%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG148+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 18:30:31 EDT 2022 % Result : Unsatisfiable 9.82s 10.09s % Output : Proof 10.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : ALG148+1 : TPTP v8.1.0. Released v2.7.0. % 0.00/0.11 % Command : run_zenon %s %d % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 600 % 0.10/0.30 % DateTime : Tue Jun 7 23:33:36 EDT 2022 % 0.10/0.31 % CPUTime : % 9.82/10.09 (* PROOF-FOUND *) % 9.82/10.09 % SZS status Unsatisfiable % 9.82/10.09 (* BEGIN-PROOF *) % 9.82/10.09 % SZS output start Proof % 9.82/10.09 Theorem zenon_thm : False. % 9.82/10.09 Proof. % 9.82/10.09 assert (zenon_L1_ : ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 9.82/10.09 do 0 intro. intros zenon_H1d zenon_H1e zenon_H1f. % 9.82/10.09 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H20 | zenon_intro zenon_H21 ]. % 9.82/10.09 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.82/10.09 intro zenon_D_pnotp. % 9.82/10.09 apply zenon_H1f. % 9.82/10.09 rewrite <- zenon_D_pnotp. % 9.82/10.09 exact zenon_H20. % 9.82/10.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.82/10.09 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 9.82/10.09 congruence. % 9.82/10.09 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 9.82/10.09 intro zenon_D_pnotp. % 9.82/10.09 apply zenon_H22. % 9.82/10.09 rewrite <- zenon_D_pnotp. % 9.82/10.09 exact zenon_H1d. % 9.82/10.09 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 9.82/10.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.82/10.09 congruence. % 9.82/10.09 apply zenon_H21. apply refl_equal. % 9.82/10.09 apply zenon_H23. apply sym_equal. exact zenon_H1e. % 9.82/10.09 apply zenon_H21. apply refl_equal. % 9.82/10.09 apply zenon_H21. apply refl_equal. % 9.82/10.09 (* end of lemma zenon_L1_ *) % 9.82/10.09 assert (zenon_L2_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 9.82/10.09 do 0 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H1e zenon_H27 zenon_H28. % 9.82/10.09 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 9.82/10.09 exact (zenon_H25 zenon_H2a). % 9.82/10.09 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 9.82/10.09 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 9.82/10.09 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 9.82/10.09 intro zenon_D_pnotp. % 9.82/10.09 apply zenon_H26. % 9.82/10.09 rewrite <- zenon_D_pnotp. % 9.82/10.09 exact zenon_H2d. % 9.82/10.09 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.82/10.09 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 9.82/10.09 congruence. % 9.82/10.09 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 9.82/10.09 intro zenon_D_pnotp. % 9.82/10.09 apply zenon_H2f. % 9.82/10.09 rewrite <- zenon_D_pnotp. % 9.82/10.09 exact zenon_H1e. % 9.82/10.09 cut (((e1) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 9.82/10.09 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.82/10.09 congruence. % 9.82/10.09 apply zenon_H2e. apply refl_equal. % 9.82/10.09 apply zenon_H30. apply sym_equal. exact zenon_H2c. % 9.82/10.09 apply zenon_H2e. apply refl_equal. % 9.82/10.09 apply zenon_H2e. apply refl_equal. % 9.82/10.09 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 9.82/10.09 exact (zenon_H27 zenon_H32). % 9.82/10.09 exact (zenon_H28 zenon_H31). % 9.82/10.09 (* end of lemma zenon_L2_ *) % 9.82/10.09 assert (zenon_L3_ : (~((e1) = (e1))) -> False). % 9.82/10.09 do 0 intro. intros zenon_H33. % 9.82/10.09 apply zenon_H33. apply refl_equal. % 9.82/10.09 (* end of lemma zenon_L3_ *) % 9.82/10.09 assert (zenon_L4_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H1e zenon_H34 zenon_H35. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H35. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H38. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H1e. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H39 zenon_H34). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L4_ *) % 9.92/10.09 assert (zenon_L5_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H3a zenon_H3b zenon_H3c. % 9.92/10.09 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 9.92/10.09 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H3c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H3d. % 9.92/10.09 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.92/10.09 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H3f. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H3a. % 9.92/10.09 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 9.92/10.09 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H3e. apply refl_equal. % 9.92/10.09 apply zenon_H40. apply sym_equal. exact zenon_H3b. % 9.92/10.09 apply zenon_H3e. apply refl_equal. % 9.92/10.09 apply zenon_H3e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L5_ *) % 9.92/10.09 assert (zenon_L6_ : (~((e0) = (e0))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H41. % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L6_ *) % 9.92/10.09 assert (zenon_L7_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H42 zenon_H27 zenon_H35 zenon_H1e zenon_H3c zenon_H3a zenon_H43 zenon_H44. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.92/10.09 exact (zenon_H27 zenon_H32). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.92/10.09 apply (zenon_L4_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.92/10.09 apply (zenon_L5_); trivial. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H44. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H48. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H43. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H49 zenon_H47). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L7_ *) % 9.92/10.09 assert (zenon_L8_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((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))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H4a zenon_H35 zenon_H3c zenon_H3a zenon_H44 zenon_H42 zenon_H25 zenon_H26 zenon_H1e zenon_H27 zenon_H24. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.92/10.09 apply (zenon_L2_); trivial. % 9.92/10.09 apply (zenon_L7_); trivial. % 9.92/10.09 (* end of lemma zenon_L8_ *) % 9.92/10.09 assert (zenon_L9_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H1e zenon_H4b zenon_H4c. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4f. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H1e. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H50 zenon_H4b). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L9_ *) % 9.92/10.09 assert (zenon_L10_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H51 zenon_H52 zenon_H53. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H53. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H54. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H51. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H55 zenon_H52). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L10_ *) % 9.92/10.09 assert (zenon_L11_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H24 zenon_H25 zenon_H56 zenon_H27 zenon_H57 zenon_H58. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 9.92/10.09 exact (zenon_H25 zenon_H2a). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 9.92/10.09 exact (zenon_H56 zenon_H2c). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 9.92/10.09 exact (zenon_H27 zenon_H32). % 9.92/10.09 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 9.92/10.09 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H58. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H59. % 9.92/10.09 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.92/10.09 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H5b. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H57. % 9.92/10.09 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 9.92/10.09 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H5a. apply refl_equal. % 9.92/10.09 apply zenon_H5c. apply sym_equal. exact zenon_H31. % 9.92/10.09 apply zenon_H5a. apply refl_equal. % 9.92/10.09 apply zenon_H5a. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L11_ *) % 9.92/10.09 assert (zenon_L12_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H51 zenon_H5d zenon_H5e. % 9.92/10.09 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H5f | zenon_intro zenon_H33 ]. % 9.92/10.09 cut (((e1) = (e1)) = ((e0) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H5e. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H5f. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H60. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H51. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H61 zenon_H5d). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L12_ *) % 9.92/10.09 assert (zenon_L13_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H62 zenon_H57 zenon_H4c. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4f. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H62. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H63 zenon_H57). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L13_ *) % 9.92/10.09 assert (zenon_L14_ : (((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 (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f zenon_H1d zenon_H5e zenon_H51 zenon_H57 zenon_H4c. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.92/10.09 exact (zenon_H56 zenon_H2c). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.92/10.09 apply (zenon_L1_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.92/10.09 apply (zenon_L12_); trivial. % 9.92/10.09 apply (zenon_L13_); trivial. % 9.92/10.09 (* end of lemma zenon_L14_ *) % 9.92/10.09 assert (zenon_L15_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((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 (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H67 zenon_H1f zenon_H1d zenon_H5e zenon_H4c zenon_H64 zenon_H25 zenon_H56 zenon_H58 zenon_H57 zenon_H24. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 9.92/10.09 apply (zenon_L11_); trivial. % 9.92/10.09 apply (zenon_L14_); trivial. % 9.92/10.09 (* end of lemma zenon_L15_ *) % 9.92/10.09 assert (zenon_L16_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H68 zenon_H34 zenon_H44. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H44. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H48. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H68. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H39 zenon_H34). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L16_ *) % 9.92/10.09 assert (zenon_L17_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H69 zenon_H6a zenon_H44. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H44. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H48. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H69. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H6b zenon_H6a). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L17_ *) % 9.92/10.09 assert (zenon_L18_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H69 zenon_H6c zenon_H53. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H53. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H54. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H69. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H6d zenon_H6c). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L18_ *) % 9.92/10.09 assert (zenon_L19_ : ((op (e1) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H6e zenon_H3b zenon_H6f. % 9.92/10.09 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 9.92/10.09 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H6f. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H70. % 9.92/10.09 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.92/10.09 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H72. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H6e. % 9.92/10.09 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 9.92/10.09 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H71. apply refl_equal. % 9.92/10.09 apply zenon_H40. apply sym_equal. exact zenon_H3b. % 9.92/10.09 apply zenon_H71. apply refl_equal. % 9.92/10.09 apply zenon_H71. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L19_ *) % 9.92/10.09 assert (zenon_L20_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H73 zenon_H74 zenon_H53. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H53. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H54. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H73. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H75 zenon_H74). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L20_ *) % 9.92/10.09 assert (zenon_L21_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H76 zenon_H74 zenon_H4c. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4f. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H76. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H75 zenon_H74). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L21_ *) % 9.92/10.09 assert (zenon_L22_ : (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H5e zenon_H77 zenon_H78. % 9.92/10.09 cut (((op (e2) (e1)) = (e1)) = ((e0) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H5e. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H77. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H79 zenon_H78). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L22_ *) % 9.92/10.09 assert (zenon_L23_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H7a zenon_H43 zenon_H7b. % 9.92/10.09 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H7a. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H43. % 9.92/10.09 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 9.92/10.09 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H5a. apply refl_equal. % 9.92/10.09 apply zenon_H7c. apply sym_equal. exact zenon_H7b. % 9.92/10.09 (* end of lemma zenon_L23_ *) % 9.92/10.09 assert (zenon_L24_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H7d zenon_H43 zenon_H7a zenon_H7e zenon_H7f zenon_H80. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 9.92/10.09 apply (zenon_L23_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 9.92/10.09 exact (zenon_H7e zenon_H83). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 9.92/10.09 exact (zenon_H7f zenon_H85). % 9.92/10.09 exact (zenon_H80 zenon_H84). % 9.92/10.09 (* end of lemma zenon_L24_ *) % 9.92/10.09 assert (zenon_L25_ : (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H86 zenon_H87 zenon_H7b. % 9.92/10.09 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H86. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H87. % 9.92/10.09 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 9.92/10.09 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H88. apply refl_equal. % 9.92/10.09 apply zenon_H7c. apply sym_equal. exact zenon_H7b. % 9.92/10.09 (* end of lemma zenon_L25_ *) % 9.92/10.09 assert (zenon_L26_ : (((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). % 9.92/10.09 do 0 intro. intros zenon_H7d zenon_H87 zenon_H86 zenon_H7e zenon_H7f zenon_H80. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 9.92/10.09 apply (zenon_L25_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 9.92/10.09 exact (zenon_H7e zenon_H83). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 9.92/10.09 exact (zenon_H7f zenon_H85). % 9.92/10.09 exact (zenon_H80 zenon_H84). % 9.92/10.09 (* end of lemma zenon_L26_ *) % 9.92/10.09 assert (zenon_L27_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H89 zenon_H8a zenon_H5e. % 9.92/10.09 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H5f | zenon_intro zenon_H33 ]. % 9.92/10.09 cut (((e1) = (e1)) = ((e0) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H5e. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H5f. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e3)) = (e0)) = ((e1) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H60. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H89. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H8b zenon_H8a). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L27_ *) % 9.92/10.09 assert (zenon_L28_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H8a zenon_H8d. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.92/10.09 apply (zenon_L24_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.92/10.09 apply (zenon_L26_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.92/10.09 apply (zenon_L27_); trivial. % 9.92/10.09 exact (zenon_H8d zenon_H7b). % 9.92/10.09 (* end of lemma zenon_L28_ *) % 9.92/10.09 assert (zenon_L29_ : (((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 (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H90 zenon_H4c zenon_H74 zenon_H78 zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H8d. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.92/10.09 apply (zenon_L21_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.92/10.09 apply (zenon_L22_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.92/10.09 exact (zenon_H91 zenon_H94). % 9.92/10.09 apply (zenon_L28_); trivial. % 9.92/10.09 (* end of lemma zenon_L29_ *) % 9.92/10.09 assert (zenon_L30_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H68 zenon_H4b zenon_H53. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H53. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H54. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H68. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H50 zenon_H4b). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L30_ *) % 9.92/10.09 assert (zenon_L31_ : (~((e2) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H37. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L31_ *) % 9.92/10.09 assert (zenon_L32_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H3b zenon_H52 zenon_H95. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H95. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H96. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H3b. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H55 zenon_H52). % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L32_ *) % 9.92/10.09 assert (zenon_L33_ : (((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 (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H95 zenon_H3b zenon_H62 zenon_H4c. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.92/10.09 exact (zenon_H28 zenon_H31). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.92/10.09 apply (zenon_L30_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.92/10.09 apply (zenon_L32_); trivial. % 9.92/10.09 apply (zenon_L13_); trivial. % 9.92/10.09 (* end of lemma zenon_L33_ *) % 9.92/10.09 assert (zenon_L34_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H9a zenon_H9b zenon_H35. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H35. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H38. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H9a. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H9c zenon_H9b). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L34_ *) % 9.92/10.09 assert (zenon_L35_ : (~((e3) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H4e. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L35_ *) % 9.92/10.09 assert (zenon_L36_ : (~((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H9d zenon_H83. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H7e zenon_H83). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L36_ *) % 9.92/10.09 assert (zenon_L37_ : ((op (e2) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H89 zenon_H9b zenon_H83. % 9.92/10.09 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H9f | zenon_intro zenon_H9e ]. % 9.92/10.09 apply zenon_H9f. apply sym_equal. exact zenon_H83. % 9.92/10.09 apply (zenon_notand_s _ _ zenon_H9e); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0 ]. % 9.92/10.09 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e0) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha1. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha2. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e3)) = (e0)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha4. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H89. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 9.92/10.09 congruence. % 9.92/10.09 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha5. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha2. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha7. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H9b. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 9.92/10.09 congruence. % 9.92/10.09 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha8. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha9. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 9.92/10.09 congruence. % 9.92/10.09 apply (zenon_L36_); trivial. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha0. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha9. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha7. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H9b. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 9.92/10.09 congruence. % 9.92/10.09 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha8. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha9. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 9.92/10.09 congruence. % 9.92/10.09 apply (zenon_L36_); trivial. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L37_ *) % 9.92/10.09 assert (zenon_L38_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((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))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hab zenon_H4c zenon_H3b zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_H89 zenon_H9b. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 9.92/10.09 apply (zenon_L33_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 9.92/10.09 apply (zenon_L34_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 9.92/10.09 apply (zenon_L27_); trivial. % 9.92/10.09 apply (zenon_L37_); trivial. % 9.92/10.09 (* end of lemma zenon_L38_ *) % 9.92/10.09 assert (zenon_L39_ : (((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)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((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))) -> (~((e0) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hae zenon_H44 zenon_H69 zenon_Haf zenon_H6f zenon_Hb0 zenon_H8d zenon_H7d zenon_H86 zenon_H7e zenon_H7f zenon_H80 zenon_H7a zenon_H8c zenon_H91 zenon_H74 zenon_H90 zenon_Hb1 zenon_Hab zenon_H4c zenon_H3b zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 9.92/10.09 apply (zenon_L17_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 9.92/10.09 exact (zenon_Haf zenon_Hb4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 9.92/10.09 apply (zenon_L19_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.92/10.09 apply (zenon_L20_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.92/10.09 apply (zenon_L29_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.92/10.09 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.09 apply (zenon_L38_); trivial. % 9.92/10.09 (* end of lemma zenon_L39_ *) % 9.92/10.09 assert (zenon_L40_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hb8 zenon_Hb9 zenon_H95. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H95. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H96. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hb8. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hba zenon_Hb9). % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L40_ *) % 9.92/10.09 assert (zenon_L41_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hbb zenon_Hbc zenon_Hbd. % 9.92/10.09 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hbb. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hbc. % 9.92/10.09 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 9.92/10.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hbf. apply refl_equal. % 9.92/10.09 apply zenon_Hbe. apply sym_equal. exact zenon_Hbd. % 9.92/10.09 (* end of lemma zenon_L41_ *) % 9.92/10.09 assert (zenon_L42_ : (((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). % 9.92/10.09 do 0 intro. intros zenon_Hc0 zenon_H53 zenon_H68 zenon_Hc1 zenon_H95 zenon_Hb8 zenon_Hbb zenon_Hbc. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.92/10.09 apply (zenon_L30_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.92/10.09 exact (zenon_Hc1 zenon_Hc4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.92/10.09 apply (zenon_L40_); trivial. % 9.92/10.09 apply (zenon_L41_); trivial. % 9.92/10.09 (* end of lemma zenon_L42_ *) % 9.92/10.09 assert (zenon_L43_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hc5 zenon_H73 zenon_Hc6 zenon_H91 zenon_Hc7 zenon_Hc8. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 9.92/10.09 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hc6. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H73. % 9.92/10.09 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 9.92/10.09 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hcb. apply refl_equal. % 9.92/10.09 apply zenon_Hca. apply sym_equal. exact zenon_Hb7. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 9.92/10.09 exact (zenon_H91 zenon_H94). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 9.92/10.09 exact (zenon_Hc7 zenon_H3a). % 9.92/10.09 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.09 (* end of lemma zenon_L43_ *) % 9.92/10.09 assert (zenon_L44_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hce zenon_Hcf zenon_Hd0. % 9.92/10.09 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hce. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hcf. % 9.92/10.09 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 9.92/10.09 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hcb. apply refl_equal. % 9.92/10.09 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 9.92/10.09 (* end of lemma zenon_L44_ *) % 9.92/10.09 assert (zenon_L45_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hd2 zenon_Hcf zenon_Hce zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.92/10.09 apply (zenon_L43_); trivial. % 9.92/10.09 apply (zenon_L44_); trivial. % 9.92/10.09 (* end of lemma zenon_L45_ *) % 9.92/10.09 assert (zenon_L46_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hd3 zenon_H68 zenon_H78. % 9.92/10.09 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hd3. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H68. % 9.92/10.09 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 9.92/10.09 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H2e. apply refl_equal. % 9.92/10.09 apply zenon_Hd4. apply sym_equal. exact zenon_H78. % 9.92/10.09 (* end of lemma zenon_L46_ *) % 9.92/10.09 assert (zenon_L47_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H35 zenon_Hcf zenon_H76. % 9.92/10.09 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H35. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hcf. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hd5 zenon_H76). % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L47_ *) % 9.92/10.09 assert (zenon_L48_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H77 zenon_Hb9 zenon_H4c. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e2) (e1)) = (e1)) = ((e3) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4f. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H77. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hba zenon_Hb9). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L48_ *) % 9.92/10.09 assert (zenon_L49_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H90 zenon_Hcf zenon_H35 zenon_H4c zenon_Hb9 zenon_H91 zenon_H89 zenon_H5e. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.92/10.09 apply (zenon_L47_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.92/10.09 apply (zenon_L48_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.92/10.09 exact (zenon_H91 zenon_H94). % 9.92/10.09 apply (zenon_L27_); trivial. % 9.92/10.09 (* end of lemma zenon_L49_ *) % 9.92/10.09 assert (zenon_L50_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H95 zenon_Hbd zenon_Hd6. % 9.92/10.09 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H95. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hbd. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hd7 zenon_Hd6). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L50_ *) % 9.92/10.09 assert (zenon_L51_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H95 zenon_Hbc zenon_Hd8. % 9.92/10.09 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H95. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hbc. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hd9 zenon_Hd8). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L51_ *) % 9.92/10.09 assert (zenon_L52_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (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 (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hda zenon_H5e zenon_H35 zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H3b zenon_H4c zenon_Hab zenon_Hb1 zenon_H90 zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H8d zenon_Hb0 zenon_H6f zenon_Haf zenon_H69 zenon_H44 zenon_Hae zenon_H95 zenon_Hd8. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.92/10.09 exact (zenon_H28 zenon_H31). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.92/10.09 apply (zenon_L18_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.92/10.09 apply (zenon_L39_); trivial. % 9.92/10.09 apply (zenon_L51_); trivial. % 9.92/10.09 (* end of lemma zenon_L52_ *) % 9.92/10.09 assert (zenon_L53_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (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 (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hdd zenon_H27 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hd3 zenon_Hc1 zenon_Hc0 zenon_Hbb zenon_Hde zenon_Hda zenon_H5e zenon_H35 zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H3b zenon_H4c zenon_Hab zenon_Hb1 zenon_H90 zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H8d zenon_Hb0 zenon_H6f zenon_Haf zenon_H69 zenon_H44 zenon_Hae zenon_H95. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.92/10.09 exact (zenon_H27 zenon_H32). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.92/10.09 apply (zenon_L17_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.92/10.09 exact (zenon_H28 zenon_H31). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.92/10.09 apply (zenon_L18_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.92/10.09 apply (zenon_L39_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.92/10.09 apply (zenon_L16_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.92/10.09 exact (zenon_Haf zenon_Hb4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.92/10.09 apply (zenon_L42_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.92/10.09 apply (zenon_L30_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.92/10.09 exact (zenon_Hc1 zenon_Hc4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.92/10.09 apply (zenon_L45_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.92/10.09 apply (zenon_L46_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.92/10.09 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.09 apply (zenon_L49_); trivial. % 9.92/10.09 apply (zenon_L50_); trivial. % 9.92/10.09 apply (zenon_L52_); trivial. % 9.92/10.09 (* end of lemma zenon_L53_ *) % 9.92/10.09 assert (zenon_L54_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H47 zenon_H57 zenon_H95. % 9.92/10.09 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.09 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H95. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H4d. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H96. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H47. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H63 zenon_H57). % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L54_ *) % 9.92/10.09 assert (zenon_L55_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_He3 zenon_He4 zenon_H7b. % 9.92/10.09 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_He3. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_He4. % 9.92/10.09 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 9.92/10.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hbf. apply refl_equal. % 9.92/10.09 apply zenon_H7c. apply sym_equal. exact zenon_H7b. % 9.92/10.09 (* end of lemma zenon_L55_ *) % 9.92/10.09 assert (zenon_L56_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H7d zenon_He4 zenon_He3 zenon_H7e zenon_H7f zenon_H80. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 9.92/10.09 apply (zenon_L55_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 9.92/10.09 exact (zenon_H7e zenon_H83). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 9.92/10.09 exact (zenon_H7f zenon_H85). % 9.92/10.09 exact (zenon_H80 zenon_H84). % 9.92/10.09 (* end of lemma zenon_L56_ *) % 9.92/10.09 assert (zenon_L57_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H44 zenon_Hb8 zenon_H78. % 9.92/10.09 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H44. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hb8. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H79 zenon_H78). % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L57_ *) % 9.92/10.09 assert (zenon_L58_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hbb zenon_He4 zenon_He5. % 9.92/10.09 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hbb. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_He4. % 9.92/10.09 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 9.92/10.09 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hbf. apply refl_equal. % 9.92/10.09 apply zenon_He6. apply sym_equal. exact zenon_He5. % 9.92/10.09 (* end of lemma zenon_L58_ *) % 9.92/10.09 assert (zenon_L59_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_He7 zenon_H53 zenon_H4b zenon_He8 zenon_Hb8 zenon_H44 zenon_Hbb zenon_He4. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.92/10.09 apply (zenon_L30_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.92/10.09 exact (zenon_He8 zenon_Heb). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.92/10.09 apply (zenon_L57_); trivial. % 9.92/10.09 apply (zenon_L58_); trivial. % 9.92/10.09 (* end of lemma zenon_L59_ *) % 9.92/10.09 assert (zenon_L60_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hec zenon_Hbd zenon_Hed. % 9.92/10.09 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hec. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hbd. % 9.92/10.09 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 9.92/10.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hef. apply refl_equal. % 9.92/10.09 apply zenon_Hee. apply sym_equal. exact zenon_Hed. % 9.92/10.09 (* end of lemma zenon_L60_ *) % 9.92/10.09 assert (zenon_L61_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hc0 zenon_He4 zenon_Hbb zenon_H44 zenon_He8 zenon_H53 zenon_He7 zenon_Hc1 zenon_H95 zenon_Hb8 zenon_Hec zenon_Hed. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.92/10.09 apply (zenon_L59_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.92/10.09 exact (zenon_Hc1 zenon_Hc4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.92/10.09 apply (zenon_L40_); trivial. % 9.92/10.09 apply (zenon_L60_); trivial. % 9.92/10.09 (* end of lemma zenon_L61_ *) % 9.92/10.09 assert (zenon_L62_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_He4 zenon_Hf0 zenon_H5e. % 9.92/10.09 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H5f | zenon_intro zenon_H33 ]. % 9.92/10.09 cut (((e1) = (e1)) = ((e0) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H5e. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H5f. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H60. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_He4. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hf1 zenon_Hf0). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L62_ *) % 9.92/10.09 assert (zenon_L63_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hf2 zenon_Hd6 zenon_H35. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H35. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e3) (e1)) = (e1)) = ((e2) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H38. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hf2. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hd7 zenon_Hd6). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L63_ *) % 9.92/10.09 assert (zenon_L64_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H4c zenon_Hed zenon_Hf3. % 9.92/10.09 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hed. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hf4 zenon_Hf3). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L64_ *) % 9.92/10.09 assert (zenon_L65_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hf5 zenon_H5e zenon_He4 zenon_H35 zenon_Hd6 zenon_Hed zenon_H4c zenon_H7e. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.92/10.09 apply (zenon_L62_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.92/10.09 apply (zenon_L63_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.92/10.09 apply (zenon_L64_); trivial. % 9.92/10.09 exact (zenon_H7e zenon_H83). % 9.92/10.09 (* end of lemma zenon_L65_ *) % 9.92/10.09 assert (zenon_L66_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((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 (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hde zenon_H68 zenon_Haf zenon_Hec zenon_H95 zenon_Hc1 zenon_He7 zenon_H53 zenon_He8 zenon_H44 zenon_Hbb zenon_Hc0 zenon_Hf5 zenon_H5e zenon_He4 zenon_H35 zenon_Hed zenon_H4c zenon_H7e. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.92/10.09 apply (zenon_L16_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.92/10.09 exact (zenon_Haf zenon_Hb4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.92/10.09 apply (zenon_L61_); trivial. % 9.92/10.09 apply (zenon_L65_); trivial. % 9.92/10.09 (* end of lemma zenon_L66_ *) % 9.92/10.09 assert (zenon_L67_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hf8 zenon_H44 zenon_H68 zenon_Haf zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.92/10.09 apply (zenon_L56_); trivial. % 9.92/10.09 apply (zenon_L66_); trivial. % 9.92/10.09 (* end of lemma zenon_L67_ *) % 9.92/10.09 assert (zenon_L68_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H84 zenon_H57 zenon_H7a. % 9.92/10.09 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 9.92/10.09 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H7a. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hf9. % 9.92/10.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.92/10.09 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hfb. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H84. % 9.92/10.09 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 9.92/10.09 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hfa. apply refl_equal. % 9.92/10.09 apply zenon_Hfc. apply sym_equal. exact zenon_H57. % 9.92/10.09 apply zenon_Hfa. apply refl_equal. % 9.92/10.09 apply zenon_Hfa. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L68_ *) % 9.92/10.09 assert (zenon_L69_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hfd zenon_H68 zenon_H51. % 9.92/10.09 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Hfd. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H68. % 9.92/10.09 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 9.92/10.09 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H2e. apply refl_equal. % 9.92/10.09 apply zenon_Hfe. apply sym_equal. exact zenon_H51. % 9.92/10.09 (* end of lemma zenon_L69_ *) % 9.92/10.09 assert (zenon_L70_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H5d zenon_H3b zenon_H35. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H35. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e2)) = (e1)) = ((e2) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H38. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H5d. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_Hff zenon_H3b). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L70_ *) % 9.92/10.09 assert (zenon_L71_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H5e zenon_H100 zenon_H101. % 9.92/10.09 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H5e. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H100. % 9.92/10.09 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.09 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H102 zenon_H101). % 9.92/10.09 apply zenon_H33. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L71_ *) % 9.92/10.09 assert (zenon_L72_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H103 zenon_H35 zenon_H3b zenon_H101 zenon_H5e zenon_H91 zenon_H4c zenon_Hed. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.92/10.09 apply (zenon_L70_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.92/10.09 apply (zenon_L71_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.92/10.09 exact (zenon_H91 zenon_H94). % 9.92/10.09 apply (zenon_L64_); trivial. % 9.92/10.09 (* end of lemma zenon_L72_ *) % 9.92/10.09 assert (zenon_L73_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H53 zenon_Hed zenon_H106. % 9.92/10.09 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H53. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hed. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H107 zenon_H106). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L73_ *) % 9.92/10.09 assert (zenon_L74_ : (((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)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H108 zenon_H68 zenon_Hfd zenon_H4c zenon_H91 zenon_H5e zenon_H3b zenon_H35 zenon_H103 zenon_Hb1 zenon_H53 zenon_Hed. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.92/10.09 apply (zenon_L69_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.92/10.09 apply (zenon_L72_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.92/10.09 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.09 apply (zenon_L73_); trivial. % 9.92/10.09 (* end of lemma zenon_L74_ *) % 9.92/10.09 assert (zenon_L75_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hed zenon_H52 zenon_H10b. % 9.92/10.09 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 9.92/10.09 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H10b. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H10c. % 9.92/10.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.92/10.09 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H10e. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hed. % 9.92/10.09 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 9.92/10.09 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H10d. apply refl_equal. % 9.92/10.09 apply zenon_H10f. apply sym_equal. exact zenon_H52. % 9.92/10.09 apply zenon_H10d. apply refl_equal. % 9.92/10.09 apply zenon_H10d. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L75_ *) % 9.92/10.09 assert (zenon_L76_ : (((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 (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H10b zenon_Hed zenon_H47 zenon_H95. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.92/10.09 exact (zenon_H28 zenon_H31). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.92/10.09 apply (zenon_L30_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.92/10.09 apply (zenon_L75_); trivial. % 9.92/10.09 apply (zenon_L54_); trivial. % 9.92/10.09 (* end of lemma zenon_L76_ *) % 9.92/10.09 assert (zenon_L77_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_Hb1 zenon_H103 zenon_H35 zenon_H5e zenon_H91 zenon_H4c zenon_Hfd zenon_H108 zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H10b zenon_Hed zenon_H95. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.92/10.09 exact (zenon_H27 zenon_H32). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.92/10.09 apply (zenon_L16_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.92/10.09 apply (zenon_L74_); trivial. % 9.92/10.09 apply (zenon_L76_); trivial. % 9.92/10.09 (* end of lemma zenon_L77_ *) % 9.92/10.09 assert (zenon_L78_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H110 zenon_H1d zenon_H77. % 9.92/10.09 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H110. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H1d. % 9.92/10.09 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 9.92/10.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H21. apply refl_equal. % 9.92/10.09 apply zenon_H111. apply sym_equal. exact zenon_H77. % 9.92/10.09 (* end of lemma zenon_L78_ *) % 9.92/10.09 assert (zenon_L79_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H112 zenon_Hcf zenon_Hb8. % 9.92/10.09 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H112. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hcf. % 9.92/10.09 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 9.92/10.09 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hcb. apply refl_equal. % 9.92/10.09 apply zenon_H113. apply sym_equal. exact zenon_Hb8. % 9.92/10.09 (* end of lemma zenon_L79_ *) % 9.92/10.09 assert (zenon_L80_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hbd zenon_Hb9 zenon_H114. % 9.92/10.09 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H115 | zenon_intro zenon_Hef ]. % 9.92/10.09 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H114. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H115. % 9.92/10.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.92/10.09 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H116. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Hbd. % 9.92/10.09 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 9.92/10.09 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_Hef. apply refl_equal. % 9.92/10.09 apply zenon_H117. apply sym_equal. exact zenon_Hb9. % 9.92/10.09 apply zenon_Hef. apply refl_equal. % 9.92/10.09 apply zenon_Hef. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L80_ *) % 9.92/10.09 assert (zenon_L81_ : (((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) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H118 zenon_H68 zenon_Hd3 zenon_H1d zenon_H110 zenon_Hcf zenon_H112 zenon_Hbd zenon_H114. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H78 | zenon_intro zenon_H119 ]. % 9.92/10.09 apply (zenon_L46_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H77 | zenon_intro zenon_H11a ]. % 9.92/10.09 apply (zenon_L78_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hb9 ]. % 9.92/10.09 apply (zenon_L79_); trivial. % 9.92/10.09 apply (zenon_L80_); trivial. % 9.92/10.09 (* end of lemma zenon_L81_ *) % 9.92/10.09 assert (zenon_L82_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((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))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hb0 zenon_H74 zenon_Hb8 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H3b zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_H9b. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.92/10.09 apply (zenon_L20_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.92/10.09 apply (zenon_L57_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.92/10.09 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.09 apply (zenon_L38_); trivial. % 9.92/10.09 (* end of lemma zenon_L82_ *) % 9.92/10.09 assert (zenon_L83_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((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))) -> (~((e0) = (e1))) -> (~((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)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hda zenon_Hbd zenon_Hb0 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H3b zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_Haf zenon_Hde zenon_H6f zenon_H69 zenon_Hae zenon_H95 zenon_Hd8. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.92/10.09 exact (zenon_H28 zenon_H31). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.92/10.09 apply (zenon_L18_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 9.92/10.09 apply (zenon_L17_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 9.92/10.09 exact (zenon_Haf zenon_Hb4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 9.92/10.09 apply (zenon_L19_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.92/10.09 apply (zenon_L16_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.92/10.09 exact (zenon_Haf zenon_Hb4). % 9.92/10.09 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.92/10.09 apply (zenon_L82_); trivial. % 9.92/10.09 apply (zenon_L50_); trivial. % 9.92/10.09 apply (zenon_L51_); trivial. % 9.92/10.09 (* end of lemma zenon_L83_ *) % 9.92/10.09 assert (zenon_L84_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((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))) -> (~((e0) = (e1))) -> (~((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)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H114 zenon_H112 zenon_H110 zenon_H1d zenon_Hd3 zenon_H118 zenon_Hda zenon_Hbd zenon_Hb0 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H3b zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_Haf zenon_Hde zenon_H6f zenon_H69 zenon_Hae zenon_H95. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.92/10.09 exact (zenon_H27 zenon_H32). % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.92/10.09 apply (zenon_L17_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.92/10.09 apply (zenon_L81_); trivial. % 9.92/10.09 apply (zenon_L83_); trivial. % 9.92/10.09 (* end of lemma zenon_L84_ *) % 9.92/10.09 assert (zenon_L85_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H11b zenon_H68 zenon_H43. % 9.92/10.09 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H11b. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H68. % 9.92/10.09 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 9.92/10.09 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H2e. apply refl_equal. % 9.92/10.09 apply zenon_H11c. apply sym_equal. exact zenon_H43. % 9.92/10.09 (* end of lemma zenon_L85_ *) % 9.92/10.09 assert (zenon_L86_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H7a zenon_H62 zenon_H83. % 9.92/10.09 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H7a. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H62. % 9.92/10.09 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 9.92/10.09 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H5a. apply refl_equal. % 9.92/10.09 apply zenon_H9f. apply sym_equal. exact zenon_H83. % 9.92/10.09 (* end of lemma zenon_L86_ *) % 9.92/10.09 assert (zenon_L87_ : (((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). % 9.92/10.09 do 0 intro. intros zenon_H7d zenon_H8d zenon_H62 zenon_H7a zenon_H7f zenon_H80. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 9.92/10.09 exact (zenon_H8d zenon_H7b). % 9.92/10.09 apply (zenon_or_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 9.92/10.09 apply (zenon_L86_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 9.92/10.09 exact (zenon_H7f zenon_H85). % 9.92/10.09 exact (zenon_H80 zenon_H84). % 9.92/10.09 (* end of lemma zenon_L87_ *) % 9.92/10.09 assert (zenon_L88_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H11d zenon_H1d zenon_H9a. % 9.92/10.09 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H11d. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H1d. % 9.92/10.09 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 9.92/10.09 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.92/10.09 congruence. % 9.92/10.09 apply zenon_H21. apply refl_equal. % 9.92/10.09 apply zenon_H11e. apply sym_equal. exact zenon_H9a. % 9.92/10.09 (* end of lemma zenon_L88_ *) % 9.92/10.09 assert (zenon_L89_ : (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H4c zenon_H11f zenon_H8a. % 9.92/10.09 cut (((op (e2) (e3)) = (e3)) = ((e1) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H4c. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H11f. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H8b zenon_H8a). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L89_ *) % 9.92/10.09 assert (zenon_L90_ : ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (op (op (e3) (e3)) (e3)))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H87 zenon_H83 zenon_H120. % 9.92/10.09 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H120. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha9. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H121. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H87. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 9.92/10.09 congruence. % 9.92/10.09 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha8. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha9. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 9.92/10.09 congruence. % 9.92/10.09 apply (zenon_L36_); trivial. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L90_ *) % 9.92/10.09 assert (zenon_L91_ : ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H47 zenon_H87 zenon_H83. % 9.92/10.09 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H9f | zenon_intro zenon_H122 ]. % 9.92/10.09 apply zenon_H9f. apply sym_equal. exact zenon_H83. % 9.92/10.09 apply (zenon_notand_s _ _ zenon_H122); [ zenon_intro zenon_H123 | zenon_intro zenon_H120 ]. % 9.92/10.09 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e2) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H123. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha2. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e0) (e3)) = (e2)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H124. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H47. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 9.92/10.09 congruence. % 9.92/10.09 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H125. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha2. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.92/10.09 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H121. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H87. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 9.92/10.09 congruence. % 9.92/10.09 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_Ha8. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_Ha9. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.92/10.09 cut (((op (op (e3) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 9.92/10.09 congruence. % 9.92/10.09 apply (zenon_L36_); trivial. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_Haa. apply refl_equal. % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply zenon_Ha3. apply refl_equal. % 9.92/10.09 apply (zenon_L90_); trivial. % 9.92/10.09 (* end of lemma zenon_L91_ *) % 9.92/10.09 assert (zenon_L92_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H87 zenon_H9b zenon_H44. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H44. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e1) (e3)) = (e0)) = ((e2) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H48. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H87. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H9c zenon_H9b). % 9.92/10.09 apply zenon_H41. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 apply zenon_H37. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L92_ *) % 9.92/10.09 assert (zenon_L93_ : (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H95 zenon_H11f zenon_Hd0. % 9.92/10.09 cut (((op (e2) (e3)) = (e3)) = ((e2) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H95. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H11f. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e2) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H127 zenon_Hd0). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L93_ *) % 9.92/10.09 assert (zenon_L94_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H128 zenon_H83 zenon_H44 zenon_H87 zenon_H11f zenon_H95 zenon_H7f. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 9.92/10.09 apply (zenon_L91_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 9.92/10.09 apply (zenon_L92_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 9.92/10.09 apply (zenon_L93_); trivial. % 9.92/10.09 exact (zenon_H7f zenon_H85). % 9.92/10.09 (* end of lemma zenon_L94_ *) % 9.92/10.09 assert (zenon_L95_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_Hab zenon_H80 zenon_H7a zenon_H8d zenon_H7d zenon_H1d zenon_H11d zenon_H4c zenon_H128 zenon_H44 zenon_H87 zenon_H11f zenon_H95 zenon_H7f. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 9.92/10.09 apply (zenon_L87_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 9.92/10.09 apply (zenon_L88_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 9.92/10.09 apply (zenon_L89_); trivial. % 9.92/10.09 apply (zenon_L94_); trivial. % 9.92/10.09 (* end of lemma zenon_L95_ *) % 9.92/10.09 assert (zenon_L96_ : (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> False). % 9.92/10.09 do 0 intro. intros zenon_H53 zenon_H11f zenon_H89. % 9.92/10.09 cut (((op (e2) (e3)) = (e3)) = ((e0) = (e3))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H53. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H11f. % 9.92/10.09 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.09 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 9.92/10.09 congruence. % 9.92/10.09 exact (zenon_H12b zenon_H89). % 9.92/10.09 apply zenon_H4e. apply refl_equal. % 9.92/10.09 (* end of lemma zenon_L96_ *) % 9.92/10.09 assert (zenon_L97_ : (((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)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H8c zenon_H68 zenon_H11b zenon_H7f zenon_H95 zenon_H44 zenon_H128 zenon_H4c zenon_H11d zenon_H1d zenon_H7d zenon_H7a zenon_H80 zenon_Hab zenon_H11f zenon_H53 zenon_H8d. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.92/10.09 apply (zenon_L85_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.92/10.09 apply (zenon_L95_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.92/10.09 apply (zenon_L96_); trivial. % 9.92/10.09 exact (zenon_H8d zenon_H7b). % 9.92/10.09 (* end of lemma zenon_L97_ *) % 9.92/10.09 assert (zenon_L98_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.09 do 0 intro. intros zenon_H12c zenon_H73 zenon_H114 zenon_Hbd zenon_Hc8 zenon_H8c zenon_H68 zenon_H11b zenon_H7f zenon_H95 zenon_H44 zenon_H128 zenon_H4c zenon_H11d zenon_H1d zenon_H7d zenon_H7a zenon_H80 zenon_Hab zenon_H53 zenon_H8d. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.92/10.09 apply (zenon_L20_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.92/10.09 apply (zenon_L80_); trivial. % 9.92/10.09 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.92/10.09 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.09 apply (zenon_L97_); trivial. % 9.92/10.09 (* end of lemma zenon_L98_ *) % 9.92/10.09 assert (zenon_L99_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 9.92/10.09 do 0 intro. intros zenon_He4 zenon_Hd8 zenon_H44. % 9.92/10.09 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.92/10.09 cut (((e2) = (e2)) = ((e0) = (e2))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H44. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_H36. % 9.92/10.09 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.09 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 9.92/10.09 congruence. % 9.92/10.09 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 9.92/10.09 intro zenon_D_pnotp. % 9.92/10.09 apply zenon_H48. % 9.92/10.09 rewrite <- zenon_D_pnotp. % 9.92/10.09 exact zenon_He4. % 9.92/10.09 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.09 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_Hd9 zenon_Hd8). % 9.92/10.10 apply zenon_H41. apply refl_equal. % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L99_ *) % 9.92/10.10 assert (zenon_L100_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H12f zenon_H2a zenon_H69. % 9.92/10.10 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H12f. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H2a. % 9.92/10.10 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 9.92/10.10 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H131. apply refl_equal. % 9.92/10.10 apply zenon_H130. apply sym_equal. exact zenon_H69. % 9.92/10.10 (* end of lemma zenon_L100_ *) % 9.92/10.10 assert (zenon_L101_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H132 zenon_H2a zenon_H51. % 9.92/10.10 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H132. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H2a. % 9.92/10.10 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 9.92/10.10 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H131. apply refl_equal. % 9.92/10.10 apply zenon_Hfe. apply sym_equal. exact zenon_H51. % 9.92/10.10 (* end of lemma zenon_L101_ *) % 9.92/10.10 assert (zenon_L102_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H3c zenon_H5d zenon_H94. % 9.92/10.10 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H3c. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H5d. % 9.92/10.10 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 9.92/10.10 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H134. apply refl_equal. % 9.92/10.10 apply zenon_H133. apply sym_equal. exact zenon_H94. % 9.92/10.10 (* end of lemma zenon_L102_ *) % 9.92/10.10 assert (zenon_L103_ : (((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). % 9.92/10.10 do 0 intro. intros zenon_Hc5 zenon_Hb1 zenon_H5d zenon_H3c zenon_Hc7 zenon_Hc8. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 9.92/10.10 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 9.92/10.10 apply (zenon_L102_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 9.92/10.10 exact (zenon_Hc7 zenon_H3a). % 9.92/10.10 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.10 (* end of lemma zenon_L103_ *) % 9.92/10.10 assert (zenon_L104_ : ((op (e3) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H135 zenon_H3b zenon_H10b. % 9.92/10.10 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H10b. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H10c. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H10e. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H135. % 9.92/10.10 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H10d. apply refl_equal. % 9.92/10.10 apply zenon_H40. apply sym_equal. exact zenon_H3b. % 9.92/10.10 apply zenon_H10d. apply refl_equal. % 9.92/10.10 apply zenon_H10d. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L104_ *) % 9.92/10.10 assert (zenon_L105_ : (~((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H136 zenon_H94. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_H91 zenon_H94). % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L105_ *) % 9.92/10.10 assert (zenon_L106_ : ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H101 zenon_H94 zenon_H137. % 9.92/10.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H137. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H138. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H13a. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H101. % 9.92/10.10 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.10 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 9.92/10.10 congruence. % 9.92/10.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H13b. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H138. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 9.92/10.10 congruence. % 9.92/10.10 apply (zenon_L105_); trivial. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H41. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L106_ *) % 9.92/10.10 assert (zenon_L107_ : ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H52 zenon_H101 zenon_H94. % 9.92/10.10 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H133 | zenon_intro zenon_H13c ]. % 9.92/10.10 apply zenon_H133. apply sym_equal. exact zenon_H94. % 9.92/10.10 apply (zenon_notand_s _ _ zenon_H13c); [ zenon_intro zenon_H13d | zenon_intro zenon_H137 ]. % 9.92/10.10 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e3) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H13d. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H13e. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e0) (e2)) = (e3)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H140. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H52. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 9.92/10.10 congruence. % 9.92/10.10 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H141. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H13e. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H13a. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H101. % 9.92/10.10 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.10 cut (((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 9.92/10.10 congruence. % 9.92/10.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (e2) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H13b. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H138. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 9.92/10.10 congruence. % 9.92/10.10 apply (zenon_L105_); trivial. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H41. apply refl_equal. % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply (zenon_L106_); trivial. % 9.92/10.10 (* end of lemma zenon_L107_ *) % 9.92/10.10 assert (zenon_L108_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hc5 zenon_Hb1 zenon_H101 zenon_H52 zenon_Hc7 zenon_Hc8. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 9.92/10.10 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 9.92/10.10 apply (zenon_L107_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 9.92/10.10 exact (zenon_Hc7 zenon_H3a). % 9.92/10.10 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.10 (* end of lemma zenon_L108_ *) % 9.92/10.10 assert (zenon_L109_ : ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H135 zenon_Hed zenon_H95. % 9.92/10.10 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.10 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H95. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H4d. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e3) (e2)) = (e2)) = ((e3) = (e2))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H96. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H135. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (e3) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_H143 zenon_Hed). % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L109_ *) % 9.92/10.10 assert (zenon_L110_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hf8 zenon_H95 zenon_H12f zenon_H2a zenon_He8 zenon_H144 zenon_H135 zenon_H10b zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H7e zenon_H86 zenon_H145. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 9.92/10.10 apply (zenon_L100_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 9.92/10.10 exact (zenon_He8 zenon_Heb). % 9.92/10.10 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H51 | zenon_intro zenon_H148 ]. % 9.92/10.10 apply (zenon_L101_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H5d | zenon_intro zenon_H149 ]. % 9.92/10.10 apply (zenon_L103_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H3b | zenon_intro zenon_H52 ]. % 9.92/10.10 apply (zenon_L104_); trivial. % 9.92/10.10 apply (zenon_L108_); trivial. % 9.92/10.10 apply (zenon_L26_); trivial. % 9.92/10.10 apply (zenon_L109_); trivial. % 9.92/10.10 (* end of lemma zenon_L110_ *) % 9.92/10.10 assert (zenon_L111_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H14a zenon_H2a zenon_He4. % 9.92/10.10 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H14a. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H2a. % 9.92/10.10 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 9.92/10.10 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H131. apply refl_equal. % 9.92/10.10 apply zenon_H14b. apply sym_equal. exact zenon_He4. % 9.92/10.10 (* end of lemma zenon_L111_ *) % 9.92/10.10 assert (zenon_L112_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H53 zenon_Hbd zenon_He5. % 9.92/10.10 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H53. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hbd. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_H14c zenon_He5). % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L112_ *) % 9.92/10.10 assert (zenon_L113_ : (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H44 zenon_H135 zenon_H106. % 9.92/10.10 cut (((op (e3) (e2)) = (e2)) = ((e0) = (e2))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H44. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H135. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_H107 zenon_H106). % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L113_ *) % 9.92/10.10 assert (zenon_L114_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H14d zenon_H2a zenon_H14a zenon_Hbd zenon_H53 zenon_H135 zenon_H44 zenon_H8d. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 9.92/10.10 apply (zenon_L111_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 9.92/10.10 apply (zenon_L112_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 9.92/10.10 apply (zenon_L113_); trivial. % 9.92/10.10 exact (zenon_H8d zenon_H7b). % 9.92/10.10 (* end of lemma zenon_L114_ *) % 9.92/10.10 assert (zenon_L115_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H2a zenon_He8 zenon_H144 zenon_H135 zenon_H10b zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_L110_); trivial. % 9.92/10.10 apply (zenon_L114_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_L110_); trivial. % 9.92/10.10 apply (zenon_L41_); trivial. % 9.92/10.10 (* end of lemma zenon_L115_ *) % 9.92/10.10 assert (zenon_L116_ : ((op (e3) (e2)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H135 zenon_H3a zenon_H152. % 9.92/10.10 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e2) (e2)) = (op (e3) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H152. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H10c. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e2) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H153. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H135. % 9.92/10.10 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 9.92/10.10 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H10d. apply refl_equal. % 9.92/10.10 apply zenon_H154. apply sym_equal. exact zenon_H3a. % 9.92/10.10 apply zenon_H10d. apply refl_equal. % 9.92/10.10 apply zenon_H10d. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L116_ *) % 9.92/10.10 assert (zenon_L117_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H155 zenon_H101 zenon_Hb7. % 9.92/10.10 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H155. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H101. % 9.92/10.10 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 9.92/10.10 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H71. apply refl_equal. % 9.92/10.10 apply zenon_Hca. apply sym_equal. exact zenon_Hb7. % 9.92/10.10 (* end of lemma zenon_L117_ *) % 9.92/10.10 assert (zenon_L118_ : (((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). % 9.92/10.10 do 0 intro. intros zenon_Hc5 zenon_H101 zenon_H155 zenon_H91 zenon_Hc7 zenon_Hc8. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 9.92/10.10 apply (zenon_L117_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 9.92/10.10 exact (zenon_H91 zenon_H94). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 9.92/10.10 exact (zenon_Hc7 zenon_H3a). % 9.92/10.10 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.10 (* end of lemma zenon_L118_ *) % 9.92/10.10 assert (zenon_L119_ : (((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 (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). % 9.92/10.10 do 0 intro. intros zenon_H145 zenon_H2a zenon_H12f zenon_He8 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_Hc5 zenon_H7d zenon_H86 zenon_H7e zenon_H7f zenon_H80. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 9.92/10.10 apply (zenon_L100_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 9.92/10.10 exact (zenon_He8 zenon_Heb). % 9.92/10.10 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 9.92/10.10 apply (zenon_L118_); trivial. % 9.92/10.10 apply (zenon_L26_); trivial. % 9.92/10.10 (* end of lemma zenon_L119_ *) % 9.92/10.10 assert (zenon_L120_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((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 (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hf8 zenon_H135 zenon_H95 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_H7d zenon_H80 zenon_H7e zenon_H86 zenon_H145. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.92/10.10 apply (zenon_L119_); trivial. % 9.92/10.10 apply (zenon_L109_); trivial. % 9.92/10.10 (* end of lemma zenon_L120_ *) % 9.92/10.10 assert (zenon_L121_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((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 (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H150 zenon_Hbb zenon_Hf8 zenon_H135 zenon_H95 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_L120_); trivial. % 9.92/10.10 apply (zenon_L114_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_L120_); trivial. % 9.92/10.10 apply (zenon_L41_); trivial. % 9.92/10.10 (* end of lemma zenon_L121_ *) % 9.92/10.10 assert (zenon_L122_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H2a zenon_He8 zenon_H144 zenon_H135 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_L115_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_L121_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 apply (zenon_L79_); trivial. % 9.92/10.10 (* end of lemma zenon_L122_ *) % 9.92/10.10 assert (zenon_L123_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H159 zenon_H15a zenon_H100. % 9.92/10.10 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H159. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H15a. % 9.92/10.10 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 9.92/10.10 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H15c. apply refl_equal. % 9.92/10.10 apply zenon_H15b. apply sym_equal. exact zenon_H100. % 9.92/10.10 (* end of lemma zenon_L123_ *) % 9.92/10.10 assert (zenon_L124_ : (((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 (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H144 zenon_H2a zenon_H132 zenon_H3c zenon_H10b zenon_H135 zenon_H101 zenon_H94. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H51 | zenon_intro zenon_H148 ]. % 9.92/10.10 apply (zenon_L101_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H5d | zenon_intro zenon_H149 ]. % 9.92/10.10 apply (zenon_L102_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H3b | zenon_intro zenon_H52 ]. % 9.92/10.10 apply (zenon_L104_); trivial. % 9.92/10.10 apply (zenon_L107_); trivial. % 9.92/10.10 (* end of lemma zenon_L124_ *) % 9.92/10.10 assert (zenon_L125_ : (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H35 zenon_H135 zenon_Hf3. % 9.92/10.10 cut (((op (e3) (e2)) = (e2)) = ((e1) = (e2))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H35. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H135. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_Hf4 zenon_Hf3). % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L125_ *) % 9.92/10.10 assert (zenon_L126_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (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))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H103 zenon_Hc8 zenon_Hc7 zenon_Hb1 zenon_Hc5 zenon_H15a zenon_H159 zenon_H101 zenon_H10b zenon_H3c zenon_H132 zenon_H2a zenon_H144 zenon_H35 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.92/10.10 apply (zenon_L103_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.92/10.10 apply (zenon_L123_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.92/10.10 apply (zenon_L124_); trivial. % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 (* end of lemma zenon_L126_ *) % 9.92/10.10 assert (zenon_L127_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H108 zenon_H35 zenon_H144 zenon_H2a zenon_H132 zenon_H3c zenon_H10b zenon_H159 zenon_H15a zenon_Hc5 zenon_Hc7 zenon_Hc8 zenon_H103 zenon_Hb1 zenon_H44 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.92/10.10 apply (zenon_L101_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.92/10.10 apply (zenon_L126_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.92/10.10 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.10 apply (zenon_L113_); trivial. % 9.92/10.10 (* end of lemma zenon_L127_ *) % 9.92/10.10 assert (zenon_L128_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H3c zenon_H51 zenon_Hb7. % 9.92/10.10 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H3c. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H51. % 9.92/10.10 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hca]. % 9.92/10.10 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H134. apply refl_equal. % 9.92/10.10 apply zenon_Hca. apply sym_equal. exact zenon_Hb7. % 9.92/10.10 (* end of lemma zenon_L128_ *) % 9.92/10.10 assert (zenon_L129_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hc5 zenon_H51 zenon_H3c zenon_H91 zenon_Hc7 zenon_Hc8. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 9.92/10.10 apply (zenon_L128_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 9.92/10.10 exact (zenon_H91 zenon_H94). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 9.92/10.10 exact (zenon_Hc7 zenon_H3a). % 9.92/10.10 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.10 (* end of lemma zenon_L129_ *) % 9.92/10.10 assert (zenon_L130_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H5d zenon_H52 zenon_H4c. % 9.92/10.10 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.10 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H4c. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H4d. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H4f. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H5d. % 9.92/10.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.10 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_H55 zenon_H52). % 9.92/10.10 apply zenon_H33. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L130_ *) % 9.92/10.10 assert (zenon_L131_ : (~((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H15d zenon_Hb7. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L131_ *) % 9.92/10.10 assert (zenon_L132_ : ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (op (op (e2) (e2)) (e2)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H5d zenon_Hb7 zenon_H15e. % 9.92/10.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H15e. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H138. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H15f. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H5d. % 9.92/10.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.10 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 9.92/10.10 congruence. % 9.92/10.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H160. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H138. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 9.92/10.10 congruence. % 9.92/10.10 apply (zenon_L131_); trivial. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H33. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L132_ *) % 9.92/10.10 assert (zenon_L133_ : ((op (e1) (e2)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H161 zenon_H5d zenon_Hb7. % 9.92/10.10 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_Hca | zenon_intro zenon_H162 ]. % 9.92/10.10 apply zenon_Hca. apply sym_equal. exact zenon_Hb7. % 9.92/10.10 apply (zenon_notand_s _ _ zenon_H162); [ zenon_intro zenon_H13d | zenon_intro zenon_H15e ]. % 9.92/10.10 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e3) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H13d. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H13e. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e1) (e2)) = (e3)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H140. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H161. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 9.92/10.10 congruence. % 9.92/10.10 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H163. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H13e. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 9.92/10.10 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H15f. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H5d. % 9.92/10.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.10 cut (((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 9.92/10.10 congruence. % 9.92/10.10 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (e2) (e2)) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H160. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H138. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.92/10.10 cut (((op (op (e2) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 9.92/10.10 congruence. % 9.92/10.10 apply (zenon_L131_); trivial. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H139. apply refl_equal. % 9.92/10.10 apply zenon_H33. apply refl_equal. % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply zenon_H13f. apply refl_equal. % 9.92/10.10 apply (zenon_L132_); trivial. % 9.92/10.10 (* end of lemma zenon_L133_ *) % 9.92/10.10 assert (zenon_L134_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H165 zenon_H4c zenon_Hb7 zenon_H5d zenon_Hc8 zenon_H135 zenon_H95. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H52 | zenon_intro zenon_H166 ]. % 9.92/10.10 apply (zenon_L130_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 9.92/10.10 apply (zenon_L133_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hed ]. % 9.92/10.10 exact (zenon_Hc8 zenon_Hcd). % 9.92/10.10 apply (zenon_L109_); trivial. % 9.92/10.10 (* end of lemma zenon_L134_ *) % 9.92/10.10 assert (zenon_L135_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H103 zenon_H95 zenon_Hc8 zenon_Hb7 zenon_H4c zenon_H165 zenon_H15a zenon_H159 zenon_H91 zenon_H35 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.92/10.10 apply (zenon_L134_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.92/10.10 apply (zenon_L123_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.92/10.10 exact (zenon_H91 zenon_H94). % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 (* end of lemma zenon_L135_ *) % 9.92/10.10 assert (zenon_L136_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H108 zenon_H3c zenon_Hc7 zenon_H155 zenon_Hc5 zenon_H35 zenon_H91 zenon_H159 zenon_H15a zenon_H165 zenon_H4c zenon_Hc8 zenon_H95 zenon_H103 zenon_H44 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.92/10.10 apply (zenon_L129_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.92/10.10 apply (zenon_L118_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.92/10.10 apply (zenon_L135_); trivial. % 9.92/10.10 apply (zenon_L113_); trivial. % 9.92/10.10 (* end of lemma zenon_L136_ *) % 9.92/10.10 assert (zenon_L137_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H158 zenon_H152 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H3c zenon_H155 zenon_H103 zenon_H35 zenon_H15a zenon_H159 zenon_H4c zenon_H95 zenon_H135 zenon_H165 zenon_H44 zenon_H108. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_L136_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 (* end of lemma zenon_L137_ *) % 9.92/10.10 assert (zenon_L138_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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 (e1) (e0)))) -> (~((e2) = (e3))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H135 zenon_H144 zenon_H2a zenon_H12f zenon_H95 zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.92/10.10 apply (zenon_L122_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_L127_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.92/10.10 apply (zenon_L137_); trivial. % 9.92/10.10 apply (zenon_L79_); trivial. % 9.92/10.10 (* end of lemma zenon_L138_ *) % 9.92/10.10 assert (zenon_L139_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H4c zenon_Hbc zenon_Hf0. % 9.92/10.10 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H4c. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hbc. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_Hf1 zenon_Hf0). % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L139_ *) % 9.92/10.10 assert (zenon_L140_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H169 zenon_H1d zenon_Hf2. % 9.92/10.10 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H169. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H1d. % 9.92/10.10 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 9.92/10.10 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H21. apply refl_equal. % 9.92/10.10 apply zenon_H16a. apply sym_equal. exact zenon_Hf2. % 9.92/10.10 (* end of lemma zenon_L140_ *) % 9.92/10.10 assert (zenon_L141_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hf5 zenon_H5e zenon_He4 zenon_H1d zenon_H169 zenon_H135 zenon_H35 zenon_H7a zenon_H62. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.92/10.10 apply (zenon_L62_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.92/10.10 apply (zenon_L140_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 apply (zenon_L86_); trivial. % 9.92/10.10 (* end of lemma zenon_L141_ *) % 9.92/10.10 assert (zenon_L142_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H14d zenon_H62 zenon_H7a zenon_H35 zenon_H169 zenon_H1d zenon_H5e zenon_Hf5 zenon_Hbd zenon_H53 zenon_H135 zenon_H44 zenon_H8d. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 9.92/10.10 apply (zenon_L141_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 9.92/10.10 apply (zenon_L112_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 9.92/10.10 apply (zenon_L113_); trivial. % 9.92/10.10 exact (zenon_H8d zenon_H7b). % 9.92/10.10 (* end of lemma zenon_L142_ *) % 9.92/10.10 assert (zenon_L143_ : (((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H14d zenon_H7a zenon_H35 zenon_H169 zenon_H1d zenon_H5e zenon_Hf5 zenon_Hbd zenon_H53 zenon_H135 zenon_H44 zenon_H8d. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.92/10.10 exact (zenon_H56 zenon_H2c). % 9.92/10.10 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.92/10.10 apply (zenon_L1_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.92/10.10 apply (zenon_L103_); trivial. % 9.92/10.10 apply (zenon_L142_); trivial. % 9.92/10.10 (* end of lemma zenon_L143_ *) % 9.92/10.10 assert (zenon_L144_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (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))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H16b zenon_Hf0 zenon_H4c zenon_H8d zenon_H44 zenon_H53 zenon_Hf5 zenon_H5e zenon_H1d zenon_H169 zenon_H35 zenon_H7a zenon_H14d zenon_Hc5 zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_H1f zenon_H56 zenon_H64 zenon_H95 zenon_H135 zenon_H80. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbc | zenon_intro zenon_H16c ]. % 9.92/10.10 apply (zenon_L139_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_Hbd | zenon_intro zenon_H16d ]. % 9.92/10.10 apply (zenon_L143_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hed | zenon_intro zenon_H84 ]. % 9.92/10.10 apply (zenon_L109_); trivial. % 9.92/10.10 exact (zenon_H80 zenon_H84). % 9.92/10.10 (* end of lemma zenon_L144_ *) % 9.92/10.10 assert (zenon_L145_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hf5 zenon_Hbc zenon_H4c zenon_H1d zenon_H169 zenon_H135 zenon_H35 zenon_H7e. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.92/10.10 apply (zenon_L139_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.92/10.10 apply (zenon_L140_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 exact (zenon_H7e zenon_H83). % 9.92/10.10 (* end of lemma zenon_L145_ *) % 9.92/10.10 assert (zenon_L146_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H151 zenon_Hbb zenon_H4c zenon_Hbc zenon_H169 zenon_H1d zenon_H35 zenon_H135 zenon_Hf5. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_L145_); trivial. % 9.92/10.10 apply (zenon_L41_); trivial. % 9.92/10.10 (* end of lemma zenon_L146_ *) % 9.92/10.10 assert (zenon_L147_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H150 zenon_Hbb zenon_H4c zenon_H64 zenon_Hf5 zenon_H7a zenon_H135 zenon_H35 zenon_H169 zenon_H5e zenon_H53 zenon_H44 zenon_H14d zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_H95 zenon_H80 zenon_H16b zenon_H151. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.92/10.10 apply (zenon_L144_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.92/10.10 apply (zenon_L140_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 exact (zenon_H7e zenon_H83). % 9.92/10.10 apply (zenon_L143_); trivial. % 9.92/10.10 apply (zenon_L146_); trivial. % 9.92/10.10 (* end of lemma zenon_L147_ *) % 9.92/10.10 assert (zenon_L148_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((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)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H158 zenon_H152 zenon_H151 zenon_H16b zenon_H80 zenon_H95 zenon_H56 zenon_H1f zenon_H1d zenon_Hc5 zenon_Hc8 zenon_H3c zenon_Hb1 zenon_H14d zenon_H44 zenon_H53 zenon_H5e zenon_H169 zenon_H35 zenon_H135 zenon_H7a zenon_Hf5 zenon_H64 zenon_H4c zenon_Hbb zenon_H150. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_L147_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 (* end of lemma zenon_L148_ *) % 9.92/10.10 assert (zenon_L149_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H16e zenon_H1d zenon_H100. % 9.92/10.10 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H16e. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H1d. % 9.92/10.10 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 9.92/10.10 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H21. apply refl_equal. % 9.92/10.10 apply zenon_H15b. apply sym_equal. exact zenon_H100. % 9.92/10.10 (* end of lemma zenon_L149_ *) % 9.92/10.10 assert (zenon_L150_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H103 zenon_H95 zenon_Hc8 zenon_Hb7 zenon_H4c zenon_H165 zenon_H1d zenon_H16e zenon_H91 zenon_H35 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.92/10.10 apply (zenon_L134_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.92/10.10 apply (zenon_L149_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.92/10.10 exact (zenon_H91 zenon_H94). % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 (* end of lemma zenon_L150_ *) % 9.92/10.10 assert (zenon_L151_ : (((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H144 zenon_H68 zenon_Hfd zenon_H3c zenon_H10b zenon_H135 zenon_H101 zenon_H94. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H51 | zenon_intro zenon_H148 ]. % 9.92/10.10 apply (zenon_L69_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H5d | zenon_intro zenon_H149 ]. % 9.92/10.10 apply (zenon_L102_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H3b | zenon_intro zenon_H52 ]. % 9.92/10.10 apply (zenon_L104_); trivial. % 9.92/10.10 apply (zenon_L107_); trivial. % 9.92/10.10 (* end of lemma zenon_L151_ *) % 9.92/10.10 assert (zenon_L152_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (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))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (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))))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H103 zenon_Hc8 zenon_Hc7 zenon_Hb1 zenon_Hc5 zenon_H1d zenon_H16e zenon_H101 zenon_H10b zenon_H3c zenon_Hfd zenon_H68 zenon_H144 zenon_H35 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.92/10.10 apply (zenon_L103_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.92/10.10 apply (zenon_L149_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.92/10.10 apply (zenon_L151_); trivial. % 9.92/10.10 apply (zenon_L125_); trivial. % 9.92/10.10 (* end of lemma zenon_L152_ *) % 9.92/10.10 assert (zenon_L153_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (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)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H108 zenon_H35 zenon_H144 zenon_H68 zenon_Hfd zenon_H3c zenon_H10b zenon_H16e zenon_H1d zenon_Hc5 zenon_Hc7 zenon_Hc8 zenon_H103 zenon_Hb1 zenon_H44 zenon_H135. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.92/10.10 apply (zenon_L69_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.92/10.10 apply (zenon_L152_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.92/10.10 exact (zenon_Hb1 zenon_Hb7). % 9.92/10.10 apply (zenon_L113_); trivial. % 9.92/10.10 (* end of lemma zenon_L153_ *) % 9.92/10.10 assert (zenon_L154_ : ((op (e3) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hbc zenon_H6c zenon_H16f. % 9.92/10.10 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H170 | zenon_intro zenon_Hbf ]. % 9.92/10.10 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H16f. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H170. % 9.92/10.10 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.92/10.10 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H171. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hbc. % 9.92/10.10 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 9.92/10.10 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_Hbf. apply refl_equal. % 9.92/10.10 apply zenon_H172. apply sym_equal. exact zenon_H6c. % 9.92/10.10 apply zenon_Hbf. apply refl_equal. % 9.92/10.10 apply zenon_Hbf. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L154_ *) % 9.92/10.10 assert (zenon_L155_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hcf zenon_H74 zenon_H95. % 9.92/10.10 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.92/10.10 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H95. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H4d. % 9.92/10.10 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.92/10.10 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H96. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hcf. % 9.92/10.10 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.92/10.10 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_H75 zenon_H74). % 9.92/10.10 apply zenon_H37. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 apply zenon_H4e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L155_ *) % 9.92/10.10 assert (zenon_L156_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H151 zenon_H28 zenon_H16b zenon_H80 zenon_H135 zenon_H95 zenon_Hd3 zenon_H68 zenon_H110 zenon_H1d zenon_H112 zenon_Hcf zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H35 zenon_H169 zenon_H4c zenon_Hda. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.92/10.10 exact (zenon_H28 zenon_H31). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbc | zenon_intro zenon_H16c ]. % 9.92/10.10 apply (zenon_L154_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_Hbd | zenon_intro zenon_H16d ]. % 9.92/10.10 apply (zenon_L81_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hed | zenon_intro zenon_H84 ]. % 9.92/10.10 apply (zenon_L109_); trivial. % 9.92/10.10 exact (zenon_H80 zenon_H84). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.92/10.10 apply (zenon_L155_); trivial. % 9.92/10.10 apply (zenon_L145_); trivial. % 9.92/10.10 apply (zenon_L81_); trivial. % 9.92/10.10 (* end of lemma zenon_L156_ *) % 9.92/10.10 assert (zenon_L157_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H156 zenon_Hda zenon_H4c zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_Hd3 zenon_H95 zenon_H80 zenon_H16b zenon_H28 zenon_H151 zenon_H108 zenon_H44 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H16e zenon_H1d zenon_H144 zenon_H135 zenon_H10b zenon_H35 zenon_H103 zenon_H68 zenon_Hfd zenon_H152 zenon_H158. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_L153_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 apply (zenon_L156_); trivial. % 9.92/10.10 (* end of lemma zenon_L157_ *) % 9.92/10.10 assert (zenon_L158_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H173 zenon_Hf8 zenon_H12f zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14a zenon_H159 zenon_H168 zenon_H156 zenon_H155 zenon_H103 zenon_H16e zenon_H165 zenon_H108 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H4c zenon_H64 zenon_Hf5 zenon_H7a zenon_H35 zenon_H169 zenon_H5e zenon_H53 zenon_H44 zenon_H14d zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H1f zenon_H95 zenon_H16b zenon_H151 zenon_H158 zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_H144 zenon_H10b zenon_Hfd zenon_H174 zenon_H152 zenon_H135 zenon_H80. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 9.92/10.10 apply (zenon_L138_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.92/10.10 apply (zenon_L148_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.92/10.10 apply (zenon_L129_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.92/10.10 apply (zenon_L118_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.92/10.10 apply (zenon_L150_); trivial. % 9.92/10.10 apply (zenon_L113_); trivial. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 apply (zenon_L79_); trivial. % 9.92/10.10 apply (zenon_L157_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 9.92/10.10 apply (zenon_L116_); trivial. % 9.92/10.10 exact (zenon_H80 zenon_H84). % 9.92/10.10 (* end of lemma zenon_L158_ *) % 9.92/10.10 assert (zenon_L159_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (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)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (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)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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 (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H177 zenon_He4 zenon_Hbd zenon_H80 zenon_H152 zenon_H174 zenon_Hfd zenon_H10b zenon_H144 zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H158 zenon_H151 zenon_H16b zenon_H95 zenon_H1f zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H14d zenon_H44 zenon_H53 zenon_H5e zenon_H169 zenon_H35 zenon_H7a zenon_Hf5 zenon_H64 zenon_H4c zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H108 zenon_H165 zenon_H16e zenon_H103 zenon_H155 zenon_H156 zenon_H168 zenon_H159 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_H12f zenon_Hf8 zenon_H173 zenon_H7f. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 9.92/10.10 apply (zenon_L99_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 9.92/10.10 apply (zenon_L50_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 9.92/10.10 apply (zenon_L158_); trivial. % 9.92/10.10 exact (zenon_H7f zenon_H85). % 9.92/10.10 (* end of lemma zenon_L159_ *) % 9.92/10.10 assert (zenon_L160_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hec zenon_H44 zenon_He4 zenon_H95 zenon_Hbd zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.92/10.10 apply (zenon_L159_); trivial. % 9.92/10.10 apply (zenon_L60_); trivial. % 9.92/10.10 (* end of lemma zenon_L160_ *) % 9.92/10.10 assert (zenon_L161_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H84 zenon_Hbd zenon_H17a. % 9.92/10.10 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 9.92/10.10 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H17a. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hf9. % 9.92/10.10 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.92/10.10 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H17b. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H84. % 9.92/10.10 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 9.92/10.10 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_Hfa. apply refl_equal. % 9.92/10.10 apply zenon_Hbe. apply sym_equal. exact zenon_Hbd. % 9.92/10.10 apply zenon_Hfa. apply refl_equal. % 9.92/10.10 apply zenon_Hfa. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L161_ *) % 9.92/10.10 assert (zenon_L162_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hd0 zenon_H9b zenon_H17c. % 9.92/10.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H17c. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H17d. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H17f. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hd0. % 9.92/10.10 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H17e. apply refl_equal. % 9.92/10.10 apply zenon_H180. apply sym_equal. exact zenon_H9b. % 9.92/10.10 apply zenon_H17e. apply refl_equal. % 9.92/10.10 apply zenon_H17e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L162_ *) % 9.92/10.10 assert (zenon_L163_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hd0 zenon_H47 zenon_H181. % 9.92/10.10 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H181. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H17d. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H182. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hd0. % 9.92/10.10 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 9.92/10.10 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H17e. apply refl_equal. % 9.92/10.10 apply zenon_H183. apply sym_equal. exact zenon_H47. % 9.92/10.10 apply zenon_H17e. apply refl_equal. % 9.92/10.10 apply zenon_H17e. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L163_ *) % 9.92/10.10 assert (zenon_L164_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H184 zenon_Hb8 zenon_Hd0. % 9.92/10.10 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H184. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_Hb8. % 9.92/10.10 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 9.92/10.10 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H185. apply refl_equal. % 9.92/10.10 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 9.92/10.10 (* end of lemma zenon_L164_ *) % 9.92/10.10 assert (zenon_L165_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H73 zenon_H76 zenon_H5e. % 9.92/10.10 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H5f | zenon_intro zenon_H33 ]. % 9.92/10.10 cut (((e1) = (e1)) = ((e0) = (e1))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H5e. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H5f. % 9.92/10.10 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.92/10.10 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 9.92/10.10 congruence. % 9.92/10.10 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H60. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H73. % 9.92/10.10 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.92/10.10 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 9.92/10.10 congruence. % 9.92/10.10 exact (zenon_Hd5 zenon_H76). % 9.92/10.10 apply zenon_H41. apply refl_equal. % 9.92/10.10 apply zenon_H33. apply refl_equal. % 9.92/10.10 apply zenon_H33. apply refl_equal. % 9.92/10.10 (* end of lemma zenon_L165_ *) % 9.92/10.10 assert (zenon_L166_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H17c zenon_H9a zenon_H8a. % 9.92/10.10 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H17c. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H9a. % 9.92/10.10 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H186]. % 9.92/10.10 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H88. apply refl_equal. % 9.92/10.10 apply zenon_H186. apply sym_equal. exact zenon_H8a. % 9.92/10.10 (* end of lemma zenon_L166_ *) % 9.92/10.10 assert (zenon_L167_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 9.92/10.10 do 0 intro. intros zenon_H187 zenon_H57 zenon_H188. % 9.92/10.10 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 9.92/10.10 intro zenon_D_pnotp. % 9.92/10.10 apply zenon_H187. % 9.92/10.10 rewrite <- zenon_D_pnotp. % 9.92/10.10 exact zenon_H57. % 9.92/10.10 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 9.92/10.10 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.92/10.10 congruence. % 9.92/10.10 apply zenon_H5a. apply refl_equal. % 9.92/10.10 apply zenon_H189. apply sym_equal. exact zenon_H188. % 9.92/10.10 (* end of lemma zenon_L167_ *) % 9.92/10.10 assert (zenon_L168_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((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)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 9.92/10.10 do 0 intro. intros zenon_Hc0 zenon_H53 zenon_H68 zenon_Hc1 zenon_H57 zenon_H187 zenon_Hd0 zenon_H17c zenon_H86 zenon_H18a zenon_H5e zenon_H7d zenon_H7e zenon_H7f zenon_H80 zenon_H7a zenon_H8c zenon_H91 zenon_H4c zenon_H73 zenon_H90 zenon_H95 zenon_Hd6. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.92/10.10 apply (zenon_L30_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.92/10.10 exact (zenon_Hc1 zenon_Hc4). % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.92/10.10 apply (zenon_L165_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.92/10.10 apply (zenon_L48_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.92/10.10 exact (zenon_H91 zenon_H94). % 9.92/10.10 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.92/10.10 apply (zenon_L24_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.92/10.10 apply (zenon_L26_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.92/10.10 apply (zenon_L27_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 9.92/10.10 apply (zenon_L25_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 9.92/10.10 apply (zenon_L166_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 9.92/10.10 apply (zenon_L162_); trivial. % 9.92/10.10 apply (zenon_L167_); trivial. % 9.92/10.10 apply (zenon_L50_); trivial. % 9.92/10.10 (* end of lemma zenon_L168_ *) % 9.92/10.10 assert (zenon_L169_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (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))))) -> (~((e0) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.92/10.10 do 0 intro. intros zenon_H42 zenon_H27 zenon_H95 zenon_H90 zenon_H73 zenon_H4c zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H7d zenon_H5e zenon_H18a zenon_H86 zenon_H17c zenon_H187 zenon_Hc1 zenon_H68 zenon_H53 zenon_Hc0 zenon_H184 zenon_Haf zenon_H44 zenon_Hde zenon_H28 zenon_H97 zenon_Hd0 zenon_H181. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.92/10.10 exact (zenon_H27 zenon_H32). % 9.92/10.10 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.92/10.10 apply (zenon_L16_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.92/10.10 exact (zenon_H28 zenon_H31). % 9.92/10.10 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.92/10.10 apply (zenon_L30_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.92/10.10 apply (zenon_L32_); trivial. % 9.92/10.10 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.94/10.11 exact (zenon_Haf zenon_Hb4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.94/10.11 apply (zenon_L164_); trivial. % 9.94/10.11 apply (zenon_L168_); trivial. % 9.94/10.11 apply (zenon_L163_); trivial. % 9.94/10.11 (* end of lemma zenon_L169_ *) % 9.94/10.11 assert (zenon_L170_ : (((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). % 9.94/10.11 do 0 intro. intros zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H95 zenon_H3b zenon_H84 zenon_H7a. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.94/10.11 exact (zenon_H28 zenon_H31). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.94/10.11 apply (zenon_L30_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.94/10.11 apply (zenon_L32_); trivial. % 9.94/10.11 apply (zenon_L68_); trivial. % 9.94/10.11 (* end of lemma zenon_L170_ *) % 9.94/10.11 assert (zenon_L171_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H7a zenon_H84 zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_Hd0 zenon_H181. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_L170_); trivial. % 9.94/10.11 apply (zenon_L163_); trivial. % 9.94/10.11 (* end of lemma zenon_L171_ *) % 9.94/10.11 assert (zenon_L172_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (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)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hd2 zenon_H27 zenon_H44 zenon_H68 zenon_H97 zenon_H84 zenon_H7a zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.94/10.11 apply (zenon_L43_); trivial. % 9.94/10.11 apply (zenon_L171_); trivial. % 9.94/10.11 (* end of lemma zenon_L172_ *) % 9.94/10.11 assert (zenon_L173_ : (((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). % 9.94/10.11 do 0 intro. intros zenon_Hc0 zenon_H53 zenon_H68 zenon_Hc1 zenon_H95 zenon_Hb8 zenon_H84 zenon_H17a. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.94/10.11 apply (zenon_L30_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_L40_); trivial. % 9.94/10.11 apply (zenon_L161_); trivial. % 9.94/10.11 (* end of lemma zenon_L173_ *) % 9.94/10.11 assert (zenon_L174_ : ((~((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 (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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 (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H157 zenon_Hc1 zenon_H17a zenon_Hc0 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H68 zenon_H44 zenon_H27 zenon_Hd2. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.94/10.11 apply (zenon_L172_); trivial. % 9.94/10.11 apply (zenon_L173_); trivial. % 9.94/10.11 (* end of lemma zenon_L174_ *) % 9.94/10.11 assert (zenon_L175_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H18d zenon_Hd2 zenon_Hc6 zenon_Hc7 zenon_Hc5 zenon_H17a zenon_H157 zenon_H27 zenon_H44 zenon_H68 zenon_H97 zenon_Haf zenon_H184 zenon_Hd0 zenon_Hc0 zenon_H5e zenon_H73 zenon_H4c zenon_H91 zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7e zenon_H7f zenon_H7d zenon_H90 zenon_Hc1 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.94/10.11 apply (zenon_L169_); trivial. % 9.94/10.11 apply (zenon_L174_); trivial. % 9.94/10.11 (* end of lemma zenon_L175_ *) % 9.94/10.11 assert (zenon_L176_ : ((~((op (e3) (e3)) = (e1)))\/((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 (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H151 zenon_H25 zenon_H42 zenon_H181 zenon_Haf zenon_H6f zenon_H17c zenon_Hd0 zenon_Hae zenon_H68 zenon_H44 zenon_H27 zenon_H18d zenon_Hd2 zenon_Hc6 zenon_Hc7 zenon_Hc5 zenon_H17a zenon_H157 zenon_H97 zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H91 zenon_H8c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hc1 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H35 zenon_Hb1 zenon_H108 zenon_Hf8. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.94/10.11 exact (zenon_H25 zenon_H2a). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 9.94/10.11 apply (zenon_L17_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 9.94/10.11 exact (zenon_Haf zenon_Hb4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 9.94/10.11 apply (zenon_L19_); trivial. % 9.94/10.11 apply (zenon_L162_); trivial. % 9.94/10.11 apply (zenon_L163_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.94/10.11 apply (zenon_L175_); trivial. % 9.94/10.11 apply (zenon_L56_); trivial. % 9.94/10.11 apply (zenon_L171_); trivial. % 9.94/10.11 apply (zenon_L77_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.94/10.11 exact (zenon_Haf zenon_Hb4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.94/10.11 apply (zenon_L164_); trivial. % 9.94/10.11 apply (zenon_L50_); trivial. % 9.94/10.11 (* end of lemma zenon_L176_ *) % 9.94/10.11 assert (zenon_L177_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_He8 zenon_Hec zenon_Hf8 zenon_H27 zenon_H44 zenon_H68 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Haf zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hc1 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H57 zenon_H42 zenon_H25 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H64 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H1d zenon_H112 zenon_H114 zenon_H118 zenon_H17a. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.94/10.11 exact (zenon_H25 zenon_H2a). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_L53_); trivial. % 9.94/10.11 apply (zenon_L54_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.94/10.11 apply (zenon_L43_); trivial. % 9.94/10.11 apply (zenon_L67_); trivial. % 9.94/10.11 apply (zenon_L68_); trivial. % 9.94/10.11 apply (zenon_L77_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.94/10.11 exact (zenon_H25 zenon_H2a). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_L84_); trivial. % 9.94/10.11 apply (zenon_L54_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.94/10.11 apply (zenon_L98_); trivial. % 9.94/10.11 apply (zenon_L160_); trivial. % 9.94/10.11 apply (zenon_L161_); trivial. % 9.94/10.11 apply (zenon_L60_); trivial. % 9.94/10.11 apply (zenon_L176_); trivial. % 9.94/10.11 (* end of lemma zenon_L177_ *) % 9.94/10.11 assert (zenon_L178_ : (((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 (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H57 zenon_H95. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_L5_); trivial. % 9.94/10.11 apply (zenon_L54_); trivial. % 9.94/10.11 (* end of lemma zenon_L178_ *) % 9.94/10.11 assert (zenon_L179_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((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))) -> (~((e0) = (e1))) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hae zenon_H69 zenon_Haf zenon_H6f zenon_Hb0 zenon_H74 zenon_Hb8 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H3b zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 9.94/10.11 apply (zenon_L17_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 9.94/10.11 exact (zenon_Haf zenon_Hb4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 9.94/10.11 apply (zenon_L19_); trivial. % 9.94/10.11 apply (zenon_L82_); trivial. % 9.94/10.11 (* end of lemma zenon_L179_ *) % 9.94/10.11 assert (zenon_L180_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (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 (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hda zenon_H5e zenon_H35 zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H3b zenon_H4c zenon_Hab zenon_Hb1 zenon_H44 zenon_Hb8 zenon_Hb0 zenon_H6f zenon_Haf zenon_H69 zenon_Hae zenon_H95 zenon_Hd8. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.94/10.11 exact (zenon_H28 zenon_H31). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.94/10.11 apply (zenon_L18_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.94/10.11 apply (zenon_L179_); trivial. % 9.94/10.11 apply (zenon_L51_); trivial. % 9.94/10.11 (* end of lemma zenon_L180_ *) % 9.94/10.11 assert (zenon_L181_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (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 (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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))))) -> (~((e2) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H112 zenon_Hda zenon_H5e zenon_H35 zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H3b zenon_H4c zenon_Hab zenon_Hb1 zenon_H44 zenon_Hb8 zenon_Hb0 zenon_H6f zenon_Haf zenon_H69 zenon_Hae zenon_H95. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.94/10.11 apply (zenon_L17_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.94/10.11 apply (zenon_L79_); trivial. % 9.94/10.11 apply (zenon_L180_); trivial. % 9.94/10.11 (* end of lemma zenon_L181_ *) % 9.94/10.11 assert (zenon_L182_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hc0 zenon_Hc1 zenon_Hb8 zenon_H12c zenon_H73 zenon_H114 zenon_Hc8 zenon_H8c zenon_H68 zenon_H11b zenon_H7f zenon_H95 zenon_H44 zenon_H128 zenon_H4c zenon_H11d zenon_H1d zenon_H7d zenon_H7a zenon_H80 zenon_Hab zenon_H53 zenon_H8d. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.94/10.11 apply (zenon_L30_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_L40_); trivial. % 9.94/10.11 apply (zenon_L98_); trivial. % 9.94/10.11 (* end of lemma zenon_L182_ *) % 9.94/10.11 assert (zenon_L183_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hc0 zenon_H53 zenon_H68 zenon_Hc1 zenon_H95 zenon_Hb8 zenon_Hec zenon_Hed. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.94/10.11 apply (zenon_L30_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_L40_); trivial. % 9.94/10.11 apply (zenon_L60_); trivial. % 9.94/10.11 (* end of lemma zenon_L183_ *) % 9.94/10.11 assert (zenon_L184_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H34 zenon_H4b zenon_H95. % 9.94/10.11 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.94/10.11 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H95. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H4d. % 9.94/10.11 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.94/10.11 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.94/10.11 congruence. % 9.94/10.11 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H96. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H34. % 9.94/10.11 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.94/10.11 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 9.94/10.11 congruence. % 9.94/10.11 exact (zenon_H50 zenon_H4b). % 9.94/10.11 apply zenon_H37. apply refl_equal. % 9.94/10.11 apply zenon_H4e. apply refl_equal. % 9.94/10.11 apply zenon_H4e. apply refl_equal. % 9.94/10.11 (* end of lemma zenon_L184_ *) % 9.94/10.11 assert (zenon_L185_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_He7 zenon_He8 zenon_H44 zenon_Hc0 zenon_H34 zenon_Hc1 zenon_H95 zenon_Hb8 zenon_H53. % 9.94/10.11 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.94/10.11 exact (zenon_He8 zenon_Heb). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.94/10.11 apply (zenon_L57_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.94/10.11 apply (zenon_L184_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_L40_); trivial. % 9.94/10.11 apply (zenon_L112_); trivial. % 9.94/10.11 (* end of lemma zenon_L185_ *) % 9.94/10.11 assert (zenon_L186_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hf8 zenon_He7 zenon_Hbb zenon_Hb8 zenon_H44 zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.94/10.11 apply (zenon_L56_); trivial. % 9.94/10.11 apply (zenon_L61_); trivial. % 9.94/10.11 (* end of lemma zenon_L186_ *) % 9.94/10.11 assert (zenon_L187_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_H44 zenon_Hb8 zenon_Hbb zenon_He7 zenon_Hf8. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_L186_); trivial. % 9.94/10.11 apply (zenon_L160_); trivial. % 9.94/10.11 (* end of lemma zenon_L187_ *) % 9.94/10.11 assert (zenon_L188_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H18e zenon_He3 zenon_Hde zenon_Hf5 zenon_He7 zenon_Hbb zenon_He8 zenon_Hec zenon_Hf8 zenon_Hc1 zenon_H12c zenon_H11b zenon_H128 zenon_H1d zenon_H11d zenon_H8d zenon_H7a zenon_H7d zenon_H8c zenon_H114 zenon_Hc0 zenon_H27 zenon_H44 zenon_H68 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_Hb1 zenon_Hab zenon_H5e zenon_H35 zenon_H95 zenon_H4c zenon_H97 zenon_Hb0 zenon_H6f zenon_Haf zenon_Hda zenon_Hb8 zenon_H112 zenon_H57 zenon_H42 zenon_H25 zenon_H18d zenon_H173 zenon_H16e zenon_H64 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_Hd3 zenon_H110 zenon_H118 zenon_H17a. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.94/10.11 exact (zenon_H25 zenon_H2a). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L16_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_L181_); trivial. % 9.94/10.11 apply (zenon_L54_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.94/10.11 apply (zenon_L182_); trivial. % 9.94/10.11 apply (zenon_L67_); trivial. % 9.94/10.11 apply (zenon_L68_); trivial. % 9.94/10.11 apply (zenon_L183_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.94/10.11 exact (zenon_H25 zenon_H2a). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.11 apply (zenon_L185_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.94/10.11 exact (zenon_H27 zenon_H32). % 9.94/10.11 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.94/10.11 apply (zenon_L17_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.94/10.11 apply (zenon_L81_); trivial. % 9.94/10.11 apply (zenon_L180_); trivial. % 9.94/10.11 apply (zenon_L54_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.94/10.11 apply (zenon_L98_); trivial. % 9.94/10.11 apply (zenon_L187_); trivial. % 9.94/10.11 apply (zenon_L161_); trivial. % 9.94/10.11 apply (zenon_L60_); trivial. % 9.94/10.11 apply (zenon_L164_); trivial. % 9.94/10.11 (* end of lemma zenon_L188_ *) % 9.94/10.11 assert (zenon_L189_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_He8 zenon_Hec zenon_Hf8 zenon_H27 zenon_H44 zenon_H68 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Haf zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hc1 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H57 zenon_H42 zenon_H25 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H64 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H1d zenon_H112 zenon_H114 zenon_H118 zenon_H17a. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.94/10.11 apply (zenon_L177_); trivial. % 9.94/10.11 apply (zenon_L178_); trivial. % 9.94/10.11 apply (zenon_L188_); trivial. % 9.94/10.11 (* end of lemma zenon_L189_ *) % 9.94/10.11 assert (zenon_L190_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H191 zenon_He8 zenon_H192 zenon_Haf zenon_Hc1. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.94/10.11 exact (zenon_He8 zenon_Heb). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.94/10.11 exact (zenon_H192 zenon_H1d). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.94/10.11 exact (zenon_Haf zenon_Hb4). % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 (* end of lemma zenon_L190_ *) % 9.94/10.11 assert (zenon_L191_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H191 zenon_H69 zenon_H195 zenon_H192 zenon_Haf zenon_Hc1. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.94/10.11 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H195. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H69. % 9.94/10.11 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 9.94/10.11 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 9.94/10.11 congruence. % 9.94/10.11 apply zenon_H15c. apply refl_equal. % 9.94/10.11 apply zenon_H196. apply sym_equal. exact zenon_Heb. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.94/10.11 exact (zenon_H192 zenon_H1d). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.94/10.11 exact (zenon_Haf zenon_Hb4). % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 (* end of lemma zenon_L191_ *) % 9.94/10.11 assert (zenon_L192_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 9.94/10.11 do 0 intro. intros zenon_H5e zenon_H9a zenon_H87. % 9.94/10.11 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H5e. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H9a. % 9.94/10.11 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.11 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 9.94/10.11 congruence. % 9.94/10.11 exact (zenon_H197 zenon_H87). % 9.94/10.11 apply zenon_H33. apply refl_equal. % 9.94/10.11 (* end of lemma zenon_L192_ *) % 9.94/10.11 assert (zenon_L193_ : (((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). % 9.94/10.11 do 0 intro. intros zenon_H145 zenon_H2a zenon_H12f zenon_He8 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_Hc5 zenon_H5e zenon_H9a. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 9.94/10.11 apply (zenon_L100_); trivial. % 9.94/10.11 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 9.94/10.11 exact (zenon_He8 zenon_Heb). % 9.94/10.11 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 9.94/10.11 apply (zenon_L118_); trivial. % 9.94/10.11 apply (zenon_L192_); trivial. % 9.94/10.11 (* end of lemma zenon_L193_ *) % 9.94/10.11 assert (zenon_L194_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 9.94/10.11 do 0 intro. intros zenon_H198 zenon_H15a zenon_H9a. % 9.94/10.11 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H198. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H15a. % 9.94/10.11 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 9.94/10.11 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 9.94/10.11 congruence. % 9.94/10.11 apply zenon_H15c. apply refl_equal. % 9.94/10.11 apply zenon_H11e. apply sym_equal. exact zenon_H9a. % 9.94/10.11 (* end of lemma zenon_L194_ *) % 9.94/10.11 assert (zenon_L195_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H6e zenon_H6a zenon_H159. % 9.94/10.11 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 9.94/10.11 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H159. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H70. % 9.94/10.11 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.94/10.11 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 9.94/10.11 congruence. % 9.94/10.11 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H199. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H6e. % 9.94/10.11 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 9.94/10.11 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.94/10.11 congruence. % 9.94/10.11 apply zenon_H71. apply refl_equal. % 9.94/10.11 apply zenon_H19a. apply sym_equal. exact zenon_H6a. % 9.94/10.11 apply zenon_H71. apply refl_equal. % 9.94/10.11 apply zenon_H71. apply refl_equal. % 9.94/10.11 (* end of lemma zenon_L195_ *) % 9.94/10.11 assert (zenon_L196_ : ((op (e2) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_H77 zenon_H1e zenon_Hd3. % 9.94/10.11 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H19b | zenon_intro zenon_H185 ]. % 9.94/10.11 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_Hd3. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H19b. % 9.94/10.11 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 9.94/10.11 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 9.94/10.11 congruence. % 9.94/10.11 cut (((op (e2) (e1)) = (e1)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H19c. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H77. % 9.94/10.11 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 9.94/10.11 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 9.94/10.11 congruence. % 9.94/10.11 apply zenon_H185. apply refl_equal. % 9.94/10.11 apply zenon_H23. apply sym_equal. exact zenon_H1e. % 9.94/10.11 apply zenon_H185. apply refl_equal. % 9.94/10.11 apply zenon_H185. apply refl_equal. % 9.94/10.11 (* end of lemma zenon_L196_ *) % 9.94/10.11 assert (zenon_L197_ : (~((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 9.94/10.11 do 0 intro. intros zenon_H19d zenon_Hc4. % 9.94/10.11 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.11 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 9.94/10.11 congruence. % 9.94/10.11 exact (zenon_Hc1 zenon_Hc4). % 9.94/10.11 apply zenon_H33. apply refl_equal. % 9.94/10.11 (* end of lemma zenon_L197_ *) % 9.94/10.11 assert (zenon_L198_ : ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 9.94/10.11 do 0 intro. intros zenon_He5 zenon_Hc4 zenon_H19e. % 9.94/10.11 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 9.94/10.11 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H19e. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H19f. % 9.94/10.11 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.94/10.11 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 9.94/10.11 congruence. % 9.94/10.11 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H1a1. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_He5. % 9.94/10.11 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.94/10.11 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 9.94/10.11 congruence. % 9.94/10.11 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 9.94/10.11 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 9.94/10.11 intro zenon_D_pnotp. % 9.94/10.11 apply zenon_H1a2. % 9.94/10.11 rewrite <- zenon_D_pnotp. % 9.94/10.11 exact zenon_H19f. % 9.94/10.11 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.94/10.11 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 9.94/10.11 congruence. % 9.94/10.11 apply (zenon_L197_); trivial. % 9.94/10.11 apply zenon_H1a0. apply refl_equal. % 9.94/10.12 apply zenon_H1a0. apply refl_equal. % 9.94/10.12 apply zenon_H41. apply refl_equal. % 9.94/10.12 apply zenon_H1a0. apply refl_equal. % 9.94/10.12 apply zenon_H1a0. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L198_ *) % 9.94/10.12 assert (zenon_L199_ : ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 9.94/10.12 do 0 intro. intros zenon_H34 zenon_He5 zenon_Hc4. % 9.94/10.12 apply (zenon_notand_s _ _ ax28); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a3 ]. % 9.94/10.12 apply zenon_H1a4. apply sym_equal. exact zenon_Hc4. % 9.94/10.12 apply (zenon_notand_s _ _ zenon_H1a3); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H19e ]. % 9.94/10.12 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1a7 ]. % 9.94/10.12 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e2) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1a5. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H1a6. % 9.94/10.12 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 9.94/10.12 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e0) (e1)) = (e2)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e2))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1a8. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H34. % 9.94/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.94/10.12 cut (((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 9.94/10.12 congruence. % 9.94/10.12 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1a7 ]. % 9.94/10.12 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1a9. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H1a6. % 9.94/10.12 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 9.94/10.12 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.12 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1a1. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_He5. % 9.94/10.12 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.94/10.12 cut (((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 9.94/10.12 congruence. % 9.94/10.12 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 9.94/10.12 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e3) (e1)) = (op (op (e1) (e1)) (e1)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1a2. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H19f. % 9.94/10.12 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.94/10.12 cut (((op (op (e1) (e1)) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 9.94/10.12 congruence. % 9.94/10.12 apply (zenon_L197_); trivial. % 9.94/10.12 apply zenon_H1a0. apply refl_equal. % 9.94/10.12 apply zenon_H1a0. apply refl_equal. % 9.94/10.12 apply zenon_H41. apply refl_equal. % 9.94/10.12 apply zenon_H33. apply refl_equal. % 9.94/10.12 apply zenon_H1a7. apply refl_equal. % 9.94/10.12 apply zenon_H1a7. apply refl_equal. % 9.94/10.12 apply zenon_H37. apply refl_equal. % 9.94/10.12 apply zenon_H1a7. apply refl_equal. % 9.94/10.12 apply zenon_H1a7. apply refl_equal. % 9.94/10.12 apply (zenon_L198_); trivial. % 9.94/10.12 (* end of lemma zenon_L199_ *) % 9.94/10.12 assert (zenon_L200_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H42 zenon_H27 zenon_Hbd zenon_H53 zenon_H5e zenon_H77 zenon_He8 zenon_H44 zenon_He7 zenon_H35 zenon_H5d zenon_Hd0 zenon_H181. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.94/10.12 apply (zenon_L16_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.94/10.12 exact (zenon_He8 zenon_Heb). % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.94/10.12 apply (zenon_L22_); trivial. % 9.94/10.12 apply (zenon_L112_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.12 apply (zenon_L70_); trivial. % 9.94/10.12 apply (zenon_L163_); trivial. % 9.94/10.12 (* end of lemma zenon_L200_ *) % 9.94/10.12 assert (zenon_L201_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_He7 zenon_H44 zenon_He8 zenon_H77 zenon_H5e zenon_H53 zenon_H27 zenon_H42 zenon_H4c zenon_H95 zenon_Hc0 zenon_H35 zenon_H5d zenon_Hd0 zenon_H181. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.94/10.12 apply (zenon_L16_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.94/10.12 exact (zenon_He8 zenon_Heb). % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.94/10.12 apply (zenon_L22_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.94/10.12 apply (zenon_L184_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.94/10.12 apply (zenon_L199_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.94/10.12 apply (zenon_L48_); trivial. % 9.94/10.12 apply (zenon_L200_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.12 apply (zenon_L70_); trivial. % 9.94/10.12 apply (zenon_L163_); trivial. % 9.94/10.12 (* end of lemma zenon_L201_ *) % 9.94/10.12 assert (zenon_L202_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H9a zenon_H62 zenon_H187. % 9.94/10.12 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H1ab | zenon_intro zenon_H88 ]. % 9.94/10.12 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H187. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H1ab. % 9.94/10.12 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.94/10.12 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1ac. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H9a. % 9.94/10.12 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 9.94/10.12 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.94/10.12 congruence. % 9.94/10.12 apply zenon_H88. apply refl_equal. % 9.94/10.12 apply zenon_H1ad. apply sym_equal. exact zenon_H62. % 9.94/10.12 apply zenon_H88. apply refl_equal. % 9.94/10.12 apply zenon_H88. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L202_ *) % 9.94/10.12 assert (zenon_L203_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H77 zenon_Hb8 zenon_H35. % 9.94/10.12 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.94/10.12 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H35. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H36. % 9.94/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.94/10.12 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e2) (e1)) = (e1)) = ((e2) = (e1))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H38. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H77. % 9.94/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.12 cut (((op (e2) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 9.94/10.12 congruence. % 9.94/10.12 exact (zenon_H1ae zenon_Hb8). % 9.94/10.12 apply zenon_H33. apply refl_equal. % 9.94/10.12 apply zenon_H37. apply refl_equal. % 9.94/10.12 apply zenon_H37. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L203_ *) % 9.94/10.12 assert (zenon_L204_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (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)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H157 zenon_H145 zenon_H9a zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H64 zenon_H187 zenon_H27 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H35 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H77 zenon_Hd3 zenon_H56 zenon_Hd2. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.94/10.12 apply (zenon_L193_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.94/10.12 exact (zenon_H56 zenon_H2c). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.94/10.12 apply (zenon_L196_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.94/10.12 apply (zenon_L201_); trivial. % 9.94/10.12 apply (zenon_L202_); trivial. % 9.94/10.12 apply (zenon_L203_); trivial. % 9.94/10.12 (* end of lemma zenon_L204_ *) % 9.94/10.12 assert (zenon_L205_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H1af zenon_Hd2 zenon_H56 zenon_Hd3 zenon_H77 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H35 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H27 zenon_H187 zenon_H64 zenon_H12f zenon_H2a zenon_Hc5 zenon_Hc7 zenon_H155 zenon_H5e zenon_H145 zenon_H157 zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.94/10.12 apply (zenon_L190_); trivial. % 9.94/10.12 apply (zenon_L204_); trivial. % 9.94/10.12 (* end of lemma zenon_L205_ *) % 9.94/10.12 assert (zenon_L206_ : (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> False). % 9.94/10.12 do 0 intro. intros zenon_H5e zenon_Hf2 zenon_He5. % 9.94/10.12 cut (((op (e3) (e1)) = (e1)) = ((e0) = (e1))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H5e. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_Hf2. % 9.94/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.12 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 9.94/10.12 congruence. % 9.94/10.12 exact (zenon_H14c zenon_He5). % 9.94/10.12 apply zenon_H33. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L206_ *) % 9.94/10.12 assert (zenon_L207_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.94/10.12 do 0 intro. intros zenon_Hf2 zenon_Hbd zenon_H4c. % 9.94/10.12 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.94/10.12 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H4c. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H4d. % 9.94/10.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.94/10.12 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e3) (e1)) = (e1)) = ((e3) = (e1))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H4f. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_Hf2. % 9.94/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.12 cut (((op (e3) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 9.94/10.12 congruence. % 9.94/10.12 exact (zenon_H1b0 zenon_Hbd). % 9.94/10.12 apply zenon_H33. apply refl_equal. % 9.94/10.12 apply zenon_H4e. apply refl_equal. % 9.94/10.12 apply zenon_H4e. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L207_ *) % 9.94/10.12 assert (zenon_L208_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H16b zenon_Hd8 zenon_H95 zenon_H4c zenon_Hf2 zenon_H106 zenon_H53 zenon_H80. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbc | zenon_intro zenon_H16c ]. % 9.94/10.12 apply (zenon_L51_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_Hbd | zenon_intro zenon_H16d ]. % 9.94/10.12 apply (zenon_L207_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hed | zenon_intro zenon_H84 ]. % 9.94/10.12 apply (zenon_L73_); trivial. % 9.94/10.12 exact (zenon_H80 zenon_H84). % 9.94/10.12 (* end of lemma zenon_L208_ *) % 9.94/10.12 assert (zenon_L209_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H14d zenon_H44 zenon_H5e zenon_H80 zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_Hd8 zenon_H16b zenon_H8d. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 9.94/10.12 apply (zenon_L99_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 9.94/10.12 apply (zenon_L206_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 9.94/10.12 apply (zenon_L208_); trivial. % 9.94/10.12 exact (zenon_H8d zenon_H7b). % 9.94/10.12 (* end of lemma zenon_L209_ *) % 9.94/10.12 assert (zenon_L210_ : (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((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 (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H8d zenon_H16b zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H5e zenon_H44 zenon_H14d zenon_H1af zenon_Hd2 zenon_H56 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H35 zenon_H42 zenon_H27 zenon_H187 zenon_H64 zenon_H12f zenon_H2a zenon_Hc5 zenon_Hc7 zenon_H155 zenon_H145 zenon_H157 zenon_He8 zenon_H192 zenon_Haf zenon_H191 zenon_H1b1 zenon_H76 zenon_H159 zenon_Hdd zenon_H6f zenon_H6e zenon_Hd0 zenon_H181. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.94/10.12 apply (zenon_L195_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.94/10.12 apply (zenon_L47_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.94/10.12 apply (zenon_L4_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.94/10.12 exact (zenon_H192 zenon_H1d). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.94/10.12 apply (zenon_L205_); trivial. % 9.94/10.12 apply (zenon_L209_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.94/10.12 apply (zenon_L19_); trivial. % 9.94/10.12 apply (zenon_L163_); trivial. % 9.94/10.12 (* end of lemma zenon_L210_ *) % 9.94/10.12 assert (zenon_L211_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.94/10.12 do 0 intro. intros zenon_Hf0 zenon_Hd8 zenon_H35. % 9.94/10.12 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.94/10.12 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H35. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H36. % 9.94/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.94/10.12 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H38. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_Hf0. % 9.94/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.94/10.12 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 9.94/10.12 congruence. % 9.94/10.12 exact (zenon_Hd9 zenon_Hd8). % 9.94/10.12 apply zenon_H33. apply refl_equal. % 9.94/10.12 apply zenon_H37. apply refl_equal. % 9.94/10.12 apply zenon_H37. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L211_ *) % 9.94/10.12 assert (zenon_L212_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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 (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H1b4 zenon_H9a zenon_H198 zenon_H181 zenon_H6f zenon_H1b1 zenon_H191 zenon_Haf zenon_H192 zenon_He8 zenon_H157 zenon_H145 zenon_H155 zenon_Hc7 zenon_Hc5 zenon_H2a zenon_H12f zenon_H64 zenon_H187 zenon_H42 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_H56 zenon_Hd2 zenon_H1af zenon_H14d zenon_H44 zenon_H5e zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H16b zenon_H8d zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_Hd0 zenon_Hce zenon_H35. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.94/10.12 exact (zenon_H56 zenon_H2c). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.94/10.12 apply (zenon_L194_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.94/10.12 apply (zenon_L210_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.94/10.12 apply (zenon_L195_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.94/10.12 apply (zenon_L44_); trivial. % 9.94/10.12 apply (zenon_L211_); trivial. % 9.94/10.12 (* end of lemma zenon_L212_ *) % 9.94/10.12 assert (zenon_L213_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 9.94/10.12 do 0 intro. intros zenon_H58 zenon_H2a zenon_H43. % 9.94/10.12 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H58. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H2a. % 9.94/10.12 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 9.94/10.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 9.94/10.12 congruence. % 9.94/10.12 apply zenon_H131. apply refl_equal. % 9.94/10.12 apply zenon_H11c. apply sym_equal. exact zenon_H43. % 9.94/10.12 (* end of lemma zenon_L213_ *) % 9.94/10.12 assert (zenon_L214_ : (((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H1b7 zenon_H2a zenon_H58 zenon_H187 zenon_H9a zenon_H181 zenon_Hd0 zenon_H84 zenon_H7a. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H43 | zenon_intro zenon_H1b8 ]. % 9.94/10.12 apply (zenon_L213_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H62 | zenon_intro zenon_H1b9 ]. % 9.94/10.12 apply (zenon_L202_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 9.94/10.12 apply (zenon_L163_); trivial. % 9.94/10.12 apply (zenon_L68_); trivial. % 9.94/10.12 (* end of lemma zenon_L214_ *) % 9.94/10.12 assert (zenon_L215_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((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)) = (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). % 9.94/10.12 do 0 intro. intros zenon_Hd2 zenon_H58 zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc7 zenon_H91 zenon_H155 zenon_H5e zenon_H9a zenon_H145. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.94/10.12 apply (zenon_L193_); trivial. % 9.94/10.12 apply (zenon_L214_); trivial. % 9.94/10.12 (* end of lemma zenon_L215_ *) % 9.94/10.12 assert (zenon_L216_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 9.94/10.12 do 0 intro. intros zenon_H1ba zenon_H2a zenon_H73. % 9.94/10.12 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1ba. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H2a. % 9.94/10.12 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 9.94/10.12 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 9.94/10.12 congruence. % 9.94/10.12 apply zenon_H131. apply refl_equal. % 9.94/10.12 apply zenon_H1bb. apply sym_equal. exact zenon_H73. % 9.94/10.12 (* end of lemma zenon_L216_ *) % 9.94/10.12 assert (zenon_L217_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 9.94/10.12 do 0 intro. intros zenon_H1bc zenon_H15a zenon_H76. % 9.94/10.12 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1bc. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H15a. % 9.94/10.12 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 9.94/10.12 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 9.94/10.12 congruence. % 9.94/10.12 apply zenon_H15c. apply refl_equal. % 9.94/10.12 apply zenon_H1bd. apply sym_equal. exact zenon_H76. % 9.94/10.12 (* end of lemma zenon_L217_ *) % 9.94/10.12 assert (zenon_L218_ : ((op (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_Hcf zenon_H6a zenon_H1bc. % 9.94/10.12 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_H1be | zenon_intro zenon_Hcb ]. % 9.94/10.12 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1bc. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H1be. % 9.94/10.12 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 9.94/10.12 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1bf. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_Hcf. % 9.94/10.12 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 9.94/10.12 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 9.94/10.12 congruence. % 9.94/10.12 apply zenon_Hcb. apply refl_equal. % 9.94/10.12 apply zenon_H19a. apply sym_equal. exact zenon_H6a. % 9.94/10.12 apply zenon_Hcb. apply refl_equal. % 9.94/10.12 apply zenon_Hcb. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L218_ *) % 9.94/10.12 assert (zenon_L219_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_Hbc zenon_H74 zenon_H1c0. % 9.94/10.12 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H170 | zenon_intro zenon_Hbf ]. % 9.94/10.12 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1c0. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_H170. % 9.94/10.12 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.94/10.12 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 9.94/10.12 congruence. % 9.94/10.12 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 9.94/10.12 intro zenon_D_pnotp. % 9.94/10.12 apply zenon_H1c1. % 9.94/10.12 rewrite <- zenon_D_pnotp. % 9.94/10.12 exact zenon_Hbc. % 9.94/10.12 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 9.94/10.12 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.94/10.12 congruence. % 9.94/10.12 apply zenon_Hbf. apply refl_equal. % 9.94/10.12 apply zenon_H1c2. apply sym_equal. exact zenon_H74. % 9.94/10.12 apply zenon_Hbf. apply refl_equal. % 9.94/10.12 apply zenon_Hbf. apply refl_equal. % 9.94/10.12 (* end of lemma zenon_L219_ *) % 9.94/10.12 assert (zenon_L220_ : (((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 (e1) (e0)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H1c3 zenon_H2a zenon_H1ba zenon_H15a zenon_H1bc zenon_H6a zenon_Hbc zenon_H1c0. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H73 | zenon_intro zenon_H1c4 ]. % 9.94/10.12 apply (zenon_L216_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H76 | zenon_intro zenon_H1c5 ]. % 9.94/10.12 apply (zenon_L217_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H74 ]. % 9.94/10.12 apply (zenon_L218_); trivial. % 9.94/10.12 apply (zenon_L219_); trivial. % 9.94/10.12 (* end of lemma zenon_L220_ *) % 9.94/10.12 assert (zenon_L221_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 9.94/10.12 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H1c0 zenon_H1bc zenon_H15a zenon_H1ba zenon_H2a zenon_H1c3 zenon_Hd0 zenon_Hce zenon_H95 zenon_Hbc. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.94/10.12 apply (zenon_L220_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.94/10.12 apply (zenon_L44_); trivial. % 9.94/10.12 apply (zenon_L51_); trivial. % 9.94/10.12 (* end of lemma zenon_L221_ *) % 9.94/10.12 assert (zenon_L222_ : (((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) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((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)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((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). % 9.94/10.12 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_Hce zenon_Hd0 zenon_H1c3 zenon_H2a zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H95 zenon_H35 zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_H4c zenon_Hbc. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.94/10.12 exact (zenon_H56 zenon_H2c). % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.94/10.12 apply (zenon_L221_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.94/10.12 exact (zenon_H27 zenon_H32). % 9.94/10.12 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.94/10.12 apply (zenon_L195_); trivial. % 9.94/10.12 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.94/10.12 apply (zenon_L47_); trivial. % 9.94/10.12 apply (zenon_L51_); trivial. % 9.94/10.12 apply (zenon_L139_); trivial. % 9.94/10.12 (* end of lemma zenon_L222_ *) % 9.94/10.12 assert (zenon_L223_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 9.94/10.12 do 0 intro. intros zenon_H3a zenon_H6e zenon_H155. % 9.95/10.12 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 9.95/10.12 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H155. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H3d. % 9.95/10.12 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.12 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1c6. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H3a. % 9.95/10.12 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 9.95/10.12 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.12 congruence. % 9.95/10.12 apply zenon_H3e. apply refl_equal. % 9.95/10.12 apply zenon_H1c7. apply sym_equal. exact zenon_H6e. % 9.95/10.12 apply zenon_H3e. apply refl_equal. % 9.95/10.12 apply zenon_H3e. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L223_ *) % 9.95/10.12 assert (zenon_L224_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H191 zenon_He8 zenon_H192 zenon_H16e zenon_H6e zenon_Hc1. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.95/10.12 exact (zenon_He8 zenon_Heb). % 9.95/10.12 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.95/10.12 exact (zenon_H192 zenon_H1d). % 9.95/10.12 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.95/10.12 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H16e. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H70. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1c8. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H6e. % 9.95/10.12 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.95/10.12 congruence. % 9.95/10.12 apply zenon_H71. apply refl_equal. % 9.95/10.12 apply zenon_H1c9. apply sym_equal. exact zenon_Hb4. % 9.95/10.12 apply zenon_H71. apply refl_equal. % 9.95/10.12 apply zenon_H71. apply refl_equal. % 9.95/10.12 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.12 (* end of lemma zenon_L224_ *) % 9.95/10.12 assert (zenon_L225_ : (((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 (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). % 9.95/10.12 do 0 intro. intros zenon_H145 zenon_H2a zenon_H12f zenon_He8 zenon_H100 zenon_H5e zenon_H7d zenon_H86 zenon_H7e zenon_H7f zenon_H80. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 9.95/10.12 apply (zenon_L100_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 9.95/10.12 exact (zenon_He8 zenon_Heb). % 9.95/10.12 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 9.95/10.12 apply (zenon_L71_); trivial. % 9.95/10.12 apply (zenon_L26_); trivial. % 9.95/10.12 (* end of lemma zenon_L225_ *) % 9.95/10.12 assert (zenon_L226_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H18d zenon_H58 zenon_H187 zenon_H9a zenon_H181 zenon_Hd0 zenon_H7a zenon_H1b7 zenon_H12f zenon_H2a zenon_He8 zenon_H5e zenon_H100 zenon_H7d zenon_H7f zenon_H7e zenon_H86 zenon_H145. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.12 apply (zenon_L225_); trivial. % 9.95/10.12 apply (zenon_L214_); trivial. % 9.95/10.12 (* end of lemma zenon_L226_ *) % 9.95/10.12 assert (zenon_L227_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H42 zenon_H27 zenon_H35 zenon_H1e zenon_H6f zenon_H6e zenon_Hd0 zenon_H181. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.12 exact (zenon_H27 zenon_H32). % 9.95/10.12 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.12 apply (zenon_L4_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.12 apply (zenon_L19_); trivial. % 9.95/10.12 apply (zenon_L163_); trivial. % 9.95/10.12 (* end of lemma zenon_L227_ *) % 9.95/10.12 assert (zenon_L228_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H100 zenon_H5d zenon_H6f. % 9.95/10.12 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H70 | zenon_intro zenon_H71 ]. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H6f. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H70. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H72. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H100. % 9.95/10.12 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 9.95/10.12 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.95/10.12 congruence. % 9.95/10.12 apply zenon_H71. apply refl_equal. % 9.95/10.12 apply zenon_H1ca. apply sym_equal. exact zenon_H5d. % 9.95/10.12 apply zenon_H71. apply refl_equal. % 9.95/10.12 apply zenon_H71. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L228_ *) % 9.95/10.12 assert (zenon_L229_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H62 zenon_H5d zenon_H1cb. % 9.95/10.12 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1cb. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H59. % 9.95/10.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1cc. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H62. % 9.95/10.12 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.95/10.12 congruence. % 9.95/10.12 apply zenon_H5a. apply refl_equal. % 9.95/10.12 apply zenon_H1ca. apply sym_equal. exact zenon_H5d. % 9.95/10.12 apply zenon_H5a. apply refl_equal. % 9.95/10.12 apply zenon_H5a. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L229_ *) % 9.95/10.12 assert (zenon_L230_ : (((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) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.12 do 0 intro. intros zenon_H103 zenon_H1cb zenon_H62 zenon_H101 zenon_H5e zenon_H91 zenon_H4c zenon_Hed. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.95/10.12 apply (zenon_L229_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.95/10.12 apply (zenon_L71_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.95/10.12 exact (zenon_H91 zenon_H94). % 9.95/10.12 apply (zenon_L64_); trivial. % 9.95/10.12 (* end of lemma zenon_L230_ *) % 9.95/10.12 assert (zenon_L231_ : (((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)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((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 (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.12 do 0 intro. intros zenon_H108 zenon_H2a zenon_H132 zenon_H4c zenon_H91 zenon_H5e zenon_H62 zenon_H1cb zenon_H103 zenon_Hb1 zenon_H53 zenon_Hed. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.95/10.12 apply (zenon_L101_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.95/10.12 apply (zenon_L230_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.95/10.12 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.12 apply (zenon_L73_); trivial. % 9.95/10.12 (* end of lemma zenon_L231_ *) % 9.95/10.12 assert (zenon_L232_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.12 do 0 intro. intros zenon_Hf8 zenon_H56 zenon_H42 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H108 zenon_H53 zenon_Hb1 zenon_H1cb zenon_H91 zenon_H4c zenon_H103 zenon_H132 zenon_H64 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H1b7 zenon_H7a zenon_Hd0 zenon_H181 zenon_H9a zenon_H187 zenon_H58 zenon_H18d. % 9.95/10.12 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.12 apply (zenon_L226_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.12 exact (zenon_H56 zenon_H2c). % 9.95/10.12 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.12 apply (zenon_L227_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.12 apply (zenon_L228_); trivial. % 9.95/10.12 apply (zenon_L231_); trivial. % 9.95/10.12 (* end of lemma zenon_L232_ *) % 9.95/10.12 assert (zenon_L233_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H158 zenon_H145 zenon_H9a zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_Hf8 zenon_H56 zenon_H42 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H108 zenon_H53 zenon_Hb1 zenon_H1cb zenon_H4c zenon_H103 zenon_H132 zenon_H64 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H1b7 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_H18d zenon_Hd2. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.12 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.12 apply (zenon_L193_); trivial. % 9.95/10.12 apply (zenon_L232_); trivial. % 9.95/10.12 apply (zenon_L223_); trivial. % 9.95/10.12 (* end of lemma zenon_L233_ *) % 9.95/10.12 assert (zenon_L234_ : (((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 (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 9.95/10.12 do 0 intro. intros zenon_H90 zenon_Hcf zenon_H35 zenon_Hd3 zenon_H1e zenon_H91 zenon_H17c zenon_H9a. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.12 apply (zenon_L47_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.12 apply (zenon_L196_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.12 exact (zenon_H91 zenon_H94). % 9.95/10.12 apply (zenon_L166_); trivial. % 9.95/10.12 (* end of lemma zenon_L234_ *) % 9.95/10.12 assert (zenon_L235_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H64 zenon_H56 zenon_H17c zenon_H91 zenon_Hd3 zenon_H35 zenon_Hcf zenon_H90 zenon_H6f zenon_H100 zenon_H9a zenon_H187. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.12 exact (zenon_H56 zenon_H2c). % 9.95/10.12 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.12 apply (zenon_L234_); trivial. % 9.95/10.12 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.12 apply (zenon_L228_); trivial. % 9.95/10.12 apply (zenon_L202_); trivial. % 9.95/10.12 (* end of lemma zenon_L235_ *) % 9.95/10.12 assert (zenon_L236_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H15a zenon_H6c zenon_H4c. % 9.95/10.12 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.95/10.12 cut (((e3) = (e3)) = ((e1) = (e3))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H4c. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H4d. % 9.95/10.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.12 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H4f. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H15a. % 9.95/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.12 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 9.95/10.12 congruence. % 9.95/10.12 exact (zenon_H6d zenon_H6c). % 9.95/10.12 apply zenon_H33. apply refl_equal. % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L236_ *) % 9.95/10.12 assert (zenon_L237_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H6e zenon_H161 zenon_H95. % 9.95/10.12 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.95/10.12 cut (((e3) = (e3)) = ((e2) = (e3))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H95. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H4d. % 9.95/10.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.12 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H96. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H6e. % 9.95/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.12 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 9.95/10.12 congruence. % 9.95/10.12 exact (zenon_H1cd zenon_H161). % 9.95/10.12 apply zenon_H37. apply refl_equal. % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L237_ *) % 9.95/10.12 assert (zenon_L238_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H15a zenon_H6a zenon_H35. % 9.95/10.12 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.95/10.12 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H35. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H36. % 9.95/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.12 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H38. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H15a. % 9.95/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.12 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 9.95/10.12 congruence. % 9.95/10.12 exact (zenon_H6b zenon_H6a). % 9.95/10.12 apply zenon_H33. apply refl_equal. % 9.95/10.12 apply zenon_H37. apply refl_equal. % 9.95/10.12 apply zenon_H37. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L238_ *) % 9.95/10.12 assert (zenon_L239_ : ((op (e1) (e3)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 9.95/10.12 do 0 intro. intros zenon_H188 zenon_H6c zenon_H198. % 9.95/10.12 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H1ab | zenon_intro zenon_H88 ]. % 9.95/10.12 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H198. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H1ab. % 9.95/10.12 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.95/10.12 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1ce. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H188. % 9.95/10.12 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 9.95/10.12 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.95/10.12 congruence. % 9.95/10.12 apply zenon_H88. apply refl_equal. % 9.95/10.12 apply zenon_H172. apply sym_equal. exact zenon_H6c. % 9.95/10.12 apply zenon_H88. apply refl_equal. % 9.95/10.12 apply zenon_H88. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L239_ *) % 9.95/10.12 assert (zenon_L240_ : (~((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e0)) -> False). % 9.95/10.12 do 0 intro. intros zenon_H1cf zenon_H7b. % 9.95/10.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.12 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 9.95/10.12 congruence. % 9.95/10.12 exact (zenon_H8d zenon_H7b). % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L240_ *) % 9.95/10.12 assert (zenon_L241_ : ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 9.95/10.12 do 0 intro. intros zenon_H8a zenon_H47 zenon_H7b. % 9.95/10.12 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H7c | zenon_intro zenon_H1d0 ]. % 9.95/10.12 apply zenon_H7c. apply sym_equal. exact zenon_H7b. % 9.95/10.12 apply (zenon_notand_s _ _ zenon_H1d0); [ zenon_intro zenon_H1d1 | zenon_intro zenon_Ha0 ]. % 9.95/10.12 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e1) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d1. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha2. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e2) (e3)) = (e1)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d2. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H8a. % 9.95/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.12 cut (((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 9.95/10.12 congruence. % 9.95/10.12 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_Ha5. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha2. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_Ha7. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H47. % 9.95/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 9.95/10.12 congruence. % 9.95/10.12 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d3. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha9. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 9.95/10.12 congruence. % 9.95/10.12 apply (zenon_L240_); trivial. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_H37. apply refl_equal. % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 apply zenon_H33. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e2) = (op (op (e3) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_Ha0. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha9. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha7]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e0) (e3)) = (e2)) = ((op (op (e3) (e3)) (e3)) = (e2))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_Ha7. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H47. % 9.95/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 9.95/10.12 congruence. % 9.95/10.12 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d3. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha9. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 9.95/10.12 congruence. % 9.95/10.12 apply (zenon_L240_); trivial. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_H37. apply refl_equal. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 (* end of lemma zenon_L241_ *) % 9.95/10.12 assert (zenon_L242_ : ((op (e1) (e3)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 9.95/10.12 do 0 intro. intros zenon_H9b zenon_H62 zenon_H7b. % 9.95/10.12 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H7c | zenon_intro zenon_H1d4 ]. % 9.95/10.12 apply zenon_H7c. apply sym_equal. exact zenon_H7b. % 9.95/10.12 apply (zenon_notand_s _ _ zenon_H1d4); [ zenon_intro zenon_H123 | zenon_intro zenon_H1d5 ]. % 9.95/10.12 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e2) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H123. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha2. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e1) (e3)) = (e2)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e2))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H124. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H9b. % 9.95/10.12 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.12 cut (((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 9.95/10.12 congruence. % 9.95/10.12 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d6. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha2. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.12 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d8. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H62. % 9.95/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 9.95/10.12 congruence. % 9.95/10.12 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d3. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha9. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 9.95/10.12 congruence. % 9.95/10.12 apply (zenon_L240_); trivial. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_Haa. apply refl_equal. % 9.95/10.12 apply zenon_H33. apply refl_equal. % 9.95/10.12 apply zenon_H4e. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 apply zenon_H37. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 apply zenon_Ha3. apply refl_equal. % 9.95/10.12 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d5. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha9. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 9.95/10.12 congruence. % 9.95/10.12 cut (((op (e0) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d8. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_H62. % 9.95/10.12 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.12 cut (((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 9.95/10.12 congruence. % 9.95/10.12 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.12 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.12 intro zenon_D_pnotp. % 9.95/10.12 apply zenon_H1d3. % 9.95/10.12 rewrite <- zenon_D_pnotp. % 9.95/10.12 exact zenon_Ha9. % 9.95/10.13 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.13 cut (((op (op (e3) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 9.95/10.13 congruence. % 9.95/10.13 apply (zenon_L240_); trivial. % 9.95/10.13 apply zenon_Haa. apply refl_equal. % 9.95/10.13 apply zenon_Haa. apply refl_equal. % 9.95/10.13 apply zenon_H33. apply refl_equal. % 9.95/10.13 apply zenon_Haa. apply refl_equal. % 9.95/10.13 apply zenon_Haa. apply refl_equal. % 9.95/10.13 (* end of lemma zenon_L242_ *) % 9.95/10.13 assert (zenon_L243_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H187 zenon_H47 zenon_H9b. % 9.95/10.13 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H187. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H47. % 9.95/10.13 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 9.95/10.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_H5a. apply refl_equal. % 9.95/10.13 apply zenon_H180. apply sym_equal. exact zenon_H9b. % 9.95/10.13 (* end of lemma zenon_L243_ *) % 9.95/10.13 assert (zenon_L244_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H1b7 zenon_H7a zenon_H7b zenon_H9b zenon_H187 zenon_H188. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H43 | zenon_intro zenon_H1b8 ]. % 9.95/10.13 apply (zenon_L23_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H62 | zenon_intro zenon_H1b9 ]. % 9.95/10.13 apply (zenon_L242_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 9.95/10.13 apply (zenon_L243_); trivial. % 9.95/10.13 apply (zenon_L167_); trivial. % 9.95/10.13 (* end of lemma zenon_L244_ *) % 9.95/10.13 assert (zenon_L245_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H128 zenon_H8a zenon_H188 zenon_H187 zenon_H7b zenon_H7a zenon_H1b7 zenon_Hbc zenon_H95 zenon_Hce zenon_H1c3 zenon_H2a zenon_H1ba zenon_H15a zenon_H1bc zenon_H1c0 zenon_H27 zenon_Hdd zenon_H7f. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 9.95/10.13 apply (zenon_L241_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 9.95/10.13 apply (zenon_L244_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 9.95/10.13 apply (zenon_L221_); trivial. % 9.95/10.13 exact (zenon_H7f zenon_H85). % 9.95/10.13 (* end of lemma zenon_L245_ *) % 9.95/10.13 assert (zenon_L246_ : (((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 (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H90 zenon_Hcf zenon_H35 zenon_Hd3 zenon_H1e zenon_H91 zenon_H8c zenon_H58 zenon_H80 zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H128 zenon_H188 zenon_H187 zenon_H7a zenon_H1b7 zenon_Hbc zenon_H95 zenon_Hce zenon_H1c3 zenon_H2a zenon_H1ba zenon_H15a zenon_H1bc zenon_H1c0 zenon_H27 zenon_Hdd zenon_H7f. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.13 apply (zenon_L47_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.13 apply (zenon_L196_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.13 apply (zenon_L213_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.13 apply (zenon_L26_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.13 apply (zenon_L27_); trivial. % 9.95/10.13 apply (zenon_L245_); trivial. % 9.95/10.13 (* end of lemma zenon_L246_ *) % 9.95/10.13 assert (zenon_L247_ : (~((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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) (e3)) = (e1))) -> (~((op (e3) (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) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H7f zenon_Hdd zenon_H27 zenon_H1c0 zenon_H1bc zenon_H15a zenon_H1ba zenon_H2a zenon_H1c3 zenon_Hce zenon_H1b7 zenon_H7a zenon_H187 zenon_H188 zenon_H128 zenon_H5e zenon_H7d zenon_H86 zenon_H7e zenon_H80 zenon_H58 zenon_H8c zenon_H91 zenon_H1e zenon_Hd3 zenon_H35 zenon_H90 zenon_H95 zenon_Hbc. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.13 apply (zenon_L220_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.13 apply (zenon_L246_); trivial. % 9.95/10.13 apply (zenon_L51_); trivial. % 9.95/10.13 (* end of lemma zenon_L247_ *) % 9.95/10.13 assert (zenon_L248_ : (((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) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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) (e3)) = (e1))) -> (~((op (e3) (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) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hda zenon_H28 zenon_H198 zenon_Hcf zenon_H7f zenon_Hdd zenon_H27 zenon_H1c0 zenon_H1bc zenon_H15a zenon_H1ba zenon_H2a zenon_H1c3 zenon_Hce zenon_H1b7 zenon_H7a zenon_H187 zenon_H188 zenon_H128 zenon_H5e zenon_H7d zenon_H86 zenon_H7e zenon_H80 zenon_H58 zenon_H8c zenon_H91 zenon_H1e zenon_Hd3 zenon_H35 zenon_H90 zenon_H95. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.13 apply (zenon_L239_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_L155_); trivial. % 9.95/10.13 apply (zenon_L247_); trivial. % 9.95/10.13 (* end of lemma zenon_L248_ *) % 9.95/10.13 assert (zenon_L249_ : (((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)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hda zenon_H28 zenon_H4c zenon_H15a zenon_H53 zenon_H73 zenon_H95 zenon_Hd8. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.13 apply (zenon_L236_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_L20_); trivial. % 9.95/10.13 apply (zenon_L51_); trivial. % 9.95/10.13 (* end of lemma zenon_L249_ *) % 9.95/10.13 assert (zenon_L250_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H90 zenon_H4c zenon_H74 zenon_Hd3 zenon_H1e zenon_H91 zenon_H89 zenon_H5e. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.13 apply (zenon_L21_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.13 apply (zenon_L196_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_L27_); trivial. % 9.95/10.13 (* end of lemma zenon_L250_ *) % 9.95/10.13 assert (zenon_L251_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((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 (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((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) (e3)) = (e1))) -> (~((op (e3) (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) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H198 zenon_H4c zenon_Hb1 zenon_H8d zenon_Hda zenon_H28 zenon_H53 zenon_Hd8 zenon_Hb0 zenon_H7f zenon_Hdd zenon_H27 zenon_H1c0 zenon_H1bc zenon_H15a zenon_H1ba zenon_H2a zenon_H1c3 zenon_Hce zenon_H1b7 zenon_H7a zenon_H187 zenon_H188 zenon_H128 zenon_H5e zenon_H7d zenon_H86 zenon_H7e zenon_H80 zenon_H58 zenon_H8c zenon_H91 zenon_H1e zenon_Hd3 zenon_H35 zenon_H90 zenon_H95. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.13 apply (zenon_L239_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.13 apply (zenon_L249_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.13 apply (zenon_L29_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.13 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.13 apply (zenon_L250_); trivial. % 9.95/10.13 apply (zenon_L247_); trivial. % 9.95/10.13 (* end of lemma zenon_L251_ *) % 9.95/10.13 assert (zenon_L252_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H84 zenon_H188 zenon_H86. % 9.95/10.13 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H86. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_Hf9. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 9.95/10.13 congruence. % 9.95/10.13 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H1d9. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H84. % 9.95/10.13 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_Hfa. apply refl_equal. % 9.95/10.13 apply zenon_H189. apply sym_equal. exact zenon_H188. % 9.95/10.13 apply zenon_Hfa. apply refl_equal. % 9.95/10.13 apply zenon_Hfa. apply refl_equal. % 9.95/10.13 (* end of lemma zenon_L252_ *) % 9.95/10.13 assert (zenon_L253_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (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 (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H18d zenon_H56 zenon_Hb0 zenon_Hb1 zenon_H8d zenon_H4c zenon_H53 zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_Hd3 zenon_H91 zenon_H8c zenon_H1b7 zenon_H187 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H5e zenon_H86 zenon_H7e zenon_H7f zenon_H7d zenon_H58 zenon_H90 zenon_H1ba zenon_H2a zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H15a zenon_H35 zenon_H27 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_H64. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.13 exact (zenon_H56 zenon_H2c). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.13 apply (zenon_L238_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.13 apply (zenon_L248_); trivial. % 9.95/10.13 apply (zenon_L251_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.13 apply (zenon_L103_); trivial. % 9.95/10.13 apply (zenon_L87_); trivial. % 9.95/10.13 apply (zenon_L252_); trivial. % 9.95/10.13 (* end of lemma zenon_L253_ *) % 9.95/10.13 assert (zenon_L254_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (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))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H108 zenon_H3c zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_Hc5 zenon_Hb1 zenon_H53 zenon_Hed. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.95/10.13 apply (zenon_L129_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.95/10.13 apply (zenon_L118_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.95/10.13 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.13 apply (zenon_L73_); trivial. % 9.95/10.13 (* end of lemma zenon_L254_ *) % 9.95/10.13 assert (zenon_L255_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H8a zenon_H47. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.13 apply (zenon_L24_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.13 apply (zenon_L26_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.13 apply (zenon_L27_); trivial. % 9.95/10.13 apply (zenon_L241_); trivial. % 9.95/10.13 (* end of lemma zenon_L255_ *) % 9.95/10.13 assert (zenon_L256_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e2)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H90 zenon_H15a zenon_H1bc zenon_Hd3 zenon_H1e zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H47. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.13 apply (zenon_L217_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.13 apply (zenon_L196_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_L255_); trivial. % 9.95/10.13 (* end of lemma zenon_L256_ *) % 9.95/10.13 assert (zenon_L257_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H42 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H15a zenon_H1bc zenon_Hd3 zenon_H1e zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.13 apply (zenon_L4_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.13 apply (zenon_L19_); trivial. % 9.95/10.13 apply (zenon_L256_); trivial. % 9.95/10.13 (* end of lemma zenon_L257_ *) % 9.95/10.13 assert (zenon_L258_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H181 zenon_H62 zenon_H8a. % 9.95/10.13 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H181. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H62. % 9.95/10.13 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H186]. % 9.95/10.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_H5a. apply refl_equal. % 9.95/10.13 apply zenon_H186. apply sym_equal. exact zenon_H8a. % 9.95/10.13 (* end of lemma zenon_L258_ *) % 9.95/10.13 assert (zenon_L259_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H90 zenon_H15a zenon_H1bc zenon_Hd3 zenon_H1e zenon_H91 zenon_H181 zenon_H62. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.13 apply (zenon_L217_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.13 apply (zenon_L196_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_L258_); trivial. % 9.95/10.13 (* end of lemma zenon_L259_ *) % 9.95/10.13 assert (zenon_L260_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H62 zenon_H47 zenon_H35. % 9.95/10.13 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 9.95/10.13 cut (((e2) = (e2)) = ((e1) = (e2))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H35. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H36. % 9.95/10.13 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.13 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 9.95/10.13 congruence. % 9.95/10.13 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H38. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H62. % 9.95/10.13 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.13 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 9.95/10.13 congruence. % 9.95/10.13 exact (zenon_H49 zenon_H47). % 9.95/10.13 apply zenon_H33. apply refl_equal. % 9.95/10.13 apply zenon_H37. apply refl_equal. % 9.95/10.13 apply zenon_H37. apply refl_equal. % 9.95/10.13 (* end of lemma zenon_L260_ *) % 9.95/10.13 assert (zenon_L261_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H128 zenon_H35 zenon_H7b zenon_H62 zenon_H11f zenon_H95 zenon_H7f. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 9.95/10.13 apply (zenon_L260_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 9.95/10.13 apply (zenon_L242_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 9.95/10.13 apply (zenon_L93_); trivial. % 9.95/10.13 exact (zenon_H7f zenon_H85). % 9.95/10.13 (* end of lemma zenon_L261_ *) % 9.95/10.13 assert (zenon_L262_ : (((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)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H8c zenon_H2a zenon_H58 zenon_H80 zenon_H7e zenon_H86 zenon_H7d zenon_H53 zenon_H128 zenon_H35 zenon_H62 zenon_H11f zenon_H95 zenon_H7f. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.13 apply (zenon_L213_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.13 apply (zenon_L26_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.13 apply (zenon_L96_); trivial. % 9.95/10.13 apply (zenon_L261_); trivial. % 9.95/10.13 (* end of lemma zenon_L262_ *) % 9.95/10.13 assert (zenon_L263_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hec zenon_Hf2 zenon_Hf3. % 9.95/10.13 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_Hec. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_Hf2. % 9.95/10.13 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 9.95/10.13 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_Hef. apply refl_equal. % 9.95/10.13 apply zenon_H1da. apply sym_equal. exact zenon_Hf3. % 9.95/10.13 (* end of lemma zenon_L263_ *) % 9.95/10.13 assert (zenon_L264_ : (((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 (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H103 zenon_H1cb zenon_H62 zenon_H15a zenon_H159 zenon_H91 zenon_Hec zenon_Hf2. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 9.95/10.13 apply (zenon_L229_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 9.95/10.13 apply (zenon_L123_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_L263_); trivial. % 9.95/10.13 (* end of lemma zenon_L264_ *) % 9.95/10.13 assert (zenon_L265_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((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))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (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 (e3) (e1)) = (op (e3) (e2)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H1b1 zenon_H181 zenon_Hd3 zenon_H1bc zenon_H90 zenon_H192 zenon_H7f zenon_H95 zenon_H35 zenon_H128 zenon_H53 zenon_H7d zenon_H86 zenon_H7e zenon_H80 zenon_H58 zenon_H2a zenon_H8c zenon_Hc8 zenon_H4c zenon_Hbc zenon_H1c0 zenon_H12c zenon_H103 zenon_H1cb zenon_H62 zenon_H15a zenon_H159 zenon_H91 zenon_Hec. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.13 apply (zenon_L259_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.13 exact (zenon_H192 zenon_H1d). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.95/10.13 apply (zenon_L219_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.95/10.13 apply (zenon_L48_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.95/10.13 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.13 apply (zenon_L262_); trivial. % 9.95/10.13 apply (zenon_L264_); trivial. % 9.95/10.13 (* end of lemma zenon_L265_ *) % 9.95/10.13 assert (zenon_L266_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H84 zenon_Hbc zenon_He3. % 9.95/10.13 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_He3. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_Hf9. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 9.95/10.13 congruence. % 9.95/10.13 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H1db. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H84. % 9.95/10.13 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 9.95/10.13 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_Hfa. apply refl_equal. % 9.95/10.13 apply zenon_H1dc. apply sym_equal. exact zenon_Hbc. % 9.95/10.13 apply zenon_Hfa. apply refl_equal. % 9.95/10.13 apply zenon_Hfa. apply refl_equal. % 9.95/10.13 (* end of lemma zenon_L266_ *) % 9.95/10.13 assert (zenon_L267_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H1dd zenon_Hbc zenon_Hed. % 9.95/10.13 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H1dd. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_Hbc. % 9.95/10.13 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 9.95/10.13 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_Hbf. apply refl_equal. % 9.95/10.13 apply zenon_Hee. apply sym_equal. exact zenon_Hed. % 9.95/10.13 (* end of lemma zenon_L267_ *) % 9.95/10.13 assert (zenon_L268_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (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 (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H64 zenon_H181 zenon_H192 zenon_H12c zenon_H58 zenon_H2a zenon_H53 zenon_H128 zenon_H95 zenon_H4c zenon_Hbc zenon_H1c0 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H5e zenon_H8c zenon_H91 zenon_Hd3 zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_He3 zenon_H18d. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.13 exact (zenon_H56 zenon_H2c). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.13 apply (zenon_L257_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.13 apply (zenon_L103_); trivial. % 9.95/10.13 apply (zenon_L265_); trivial. % 9.95/10.13 apply (zenon_L266_); trivial. % 9.95/10.13 apply (zenon_L267_); trivial. % 9.95/10.13 (* end of lemma zenon_L268_ *) % 9.95/10.13 assert (zenon_L269_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (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) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (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)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H150 zenon_He3 zenon_H42 zenon_H6f zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H12c zenon_H192 zenon_H181 zenon_H1dd zenon_H1de zenon_H64 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H27 zenon_H35 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_H90 zenon_H58 zenon_H7d zenon_H7e zenon_H86 zenon_H5e zenon_H128 zenon_Hce zenon_Hdd zenon_H7a zenon_H187 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_H198 zenon_H28 zenon_H53 zenon_Hb1 zenon_Hb0 zenon_H56 zenon_H18d zenon_H6e zenon_H95 zenon_Hc1 zenon_H15a zenon_H4c zenon_H108 zenon_H155 zenon_Hf8. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.13 apply (zenon_L236_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.13 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.13 apply (zenon_L237_); trivial. % 9.95/10.13 apply (zenon_L253_); trivial. % 9.95/10.13 apply (zenon_L254_); trivial. % 9.95/10.13 apply (zenon_L268_); trivial. % 9.95/10.13 (* end of lemma zenon_L269_ *) % 9.95/10.13 assert (zenon_L270_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H17c zenon_H87 zenon_H89. % 9.95/10.13 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H17c. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H87. % 9.95/10.13 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 9.95/10.13 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_H88. apply refl_equal. % 9.95/10.13 apply zenon_H1e1. apply sym_equal. exact zenon_H89. % 9.95/10.13 (* end of lemma zenon_L270_ *) % 9.95/10.13 assert (zenon_L271_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H1e2 zenon_H95 zenon_H74 zenon_H35 zenon_H77 zenon_Hc7 zenon_H9b zenon_H17c. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 9.95/10.13 apply (zenon_L155_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 9.95/10.13 apply (zenon_L203_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 9.95/10.13 exact (zenon_Hc7 zenon_H3a). % 9.95/10.13 apply (zenon_L162_); trivial. % 9.95/10.13 (* end of lemma zenon_L271_ *) % 9.95/10.13 assert (zenon_L272_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hb0 zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_Hc7 zenon_H77 zenon_H35 zenon_H74 zenon_H95 zenon_H1e2 zenon_H187 zenon_H57. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.13 apply (zenon_L20_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.13 apply (zenon_L22_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.13 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 9.95/10.13 apply (zenon_L270_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 9.95/10.13 apply (zenon_L194_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 9.95/10.13 apply (zenon_L271_); trivial. % 9.95/10.13 apply (zenon_L167_); trivial. % 9.95/10.13 (* end of lemma zenon_L272_ *) % 9.95/10.13 assert (zenon_L273_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H64 zenon_H56 zenon_Hd3 zenon_H181 zenon_Hd0 zenon_H35 zenon_H97 zenon_Hda zenon_H28 zenon_H4c zenon_H187 zenon_H1e2 zenon_H77 zenon_Hc7 zenon_H17c zenon_H198 zenon_H18a zenon_Hb1 zenon_H5e zenon_H53 zenon_Hb0 zenon_Hdd zenon_H27 zenon_H1c0 zenon_H1bc zenon_H15a zenon_H1ba zenon_H2a zenon_H1c3 zenon_Hce zenon_H95 zenon_H42 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.13 exact (zenon_H56 zenon_H2c). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.13 apply (zenon_L196_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.13 apply (zenon_L184_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.13 apply (zenon_L130_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.13 apply (zenon_L236_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_L272_); trivial. % 9.95/10.13 apply (zenon_L221_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.13 apply (zenon_L70_); trivial. % 9.95/10.13 apply (zenon_L163_); trivial. % 9.95/10.13 apply (zenon_L87_); trivial. % 9.95/10.13 (* end of lemma zenon_L273_ *) % 9.95/10.13 assert (zenon_L274_ : (~((op (e3) (e3)) = (e0))) -> (~((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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H8d zenon_H5e zenon_H7d zenon_H86 zenon_H7e zenon_H7f zenon_H80 zenon_H7a zenon_H8c zenon_H91 zenon_H64 zenon_H56 zenon_Hd3 zenon_H181 zenon_Hd0 zenon_H35 zenon_H97 zenon_Hda zenon_H28 zenon_H4c zenon_H187 zenon_H1e2 zenon_Hc7 zenon_H17c zenon_H198 zenon_H18a zenon_Hb1 zenon_H53 zenon_Hb0 zenon_Hdd zenon_H27 zenon_H1c0 zenon_H1bc zenon_H15a zenon_H1ba zenon_H2a zenon_H1c3 zenon_Hce zenon_H42 zenon_H90 zenon_H95. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.13 apply (zenon_L238_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.13 apply (zenon_L44_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.13 apply (zenon_L236_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.13 apply (zenon_L21_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.13 apply (zenon_L273_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_L28_); trivial. % 9.95/10.13 apply (zenon_L51_); trivial. % 9.95/10.13 (* end of lemma zenon_L274_ *) % 9.95/10.13 assert (zenon_L275_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H35 zenon_Hd0 zenon_Hce zenon_Hda zenon_H28 zenon_H4c zenon_H15a zenon_H53 zenon_H73 zenon_H95. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.13 apply (zenon_L238_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.13 apply (zenon_L44_); trivial. % 9.95/10.13 apply (zenon_L249_); trivial. % 9.95/10.13 (* end of lemma zenon_L275_ *) % 9.95/10.13 assert (zenon_L276_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H187 zenon_H43 zenon_H87. % 9.95/10.13 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H187. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H43. % 9.95/10.13 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 9.95/10.13 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_H5a. apply refl_equal. % 9.95/10.13 apply zenon_H1e5. apply sym_equal. exact zenon_H87. % 9.95/10.13 (* end of lemma zenon_L276_ *) % 9.95/10.13 assert (zenon_L277_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H1b7 zenon_H87 zenon_H187 zenon_H8a zenon_H181 zenon_Hd0 zenon_H84 zenon_H7a. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H43 | zenon_intro zenon_H1b8 ]. % 9.95/10.13 apply (zenon_L276_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H62 | zenon_intro zenon_H1b9 ]. % 9.95/10.13 apply (zenon_L258_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 9.95/10.13 apply (zenon_L163_); trivial. % 9.95/10.13 apply (zenon_L68_); trivial. % 9.95/10.13 (* end of lemma zenon_L277_ *) % 9.95/10.13 assert (zenon_L278_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (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))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H8c zenon_H2a zenon_H58 zenon_H7a zenon_H84 zenon_Hd0 zenon_H181 zenon_H187 zenon_H1b7 zenon_H5e zenon_H8a zenon_H8d. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.13 apply (zenon_L213_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.13 apply (zenon_L277_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.13 apply (zenon_L27_); trivial. % 9.95/10.13 exact (zenon_H8d zenon_H7b). % 9.95/10.13 (* end of lemma zenon_L278_ *) % 9.95/10.13 assert (zenon_L279_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H18a zenon_H89 zenon_H15a zenon_H198 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 9.95/10.13 apply (zenon_L270_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 9.95/10.13 apply (zenon_L194_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 9.95/10.13 apply (zenon_L162_); trivial. % 9.95/10.13 apply (zenon_L252_); trivial. % 9.95/10.13 (* end of lemma zenon_L279_ *) % 9.95/10.13 assert (zenon_L280_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hb0 zenon_H2a zenon_H1ba zenon_H77 zenon_H5e zenon_Hb1 zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.13 apply (zenon_L216_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.13 apply (zenon_L22_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.13 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.13 apply (zenon_L279_); trivial. % 9.95/10.13 (* end of lemma zenon_L280_ *) % 9.95/10.13 assert (zenon_L281_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((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)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H64 zenon_H56 zenon_Hce zenon_H1c3 zenon_H1c0 zenon_Hdd zenon_H53 zenon_Hda zenon_H8d zenon_H1b7 zenon_H187 zenon_H58 zenon_H8c zenon_H35 zenon_H97 zenon_H28 zenon_H95 zenon_H4c zenon_H7a zenon_H27 zenon_H42 zenon_H1b1 zenon_H181 zenon_Hd3 zenon_H1bc zenon_H90 zenon_H192 zenon_H86 zenon_H84 zenon_Hd0 zenon_H17c zenon_H198 zenon_H18a zenon_Hb1 zenon_H5e zenon_H1ba zenon_H2a zenon_Hb0 zenon_H103 zenon_H1cb zenon_H15a zenon_H159 zenon_H91 zenon_Hec. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.13 exact (zenon_H56 zenon_H2c). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.13 apply (zenon_L236_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.13 apply (zenon_L275_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.13 apply (zenon_L217_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.13 apply (zenon_L22_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.13 exact (zenon_H91 zenon_H94). % 9.95/10.13 apply (zenon_L278_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.13 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.13 apply (zenon_L250_); trivial. % 9.95/10.13 apply (zenon_L221_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.13 apply (zenon_L184_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.13 apply (zenon_L130_); trivial. % 9.95/10.13 apply (zenon_L68_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.13 apply (zenon_L70_); trivial. % 9.95/10.13 apply (zenon_L163_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.13 apply (zenon_L259_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.13 exact (zenon_H192 zenon_H1d). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.13 apply (zenon_L280_); trivial. % 9.95/10.13 apply (zenon_L264_); trivial. % 9.95/10.13 (* end of lemma zenon_L281_ *) % 9.95/10.13 assert (zenon_L282_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hed zenon_H161 zenon_H1e6. % 9.95/10.13 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 9.95/10.13 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H1e6. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_H10c. % 9.95/10.13 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.95/10.13 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 9.95/10.13 congruence. % 9.95/10.13 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 9.95/10.13 intro zenon_D_pnotp. % 9.95/10.13 apply zenon_H1e7. % 9.95/10.13 rewrite <- zenon_D_pnotp. % 9.95/10.13 exact zenon_Hed. % 9.95/10.13 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 9.95/10.13 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.95/10.13 congruence. % 9.95/10.13 apply zenon_H10d. apply refl_equal. % 9.95/10.13 apply zenon_H1e8. apply sym_equal. exact zenon_H161. % 9.95/10.13 apply zenon_H10d. apply refl_equal. % 9.95/10.13 apply zenon_H10d. apply refl_equal. % 9.95/10.13 (* end of lemma zenon_L282_ *) % 9.95/10.13 assert (zenon_L283_ : (((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). % 9.95/10.13 do 0 intro. intros zenon_H1de zenon_H4c zenon_H15a zenon_Hc1 zenon_H1e6 zenon_Hed zenon_H187 zenon_H57. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.13 apply (zenon_L236_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.13 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.13 apply (zenon_L282_); trivial. % 9.95/10.13 apply (zenon_L167_); trivial. % 9.95/10.13 (* end of lemma zenon_L283_ *) % 9.95/10.13 assert (zenon_L284_ : (((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 (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)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H97 zenon_H28 zenon_H95 zenon_H34 zenon_H10b zenon_H1de zenon_H4c zenon_H15a zenon_Hc1 zenon_H1e6 zenon_Hed zenon_H187. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.13 exact (zenon_H28 zenon_H31). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.13 apply (zenon_L184_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.13 apply (zenon_L75_); trivial. % 9.95/10.13 apply (zenon_L283_); trivial. % 9.95/10.13 (* end of lemma zenon_L284_ *) % 9.95/10.13 assert (zenon_L285_ : (((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)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.13 do 0 intro. intros zenon_H108 zenon_H2a zenon_H132 zenon_H4c zenon_H91 zenon_H5e zenon_H3b zenon_H35 zenon_H103 zenon_Hb1 zenon_H53 zenon_Hed. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.95/10.13 apply (zenon_L101_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.95/10.13 apply (zenon_L72_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.95/10.13 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.13 apply (zenon_L73_); trivial. % 9.95/10.13 (* end of lemma zenon_L285_ *) % 9.95/10.13 assert (zenon_L286_ : (((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) (e2)) = (op (e3) (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 (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) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((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))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.13 do 0 intro. intros zenon_H42 zenon_H27 zenon_H187 zenon_H1e6 zenon_Hc1 zenon_H15a zenon_H1de zenon_H10b zenon_H95 zenon_H28 zenon_H97 zenon_Hed zenon_H53 zenon_Hb1 zenon_H103 zenon_H35 zenon_H5e zenon_H91 zenon_H4c zenon_H132 zenon_H2a zenon_H108 zenon_Hd0 zenon_H181. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.13 exact (zenon_H27 zenon_H32). % 9.95/10.13 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.13 apply (zenon_L284_); trivial. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.13 apply (zenon_L285_); trivial. % 9.95/10.13 apply (zenon_L163_); trivial. % 9.95/10.13 (* end of lemma zenon_L286_ *) % 9.95/10.13 assert (zenon_L287_ : ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (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)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (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 (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.13 do 0 intro. intros zenon_Hf8 zenon_Hc1 zenon_H1e6 zenon_H1de zenon_H10b zenon_H108 zenon_H132 zenon_H28 zenon_H4c zenon_H90 zenon_H7e zenon_H86 zenon_H8c zenon_H91 zenon_H56 zenon_Hd3 zenon_H42 zenon_H181 zenon_H95 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_Hdd zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H187 zenon_Hc7 zenon_H1e2 zenon_H198 zenon_H17c zenon_Hb0 zenon_H97 zenon_H7d zenon_H7a zenon_H8d zenon_H64 zenon_Hd0 zenon_Hce zenon_H15a zenon_H35 zenon_H27 zenon_H192 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_H1b7 zenon_H58 zenon_H18d. % 9.95/10.13 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.13 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.13 apply (zenon_L274_); trivial. % 9.95/10.13 apply (zenon_L281_); trivial. % 9.95/10.13 apply (zenon_L286_); trivial. % 9.95/10.13 (* end of lemma zenon_L287_ *) % 9.95/10.13 assert (zenon_L288_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H150 zenon_H6e zenon_H1b4 zenon_H18d zenon_H58 zenon_H1b7 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H192 zenon_H27 zenon_H35 zenon_H15a zenon_Hce zenon_Hd0 zenon_H64 zenon_H7a zenon_H7d zenon_H97 zenon_Hb0 zenon_H17c zenon_H198 zenon_H1e2 zenon_Hc7 zenon_H187 zenon_H18a zenon_Hb1 zenon_H5e zenon_H53 zenon_Hdd zenon_H1ba zenon_H2a zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H95 zenon_H181 zenon_H42 zenon_Hd3 zenon_H56 zenon_H91 zenon_H8c zenon_H86 zenon_H7e zenon_H90 zenon_H4c zenon_H28 zenon_H132 zenon_H108 zenon_H10b zenon_H1de zenon_H1e6 zenon_Hc1 zenon_Hf8. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L287_); trivial. % 9.95/10.14 apply (zenon_L222_); trivial. % 9.95/10.14 (* end of lemma zenon_L288_ *) % 9.95/10.14 assert (zenon_L289_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1de zenon_H16f zenon_Hbc zenon_Hc1 zenon_H95 zenon_H6e zenon_H187 zenon_H57. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.14 apply (zenon_L154_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.14 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.14 apply (zenon_L237_); trivial. % 9.95/10.14 apply (zenon_L167_); trivial. % 9.95/10.14 (* end of lemma zenon_L289_ *) % 9.95/10.14 assert (zenon_L290_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1e2 zenon_H95 zenon_H74 zenon_H35 zenon_H77 zenon_Hc7 zenon_H47 zenon_H181. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 9.95/10.14 apply (zenon_L155_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 9.95/10.14 apply (zenon_L203_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 9.95/10.14 exact (zenon_Hc7 zenon_H3a). % 9.95/10.14 apply (zenon_L163_); trivial. % 9.95/10.14 (* end of lemma zenon_L290_ *) % 9.95/10.14 assert (zenon_L291_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hab zenon_H35 zenon_H47 zenon_H15a zenon_H198 zenon_H11f zenon_H4c zenon_H7e. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 9.95/10.14 apply (zenon_L260_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 9.95/10.14 apply (zenon_L194_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 9.95/10.14 apply (zenon_L89_); trivial. % 9.95/10.14 exact (zenon_H7e zenon_H83). % 9.95/10.14 (* end of lemma zenon_L291_ *) % 9.95/10.14 assert (zenon_L292_ : (((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)) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H12c zenon_H181 zenon_Hc7 zenon_H95 zenon_H1e2 zenon_H77 zenon_Hc8 zenon_Hab zenon_H35 zenon_H47 zenon_H15a zenon_H198 zenon_H4c zenon_H7e. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.95/10.14 apply (zenon_L290_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.95/10.14 apply (zenon_L48_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.95/10.14 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.14 apply (zenon_L291_); trivial. % 9.95/10.14 (* end of lemma zenon_L292_ *) % 9.95/10.14 assert (zenon_L293_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hde zenon_H95 zenon_H4b zenon_Haf zenon_Hcf zenon_H112 zenon_Hf2 zenon_H35. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.95/10.14 apply (zenon_L184_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.95/10.14 exact (zenon_Haf zenon_Hb4). % 9.95/10.14 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.95/10.14 apply (zenon_L79_); trivial. % 9.95/10.14 apply (zenon_L63_); trivial. % 9.95/10.14 (* end of lemma zenon_L293_ *) % 9.95/10.14 assert (zenon_L294_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H97 zenon_H28 zenon_H35 zenon_H112 zenon_Hcf zenon_Haf zenon_Hde zenon_H12c zenon_H181 zenon_Hc7 zenon_H1e2 zenon_Hc8 zenon_Hab zenon_H15a zenon_H198 zenon_H7e zenon_H192 zenon_H90 zenon_H1bc zenon_Hd3 zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H5e zenon_H1b1 zenon_H4c zenon_H5d zenon_H47 zenon_H95. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.14 apply (zenon_L256_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.14 exact (zenon_H192 zenon_H1d). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.14 apply (zenon_L292_); trivial. % 9.95/10.14 apply (zenon_L293_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L130_); trivial. % 9.95/10.14 apply (zenon_L54_); trivial. % 9.95/10.14 (* end of lemma zenon_L294_ *) % 9.95/10.14 assert (zenon_L295_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (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 (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (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). % 9.95/10.14 do 0 intro. intros zenon_H64 zenon_H56 zenon_H6f zenon_H95 zenon_H4c zenon_H1b1 zenon_H5e zenon_H86 zenon_H8c zenon_H91 zenon_Hd3 zenon_H1bc zenon_H90 zenon_H192 zenon_H7e zenon_H198 zenon_H15a zenon_Hab zenon_Hc8 zenon_H1e2 zenon_Hc7 zenon_H181 zenon_H12c zenon_Hde zenon_Haf zenon_Hcf zenon_H112 zenon_H35 zenon_H28 zenon_H97 zenon_Hda zenon_H1de zenon_H16f zenon_Hc1 zenon_H6e zenon_H187 zenon_H27 zenon_H42 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_L257_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.14 exact (zenon_H27 zenon_H32). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_L184_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L130_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L236_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L155_); trivial. % 9.95/10.14 apply (zenon_L289_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.14 apply (zenon_L70_); trivial. % 9.95/10.14 apply (zenon_L294_); trivial. % 9.95/10.14 apply (zenon_L87_); trivial. % 9.95/10.14 (* end of lemma zenon_L295_ *) % 9.95/10.14 assert (zenon_L296_ : (((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). % 9.95/10.14 do 0 intro. intros zenon_Hda zenon_H28 zenon_H4c zenon_H15a zenon_H95 zenon_Hcf zenon_H84 zenon_He3. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L236_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L155_); trivial. % 9.95/10.14 apply (zenon_L266_); trivial. % 9.95/10.14 (* end of lemma zenon_L296_ *) % 9.95/10.14 assert (zenon_L297_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H191 zenon_He8 zenon_H192 zenon_Haf zenon_H188 zenon_H11d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.95/10.14 exact (zenon_He8 zenon_Heb). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.95/10.14 exact (zenon_H192 zenon_H1d). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.95/10.14 exact (zenon_Haf zenon_Hb4). % 9.95/10.14 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H1ab | zenon_intro zenon_H88 ]. % 9.95/10.14 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H11d. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H1ab. % 9.95/10.14 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.95/10.14 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1e9. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H188. % 9.95/10.14 cut (((e3) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 9.95/10.14 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H88. apply refl_equal. % 9.95/10.14 apply zenon_H1a4. apply sym_equal. exact zenon_Hc4. % 9.95/10.14 apply zenon_H88. apply refl_equal. % 9.95/10.14 apply zenon_H88. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L297_ *) % 9.95/10.14 assert (zenon_L298_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H18d zenon_H188 zenon_H12f zenon_H2a zenon_He8 zenon_H5e zenon_H100 zenon_H7d zenon_H7f zenon_H7e zenon_H86 zenon_H145. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.14 apply (zenon_L225_); trivial. % 9.95/10.14 apply (zenon_L252_); trivial. % 9.95/10.14 (* end of lemma zenon_L298_ *) % 9.95/10.14 assert (zenon_L299_ : ((~((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 (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H3c zenon_H155 zenon_Hb1 zenon_H53 zenon_H108 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H188 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_L298_); trivial. % 9.95/10.14 apply (zenon_L254_); trivial. % 9.95/10.14 (* end of lemma zenon_L299_ *) % 9.95/10.14 assert (zenon_L300_ : (((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)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H97 zenon_H28 zenon_H95 zenon_H34 zenon_H10b zenon_Hed zenon_H187 zenon_H188. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_L184_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L75_); trivial. % 9.95/10.14 apply (zenon_L167_); trivial. % 9.95/10.14 (* end of lemma zenon_L300_ *) % 9.95/10.14 assert (zenon_L301_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (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) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((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))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H42 zenon_H27 zenon_H188 zenon_H187 zenon_H10b zenon_H95 zenon_H28 zenon_H97 zenon_Hed zenon_H53 zenon_Hb1 zenon_H103 zenon_H35 zenon_H5e zenon_H91 zenon_H4c zenon_H132 zenon_H2a zenon_H108 zenon_Hd0 zenon_H181. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.14 exact (zenon_H27 zenon_H32). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.14 apply (zenon_L300_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.14 apply (zenon_L285_); trivial. % 9.95/10.14 apply (zenon_L163_); trivial. % 9.95/10.14 (* end of lemma zenon_L301_ *) % 9.95/10.14 assert (zenon_L302_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((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 (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H27 zenon_H97 zenon_H187 zenon_H10b zenon_H95 zenon_H28 zenon_H108 zenon_H53 zenon_Hb1 zenon_H35 zenon_H91 zenon_H4c zenon_H103 zenon_H132 zenon_H181 zenon_Hd0 zenon_H42 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H188 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_L298_); trivial. % 9.95/10.14 apply (zenon_L301_); trivial. % 9.95/10.14 (* end of lemma zenon_L302_ *) % 9.95/10.14 assert (zenon_L303_ : (((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 (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H144 zenon_H2a zenon_H132 zenon_H6f zenon_H100 zenon_H3c zenon_H3a zenon_Hed zenon_H10b. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H51 | zenon_intro zenon_H148 ]. % 9.95/10.14 apply (zenon_L101_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H5d | zenon_intro zenon_H149 ]. % 9.95/10.14 apply (zenon_L228_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H3b | zenon_intro zenon_H52 ]. % 9.95/10.14 apply (zenon_L5_); trivial. % 9.95/10.14 apply (zenon_L75_); trivial. % 9.95/10.14 (* end of lemma zenon_L303_ *) % 9.95/10.14 assert (zenon_L304_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H132 zenon_H6f zenon_H3c zenon_H3a zenon_H10b zenon_H144 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H188 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_L298_); trivial. % 9.95/10.14 apply (zenon_L303_); trivial. % 9.95/10.14 (* end of lemma zenon_L304_ *) % 9.95/10.14 assert (zenon_L305_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H158 zenon_H144 zenon_H6f zenon_Hf8 zenon_Hc5 zenon_H91 zenon_H3c zenon_H155 zenon_Hb1 zenon_H53 zenon_H108 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H188 zenon_H18d zenon_H27 zenon_H97 zenon_H187 zenon_H10b zenon_H95 zenon_H28 zenon_H35 zenon_H4c zenon_H103 zenon_H132 zenon_H181 zenon_H42 zenon_Hd2. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.14 apply (zenon_L299_); trivial. % 9.95/10.14 apply (zenon_L302_); trivial. % 9.95/10.14 apply (zenon_L304_); trivial. % 9.95/10.14 (* end of lemma zenon_L305_ *) % 9.95/10.14 assert (zenon_L306_ : (((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). % 9.95/10.14 do 0 intro. intros zenon_Hda zenon_H28 zenon_H4c zenon_H15a zenon_H95 zenon_Hcf zenon_H1dd zenon_Hed. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L236_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L155_); trivial. % 9.95/10.14 apply (zenon_L267_); trivial. % 9.95/10.14 (* end of lemma zenon_L306_ *) % 9.95/10.14 assert (zenon_L307_ : (((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) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hda zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_Hcf zenon_H4c zenon_Hf0. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L239_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L155_); trivial. % 9.95/10.14 apply (zenon_L139_); trivial. % 9.95/10.14 (* end of lemma zenon_L307_ *) % 9.95/10.14 assert (zenon_L308_ : (((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)))) -> (~((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)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_Hed zenon_H1dd zenon_H35 zenon_Hda zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_Hcf zenon_H4c. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.14 apply (zenon_L306_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.14 apply (zenon_L47_); trivial. % 9.95/10.14 apply (zenon_L307_); trivial. % 9.95/10.14 (* end of lemma zenon_L308_ *) % 9.95/10.14 assert (zenon_L309_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (~((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H56 zenon_Hda zenon_H1dd zenon_Hcf zenon_H95 zenon_H4c zenon_H28 zenon_H35 zenon_H198 zenon_H1b4 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H188 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_L298_); trivial. % 9.95/10.14 apply (zenon_L308_); trivial. % 9.95/10.14 (* end of lemma zenon_L309_ *) % 9.95/10.14 assert (zenon_L310_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (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)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H155 zenon_H108 zenon_H64 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H27 zenon_H35 zenon_H15a zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_H90 zenon_H58 zenon_H7d zenon_H7e zenon_H86 zenon_H5e zenon_H128 zenon_Hce zenon_Hdd zenon_H7a zenon_H187 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_H95 zenon_H188 zenon_H198 zenon_H28 zenon_H53 zenon_H4c zenon_H8d zenon_Hb1 zenon_Hb0 zenon_H56 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_L253_); trivial. % 9.95/10.14 apply (zenon_L254_); trivial. % 9.95/10.14 (* end of lemma zenon_L310_ *) % 9.95/10.14 assert (zenon_L311_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (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 (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H64 zenon_H181 zenon_H192 zenon_H12c zenon_H53 zenon_H4c zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H27 zenon_H1c3 zenon_Hbc zenon_H1c0 zenon_H15a zenon_H1bc zenon_H2a zenon_H1ba zenon_H90 zenon_H58 zenon_H7d zenon_H7e zenon_H86 zenon_H5e zenon_H128 zenon_Hce zenon_H95 zenon_Hdd zenon_H7a zenon_H187 zenon_H188 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_H35 zenon_H56 zenon_He3 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_L247_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_L103_); trivial. % 9.95/10.14 apply (zenon_L265_); trivial. % 9.95/10.14 apply (zenon_L266_); trivial. % 9.95/10.14 apply (zenon_L267_); trivial. % 9.95/10.14 (* end of lemma zenon_L311_ *) % 9.95/10.14 assert (zenon_L312_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (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)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (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 (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H10b zenon_H108 zenon_H103 zenon_H132 zenon_H28 zenon_H4c zenon_H90 zenon_H7e zenon_H86 zenon_H8c zenon_H91 zenon_H56 zenon_Hd3 zenon_H42 zenon_H181 zenon_H95 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_Hdd zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H187 zenon_Hc7 zenon_H1e2 zenon_H198 zenon_H17c zenon_Hb0 zenon_H97 zenon_H7d zenon_H7a zenon_H8d zenon_H64 zenon_Hd0 zenon_Hce zenon_H15a zenon_H35 zenon_H27 zenon_H188 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.14 apply (zenon_L274_); trivial. % 9.95/10.14 apply (zenon_L252_); trivial. % 9.95/10.14 apply (zenon_L301_); trivial. % 9.95/10.14 (* end of lemma zenon_L312_ *) % 9.95/10.14 assert (zenon_L313_ : (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H95 zenon_H188 zenon_H9b. % 9.95/10.14 cut (((op (e1) (e3)) = (e3)) = ((e2) = (e3))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H95. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H188. % 9.95/10.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.14 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 9.95/10.14 congruence. % 9.95/10.14 exact (zenon_H9c zenon_H9b). % 9.95/10.14 apply zenon_H4e. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L313_ *) % 9.95/10.14 assert (zenon_L314_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1ea zenon_H159 zenon_H35 zenon_H15a zenon_H155 zenon_H3a zenon_H95 zenon_H188 zenon_Hae. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 9.95/10.14 apply (zenon_L238_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 9.95/10.14 exact (zenon_Haf zenon_Hb4). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 9.95/10.14 apply (zenon_L223_); trivial. % 9.95/10.14 apply (zenon_L313_); trivial. % 9.95/10.14 apply (zenon_L123_); trivial. % 9.95/10.14 (* end of lemma zenon_L314_ *) % 9.95/10.14 assert (zenon_L315_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (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)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H168 zenon_Hae zenon_H95 zenon_H155 zenon_H35 zenon_H159 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_Hf8 zenon_H132 zenon_H6f zenon_H3c zenon_H3a zenon_H10b zenon_H144 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H5e zenon_H2a zenon_H12f zenon_H18d zenon_H1ea. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.14 apply (zenon_L297_); trivial. % 9.95/10.14 apply (zenon_L304_); trivial. % 9.95/10.14 apply (zenon_L314_); trivial. % 9.95/10.14 (* end of lemma zenon_L315_ *) % 9.95/10.14 assert (zenon_L316_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (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) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H158 zenon_H1ea zenon_H12f zenon_H145 zenon_H144 zenon_H6f zenon_H11d zenon_H191 zenon_Hae zenon_H168 zenon_H150 zenon_He3 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H12c zenon_H192 zenon_H181 zenon_H1dd zenon_H18d zenon_H56 zenon_Hb0 zenon_Hb1 zenon_H4c zenon_H53 zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_Hd3 zenon_H91 zenon_H8c zenon_H1b7 zenon_H187 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H5e zenon_H86 zenon_H7e zenon_H7d zenon_H58 zenon_H90 zenon_H1ba zenon_H2a zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H15a zenon_H35 zenon_H27 zenon_Hc5 zenon_H3c zenon_H64 zenon_H108 zenon_H155 zenon_Hf8 zenon_H97 zenon_H17c zenon_H1e2 zenon_H18a zenon_H42 zenon_H132 zenon_H10b zenon_Hd2. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L310_); trivial. % 9.95/10.14 apply (zenon_L311_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L312_); trivial. % 9.95/10.14 apply (zenon_L221_); trivial. % 9.95/10.14 apply (zenon_L315_); trivial. % 9.95/10.14 (* end of lemma zenon_L316_ *) % 9.95/10.14 assert (zenon_L317_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H97 zenon_H28 zenon_H95 zenon_H34 zenon_H4c zenon_H5d zenon_H187 zenon_H188. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_L184_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L130_); trivial. % 9.95/10.14 apply (zenon_L167_); trivial. % 9.95/10.14 (* end of lemma zenon_L317_ *) % 9.95/10.14 assert (zenon_L318_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (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))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H42 zenon_H27 zenon_H188 zenon_H187 zenon_H97 zenon_H28 zenon_H35 zenon_H112 zenon_Hcf zenon_Haf zenon_Hde zenon_H12c zenon_H181 zenon_Hc7 zenon_H1e2 zenon_Hc8 zenon_Hab zenon_H15a zenon_H198 zenon_H7e zenon_H192 zenon_H90 zenon_H1bc zenon_Hd3 zenon_H91 zenon_H8c zenon_H7a zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H5e zenon_H1b1 zenon_H4c zenon_H5d zenon_H95. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.14 exact (zenon_H27 zenon_H32). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.14 apply (zenon_L317_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.14 apply (zenon_L70_); trivial. % 9.95/10.14 apply (zenon_L294_); trivial. % 9.95/10.14 (* end of lemma zenon_L318_ *) % 9.95/10.14 assert (zenon_L319_ : ((~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (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 (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((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))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H1b4 zenon_H64 zenon_H8d zenon_H97 zenon_H4c zenon_H192 zenon_H12c zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_H112 zenon_Haf zenon_H1b1 zenon_H42 zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_Hcf zenon_H35 zenon_Hd3 zenon_H91 zenon_H8c zenon_H1b7 zenon_H187 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H5e zenon_H86 zenon_H7e zenon_H7d zenon_H58 zenon_H90 zenon_H1ba zenon_H2a zenon_H1bc zenon_H15a zenon_H1c0 zenon_H1c3 zenon_H27 zenon_Hda zenon_H56 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_L248_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_L318_); trivial. % 9.95/10.14 apply (zenon_L87_); trivial. % 9.95/10.14 apply (zenon_L252_); trivial. % 9.95/10.14 apply (zenon_L308_); trivial. % 9.95/10.14 (* end of lemma zenon_L319_ *) % 9.95/10.14 assert (zenon_L320_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((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 (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H64 zenon_H53 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H97 zenon_H4c zenon_H28 zenon_H192 zenon_H12c zenon_H198 zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_Hcf zenon_H112 zenon_Haf zenon_H1b1 zenon_H42 zenon_H27 zenon_H1c3 zenon_Hbc zenon_H1c0 zenon_H15a zenon_H1bc zenon_H2a zenon_H1ba zenon_H90 zenon_H58 zenon_H7d zenon_H7e zenon_H86 zenon_H5e zenon_H128 zenon_Hce zenon_H95 zenon_Hdd zenon_H7a zenon_H187 zenon_H188 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_H35 zenon_H56 zenon_Hda zenon_He3 zenon_H18d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_L247_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_L318_); trivial. % 9.95/10.14 apply (zenon_L265_); trivial. % 9.95/10.14 apply (zenon_L296_); trivial. % 9.95/10.14 apply (zenon_L306_); trivial. % 9.95/10.14 (* end of lemma zenon_L320_ *) % 9.95/10.14 assert (zenon_L321_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H3a zenon_Hcf zenon_Hc6. % 9.95/10.14 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 9.95/10.14 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_Hc6. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H3d. % 9.95/10.14 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.14 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1eb. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H3a. % 9.95/10.14 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 9.95/10.14 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H3e. apply refl_equal. % 9.95/10.14 apply zenon_H1ec. apply sym_equal. exact zenon_Hcf. % 9.95/10.14 apply zenon_H3e. apply refl_equal. % 9.95/10.14 apply zenon_H3e. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L321_ *) % 9.95/10.14 assert (zenon_L322_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e1) (e0)) = (op (e1) (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)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H67 zenon_Hab zenon_Hde zenon_H112 zenon_Hc6 zenon_H18a zenon_H1e2 zenon_H17c zenon_H64 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H58 zenon_H128 zenon_Hce zenon_Hdd zenon_H7a zenon_H1b7 zenon_H8c zenon_Hd3 zenon_Hb0 zenon_H12c zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_He3 zenon_H150 zenon_H168 zenon_Hae zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H198 zenon_H1dd zenon_Hda zenon_H56 zenon_Hd2 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H4c zenon_H35 zenon_H95 zenon_H10b zenon_H187 zenon_H97 zenon_H18d zenon_H12f zenon_H2a zenon_H5e zenon_H7d zenon_H7e zenon_H86 zenon_H145 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_H91 zenon_Hc5 zenon_Hf8 zenon_H6f zenon_H144 zenon_H158 zenon_H1ea zenon_H4a. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.14 apply (zenon_L297_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.14 apply (zenon_L305_); trivial. % 9.95/10.14 apply (zenon_L309_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.14 apply (zenon_L316_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L319_); trivial. % 9.95/10.14 apply (zenon_L320_); trivial. % 9.95/10.14 apply (zenon_L44_); trivial. % 9.95/10.14 apply (zenon_L321_); trivial. % 9.95/10.14 apply (zenon_L123_); trivial. % 9.95/10.14 apply (zenon_L213_); trivial. % 9.95/10.14 apply (zenon_L101_); trivial. % 9.95/10.14 (* end of lemma zenon_L322_ *) % 9.95/10.14 assert (zenon_L323_ : (((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). % 9.95/10.14 do 0 intro. intros zenon_H191 zenon_H68 zenon_H1f zenon_H192 zenon_Haf zenon_Hc1. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.95/10.14 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H68. % 9.95/10.14 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 9.95/10.14 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H2e. apply refl_equal. % 9.95/10.14 apply zenon_H196. apply sym_equal. exact zenon_Heb. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.95/10.14 exact (zenon_H192 zenon_H1d). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.95/10.14 exact (zenon_Haf zenon_Hb4). % 9.95/10.14 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.14 (* end of lemma zenon_L323_ *) % 9.95/10.14 assert (zenon_L324_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (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))))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1ea zenon_H15a zenon_H159 zenon_H1f zenon_H68 zenon_H192 zenon_Hc1 zenon_H191. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.14 apply (zenon_L323_); trivial. % 9.95/10.14 apply (zenon_L123_); trivial. % 9.95/10.14 (* end of lemma zenon_L324_ *) % 9.95/10.14 assert (zenon_L325_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1d zenon_H15a zenon_H195. % 9.95/10.14 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H20 | zenon_intro zenon_H21 ]. % 9.95/10.14 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H195. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H20. % 9.95/10.14 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.95/10.14 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1ed. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H1d. % 9.95/10.14 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 9.95/10.14 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H21. apply refl_equal. % 9.95/10.14 apply zenon_H1ee. apply sym_equal. exact zenon_H15a. % 9.95/10.14 apply zenon_H21. apply refl_equal. % 9.95/10.14 apply zenon_H21. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L325_ *) % 9.95/10.14 assert (zenon_L326_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (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) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1ef zenon_H195 zenon_H1ea zenon_H15a zenon_H159 zenon_H1f zenon_H68 zenon_H191 zenon_H198 zenon_H1af. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.14 apply (zenon_L324_); trivial. % 9.95/10.14 apply (zenon_L194_); trivial. % 9.95/10.14 apply (zenon_L325_); trivial. % 9.95/10.14 (* end of lemma zenon_L326_ *) % 9.95/10.14 assert (zenon_L327_ : ((op (e3) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf2 zenon_H1e zenon_H1f0. % 9.95/10.14 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H115 | zenon_intro zenon_Hef ]. % 9.95/10.14 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f0. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H115. % 9.95/10.14 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.95/10.14 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f1. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_Hf2. % 9.95/10.14 cut (((e1) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 9.95/10.14 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_Hef. apply refl_equal. % 9.95/10.14 apply zenon_H23. apply sym_equal. exact zenon_H1e. % 9.95/10.14 apply zenon_Hef. apply refl_equal. % 9.95/10.14 apply zenon_Hef. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L327_ *) % 9.95/10.14 assert (zenon_L328_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1e6 zenon_H100 zenon_Hf3. % 9.95/10.14 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1e6. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H100. % 9.95/10.14 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 9.95/10.14 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H71. apply refl_equal. % 9.95/10.14 apply zenon_H1da. apply sym_equal. exact zenon_Hf3. % 9.95/10.14 (* end of lemma zenon_L328_ *) % 9.95/10.14 assert (zenon_L329_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hf5 zenon_Hbc zenon_H4c zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.95/10.14 apply (zenon_L139_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.95/10.14 apply (zenon_L327_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.95/10.14 apply (zenon_L328_); trivial. % 9.95/10.14 exact (zenon_H7e zenon_H83). % 9.95/10.14 (* end of lemma zenon_L329_ *) % 9.95/10.14 assert (zenon_L330_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1f zenon_H34 zenon_Hb4. % 9.95/10.14 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H34. % 9.95/10.14 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 9.95/10.14 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H2e. apply refl_equal. % 9.95/10.14 apply zenon_H1c9. apply sym_equal. exact zenon_Hb4. % 9.95/10.14 (* end of lemma zenon_L330_ *) % 9.95/10.14 assert (zenon_L331_ : (((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). % 9.95/10.14 do 0 intro. intros zenon_H191 zenon_He8 zenon_H192 zenon_H34 zenon_H1f zenon_Hc1. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.95/10.14 exact (zenon_He8 zenon_Heb). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.95/10.14 exact (zenon_H192 zenon_H1d). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.95/10.14 apply (zenon_L330_); trivial. % 9.95/10.14 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.14 (* end of lemma zenon_L331_ *) % 9.95/10.14 assert (zenon_L332_ : (~((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1f2 zenon_Hb4. % 9.95/10.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.14 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 9.95/10.14 congruence. % 9.95/10.14 exact (zenon_Haf zenon_Hb4). % 9.95/10.14 apply zenon_H33. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L332_ *) % 9.95/10.14 assert (zenon_L333_ : ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (op (op (e1) (e1)) (e1)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H78 zenon_Hb4 zenon_H19e. % 9.95/10.14 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((e0) = (op (op (e1) (e1)) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H19e. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H19f. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1a1. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H78. % 9.95/10.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.14 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 9.95/10.14 congruence. % 9.95/10.14 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f3. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H19f. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 9.95/10.14 congruence. % 9.95/10.14 apply (zenon_L332_); trivial. % 9.95/10.14 apply zenon_H1a0. apply refl_equal. % 9.95/10.14 apply zenon_H1a0. apply refl_equal. % 9.95/10.14 apply zenon_H41. apply refl_equal. % 9.95/10.14 apply zenon_H1a0. apply refl_equal. % 9.95/10.14 apply zenon_H1a0. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L333_ *) % 9.95/10.14 assert (zenon_L334_ : ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H4b zenon_H78 zenon_Hb4. % 9.95/10.14 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H1f4 ]. % 9.95/10.14 apply zenon_H1c9. apply sym_equal. exact zenon_Hb4. % 9.95/10.14 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H19e ]. % 9.95/10.14 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1a7 ]. % 9.95/10.14 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((e3) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f5. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H1a6. % 9.95/10.14 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 9.95/10.14 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e0) (e1)) = (e3)) = ((op (op (op (e1) (e1)) (e1)) (e1)) = (e3))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f6. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H4b. % 9.95/10.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.14 cut (((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 9.95/10.14 congruence. % 9.95/10.14 elim (classic ((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1a7 ]. % 9.95/10.14 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1))) = ((op (e0) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1a9. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H1a6. % 9.95/10.14 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (op (op (e1) (e1)) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a7]. % 9.95/10.14 cut (((op (op (op (e1) (e1)) (e1)) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (e1)) (e1)) = (e0))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1a1. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H78. % 9.95/10.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.14 cut (((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 9.95/10.14 congruence. % 9.95/10.14 elim (classic ((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1))) = ((op (e2) (e1)) = (op (op (e1) (e1)) (e1)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1f3. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H19f. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (op (e1) (e1)) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 9.95/10.14 cut (((op (op (e1) (e1)) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 9.95/10.14 congruence. % 9.95/10.14 apply (zenon_L332_); trivial. % 9.95/10.14 apply zenon_H1a0. apply refl_equal. % 9.95/10.14 apply zenon_H1a0. apply refl_equal. % 9.95/10.14 apply zenon_H41. apply refl_equal. % 9.95/10.14 apply zenon_H33. apply refl_equal. % 9.95/10.14 apply zenon_H1a7. apply refl_equal. % 9.95/10.14 apply zenon_H1a7. apply refl_equal. % 9.95/10.14 apply zenon_H4e. apply refl_equal. % 9.95/10.14 apply zenon_H1a7. apply refl_equal. % 9.95/10.14 apply zenon_H1a7. apply refl_equal. % 9.95/10.14 apply (zenon_L333_); trivial. % 9.95/10.14 (* end of lemma zenon_L334_ *) % 9.95/10.14 assert (zenon_L335_ : (((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 (e2) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H191 zenon_He8 zenon_H192 zenon_H78 zenon_H4b zenon_Hc1. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.95/10.14 exact (zenon_He8 zenon_Heb). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.95/10.14 exact (zenon_H192 zenon_H1d). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.95/10.14 apply (zenon_L334_); trivial. % 9.95/10.14 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.14 (* end of lemma zenon_L335_ *) % 9.95/10.14 assert (zenon_L336_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hb0 zenon_H53 zenon_Hc1 zenon_H4b zenon_H192 zenon_He8 zenon_H191 zenon_Hb1 zenon_H90 zenon_H4c zenon_H74 zenon_Hd3 zenon_H1e zenon_H91 zenon_H5e. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.14 apply (zenon_L20_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.14 apply (zenon_L335_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.14 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.14 apply (zenon_L250_); trivial. % 9.95/10.14 (* end of lemma zenon_L336_ *) % 9.95/10.14 assert (zenon_L337_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H18d zenon_H188 zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.14 apply (zenon_L24_); trivial. % 9.95/10.14 apply (zenon_L252_); trivial. % 9.95/10.14 (* end of lemma zenon_L337_ *) % 9.95/10.14 assert (zenon_L338_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H7d zenon_H8d zenon_H87 zenon_H47 zenon_H7f zenon_H80. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H7b | zenon_intro zenon_H81 ]. % 9.95/10.14 exact (zenon_H8d zenon_H7b). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 9.95/10.14 apply (zenon_L91_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 9.95/10.14 exact (zenon_H7f zenon_H85). % 9.95/10.14 exact (zenon_H80 zenon_H84). % 9.95/10.14 (* end of lemma zenon_L338_ *) % 9.95/10.14 assert (zenon_L339_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H90 zenon_H74 zenon_H4c zenon_Hb9 zenon_H91 zenon_H8c zenon_H7e zenon_H7a zenon_H86 zenon_H188 zenon_H18d zenon_H80 zenon_H7f zenon_H47 zenon_H7d zenon_H5e zenon_H8d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.14 apply (zenon_L21_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.14 apply (zenon_L48_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.14 exact (zenon_H91 zenon_H94). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.14 apply (zenon_L337_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.14 apply (zenon_L338_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.14 apply (zenon_L27_); trivial. % 9.95/10.14 exact (zenon_H8d zenon_H7b). % 9.95/10.14 (* end of lemma zenon_L339_ *) % 9.95/10.14 assert (zenon_L340_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H14d zenon_H5e zenon_H53 zenon_H7f zenon_H44 zenon_H95 zenon_Hbd zenon_Hf0 zenon_H35 zenon_H177 zenon_H8d. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 9.95/10.14 apply (zenon_L62_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 9.95/10.14 apply (zenon_L112_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 9.95/10.14 apply (zenon_L211_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 9.95/10.14 apply (zenon_L50_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 9.95/10.14 apply (zenon_L113_); trivial. % 9.95/10.14 exact (zenon_H7f zenon_H85). % 9.95/10.14 exact (zenon_H8d zenon_H7b). % 9.95/10.14 (* end of lemma zenon_L340_ *) % 9.95/10.14 assert (zenon_L341_ : (((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). % 9.95/10.14 do 0 intro. intros zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H4c zenon_H5d zenon_H47 zenon_H95. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_L30_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L130_); trivial. % 9.95/10.14 apply (zenon_L54_); trivial. % 9.95/10.14 (* end of lemma zenon_L341_ *) % 9.95/10.14 assert (zenon_L342_ : (((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 (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H4c zenon_H5d zenon_H95. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.14 exact (zenon_H27 zenon_H32). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.14 apply (zenon_L16_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.14 apply (zenon_L5_); trivial. % 9.95/10.14 apply (zenon_L341_); trivial. % 9.95/10.14 (* end of lemma zenon_L342_ *) % 9.95/10.14 assert (zenon_L343_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1cb zenon_H51 zenon_H43. % 9.95/10.14 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1cb. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H51. % 9.95/10.14 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 9.95/10.14 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H134. apply refl_equal. % 9.95/10.14 apply zenon_H11c. apply sym_equal. exact zenon_H43. % 9.95/10.14 (* end of lemma zenon_L343_ *) % 9.95/10.14 assert (zenon_L344_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (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))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_H4c zenon_Hf5 zenon_Hb0 zenon_H53 zenon_H86 zenon_H1cb zenon_H51 zenon_H8c zenon_Hb1 zenon_H90 zenon_Hd3 zenon_H91 zenon_H5e zenon_H188 zenon_H198 zenon_H28 zenon_Hda zenon_H6f zenon_H100 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L239_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.14 apply (zenon_L20_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.14 apply (zenon_L21_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.14 apply (zenon_L22_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.14 exact (zenon_H91 zenon_H94). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.14 apply (zenon_L343_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.14 apply (zenon_L26_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.14 apply (zenon_L27_); trivial. % 9.95/10.14 exact (zenon_H8d zenon_H7b). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.14 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.14 apply (zenon_L250_); trivial. % 9.95/10.14 apply (zenon_L329_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_L228_); trivial. % 9.95/10.14 apply (zenon_L87_); trivial. % 9.95/10.14 (* end of lemma zenon_L344_ *) % 9.95/10.14 assert (zenon_L345_ : (((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 (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H144 zenon_H68 zenon_Hfd zenon_H6f zenon_H100 zenon_H3c zenon_H3a zenon_Hed zenon_H10b. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H51 | zenon_intro zenon_H148 ]. % 9.95/10.14 apply (zenon_L69_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H5d | zenon_intro zenon_H149 ]. % 9.95/10.14 apply (zenon_L228_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H3b | zenon_intro zenon_H52 ]. % 9.95/10.14 apply (zenon_L5_); trivial. % 9.95/10.14 apply (zenon_L75_); trivial. % 9.95/10.14 (* end of lemma zenon_L345_ *) % 9.95/10.14 assert (zenon_L346_ : (((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) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((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 (e2) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hda zenon_H28 zenon_H198 zenon_H188 zenon_H5e zenon_H91 zenon_Hd3 zenon_H90 zenon_Hb1 zenon_H191 zenon_He8 zenon_H192 zenon_H4b zenon_Hc1 zenon_H53 zenon_Hb0 zenon_Hf5 zenon_H4c zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L239_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L336_); trivial. % 9.95/10.14 apply (zenon_L329_); trivial. % 9.95/10.14 (* end of lemma zenon_L346_ *) % 9.95/10.14 assert (zenon_L347_ : (((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) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.14 do 0 intro. intros zenon_Hda zenon_H28 zenon_H198 zenon_H188 zenon_H53 zenon_H73 zenon_Hf5 zenon_H4c zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.14 apply (zenon_L239_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.14 apply (zenon_L20_); trivial. % 9.95/10.14 apply (zenon_L329_); trivial. % 9.95/10.14 (* end of lemma zenon_L347_ *) % 9.95/10.14 assert (zenon_L348_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H6f zenon_H51 zenon_H101. % 9.95/10.14 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H6f. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H51. % 9.95/10.14 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 9.95/10.14 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H134. apply refl_equal. % 9.95/10.14 apply zenon_H1f7. apply sym_equal. exact zenon_H101. % 9.95/10.14 (* end of lemma zenon_L348_ *) % 9.95/10.14 assert (zenon_L349_ : (((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 (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1f8 zenon_H51 zenon_H6f zenon_H5d zenon_H155 zenon_H3a zenon_Hed zenon_H1e6. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H101 | zenon_intro zenon_H1f9 ]. % 9.95/10.14 apply (zenon_L348_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H100 | zenon_intro zenon_H1fa ]. % 9.95/10.14 apply (zenon_L228_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H6e | zenon_intro zenon_H161 ]. % 9.95/10.14 apply (zenon_L223_); trivial. % 9.95/10.14 apply (zenon_L282_); trivial. % 9.95/10.14 (* end of lemma zenon_L349_ *) % 9.95/10.14 assert (zenon_L350_ : ((op (e2) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H11f zenon_H188 zenon_H17c. % 9.95/10.14 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 9.95/10.14 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H17c. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H17d. % 9.95/10.14 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.95/10.14 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H17f. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H11f. % 9.95/10.14 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 9.95/10.14 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H17e. apply refl_equal. % 9.95/10.14 apply zenon_H189. apply sym_equal. exact zenon_H188. % 9.95/10.14 apply zenon_H17e. apply refl_equal. % 9.95/10.14 apply zenon_H17e. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L350_ *) % 9.95/10.14 assert (zenon_L351_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H12c zenon_H53 zenon_H73 zenon_H4c zenon_H77 zenon_Hc8 zenon_H188 zenon_H17c. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.95/10.14 apply (zenon_L20_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.95/10.14 apply (zenon_L48_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.95/10.14 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.14 apply (zenon_L350_); trivial. % 9.95/10.14 (* end of lemma zenon_L351_ *) % 9.95/10.14 assert (zenon_L352_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H90 zenon_H5e zenon_H17c zenon_H188 zenon_Hc8 zenon_H4c zenon_H73 zenon_H53 zenon_H12c zenon_H91 zenon_H181 zenon_H62. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.14 apply (zenon_L165_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.14 apply (zenon_L351_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.14 exact (zenon_H91 zenon_H94). % 9.95/10.14 apply (zenon_L258_); trivial. % 9.95/10.14 (* end of lemma zenon_L352_ *) % 9.95/10.14 assert (zenon_L353_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H100 zenon_H1f0 zenon_Hf5 zenon_H198 zenon_H28 zenon_Hda zenon_H1e6 zenon_Hed zenon_H3a zenon_H155 zenon_H6f zenon_H51 zenon_H1f8 zenon_H90 zenon_H5e zenon_H17c zenon_H188 zenon_Hc8 zenon_H4c zenon_H73 zenon_H53 zenon_H12c zenon_H91 zenon_H181. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_L347_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_L349_); trivial. % 9.95/10.14 apply (zenon_L352_); trivial. % 9.95/10.14 (* end of lemma zenon_L353_ *) % 9.95/10.14 assert (zenon_L354_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1fb zenon_H3a zenon_Hd0. % 9.95/10.14 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1fb. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H3a. % 9.95/10.14 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 9.95/10.14 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.14 congruence. % 9.95/10.14 apply zenon_H3e. apply refl_equal. % 9.95/10.14 apply zenon_Hd1. apply sym_equal. exact zenon_Hd0. % 9.95/10.14 (* end of lemma zenon_L354_ *) % 9.95/10.14 assert (zenon_L355_ : (~((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H1fc zenon_H85. % 9.95/10.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.14 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 9.95/10.14 congruence. % 9.95/10.14 exact (zenon_H7f zenon_H85). % 9.95/10.14 apply zenon_H4e. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L355_ *) % 9.95/10.14 assert (zenon_L356_ : ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H62 zenon_H89 zenon_H85. % 9.95/10.14 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H1fe | zenon_intro zenon_H1fd ]. % 9.95/10.14 apply zenon_H1fe. apply sym_equal. exact zenon_H85. % 9.95/10.14 apply (zenon_notand_s _ _ zenon_H1fd); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H120 ]. % 9.95/10.14 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.14 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e1) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1d1. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_Ha2. % 9.95/10.14 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.14 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e0) (e3)) = (e1)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e1))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1d2. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H62. % 9.95/10.14 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.14 cut (((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 9.95/10.14 congruence. % 9.95/10.14 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.14 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e0) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H125. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_Ha2. % 9.95/10.14 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.14 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e2) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H121. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H89. % 9.95/10.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.14 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 9.95/10.14 congruence. % 9.95/10.14 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1ff. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_Ha9. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 9.95/10.14 congruence. % 9.95/10.14 apply (zenon_L355_); trivial. % 9.95/10.14 apply zenon_Haa. apply refl_equal. % 9.95/10.14 apply zenon_Haa. apply refl_equal. % 9.95/10.14 apply zenon_H41. apply refl_equal. % 9.95/10.14 apply zenon_H4e. apply refl_equal. % 9.95/10.14 apply zenon_Ha3. apply refl_equal. % 9.95/10.14 apply zenon_Ha3. apply refl_equal. % 9.95/10.14 apply zenon_H33. apply refl_equal. % 9.95/10.14 apply zenon_Ha3. apply refl_equal. % 9.95/10.14 apply zenon_Ha3. apply refl_equal. % 9.95/10.14 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e0) = (op (op (e3) (e3)) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H120. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_Ha9. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 9.95/10.14 congruence. % 9.95/10.14 cut (((op (e2) (e3)) = (e0)) = ((op (op (e3) (e3)) (e3)) = (e0))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H121. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_H89. % 9.95/10.14 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.14 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 9.95/10.14 congruence. % 9.95/10.14 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.14 intro zenon_D_pnotp. % 9.95/10.14 apply zenon_H1ff. % 9.95/10.14 rewrite <- zenon_D_pnotp. % 9.95/10.14 exact zenon_Ha9. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.14 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 9.95/10.14 congruence. % 9.95/10.14 apply (zenon_L355_); trivial. % 9.95/10.14 apply zenon_Haa. apply refl_equal. % 9.95/10.14 apply zenon_Haa. apply refl_equal. % 9.95/10.14 apply zenon_H41. apply refl_equal. % 9.95/10.14 apply zenon_Haa. apply refl_equal. % 9.95/10.14 apply zenon_Haa. apply refl_equal. % 9.95/10.14 (* end of lemma zenon_L356_ *) % 9.95/10.14 assert (zenon_L357_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H128 zenon_H35 zenon_H188 zenon_H95 zenon_H3a zenon_H1fb zenon_H62 zenon_H89. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 9.95/10.14 apply (zenon_L260_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 9.95/10.14 apply (zenon_L313_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 9.95/10.14 apply (zenon_L354_); trivial. % 9.95/10.14 apply (zenon_L356_); trivial. % 9.95/10.14 (* end of lemma zenon_L357_ *) % 9.95/10.14 assert (zenon_L358_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 9.95/10.14 do 0 intro. intros zenon_H187 zenon_Hd3 zenon_H97 zenon_H1fb zenon_H3a zenon_H95 zenon_H188 zenon_H35 zenon_H128 zenon_Hb1 zenon_H191 zenon_He8 zenon_H192 zenon_Hc1 zenon_H64 zenon_H56 zenon_H7e zenon_H100 zenon_H1f0 zenon_Hf5 zenon_H198 zenon_H28 zenon_Hda zenon_H1e6 zenon_H155 zenon_H6f zenon_H51 zenon_H1f8 zenon_H90 zenon_H5e zenon_H17c zenon_Hc8 zenon_H53 zenon_H12c zenon_H91 zenon_H181 zenon_Hb0 zenon_H10b zenon_Hed zenon_H4c. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.14 exact (zenon_H56 zenon_H2c). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_L346_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L75_); trivial. % 9.95/10.14 apply (zenon_L167_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.14 apply (zenon_L228_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.14 exact (zenon_H28 zenon_H31). % 9.95/10.14 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.14 apply (zenon_L353_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.14 apply (zenon_L335_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.14 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.14 apply (zenon_L357_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.14 apply (zenon_L75_); trivial. % 9.95/10.14 apply (zenon_L13_); trivial. % 9.95/10.14 (* end of lemma zenon_L358_ *) % 9.95/10.14 assert (zenon_L359_ : (((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) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.14 do 0 intro. intros zenon_H108 zenon_H43 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_Hed. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.95/10.14 apply (zenon_L343_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.95/10.14 apply (zenon_L71_); trivial. % 9.95/10.14 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.95/10.14 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.14 apply (zenon_L73_); trivial. % 9.95/10.14 (* end of lemma zenon_L359_ *) % 9.95/10.14 assert (zenon_L360_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (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)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.15 do 0 intro. intros zenon_H200 zenon_H25 zenon_H3c zenon_Hfd zenon_H144 zenon_H4c zenon_H10b zenon_Hb0 zenon_H181 zenon_H91 zenon_H12c zenon_Hc8 zenon_H17c zenon_H90 zenon_H1f8 zenon_H6f zenon_H155 zenon_H1e6 zenon_Hda zenon_H28 zenon_H198 zenon_Hf5 zenon_H1f0 zenon_H7e zenon_H56 zenon_H64 zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H128 zenon_H35 zenon_H188 zenon_H95 zenon_H3a zenon_H1fb zenon_H97 zenon_Hd3 zenon_H187 zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_Hed. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.15 exact (zenon_H25 zenon_H2a). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.15 apply (zenon_L345_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.15 apply (zenon_L358_); trivial. % 9.95/10.15 apply (zenon_L359_); trivial. % 9.95/10.15 (* end of lemma zenon_L360_ *) % 9.95/10.15 assert (zenon_L361_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_Hc8 zenon_H17c zenon_H12c zenon_H187 zenon_H108 zenon_H200 zenon_H1cb zenon_H6f zenon_H56 zenon_H1b4 zenon_H27 zenon_Hc1 zenon_H192 zenon_He8 zenon_H3c zenon_H3a zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_Hb1 zenon_H53 zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H8d zenon_H8c zenon_H14d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hc0 zenon_H42 zenon_H28 zenon_H188 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H191 zenon_H1f zenon_H159 zenon_H1ea zenon_H195 zenon_H1ef zenon_H97 zenon_H64 zenon_H25. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.15 exact (zenon_H25 zenon_H2a). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.15 exact (zenon_H56 zenon_H2c). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.15 exact (zenon_H56 zenon_H2c). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.15 apply (zenon_L326_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.15 exact (zenon_H28 zenon_H31). % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.15 apply (zenon_L239_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.15 apply (zenon_L21_); trivial. % 9.95/10.15 apply (zenon_L329_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.15 exact (zenon_H27 zenon_H32). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.15 apply (zenon_L331_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.15 apply (zenon_L5_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.15 exact (zenon_H28 zenon_H31). % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.15 apply (zenon_L239_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.95/10.15 apply (zenon_L336_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.95/10.15 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.95/10.15 apply (zenon_L339_); trivial. % 9.95/10.15 apply (zenon_L340_); trivial. % 9.95/10.15 apply (zenon_L139_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.15 apply (zenon_L342_); trivial. % 9.95/10.15 apply (zenon_L87_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.15 apply (zenon_L344_); trivial. % 9.95/10.15 apply (zenon_L24_); trivial. % 9.95/10.15 apply (zenon_L252_); trivial. % 9.95/10.15 apply (zenon_L360_); trivial. % 9.95/10.15 (* end of lemma zenon_L361_ *) % 9.95/10.15 assert (zenon_L362_ : (((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). % 9.95/10.15 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H4c zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H62 zenon_H35. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.15 exact (zenon_H27 zenon_H32). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.15 apply (zenon_L16_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.15 apply (zenon_L33_); trivial. % 9.95/10.15 apply (zenon_L260_); trivial. % 9.95/10.15 (* end of lemma zenon_L362_ *) % 9.95/10.15 assert (zenon_L363_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (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). % 9.95/10.15 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hbc zenon_Hf5 zenon_H6f zenon_H100 zenon_H42 zenon_H27 zenon_H44 zenon_H4c zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.15 exact (zenon_H56 zenon_H2c). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.15 apply (zenon_L329_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.15 apply (zenon_L228_); trivial. % 9.95/10.15 apply (zenon_L362_); trivial. % 9.95/10.15 (* end of lemma zenon_L363_ *) % 9.95/10.15 assert (zenon_L364_ : (((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)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hf5 zenon_Hbc zenon_H4c zenon_He5 zenon_H5e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.95/10.15 apply (zenon_L139_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.95/10.15 apply (zenon_L206_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.95/10.15 apply (zenon_L328_); trivial. % 9.95/10.15 exact (zenon_H7e zenon_H83). % 9.95/10.15 (* end of lemma zenon_L364_ *) % 9.95/10.15 assert (zenon_L365_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.15 do 0 intro. intros zenon_He7 zenon_H51 zenon_Hfd zenon_Hc1 zenon_H4b zenon_H192 zenon_He8 zenon_H191 zenon_Hf5 zenon_Hbc zenon_H4c zenon_H5e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.15 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.95/10.15 apply (zenon_L69_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.95/10.15 exact (zenon_He8 zenon_Heb). % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.95/10.15 apply (zenon_L335_); trivial. % 9.95/10.15 apply (zenon_L364_); trivial. % 9.95/10.15 (* end of lemma zenon_L365_ *) % 9.95/10.15 assert (zenon_L366_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H16b zenon_Hd8 zenon_H95 zenon_H114 zenon_Hb9 zenon_H10b zenon_H52 zenon_H80. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbc | zenon_intro zenon_H16c ]. % 9.95/10.15 apply (zenon_L51_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_Hbd | zenon_intro zenon_H16d ]. % 9.95/10.15 apply (zenon_L80_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hed | zenon_intro zenon_H84 ]. % 9.95/10.15 apply (zenon_L75_); trivial. % 9.95/10.15 exact (zenon_H80 zenon_H84). % 9.95/10.15 (* end of lemma zenon_L366_ *) % 9.95/10.15 assert (zenon_L367_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H158 zenon_H135 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.15 apply (zenon_L129_); trivial. % 9.95/10.15 apply (zenon_L116_); trivial. % 9.95/10.15 (* end of lemma zenon_L367_ *) % 9.95/10.15 assert (zenon_L368_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H177 zenon_H80 zenon_H52 zenon_H10b zenon_Hb9 zenon_H114 zenon_H95 zenon_H16b zenon_H35 zenon_Hf2 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 9.95/10.15 apply (zenon_L366_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 9.95/10.15 apply (zenon_L63_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 9.95/10.15 apply (zenon_L367_); trivial. % 9.95/10.15 exact (zenon_H7f zenon_H85). % 9.95/10.15 (* end of lemma zenon_L368_ *) % 9.95/10.15 assert (zenon_L369_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hc0 zenon_Hb4 zenon_H78 zenon_Hc1 zenon_H7f zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H35 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H52 zenon_H80 zenon_H177 zenon_Hf2 zenon_H4c. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.95/10.15 apply (zenon_L334_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.95/10.15 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.95/10.15 apply (zenon_L368_); trivial. % 9.95/10.15 apply (zenon_L207_); trivial. % 9.95/10.15 (* end of lemma zenon_L369_ *) % 9.95/10.15 assert (zenon_L370_ : (((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 (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H64 zenon_H56 zenon_H97 zenon_H28 zenon_H7e zenon_H1e6 zenon_H100 zenon_H5e zenon_Hbc zenon_Hf5 zenon_H1b1 zenon_H1f0 zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H177 zenon_H80 zenon_H10b zenon_H114 zenon_H95 zenon_H16b zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f zenon_Hc1 zenon_Hc0 zenon_H44 zenon_H35 zenon_Hfd zenon_He7 zenon_H4c. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.15 exact (zenon_H56 zenon_H2c). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.15 apply (zenon_L329_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.15 apply (zenon_L12_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.15 exact (zenon_H28 zenon_H31). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.15 apply (zenon_L365_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.95/10.15 apply (zenon_L69_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.95/10.15 exact (zenon_He8 zenon_Heb). % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.15 apply (zenon_L329_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.15 exact (zenon_H192 zenon_H1d). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.15 apply (zenon_L22_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.95/10.15 apply (zenon_L331_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.95/10.15 apply (zenon_L369_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.95/10.15 apply (zenon_L57_); trivial. % 9.95/10.15 apply (zenon_L63_); trivial. % 9.95/10.15 apply (zenon_L364_); trivial. % 9.95/10.15 apply (zenon_L13_); trivial. % 9.95/10.15 (* end of lemma zenon_L370_ *) % 9.95/10.15 assert (zenon_L371_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (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 (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H200 zenon_H25 zenon_H53 zenon_H27 zenon_H42 zenon_H6f zenon_H4c zenon_He7 zenon_Hfd zenon_H35 zenon_H44 zenon_Hc0 zenon_Hc1 zenon_H158 zenon_H152 zenon_H3c zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H177 zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hde zenon_H1f0 zenon_H1b1 zenon_Hf5 zenon_Hbc zenon_H5e zenon_H100 zenon_H1e6 zenon_H28 zenon_H97 zenon_H56 zenon_H64 zenon_H7d zenon_H7a zenon_H7e zenon_H7f zenon_H80. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.15 exact (zenon_H25 zenon_H2a). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.15 apply (zenon_L363_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.15 apply (zenon_L370_); trivial. % 9.95/10.15 apply (zenon_L24_); trivial. % 9.95/10.15 (* end of lemma zenon_L371_ *) % 9.95/10.15 assert (zenon_L372_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((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))) -> (~((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) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hf8 zenon_H144 zenon_H3a zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_Hda zenon_Hb1 zenon_H90 zenon_Hd3 zenon_Hb0 zenon_H198 zenon_H187 zenon_H108 zenon_H1cb zenon_H200 zenon_H7a zenon_H7d zenon_H5e zenon_H1b1 zenon_H1f zenon_Hc0 zenon_H16b zenon_H10b zenon_H114 zenon_H158 zenon_H152 zenon_H3c zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H177 zenon_Hde zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_H192 zenon_He7 zenon_H56 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hbc zenon_H4c zenon_H6f zenon_H42 zenon_H35 zenon_H28 zenon_H53 zenon_H95 zenon_H97 zenon_H44 zenon_H27 zenon_H64 zenon_H25 zenon_H86 zenon_H188 zenon_H18d. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.15 apply (zenon_L371_); trivial. % 9.95/10.15 apply (zenon_L252_); trivial. % 9.95/10.15 apply (zenon_L360_); trivial. % 9.95/10.15 (* end of lemma zenon_L372_ *) % 9.95/10.15 assert (zenon_L373_ : (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> False). % 9.95/10.15 do 0 intro. intros zenon_H4c zenon_H188 zenon_H9a. % 9.95/10.15 cut (((op (e1) (e3)) = (e3)) = ((e1) = (e3))). % 9.95/10.15 intro zenon_D_pnotp. % 9.95/10.15 apply zenon_H4c. % 9.95/10.15 rewrite <- zenon_D_pnotp. % 9.95/10.15 exact zenon_H188. % 9.95/10.15 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.15 cut (((op (e1) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 9.95/10.15 congruence. % 9.95/10.15 exact (zenon_H203 zenon_H9a). % 9.95/10.15 apply zenon_H4e. apply refl_equal. % 9.95/10.15 (* end of lemma zenon_L373_ *) % 9.95/10.15 assert (zenon_L374_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hf8 zenon_H1cb zenon_H5e zenon_H100 zenon_Hb1 zenon_H53 zenon_H108 zenon_H7d zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H188 zenon_H18d. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.15 apply (zenon_L337_); trivial. % 9.95/10.15 apply (zenon_L359_); trivial. % 9.95/10.15 (* end of lemma zenon_L374_ *) % 9.95/10.15 assert (zenon_L375_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (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)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H168 zenon_Hae zenon_H95 zenon_H155 zenon_H35 zenon_H159 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H3a zenon_Hc6 zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7d zenon_H108 zenon_H53 zenon_H5e zenon_H1cb zenon_Hf8 zenon_H1ea. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.15 apply (zenon_L297_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.15 apply (zenon_L374_); trivial. % 9.95/10.15 apply (zenon_L321_); trivial. % 9.95/10.15 apply (zenon_L314_); trivial. % 9.95/10.15 (* end of lemma zenon_L375_ *) % 9.95/10.15 assert (zenon_L376_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H18d zenon_H56 zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H53 zenon_H90 zenon_H1cb zenon_H51 zenon_H7d zenon_H7f zenon_H7e zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hd3 zenon_Hb0 zenon_H188 zenon_H198 zenon_H28 zenon_H6f zenon_H7a zenon_H64. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.15 apply (zenon_L344_); trivial. % 9.95/10.15 apply (zenon_L252_); trivial. % 9.95/10.15 (* end of lemma zenon_L376_ *) % 9.95/10.15 assert (zenon_L377_ : ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (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))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hf8 zenon_H97 zenon_H187 zenon_H10b zenon_He8 zenon_H192 zenon_Hc1 zenon_H191 zenon_H12c zenon_H17c zenon_Hc8 zenon_H181 zenon_H155 zenon_H3a zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_H35 zenon_H64 zenon_H7a zenon_H6f zenon_H28 zenon_H198 zenon_H188 zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H4c zenon_H5e zenon_H91 zenon_H8c zenon_H8d zenon_H86 zenon_H7e zenon_H7d zenon_H51 zenon_H1cb zenon_H90 zenon_H53 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H56 zenon_H18d. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.15 apply (zenon_L376_); trivial. % 9.95/10.15 apply (zenon_L358_); trivial. % 9.95/10.15 (* end of lemma zenon_L377_ *) % 9.95/10.15 assert (zenon_L378_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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 (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.15 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H64 zenon_H28 zenon_He7 zenon_H192 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hfd zenon_Hde zenon_H44 zenon_H177 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H3c zenon_H152 zenon_H158 zenon_H35 zenon_H95 zenon_H114 zenon_H10b zenon_H16b zenon_Hc0 zenon_H1f zenon_H1b1 zenon_H97 zenon_H51 zenon_H5e zenon_H4c zenon_Hbc zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H56 zenon_He3 zenon_H18d. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.15 apply (zenon_L370_); trivial. % 9.95/10.15 apply (zenon_L266_); trivial. % 9.95/10.15 apply (zenon_L267_); trivial. % 9.95/10.15 (* end of lemma zenon_L378_ *) % 9.95/10.15 assert (zenon_L379_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((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 (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)) = (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) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H173 zenon_H103 zenon_Hec zenon_H1b7 zenon_Hdd zenon_Hce zenon_H58 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1e2 zenon_H18a zenon_H112 zenon_Hab zenon_H67 zenon_H1dd zenon_He3 zenon_H168 zenon_Hae zenon_H191 zenon_H11d zenon_H192 zenon_Hd2 zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H187 zenon_H108 zenon_H200 zenon_H1cb zenon_H6f zenon_H56 zenon_H1b4 zenon_H3c zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_H53 zenon_H18d zenon_H7a zenon_H7d zenon_H8c zenon_H14d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hc0 zenon_H42 zenon_H4c zenon_Hf5 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H1f zenon_H159 zenon_H1ea zenon_H195 zenon_H1ef zenon_H97 zenon_H64 zenon_H1b1 zenon_H16b zenon_H114 zenon_H158 zenon_H152 zenon_Hc5 zenon_Hde zenon_He7 zenon_H150 zenon_Hc6 zenon_H156 zenon_H4a zenon_H132 zenon_H145 zenon_H12f zenon_H204 zenon_H188 zenon_H86. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 9.95/10.15 apply (zenon_L322_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 9.95/10.15 exact (zenon_H192 zenon_H1d). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.15 apply (zenon_L297_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.15 apply (zenon_L361_); trivial. % 9.95/10.15 apply (zenon_L372_); trivial. % 9.95/10.15 apply (zenon_L354_); trivial. % 9.95/10.15 apply (zenon_L321_); trivial. % 9.95/10.15 apply (zenon_L373_); trivial. % 9.95/10.15 apply (zenon_L314_); trivial. % 9.95/10.15 apply (zenon_L375_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.15 apply (zenon_L297_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.15 apply (zenon_L377_); trivial. % 9.95/10.15 apply (zenon_L378_); trivial. % 9.95/10.15 apply (zenon_L354_); trivial. % 9.95/10.15 apply (zenon_L321_); trivial. % 9.95/10.15 apply (zenon_L373_); trivial. % 9.95/10.15 apply (zenon_L314_); trivial. % 9.95/10.15 apply (zenon_L375_); trivial. % 9.95/10.15 apply (zenon_L315_); trivial. % 9.95/10.15 apply (zenon_L252_); trivial. % 9.95/10.15 (* end of lemma zenon_L379_ *) % 9.95/10.15 assert (zenon_L380_ : (((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 (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((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 (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)) = (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) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.15 do 0 intro. intros zenon_H1de zenon_H15a zenon_Hc1 zenon_Hed zenon_H173 zenon_H103 zenon_Hec zenon_H1b7 zenon_Hdd zenon_Hce zenon_H58 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1e2 zenon_H18a zenon_H112 zenon_Hab zenon_H67 zenon_H1dd zenon_He3 zenon_H168 zenon_Hae zenon_H191 zenon_H11d zenon_H192 zenon_Hd2 zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H187 zenon_H108 zenon_H200 zenon_H1cb zenon_H6f zenon_H56 zenon_H1b4 zenon_H3c zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_H53 zenon_H18d zenon_H7a zenon_H7d zenon_H8c zenon_H14d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hc0 zenon_H42 zenon_H4c zenon_Hf5 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H1f zenon_H159 zenon_H1ea zenon_H195 zenon_H1ef zenon_H97 zenon_H64 zenon_H1b1 zenon_H16b zenon_H114 zenon_H158 zenon_H152 zenon_Hc5 zenon_Hde zenon_He7 zenon_H150 zenon_Hc6 zenon_H156 zenon_H4a zenon_H132 zenon_H145 zenon_H12f zenon_H204 zenon_H86. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.15 apply (zenon_L236_); trivial. % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.15 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.15 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.15 apply (zenon_L282_); trivial. % 9.95/10.15 apply (zenon_L379_); trivial. % 9.95/10.15 (* end of lemma zenon_L380_ *) % 9.95/10.15 assert (zenon_L381_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((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)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H18d zenon_He3 zenon_H56 zenon_H42 zenon_H1bc zenon_H15a zenon_Hd3 zenon_H91 zenon_H8c zenon_H5e zenon_H86 zenon_H7a zenon_H7e zenon_H7f zenon_H7d zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H1b1 zenon_Haf zenon_H112 zenon_Hcf zenon_Hde zenon_H1e2 zenon_H181 zenon_Hc7 zenon_Hc8 zenon_Hab zenon_H198 zenon_H12c zenon_H192 zenon_H28 zenon_H95 zenon_H4c zenon_H1de zenon_H187 zenon_Hc1 zenon_Hbc zenon_H16f zenon_H97 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1c0 zenon_H128 zenon_H53 zenon_H2a zenon_H58 zenon_H64. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.16 exact (zenon_H56 zenon_H2c). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.16 apply (zenon_L257_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.16 exact (zenon_H28 zenon_H31). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.16 apply (zenon_L184_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.16 apply (zenon_L130_); trivial. % 9.95/10.16 apply (zenon_L289_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.16 apply (zenon_L70_); trivial. % 9.95/10.16 apply (zenon_L294_); trivial. % 9.95/10.16 apply (zenon_L265_); trivial. % 9.95/10.16 apply (zenon_L266_); trivial. % 9.95/10.16 (* end of lemma zenon_L381_ *) % 9.95/10.16 assert (zenon_L382_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 9.95/10.16 do 0 intro. intros zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H6e zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_H2a zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_H192 zenon_H191 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.16 apply (zenon_L190_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.16 apply (zenon_L193_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.16 apply (zenon_L212_); trivial. % 9.95/10.16 apply (zenon_L215_); trivial. % 9.95/10.16 apply (zenon_L222_); trivial. % 9.95/10.16 apply (zenon_L223_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.16 apply (zenon_L224_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.16 apply (zenon_L233_); trivial. % 9.95/10.16 apply (zenon_L235_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.16 apply (zenon_L269_); trivial. % 9.95/10.16 apply (zenon_L288_); trivial. % 9.95/10.16 apply (zenon_L223_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.16 apply (zenon_L295_); trivial. % 9.95/10.16 apply (zenon_L296_); trivial. % 9.95/10.16 apply (zenon_L380_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.16 apply (zenon_L381_); trivial. % 9.95/10.16 apply (zenon_L267_); trivial. % 9.95/10.16 apply (zenon_L44_); trivial. % 9.95/10.16 apply (zenon_L321_); trivial. % 9.95/10.16 apply (zenon_L194_); trivial. % 9.95/10.16 apply (zenon_L123_); trivial. % 9.95/10.16 apply (zenon_L213_); trivial. % 9.95/10.16 apply (zenon_L101_); trivial. % 9.95/10.16 (* end of lemma zenon_L382_ *) % 9.95/10.16 assert (zenon_L383_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hda zenon_H28 zenon_H53 zenon_H69 zenon_H4c zenon_H76 zenon_H95 zenon_Hd8. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.16 exact (zenon_H28 zenon_H31). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.16 apply (zenon_L18_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.16 apply (zenon_L21_); trivial. % 9.95/10.16 apply (zenon_L51_); trivial. % 9.95/10.16 (* end of lemma zenon_L383_ *) % 9.95/10.16 assert (zenon_L384_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_H35 zenon_Hda zenon_H28 zenon_H53 zenon_H69 zenon_H4c zenon_H76 zenon_H95. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.16 apply (zenon_L195_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.16 apply (zenon_L47_); trivial. % 9.95/10.16 apply (zenon_L383_); trivial. % 9.95/10.16 (* end of lemma zenon_L384_ *) % 9.95/10.16 assert (zenon_L385_ : (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H205 zenon_H11f zenon_H84. % 9.95/10.16 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H205. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H11f. % 9.95/10.16 cut (((e3) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 9.95/10.16 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 9.95/10.16 congruence. % 9.95/10.16 apply zenon_H17e. apply refl_equal. % 9.95/10.16 apply zenon_H206. apply sym_equal. exact zenon_H84. % 9.95/10.16 (* end of lemma zenon_L385_ *) % 9.95/10.16 assert (zenon_L386_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H12c zenon_H95 zenon_Hcf zenon_H4c zenon_H77 zenon_Hc8 zenon_H205 zenon_H84. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.95/10.16 apply (zenon_L155_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.95/10.16 apply (zenon_L48_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.95/10.16 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.16 apply (zenon_L385_); trivial. % 9.95/10.16 (* end of lemma zenon_L386_ *) % 9.95/10.16 assert (zenon_L387_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hf2 zenon_Hf0 zenon_Hbb. % 9.95/10.16 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H115 | zenon_intro zenon_Hef ]. % 9.95/10.16 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_Hbb. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H115. % 9.95/10.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.95/10.16 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 9.95/10.16 congruence. % 9.95/10.16 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H207. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_Hf2. % 9.95/10.16 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 9.95/10.16 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 9.95/10.16 congruence. % 9.95/10.16 apply zenon_Hef. apply refl_equal. % 9.95/10.16 apply zenon_H208. apply sym_equal. exact zenon_Hf0. % 9.95/10.16 apply zenon_Hef. apply refl_equal. % 9.95/10.16 apply zenon_Hef. apply refl_equal. % 9.95/10.16 (* end of lemma zenon_L387_ *) % 9.95/10.16 assert (zenon_L388_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H1b1 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H35 zenon_H90 zenon_H192 zenon_H84 zenon_H205 zenon_Hc8 zenon_H4c zenon_Hcf zenon_H95 zenon_H12c zenon_Hf0 zenon_Hbb. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.16 apply (zenon_L234_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.16 exact (zenon_H192 zenon_H1d). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.16 apply (zenon_L386_); trivial. % 9.95/10.16 apply (zenon_L387_); trivial. % 9.95/10.16 (* end of lemma zenon_L388_ *) % 9.95/10.16 assert (zenon_L389_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_Hbb zenon_H12c zenon_H95 zenon_H4c zenon_Hc8 zenon_H205 zenon_H84 zenon_H192 zenon_H90 zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H1b1 zenon_Hf0 zenon_H35. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.16 apply (zenon_L195_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.16 apply (zenon_L388_); trivial. % 9.95/10.16 apply (zenon_L211_); trivial. % 9.95/10.16 (* end of lemma zenon_L389_ *) % 9.95/10.16 assert (zenon_L390_ : (((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 (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)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H1af zenon_H198 zenon_H191 zenon_H68 zenon_H1f zenon_H1ea zenon_H195 zenon_H1ef zenon_H44 zenon_H35 zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_He4 zenon_H5e. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.16 exact (zenon_H56 zenon_H2c). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.16 apply (zenon_L326_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.16 apply (zenon_L195_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.16 apply (zenon_L47_); trivial. % 9.95/10.16 apply (zenon_L99_); trivial. % 9.95/10.16 apply (zenon_L62_); trivial. % 9.95/10.16 (* end of lemma zenon_L390_ *) % 9.95/10.16 assert (zenon_L391_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (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 (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (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) (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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H18e zenon_H25 zenon_H1b1 zenon_H9a zenon_H17c zenon_Hd3 zenon_H90 zenon_H192 zenon_H205 zenon_Hc8 zenon_H4c zenon_H12c zenon_Hbb zenon_Hda zenon_Hc5 zenon_Hc7 zenon_H91 zenon_Hc6 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_Hd2 zenon_H1b4 zenon_H56 zenon_H1af zenon_H198 zenon_H191 zenon_H68 zenon_H1f zenon_H1ea zenon_H195 zenon_H1ef zenon_H44 zenon_H35 zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_H5e. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.95/10.16 exact (zenon_H25 zenon_H2a). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.16 exact (zenon_H56 zenon_H2c). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.16 apply (zenon_L194_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.16 apply (zenon_L384_); trivial. % 9.95/10.16 apply (zenon_L389_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.95/10.16 apply (zenon_L172_); trivial. % 9.95/10.16 apply (zenon_L390_); trivial. % 9.95/10.16 (* end of lemma zenon_L391_ *) % 9.95/10.16 assert (zenon_L392_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((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 (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H18a zenon_H8a zenon_H17c zenon_H47 zenon_H187 zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 9.95/10.16 apply (zenon_L276_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 9.95/10.16 apply (zenon_L166_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 9.95/10.16 apply (zenon_L243_); trivial. % 9.95/10.16 apply (zenon_L337_); trivial. % 9.95/10.16 (* end of lemma zenon_L392_ *) % 9.95/10.16 assert (zenon_L393_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (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 (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (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) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H90 zenon_H1bc zenon_H4c zenon_H198 zenon_H15a zenon_H35 zenon_Hab zenon_Hc8 zenon_H1e2 zenon_H95 zenon_Hc7 zenon_H181 zenon_H12c zenon_H91 zenon_H18a zenon_H17c zenon_H47 zenon_H187 zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.16 apply (zenon_L217_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.16 apply (zenon_L292_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.16 exact (zenon_H91 zenon_H94). % 9.95/10.16 apply (zenon_L392_); trivial. % 9.95/10.16 (* end of lemma zenon_L393_ *) % 9.95/10.16 assert (zenon_L394_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (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 (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (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) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H42 zenon_H27 zenon_H1e zenon_H6f zenon_H6e zenon_H90 zenon_H1bc zenon_H4c zenon_H198 zenon_H15a zenon_H35 zenon_Hab zenon_Hc8 zenon_H1e2 zenon_H95 zenon_Hc7 zenon_H181 zenon_H12c zenon_H91 zenon_H18a zenon_H17c zenon_H187 zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.16 apply (zenon_L4_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.16 apply (zenon_L19_); trivial. % 9.95/10.16 apply (zenon_L393_); trivial. % 9.95/10.16 (* end of lemma zenon_L394_ *) % 9.95/10.16 assert (zenon_L395_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hb0 zenon_H76 zenon_H44 zenon_Hb1 zenon_H12c zenon_H5e zenon_H91 zenon_H1e zenon_Hd3 zenon_H4c zenon_H90 zenon_H95 zenon_Hb8 zenon_Hc8 zenon_H53. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.16 apply (zenon_L165_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.16 apply (zenon_L57_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.16 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.95/10.16 apply (zenon_L250_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.95/10.16 apply (zenon_L40_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.95/10.16 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.16 apply (zenon_L96_); trivial. % 9.95/10.16 (* end of lemma zenon_L395_ *) % 9.95/10.16 assert (zenon_L396_ : (((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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H198 zenon_H1b1 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H35 zenon_H90 zenon_H192 zenon_H84 zenon_H205 zenon_Hc8 zenon_H4c zenon_Hcf zenon_H95 zenon_H12c zenon_Hbb. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.16 exact (zenon_H56 zenon_H2c). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.16 apply (zenon_L194_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.16 apply (zenon_L47_); trivial. % 9.95/10.16 apply (zenon_L388_); trivial. % 9.95/10.16 (* end of lemma zenon_L396_ *) % 9.95/10.16 assert (zenon_L397_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e1)) = (e1))) -> (~((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))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hd2 zenon_Hce zenon_H56 zenon_H198 zenon_H9a zenon_H35 zenon_Hcf zenon_H1b1 zenon_Hbb zenon_H95 zenon_H4c zenon_H205 zenon_H84 zenon_H12c zenon_H192 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.16 apply (zenon_L396_); trivial. % 9.95/10.16 apply (zenon_L44_); trivial. % 9.95/10.16 (* end of lemma zenon_L397_ *) % 9.95/10.16 assert (zenon_L398_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H114 zenon_Hb8 zenon_Hd6. % 9.95/10.16 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H114. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_Hb8. % 9.95/10.16 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 9.95/10.16 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 9.95/10.16 congruence. % 9.95/10.16 apply zenon_H185. apply refl_equal. % 9.95/10.16 apply zenon_H209. apply sym_equal. exact zenon_Hd6. % 9.95/10.16 (* end of lemma zenon_L398_ *) % 9.95/10.16 assert (zenon_L399_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hc0 zenon_H95 zenon_He5 zenon_H34 zenon_H4c zenon_H77 zenon_H84 zenon_H17a. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 9.95/10.16 apply (zenon_L184_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 9.95/10.16 apply (zenon_L199_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 9.95/10.16 apply (zenon_L48_); trivial. % 9.95/10.16 apply (zenon_L161_); trivial. % 9.95/10.16 (* end of lemma zenon_L399_ *) % 9.95/10.16 assert (zenon_L400_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H34 zenon_H4c zenon_H77 zenon_H84 zenon_H17a. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 9.95/10.16 apply (zenon_L16_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 9.95/10.16 exact (zenon_He8 zenon_Heb). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 9.95/10.16 apply (zenon_L22_); trivial. % 9.95/10.16 apply (zenon_L399_); trivial. % 9.95/10.16 (* end of lemma zenon_L400_ *) % 9.95/10.16 assert (zenon_L401_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H90 zenon_Hcf zenon_H35 zenon_H17a zenon_H84 zenon_H4c zenon_H34 zenon_H95 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_He7 zenon_H91 zenon_H17c zenon_H9a. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.16 apply (zenon_L47_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.16 apply (zenon_L400_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.16 exact (zenon_H91 zenon_H94). % 9.95/10.16 apply (zenon_L166_); trivial. % 9.95/10.16 (* end of lemma zenon_L401_ *) % 9.95/10.16 assert (zenon_L402_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_H9a zenon_H17c zenon_H91 zenon_He7 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H34 zenon_H4c zenon_H84 zenon_H17a zenon_H35 zenon_H90 zenon_He4 zenon_H44. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.16 apply (zenon_L195_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.16 apply (zenon_L401_); trivial. % 9.95/10.16 apply (zenon_L99_); trivial. % 9.95/10.16 (* end of lemma zenon_L402_ *) % 9.95/10.16 assert (zenon_L403_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H42 zenon_H44 zenon_He4 zenon_H90 zenon_H35 zenon_H17a zenon_H84 zenon_H4c zenon_H95 zenon_Hc0 zenon_H5e zenon_He8 zenon_He7 zenon_H91 zenon_H17c zenon_H9a zenon_H159 zenon_H27 zenon_Hdd zenon_H6f zenon_H6e zenon_Hd0 zenon_H181. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.16 apply (zenon_L402_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.16 apply (zenon_L19_); trivial. % 9.95/10.16 apply (zenon_L163_); trivial. % 9.95/10.16 (* end of lemma zenon_L403_ *) % 9.95/10.16 assert (zenon_L404_ : (((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 (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_H34 zenon_He5. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_Heb | zenon_intro zenon_H193 ]. % 9.95/10.16 exact (zenon_He8 zenon_Heb). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H1d | zenon_intro zenon_H194 ]. % 9.95/10.16 exact (zenon_H192 zenon_H1d). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hc4 ]. % 9.95/10.16 apply (zenon_L330_); trivial. % 9.95/10.16 apply (zenon_L199_); trivial. % 9.95/10.16 (* end of lemma zenon_L404_ *) % 9.95/10.16 assert (zenon_L405_ : (~((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H20a zenon_Hcd. % 9.95/10.16 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.16 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 9.95/10.16 congruence. % 9.95/10.16 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.16 apply zenon_H37. apply refl_equal. % 9.95/10.16 (* end of lemma zenon_L405_ *) % 9.95/10.16 assert (zenon_L406_ : ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (op (op (e2) (e2)) (e2)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H106 zenon_Hcd zenon_H137. % 9.95/10.16 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e0) = (op (op (e2) (e2)) (e2)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H137. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H138. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 9.95/10.16 congruence. % 9.95/10.16 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H13a. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H106. % 9.95/10.16 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.16 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 9.95/10.16 congruence. % 9.95/10.16 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H20b. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H138. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 9.95/10.16 congruence. % 9.95/10.16 apply (zenon_L405_); trivial. % 9.95/10.16 apply zenon_H139. apply refl_equal. % 9.95/10.16 apply zenon_H139. apply refl_equal. % 9.95/10.16 apply zenon_H41. apply refl_equal. % 9.95/10.16 apply zenon_H139. apply refl_equal. % 9.95/10.16 apply zenon_H139. apply refl_equal. % 9.95/10.16 (* end of lemma zenon_L406_ *) % 9.95/10.16 assert (zenon_L407_ : ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 9.95/10.16 do 0 intro. intros zenon_H5d zenon_H106 zenon_Hcd. % 9.95/10.16 apply (zenon_notand_s _ _ ax26); [ zenon_intro zenon_H20d | zenon_intro zenon_H20c ]. % 9.95/10.16 apply zenon_H20d. apply sym_equal. exact zenon_Hcd. % 9.95/10.16 apply (zenon_notand_s _ _ zenon_H20c); [ zenon_intro zenon_H20e | zenon_intro zenon_H137 ]. % 9.95/10.16 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 9.95/10.16 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e1) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H20e. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H13e. % 9.95/10.16 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 9.95/10.16 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 9.95/10.16 congruence. % 9.95/10.16 cut (((op (e0) (e2)) = (e1)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e1))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H20f. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H5d. % 9.95/10.16 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.16 cut (((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 9.95/10.16 congruence. % 9.95/10.16 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 9.95/10.16 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e0) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H141. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H13e. % 9.95/10.16 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 9.95/10.16 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 9.95/10.16 congruence. % 9.95/10.16 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 9.95/10.16 congruence. % 9.95/10.16 cut (((op (e3) (e2)) = (e0)) = ((op (op (e2) (e2)) (e2)) = (e0))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H13a. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H106. % 9.95/10.16 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.16 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 9.95/10.16 congruence. % 9.95/10.16 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 9.95/10.16 intro zenon_D_pnotp. % 9.95/10.16 apply zenon_H20b. % 9.95/10.16 rewrite <- zenon_D_pnotp. % 9.95/10.16 exact zenon_H138. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 9.95/10.16 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 9.95/10.16 congruence. % 9.95/10.16 apply (zenon_L405_); trivial. % 9.95/10.16 apply zenon_H139. apply refl_equal. % 9.95/10.16 apply zenon_H139. apply refl_equal. % 9.95/10.16 apply zenon_H41. apply refl_equal. % 9.95/10.16 apply zenon_H37. apply refl_equal. % 9.95/10.16 apply zenon_H13f. apply refl_equal. % 9.95/10.16 apply zenon_H13f. apply refl_equal. % 9.95/10.16 apply zenon_H33. apply refl_equal. % 9.95/10.16 apply zenon_H13f. apply refl_equal. % 9.95/10.16 apply zenon_H13f. apply refl_equal. % 9.95/10.16 apply (zenon_L406_); trivial. % 9.95/10.16 (* end of lemma zenon_L407_ *) % 9.95/10.16 assert (zenon_L408_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((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) (e1)) = (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 (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H14d zenon_H181 zenon_Hd0 zenon_H6e zenon_H6f zenon_Hdd zenon_H27 zenon_H159 zenon_H9a zenon_H17c zenon_H91 zenon_He7 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H35 zenon_H90 zenon_H44 zenon_H42 zenon_H34 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_Hed zenon_H53 zenon_H8d. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 9.95/10.16 apply (zenon_L403_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 9.95/10.16 apply (zenon_L404_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 9.95/10.16 apply (zenon_L73_); trivial. % 9.95/10.16 exact (zenon_H8d zenon_H7b). % 9.95/10.16 (* end of lemma zenon_L408_ *) % 9.95/10.16 assert (zenon_L409_ : (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((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))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H8d zenon_H53 zenon_Hed zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_H42 zenon_H44 zenon_H90 zenon_H35 zenon_H17a zenon_H84 zenon_H4c zenon_H95 zenon_Hc0 zenon_H5e zenon_He7 zenon_H91 zenon_H17c zenon_H9a zenon_H159 zenon_H27 zenon_Hdd zenon_H14d zenon_H6f zenon_H6e zenon_Hd0 zenon_H181. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.16 apply (zenon_L408_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.16 apply (zenon_L19_); trivial. % 9.95/10.16 apply (zenon_L163_); trivial. % 9.95/10.16 (* end of lemma zenon_L409_ *) % 9.95/10.16 assert (zenon_L410_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((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))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H165 zenon_H5d zenon_H34 zenon_H8d zenon_H53 zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_H42 zenon_H44 zenon_H90 zenon_H35 zenon_H17a zenon_H84 zenon_H4c zenon_H95 zenon_Hc0 zenon_H5e zenon_He7 zenon_H91 zenon_H17c zenon_H9a zenon_H159 zenon_H27 zenon_Hdd zenon_H14d zenon_H6f zenon_H6e zenon_Hd0 zenon_H181. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H52 | zenon_intro zenon_H166 ]. % 9.95/10.16 apply (zenon_L130_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 9.95/10.16 apply (zenon_L237_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hed ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 9.95/10.16 apply (zenon_L403_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 9.95/10.16 apply (zenon_L404_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 9.95/10.16 apply (zenon_L407_); trivial. % 9.95/10.16 exact (zenon_H8d zenon_H7b). % 9.95/10.16 apply (zenon_L409_); trivial. % 9.95/10.16 (* end of lemma zenon_L410_ *) % 9.95/10.16 assert (zenon_L411_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H18a zenon_H43 zenon_H187 zenon_H62 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 9.95/10.16 apply (zenon_L276_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 9.95/10.16 apply (zenon_L202_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 9.95/10.16 apply (zenon_L162_); trivial. % 9.95/10.16 apply (zenon_L252_); trivial. % 9.95/10.16 (* end of lemma zenon_L411_ *) % 9.95/10.16 assert (zenon_L412_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H150 zenon_He3 zenon_H56 zenon_H42 zenon_Hd0 zenon_H181 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H43 zenon_H187 zenon_H64. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.16 exact (zenon_H56 zenon_H2c). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.16 apply (zenon_L227_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.16 apply (zenon_L410_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.16 apply (zenon_L70_); trivial. % 9.95/10.16 apply (zenon_L163_); trivial. % 9.95/10.16 apply (zenon_L411_); trivial. % 9.95/10.16 apply (zenon_L266_); trivial. % 9.95/10.16 (* end of lemma zenon_L412_ *) % 9.95/10.16 assert (zenon_L413_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (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))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 9.95/10.16 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_H9a zenon_H17c zenon_H91 zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H34 zenon_H4c zenon_H84 zenon_H17a zenon_H90 zenon_Hf0 zenon_H35. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.16 apply (zenon_L195_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.16 apply (zenon_L401_); trivial. % 9.95/10.16 apply (zenon_L211_); trivial. % 9.95/10.16 (* end of lemma zenon_L413_ *) % 9.95/10.16 assert (zenon_L414_ : (((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 (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H90 zenon_Hcf zenon_H35 zenon_Hd3 zenon_H1e zenon_H91 zenon_H18a zenon_H17c zenon_H47 zenon_H187 zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.16 apply (zenon_L47_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.16 apply (zenon_L196_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.16 exact (zenon_H91 zenon_H94). % 9.95/10.16 apply (zenon_L392_); trivial. % 9.95/10.16 (* end of lemma zenon_L414_ *) % 9.95/10.16 assert (zenon_L415_ : (((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)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (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) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (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 (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 9.95/10.16 do 0 intro. intros zenon_H42 zenon_H17a zenon_H84 zenon_H4c zenon_H95 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_He7 zenon_H9a zenon_H6f zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H187 zenon_H17c zenon_H18a zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_Hf0 zenon_H35. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.16 apply (zenon_L413_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.16 apply (zenon_L19_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.16 exact (zenon_H27 zenon_H32). % 9.95/10.16 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.16 apply (zenon_L195_); trivial. % 9.95/10.16 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.16 apply (zenon_L414_); trivial. % 9.95/10.16 apply (zenon_L211_); trivial. % 9.95/10.16 (* end of lemma zenon_L415_ *) % 9.95/10.16 assert (zenon_L416_ : (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (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))))) -> (((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H18a zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_H6f zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H42 zenon_Hde zenon_Haf zenon_Hb0 zenon_H1e2 zenon_H1b4 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_H198 zenon_Hce zenon_Hd2 zenon_H114 zenon_H150 zenon_He3 zenon_H56 zenon_H181 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_H53 zenon_H165 zenon_H64 zenon_H1bc zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H9a zenon_H187. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.17 apply (zenon_L394_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 9.95/10.17 apply (zenon_L4_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 9.95/10.17 exact (zenon_Haf zenon_Hb4). % 9.95/10.17 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 9.95/10.17 apply (zenon_L395_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 9.95/10.17 apply (zenon_L397_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 9.95/10.17 apply (zenon_L398_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 9.95/10.17 exact (zenon_Hc7 zenon_H3a). % 9.95/10.17 apply (zenon_L412_); trivial. % 9.95/10.17 apply (zenon_L415_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.17 apply (zenon_L103_); trivial. % 9.95/10.17 apply (zenon_L202_); trivial. % 9.95/10.17 (* end of lemma zenon_L416_ *) % 9.95/10.17 assert (zenon_L417_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (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)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((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 (e1) (e1)) = (e1))) -> (((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)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hf8 zenon_H155 zenon_H108 zenon_H25 zenon_H18e zenon_H1ef zenon_H195 zenon_H1ea zenon_H1f zenon_H191 zenon_H1af zenon_H5e zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_H42 zenon_H181 zenon_H7a zenon_H97 zenon_H44 zenon_Hd2 zenon_H56 zenon_H198 zenon_H9a zenon_Hdd zenon_H28 zenon_H53 zenon_H4c zenon_H95 zenon_Hda zenon_H35 zenon_H6e zenon_H159 zenon_H27 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H192 zenon_H12c zenon_H84 zenon_H205 zenon_Hc8 zenon_Hbb zenon_H1b1 zenon_H1b4 zenon_H3c zenon_H1bc zenon_H7e zenon_Hab zenon_H1e2 zenon_H18a zenon_H7d zenon_H86 zenon_H18d zenon_H187 zenon_H6f zenon_Hde zenon_Hce zenon_H114 zenon_H150 zenon_He3 zenon_H14d zenon_He7 zenon_H17a zenon_Hc0 zenon_He8 zenon_H165 zenon_H64 zenon_Hb1 zenon_Hb0 zenon_Haf zenon_H200. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.17 exact (zenon_H25 zenon_H2a). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.17 apply (zenon_L391_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.17 apply (zenon_L129_); trivial. % 9.95/10.17 apply (zenon_L416_); trivial. % 9.95/10.17 apply (zenon_L254_); trivial. % 9.95/10.17 (* end of lemma zenon_L417_ *) % 9.95/10.17 assert (zenon_L418_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1b7 zenon_H51 zenon_H1cb zenon_H187 zenon_H9a zenon_H181 zenon_Hd0 zenon_H84 zenon_H7a. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H43 | zenon_intro zenon_H1b8 ]. % 9.95/10.17 apply (zenon_L343_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H62 | zenon_intro zenon_H1b9 ]. % 9.95/10.17 apply (zenon_L202_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 9.95/10.17 apply (zenon_L163_); trivial. % 9.95/10.17 apply (zenon_L68_); trivial. % 9.95/10.17 (* end of lemma zenon_L418_ *) % 9.95/10.17 assert (zenon_L419_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H200 zenon_H25 zenon_H97 zenon_H28 zenon_H7a zenon_H1cb zenon_H1b7 zenon_H150 zenon_He3 zenon_H56 zenon_H42 zenon_Hd0 zenon_H181 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H187 zenon_H64. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.17 exact (zenon_H25 zenon_H2a). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.17 apply (zenon_L171_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.17 apply (zenon_L418_); trivial. % 9.95/10.17 apply (zenon_L412_); trivial. % 9.95/10.17 (* end of lemma zenon_L419_ *) % 9.95/10.17 assert (zenon_L420_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hf5 zenon_H35 zenon_Hd8 zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 9.95/10.17 apply (zenon_L211_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 9.95/10.17 apply (zenon_L327_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 9.95/10.17 apply (zenon_L328_); trivial. % 9.95/10.17 exact (zenon_H7e zenon_H83). % 9.95/10.17 (* end of lemma zenon_L420_ *) % 9.95/10.17 assert (zenon_L421_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H159 zenon_H6e zenon_H76 zenon_Hf5 zenon_H35 zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.17 exact (zenon_H27 zenon_H32). % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.17 apply (zenon_L195_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.17 apply (zenon_L47_); trivial. % 9.95/10.17 apply (zenon_L420_); trivial. % 9.95/10.17 (* end of lemma zenon_L421_ *) % 9.95/10.17 assert (zenon_L422_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H7a zenon_H84 zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H4c zenon_H5d zenon_H95. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 9.95/10.17 exact (zenon_H27 zenon_H32). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 9.95/10.17 apply (zenon_L16_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 9.95/10.17 apply (zenon_L170_); trivial. % 9.95/10.17 apply (zenon_L341_); trivial. % 9.95/10.17 (* end of lemma zenon_L422_ *) % 9.95/10.17 assert (zenon_L423_ : (((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 (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (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)) = (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) (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). % 9.95/10.17 do 0 intro. intros zenon_H64 zenon_H1b1 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H90 zenon_H192 zenon_H205 zenon_Hc8 zenon_H12c zenon_Hbb zenon_H6e zenon_H159 zenon_Hdd zenon_Hf5 zenon_H1f0 zenon_H100 zenon_H1e6 zenon_H7e zenon_H1ef zenon_H195 zenon_H1ea zenon_H1f zenon_H191 zenon_H198 zenon_H1af zenon_H56 zenon_H1b4 zenon_H84 zenon_H7a zenon_H42 zenon_H27 zenon_H44 zenon_H4c zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.17 apply (zenon_L326_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.17 apply (zenon_L421_); trivial. % 9.95/10.17 apply (zenon_L389_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.17 apply (zenon_L422_); trivial. % 9.95/10.17 apply (zenon_L362_); trivial. % 9.95/10.17 (* end of lemma zenon_L423_ *) % 9.95/10.17 assert (zenon_L424_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (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))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hd2 zenon_H1cb zenon_H187 zenon_H9a zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H3c zenon_H51 zenon_H91 zenon_Hc7 zenon_Hc5. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.17 apply (zenon_L129_); trivial. % 9.95/10.17 apply (zenon_L418_); trivial. % 9.95/10.17 (* end of lemma zenon_L424_ *) % 9.95/10.17 assert (zenon_L425_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H158 zenon_H6e zenon_H155 zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H9a zenon_H187 zenon_H1cb zenon_Hd2. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.17 apply (zenon_L424_); trivial. % 9.95/10.17 apply (zenon_L223_); trivial. % 9.95/10.17 (* end of lemma zenon_L425_ *) % 9.95/10.17 assert (zenon_L426_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H18a zenon_H43 zenon_H187 zenon_H15a zenon_H198 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 9.95/10.17 apply (zenon_L276_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 9.95/10.17 apply (zenon_L194_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 9.95/10.17 apply (zenon_L162_); trivial. % 9.95/10.17 apply (zenon_L252_); trivial. % 9.95/10.17 (* end of lemma zenon_L426_ *) % 9.95/10.17 assert (zenon_L427_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (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))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H8c zenon_H86 zenon_H17c zenon_H198 zenon_H15a zenon_H18a zenon_H7a zenon_H84 zenon_Hd0 zenon_H181 zenon_H187 zenon_H1b7 zenon_H5e zenon_H8a zenon_H8d. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 9.95/10.17 apply (zenon_L426_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 9.95/10.17 apply (zenon_L277_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 9.95/10.17 apply (zenon_L27_); trivial. % 9.95/10.17 exact (zenon_H8d zenon_H7b). % 9.95/10.17 (* end of lemma zenon_L427_ *) % 9.95/10.17 assert (zenon_L428_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (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 (e3) (e3)) = (e0))) -> (~((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). % 9.95/10.17 do 0 intro. intros zenon_Hda zenon_H28 zenon_H5e zenon_H91 zenon_H1e zenon_Hd3 zenon_H4c zenon_H90 zenon_Hb1 zenon_H8c zenon_H86 zenon_H17c zenon_H198 zenon_H15a zenon_H18a zenon_H7a zenon_Hd0 zenon_H181 zenon_H187 zenon_H1b7 zenon_H8d zenon_H53 zenon_Hb0 zenon_H84 zenon_He3. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.17 exact (zenon_H28 zenon_H31). % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.17 apply (zenon_L236_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.17 apply (zenon_L20_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.17 apply (zenon_L21_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.17 apply (zenon_L22_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.17 exact (zenon_H91 zenon_H94). % 9.95/10.17 apply (zenon_L427_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.17 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.17 apply (zenon_L250_); trivial. % 9.95/10.17 apply (zenon_L266_); trivial. % 9.95/10.17 (* end of lemma zenon_L428_ *) % 9.95/10.17 assert (zenon_L429_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((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 (e0) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1b1 zenon_H181 zenon_Hd3 zenon_H1bc zenon_H90 zenon_H192 zenon_H78 zenon_H5e zenon_H103 zenon_H1cb zenon_H62 zenon_H15a zenon_H159 zenon_H91 zenon_Hec. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.17 apply (zenon_L259_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.17 exact (zenon_H192 zenon_H1d). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.17 apply (zenon_L22_); trivial. % 9.95/10.17 apply (zenon_L264_); trivial. % 9.95/10.17 (* end of lemma zenon_L429_ *) % 9.95/10.17 assert (zenon_L430_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1e2 zenon_He3 zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H35 zenon_H77 zenon_Hc7 zenon_H18a zenon_H89 zenon_H15a zenon_H198 zenon_H17c zenon_H84 zenon_H86. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 9.95/10.17 apply (zenon_L296_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 9.95/10.17 apply (zenon_L203_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 9.95/10.17 exact (zenon_Hc7 zenon_H3a). % 9.95/10.17 apply (zenon_L279_); trivial. % 9.95/10.17 (* end of lemma zenon_L430_ *) % 9.95/10.17 assert (zenon_L431_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((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))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hb0 zenon_H53 zenon_H74 zenon_Hec zenon_H91 zenon_H159 zenon_H62 zenon_H1cb zenon_H103 zenon_H5e zenon_H192 zenon_H90 zenon_H1bc zenon_Hd3 zenon_H181 zenon_H1b1 zenon_Hb1 zenon_H1e2 zenon_He3 zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H35 zenon_H77 zenon_Hc7 zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_H84 zenon_H86. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.17 apply (zenon_L20_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.17 apply (zenon_L429_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.17 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.17 apply (zenon_L430_); trivial. % 9.95/10.17 (* end of lemma zenon_L431_ *) % 9.95/10.17 assert (zenon_L432_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H64 zenon_H56 zenon_H51 zenon_Hec zenon_H91 zenon_H159 zenon_H15a zenon_H1cb zenon_H103 zenon_Hb0 zenon_H53 zenon_H5e zenon_H192 zenon_H90 zenon_H1bc zenon_Hd3 zenon_H181 zenon_H1b1 zenon_Hb1 zenon_H1e2 zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H35 zenon_Hc7 zenon_H18a zenon_H198 zenon_H17c zenon_H86 zenon_H8c zenon_H7a zenon_Hd0 zenon_H187 zenon_H1b7 zenon_H8d zenon_H84 zenon_He3. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.17 apply (zenon_L428_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.17 apply (zenon_L12_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.17 exact (zenon_H28 zenon_H31). % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.17 apply (zenon_L236_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 9.95/10.17 apply (zenon_L428_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 9.95/10.17 exact (zenon_H192 zenon_H1d). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 9.95/10.17 apply (zenon_L431_); trivial. % 9.95/10.17 apply (zenon_L264_); trivial. % 9.95/10.17 apply (zenon_L266_); trivial. % 9.95/10.17 (* end of lemma zenon_L432_ *) % 9.95/10.17 assert (zenon_L433_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((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) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H158 zenon_H6e zenon_H155 zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_H150 zenon_H56 zenon_Hda zenon_He3 zenon_H53 zenon_H90 zenon_H18a zenon_H84 zenon_H86 zenon_H17c zenon_H198 zenon_H187 zenon_H1b7 zenon_H7a zenon_H181 zenon_H8c zenon_H5e zenon_Hb1 zenon_Hd3 zenon_Hb0 zenon_H15a zenon_H4c zenon_H28 zenon_H192 zenon_H95 zenon_H35 zenon_H1e2 zenon_H1bc zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_H64 zenon_Hd2. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.17 apply (zenon_L129_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.17 apply (zenon_L432_); trivial. % 9.95/10.17 apply (zenon_L266_); trivial. % 9.95/10.17 apply (zenon_L223_); trivial. % 9.95/10.17 (* end of lemma zenon_L433_ *) % 9.95/10.17 assert (zenon_L434_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (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))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hd2 zenon_Hcf zenon_Hce zenon_H3c zenon_H51 zenon_H91 zenon_Hc7 zenon_Hc5. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.17 apply (zenon_L129_); trivial. % 9.95/10.17 apply (zenon_L44_); trivial. % 9.95/10.17 (* end of lemma zenon_L434_ *) % 9.95/10.17 assert (zenon_L435_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H158 zenon_Hc6 zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_Hce zenon_Hcf zenon_Hd2. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.17 apply (zenon_L434_); trivial. % 9.95/10.17 apply (zenon_L321_); trivial. % 9.95/10.17 (* end of lemma zenon_L435_ *) % 9.95/10.17 assert (zenon_L436_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((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) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((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) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H168 zenon_H150 zenon_H56 zenon_Hda zenon_He3 zenon_H53 zenon_H90 zenon_H18a zenon_H86 zenon_H17c zenon_H198 zenon_H8c zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H4c zenon_H28 zenon_H95 zenon_H35 zenon_H1e2 zenon_H1bc zenon_H103 zenon_Hec zenon_H159 zenon_H1b1 zenon_H64 zenon_Hc6 zenon_Hce zenon_H156 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H158 zenon_H155 zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H1cb zenon_Hd2 zenon_H1af. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.17 apply (zenon_L224_); trivial. % 9.95/10.17 apply (zenon_L425_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.17 apply (zenon_L433_); trivial. % 9.95/10.17 apply (zenon_L435_); trivial. % 9.95/10.17 (* end of lemma zenon_L436_ *) % 9.95/10.17 assert (zenon_L437_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (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))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H64 zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H18a zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_H6f zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H42 zenon_Hf5 zenon_H1f0 zenon_H100 zenon_H1e6 zenon_H1bc zenon_H198 zenon_Hab zenon_H1e2 zenon_H181 zenon_H12c zenon_H56 zenon_H1b4 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H9a zenon_H187. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.17 apply (zenon_L394_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.17 apply (zenon_L421_); trivial. % 9.95/10.17 apply (zenon_L415_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.17 apply (zenon_L103_); trivial. % 9.95/10.17 apply (zenon_L202_); trivial. % 9.95/10.17 (* end of lemma zenon_L437_ *) % 9.95/10.17 assert (zenon_L438_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((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)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (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) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (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 (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H25 zenon_H64 zenon_H44 zenon_H97 zenon_H7a zenon_H53 zenon_H28 zenon_H42 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H191 zenon_H198 zenon_H1af zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H35 zenon_H6e zenon_H27 zenon_H90 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H192 zenon_H12c zenon_H84 zenon_H205 zenon_Hc8 zenon_H4c zenon_H95 zenon_Hbb zenon_H1b1 zenon_H1b4 zenon_H56 zenon_H168 zenon_H150 zenon_Hda zenon_He3 zenon_H18a zenon_H86 zenon_H8c zenon_H5e zenon_Hb0 zenon_H1e2 zenon_H1bc zenon_H103 zenon_Hec zenon_Hc6 zenon_Hce zenon_H156 zenon_H16e zenon_H158 zenon_H155 zenon_Hc5 zenon_H3c zenon_H1b7 zenon_H181 zenon_H187 zenon_H1cb zenon_Hd2 zenon_Hb1 zenon_Hab zenon_Hc7 zenon_H7d zenon_H18d zenon_H6f zenon_He8 zenon_Hc0 zenon_H17a zenon_He7 zenon_H200. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.17 exact (zenon_H25 zenon_H2a). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.17 apply (zenon_L423_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.17 apply (zenon_L436_); trivial. % 9.95/10.17 apply (zenon_L437_); trivial. % 9.95/10.17 apply (zenon_L254_); trivial. % 9.95/10.17 (* end of lemma zenon_L438_ *) % 9.95/10.17 assert (zenon_L439_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1ef zenon_H195 zenon_H191 zenon_Hc1 zenon_H68 zenon_H1f zenon_H159 zenon_H15a zenon_H1ea. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 9.95/10.17 apply (zenon_L324_); trivial. % 9.95/10.17 apply (zenon_L325_); trivial. % 9.95/10.17 (* end of lemma zenon_L439_ *) % 9.95/10.17 assert (zenon_L440_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1de zenon_H53 zenon_H69 zenon_Hc1 zenon_H95 zenon_H6e zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.17 apply (zenon_L18_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.17 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.17 apply (zenon_L237_); trivial. % 9.95/10.17 apply (zenon_L337_); trivial. % 9.95/10.17 (* end of lemma zenon_L440_ *) % 9.95/10.17 assert (zenon_L441_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H101 zenon_H161 zenon_H53. % 9.95/10.17 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 9.95/10.17 cut (((e3) = (e3)) = ((e0) = (e3))). % 9.95/10.17 intro zenon_D_pnotp. % 9.95/10.17 apply zenon_H53. % 9.95/10.17 rewrite <- zenon_D_pnotp. % 9.95/10.17 exact zenon_H4d. % 9.95/10.17 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.17 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 9.95/10.17 congruence. % 9.95/10.17 cut (((op (e1) (e2)) = (e0)) = ((e3) = (e0))). % 9.95/10.17 intro zenon_D_pnotp. % 9.95/10.17 apply zenon_H54. % 9.95/10.17 rewrite <- zenon_D_pnotp. % 9.95/10.17 exact zenon_H101. % 9.95/10.17 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.17 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 9.95/10.17 congruence. % 9.95/10.17 exact (zenon_H1cd zenon_H161). % 9.95/10.17 apply zenon_H41. apply refl_equal. % 9.95/10.17 apply zenon_H4e. apply refl_equal. % 9.95/10.17 apply zenon_H4e. apply refl_equal. % 9.95/10.17 (* end of lemma zenon_L441_ *) % 9.95/10.17 assert (zenon_L442_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1dd zenon_He4 zenon_H106. % 9.95/10.17 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 9.95/10.17 intro zenon_D_pnotp. % 9.95/10.17 apply zenon_H1dd. % 9.95/10.17 rewrite <- zenon_D_pnotp. % 9.95/10.17 exact zenon_He4. % 9.95/10.17 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 9.95/10.17 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 9.95/10.17 congruence. % 9.95/10.17 apply zenon_Hbf. apply refl_equal. % 9.95/10.17 apply zenon_H210. apply sym_equal. exact zenon_H106. % 9.95/10.17 (* end of lemma zenon_L442_ *) % 9.95/10.17 assert (zenon_L443_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 9.95/10.17 do 0 intro. intros zenon_H108 zenon_H5e zenon_H53 zenon_H5d zenon_H161 zenon_H1dd zenon_He4. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 9.95/10.17 apply (zenon_L12_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 9.95/10.17 apply (zenon_L441_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 9.95/10.17 apply (zenon_L133_); trivial. % 9.95/10.17 apply (zenon_L442_); trivial. % 9.95/10.17 (* end of lemma zenon_L443_ *) % 9.95/10.17 assert (zenon_L444_ : (((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 (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H1de zenon_H4c zenon_H15a zenon_Hc1 zenon_He4 zenon_H1dd zenon_H5d zenon_H53 zenon_H5e zenon_H108 zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.17 apply (zenon_L236_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.17 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.17 apply (zenon_L443_); trivial. % 9.95/10.17 apply (zenon_L337_); trivial. % 9.95/10.17 (* end of lemma zenon_L444_ *) % 9.95/10.17 assert (zenon_L445_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 9.95/10.17 do 0 intro. intros zenon_H90 zenon_H35 zenon_H84 zenon_H205 zenon_Hc8 zenon_H4c zenon_Hcf zenon_H95 zenon_H12c zenon_H91 zenon_H181 zenon_H62. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.17 apply (zenon_L47_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.17 apply (zenon_L386_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.17 exact (zenon_H91 zenon_H94). % 9.95/10.17 apply (zenon_L258_); trivial. % 9.95/10.17 (* end of lemma zenon_L445_ *) % 9.95/10.17 assert (zenon_L446_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.95/10.17 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H15a zenon_H62 zenon_H181 zenon_H91 zenon_H12c zenon_H95 zenon_H4c zenon_Hc8 zenon_H205 zenon_H84 zenon_H35 zenon_H90 zenon_He4 zenon_H44. % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 9.95/10.17 exact (zenon_H27 zenon_H32). % 9.95/10.17 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 9.95/10.17 apply (zenon_L238_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 9.95/10.17 apply (zenon_L445_); trivial. % 9.95/10.17 apply (zenon_L99_); trivial. % 9.95/10.17 (* end of lemma zenon_L446_ *) % 9.95/10.17 assert (zenon_L447_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (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)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 9.95/10.17 do 0 intro. intros zenon_H64 zenon_H56 zenon_H187 zenon_H17c zenon_H18a zenon_Hc7 zenon_H1e2 zenon_Hab zenon_H198 zenon_H1bc zenon_H6e zenon_H6f zenon_H42 zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H108 zenon_H5e zenon_H53 zenon_H1dd zenon_Hc1 zenon_H1de zenon_Hdd zenon_H27 zenon_H15a zenon_H181 zenon_H91 zenon_H12c zenon_H95 zenon_H4c zenon_Hc8 zenon_H205 zenon_H84 zenon_H35 zenon_H90 zenon_He4 zenon_H44. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.17 exact (zenon_H56 zenon_H2c). % 9.95/10.17 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.17 apply (zenon_L394_); trivial. % 9.95/10.17 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.17 apply (zenon_L444_); trivial. % 9.95/10.17 apply (zenon_L446_); trivial. % 9.95/10.17 (* end of lemma zenon_L447_ *) % 9.95/10.17 assert (zenon_L448_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (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)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H18e zenon_H25 zenon_Hc6 zenon_Hc5 zenon_H64 zenon_H56 zenon_H187 zenon_H17c zenon_H18a zenon_Hc7 zenon_H1e2 zenon_Hab zenon_H198 zenon_H1bc zenon_H6e zenon_H6f zenon_H42 zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H108 zenon_H5e zenon_H53 zenon_H1dd zenon_Hc1 zenon_H1de zenon_Hdd zenon_H27 zenon_H15a zenon_H181 zenon_H91 zenon_H12c zenon_H95 zenon_H4c zenon_Hc8 zenon_H205 zenon_H84 zenon_H35 zenon_H90 zenon_H44. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.95/10.18 exact (zenon_H25 zenon_H2a). % 9.95/10.18 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.95/10.18 apply (zenon_L440_); trivial. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.95/10.18 apply (zenon_L43_); trivial. % 9.95/10.18 apply (zenon_L447_); trivial. % 9.95/10.18 (* end of lemma zenon_L448_ *) % 9.95/10.18 assert (zenon_L449_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((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 (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 9.95/10.18 do 0 intro. intros zenon_Hf8 zenon_H3c zenon_H155 zenon_Hb1 zenon_H25 zenon_H1de zenon_H7d zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H6e zenon_H95 zenon_Hc1 zenon_H53 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_Hc6 zenon_H64 zenon_H205 zenon_H84 zenon_H44 zenon_Hdd zenon_H108 zenon_H1dd zenon_H5e zenon_H27 zenon_H35 zenon_H6f zenon_H90 zenon_H187 zenon_H17c zenon_H18a zenon_H1e2 zenon_H181 zenon_H4c zenon_Hab zenon_H198 zenon_H12c zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_H18e. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.18 apply (zenon_L448_); trivial. % 9.95/10.18 apply (zenon_L254_); trivial. % 9.95/10.18 (* end of lemma zenon_L449_ *) % 9.95/10.18 assert (zenon_L450_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 9.95/10.18 do 0 intro. intros zenon_Hd2 zenon_H18e zenon_H56 zenon_H42 zenon_H1bc zenon_H15a zenon_H12c zenon_H198 zenon_Hab zenon_H4c zenon_H181 zenon_H1e2 zenon_H18a zenon_H17c zenon_H187 zenon_H90 zenon_H6f zenon_H35 zenon_H27 zenon_H5e zenon_H1dd zenon_H108 zenon_Hdd zenon_H44 zenon_H84 zenon_H205 zenon_H64 zenon_Hc6 zenon_H91 zenon_Hc7 zenon_Hc5 zenon_H53 zenon_Hc1 zenon_H95 zenon_H6e zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7d zenon_H1de zenon_H25 zenon_Hb1 zenon_H155 zenon_H3c zenon_Hf8. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.18 apply (zenon_L449_); trivial. % 9.95/10.18 apply (zenon_L426_); trivial. % 9.95/10.18 (* end of lemma zenon_L450_ *) % 9.95/10.18 assert (zenon_L451_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (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))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H200 zenon_Hd0 zenon_H97 zenon_H1af zenon_H1cb zenon_H1b7 zenon_H158 zenon_H192 zenon_H16e zenon_H191 zenon_H156 zenon_Hce zenon_H1b1 zenon_H159 zenon_Hec zenon_H103 zenon_H28 zenon_Hb0 zenon_Hd3 zenon_H8c zenon_He3 zenon_Hda zenon_H150 zenon_H168 zenon_Hd2 zenon_H18e zenon_H56 zenon_H42 zenon_H1bc zenon_H15a zenon_H12c zenon_H198 zenon_Hab zenon_H4c zenon_H181 zenon_H1e2 zenon_H18a zenon_H17c zenon_H187 zenon_H90 zenon_H6f zenon_H35 zenon_H27 zenon_H5e zenon_H1dd zenon_H108 zenon_Hdd zenon_H44 zenon_H84 zenon_H205 zenon_H64 zenon_Hc6 zenon_H91 zenon_Hc7 zenon_Hc5 zenon_H53 zenon_Hc1 zenon_H95 zenon_H6e zenon_H18d zenon_H86 zenon_H7a zenon_H7e zenon_H7d zenon_H1de zenon_H25 zenon_Hb1 zenon_H155 zenon_H3c zenon_Hf8. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.18 exact (zenon_H25 zenon_H2a). % 9.95/10.18 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.18 apply (zenon_L171_); trivial. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.18 apply (zenon_L436_); trivial. % 9.95/10.18 apply (zenon_L450_); trivial. % 9.95/10.18 (* end of lemma zenon_L451_ *) % 9.95/10.18 assert (zenon_L452_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (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)))) -> False). % 9.95/10.18 do 0 intro. intros zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_Haf zenon_Hb0 zenon_Hd3 zenon_H53 zenon_Hb1 zenon_H44 zenon_H5e zenon_H64 zenon_H165 zenon_H159 zenon_He8 zenon_Hc0 zenon_H17a zenon_He7 zenon_Hdd zenon_H191 zenon_H1f zenon_H14d zenon_He3 zenon_H150 zenon_H114 zenon_H1b4 zenon_H192 zenon_H84 zenon_H205 zenon_Hbb zenon_H1b1 zenon_H9a zenon_Hce zenon_Hd2 zenon_Hde zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H187 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H91 zenon_H1e2 zenon_H181 zenon_Hc7 zenon_H95 zenon_H4c zenon_Hc8 zenon_Hab zenon_H7e zenon_H198 zenon_H12c zenon_H1bc zenon_H42 zenon_Hc5 zenon_H3c. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.18 apply (zenon_L416_); trivial. % 9.95/10.18 apply (zenon_L254_); trivial. % 9.95/10.18 (* end of lemma zenon_L452_ *) % 9.95/10.18 assert (zenon_L453_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H156 zenon_H3c zenon_Hc5 zenon_H42 zenon_H1bc zenon_H12c zenon_H198 zenon_H7e zenon_Hab zenon_H4c zenon_H95 zenon_H181 zenon_H1e2 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H187 zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_Hde zenon_Hd2 zenon_Hce zenon_H9a zenon_H1b1 zenon_Hbb zenon_H205 zenon_H84 zenon_H192 zenon_H1b4 zenon_H114 zenon_H150 zenon_He3 zenon_H14d zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_Hc0 zenon_He8 zenon_H159 zenon_H165 zenon_H64 zenon_H5e zenon_H44 zenon_H53 zenon_Hd3 zenon_Hb0 zenon_Haf zenon_H56 zenon_H108 zenon_H155 zenon_Hf8 zenon_H158. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.18 apply (zenon_L452_); trivial. % 9.95/10.18 apply (zenon_L412_); trivial. % 9.95/10.18 apply (zenon_L223_); trivial. % 9.95/10.18 apply (zenon_L397_); trivial. % 9.95/10.18 (* end of lemma zenon_L453_ *) % 9.95/10.18 assert (zenon_L454_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (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)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.18 do 0 intro. intros zenon_Hf8 zenon_H155 zenon_H53 zenon_H108 zenon_H56 zenon_H1b4 zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H9a zenon_Hd3 zenon_H159 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H187 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H91 zenon_H1e2 zenon_H181 zenon_Hc7 zenon_H95 zenon_H4c zenon_Hc8 zenon_Hab zenon_H7e zenon_H198 zenon_H12c zenon_H1bc zenon_H42 zenon_Hc5 zenon_H3c zenon_Hb1 zenon_H64. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.18 apply (zenon_L437_); trivial. % 9.95/10.18 apply (zenon_L254_); trivial. % 9.95/10.18 (* end of lemma zenon_L454_ *) % 9.95/10.18 assert (zenon_L455_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((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))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H156 zenon_H205 zenon_Hbb zenon_H1b1 zenon_Hce zenon_Hd2 zenon_H165 zenon_H191 zenon_H1f zenon_H192 zenon_H14d zenon_He3 zenon_H150 zenon_H64 zenon_H3c zenon_Hc5 zenon_H42 zenon_H1bc zenon_H12c zenon_H198 zenon_H7e zenon_Hab zenon_H4c zenon_H95 zenon_H181 zenon_H1e2 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H187 zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H159 zenon_Hd3 zenon_H9a zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_He7 zenon_H1b4 zenon_H56 zenon_H108 zenon_H53 zenon_H155 zenon_Hf8 zenon_H158. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.18 apply (zenon_L454_); trivial. % 9.95/10.18 apply (zenon_L412_); trivial. % 9.95/10.18 apply (zenon_L223_); trivial. % 9.95/10.18 apply (zenon_L397_); trivial. % 9.95/10.18 (* end of lemma zenon_L455_ *) % 9.95/10.18 assert (zenon_L456_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H1af zenon_H158 zenon_Hf8 zenon_H155 zenon_H53 zenon_H108 zenon_H56 zenon_H1b4 zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H44 zenon_Hd3 zenon_H159 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H27 zenon_H35 zenon_H6f zenon_H90 zenon_H187 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H91 zenon_H1e2 zenon_H181 zenon_H95 zenon_H4c zenon_Hab zenon_H7e zenon_H198 zenon_H12c zenon_H1bc zenon_H42 zenon_Hc5 zenon_H3c zenon_H64 zenon_H150 zenon_He3 zenon_H14d zenon_H1f zenon_H165 zenon_Hd2 zenon_Hce zenon_H1b1 zenon_Hbb zenon_H205 zenon_H156 zenon_He8 zenon_H192 zenon_H16e zenon_H6e zenon_H191. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.18 apply (zenon_L224_); trivial. % 9.95/10.18 apply (zenon_L455_); trivial. % 9.95/10.18 (* end of lemma zenon_L456_ *) % 9.95/10.18 assert (zenon_L457_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((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). % 9.95/10.18 do 0 intro. intros zenon_H158 zenon_Hf8 zenon_H3c zenon_H155 zenon_Hb1 zenon_H25 zenon_H1de zenon_H7d zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H6e zenon_H95 zenon_Hc1 zenon_H53 zenon_Hc5 zenon_H91 zenon_Hc6 zenon_H64 zenon_H205 zenon_H84 zenon_H44 zenon_Hdd zenon_H108 zenon_H1dd zenon_H5e zenon_H27 zenon_H35 zenon_H6f zenon_H90 zenon_H187 zenon_H17c zenon_H18a zenon_H1e2 zenon_H181 zenon_H4c zenon_Hab zenon_H198 zenon_H12c zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_H18e zenon_Hd2. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.18 apply (zenon_L450_); trivial. % 9.95/10.18 apply (zenon_L223_); trivial. % 9.95/10.18 (* end of lemma zenon_L457_ *) % 9.95/10.18 assert (zenon_L458_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H158 zenon_Hf8 zenon_H3c zenon_H155 zenon_H25 zenon_H1de zenon_H7d zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H6e zenon_H95 zenon_H53 zenon_Hc5 zenon_H91 zenon_Hc6 zenon_H64 zenon_H205 zenon_H84 zenon_H44 zenon_Hdd zenon_H108 zenon_H1dd zenon_H5e zenon_H27 zenon_H35 zenon_H6f zenon_H90 zenon_H187 zenon_H17c zenon_H18a zenon_H1e2 zenon_H181 zenon_H4c zenon_Hab zenon_H198 zenon_H12c zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_H18e zenon_Hd2 zenon_H1e6 zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H177 zenon_Hc0 zenon_Hf5 zenon_H1f0 zenon_H1af zenon_H1f zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_He7 zenon_H204 zenon_H4a zenon_H1ea zenon_H144 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_Hda zenon_H1b4 zenon_H156 zenon_H192 zenon_H11d zenon_H191 zenon_Hae zenon_H168 zenon_H150 zenon_He3 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_Hce zenon_H128 zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H112 zenon_Hde zenon_H67. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.18 apply (zenon_L457_); trivial. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.18 apply (zenon_L448_); trivial. % 9.95/10.18 apply (zenon_L380_); trivial. % 9.95/10.18 apply (zenon_L44_); trivial. % 9.95/10.18 apply (zenon_L321_); trivial. % 9.95/10.18 apply (zenon_L194_); trivial. % 9.95/10.18 (* end of lemma zenon_L458_ *) % 9.95/10.18 assert (zenon_L459_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H4a zenon_H1af zenon_Hd2 zenon_H1cb zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H3c zenon_H51 zenon_H91 zenon_Hc5 zenon_H155 zenon_H158 zenon_H192 zenon_H16e zenon_H6e zenon_H191 zenon_H156 zenon_Hce zenon_Hc6 zenon_H64 zenon_H1b1 zenon_H159 zenon_Hec zenon_H103 zenon_H1bc zenon_H1e2 zenon_H35 zenon_H95 zenon_H4c zenon_Hb0 zenon_Hd3 zenon_H5e zenon_H8c zenon_H198 zenon_H17c zenon_H86 zenon_H18a zenon_H90 zenon_H53 zenon_He3 zenon_Hda zenon_H56 zenon_H150 zenon_H168. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.18 apply (zenon_L436_); trivial. % 9.95/10.18 apply (zenon_L343_); trivial. % 9.95/10.18 (* end of lemma zenon_L459_ *) % 9.95/10.18 assert (zenon_L460_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e1) (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H158 zenon_H6e zenon_H145 zenon_H9a zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.18 apply (zenon_L215_); trivial. % 9.95/10.18 apply (zenon_L223_); trivial. % 9.95/10.18 (* end of lemma zenon_L460_ *) % 9.95/10.18 assert (zenon_L461_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H1af zenon_Hd2 zenon_H58 zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H12f zenon_H2a zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_He8 zenon_H192 zenon_H16e zenon_H6e zenon_H191. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.18 apply (zenon_L224_); trivial. % 9.95/10.18 apply (zenon_L460_); trivial. % 9.95/10.18 (* end of lemma zenon_L461_ *) % 9.95/10.18 assert (zenon_L462_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H150 zenon_H56 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_Hdd zenon_H53 zenon_H95 zenon_Hda zenon_Hd0 zenon_Hce zenon_H35 zenon_H27 zenon_H90 zenon_H58 zenon_H2a zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H8c zenon_H91 zenon_H5e zenon_H1bc zenon_Hb1 zenon_Hd3 zenon_Hb0 zenon_H15a zenon_H4c zenon_H28 zenon_H42 zenon_H97 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H192 zenon_H64. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.18 apply (zenon_L281_); trivial. % 9.95/10.18 apply (zenon_L221_); trivial. % 9.95/10.18 (* end of lemma zenon_L462_ *) % 9.95/10.18 assert (zenon_L463_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (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 (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 9.95/10.18 do 0 intro. intros zenon_H67 zenon_H1e2 zenon_Hc6 zenon_H168 zenon_H156 zenon_H17c zenon_H18a zenon_H97 zenon_Hf8 zenon_H108 zenon_H4c zenon_H95 zenon_H18d zenon_H56 zenon_Hb0 zenon_H53 zenon_H198 zenon_Hd3 zenon_H8c zenon_Hdd zenon_Hce zenon_H128 zenon_H86 zenon_H7e zenon_H7d zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H35 zenon_H3c zenon_H64 zenon_H1de zenon_H1dd zenon_H12c zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_H6f zenon_H42 zenon_He3 zenon_H150 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H1af zenon_H4a. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.18 apply (zenon_L461_); trivial. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.18 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.18 apply (zenon_L269_); trivial. % 9.95/10.18 apply (zenon_L462_); trivial. % 9.95/10.18 apply (zenon_L223_); trivial. % 9.95/10.18 apply (zenon_L296_); trivial. % 9.95/10.18 apply (zenon_L194_); trivial. % 9.95/10.18 apply (zenon_L213_); trivial. % 9.95/10.18 apply (zenon_L459_); trivial. % 9.95/10.18 (* end of lemma zenon_L463_ *) % 9.95/10.18 assert (zenon_L464_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((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)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H157 zenon_H16f zenon_H16e zenon_Hec zenon_H103 zenon_H8c zenon_H168 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_H191 zenon_H192 zenon_H156 zenon_H1b7 zenon_H1cb zenon_H200 zenon_Hb0 zenon_H64 zenon_H165 zenon_Hc0 zenon_H17a zenon_He7 zenon_H14d zenon_He3 zenon_H150 zenon_H114 zenon_Hce zenon_Hde zenon_H6f zenon_H187 zenon_H18d zenon_H86 zenon_H7d zenon_H18a zenon_H1e2 zenon_Hab zenon_H7e zenon_H1bc zenon_H3c zenon_H1b4 zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H159 zenon_H6e zenon_H35 zenon_Hda zenon_H95 zenon_H4c zenon_H53 zenon_Hdd zenon_H198 zenon_H56 zenon_Hd2 zenon_H44 zenon_H97 zenon_H7a zenon_H181 zenon_H42 zenon_Hc6 zenon_Hc5 zenon_H5e zenon_H1af zenon_H1f zenon_H1ea zenon_H195 zenon_H1ef zenon_H18e zenon_H108 zenon_H155 zenon_Hf8 zenon_H158 zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H177 zenon_H16b zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H145 zenon_H12f zenon_H10b zenon_H132 zenon_H11d zenon_Hae zenon_H128 zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H112 zenon_H67 zenon_H1dd zenon_H1de. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 9.95/10.19 apply (zenon_L382_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 9.95/10.19 exact (zenon_H192 zenon_H1d). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 9.95/10.19 apply (zenon_L223_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.19 apply (zenon_L190_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.19 apply (zenon_L417_); trivial. % 9.95/10.19 apply (zenon_L419_); trivial. % 9.95/10.19 apply (zenon_L223_); trivial. % 9.95/10.19 apply (zenon_L397_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.19 apply (zenon_L224_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.19 apply (zenon_L438_); trivial. % 9.95/10.19 apply (zenon_L419_); trivial. % 9.95/10.19 apply (zenon_L223_); trivial. % 9.95/10.19 apply (zenon_L235_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 9.95/10.19 exact (zenon_H25 zenon_H2a). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 9.95/10.19 apply (zenon_L439_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 9.95/10.19 apply (zenon_L129_); trivial. % 9.95/10.19 apply (zenon_L448_); trivial. % 9.95/10.19 apply (zenon_L380_); trivial. % 9.95/10.19 apply (zenon_L451_); trivial. % 9.95/10.19 apply (zenon_L223_); trivial. % 9.95/10.19 apply (zenon_L296_); trivial. % 9.95/10.19 apply (zenon_L194_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.19 apply (zenon_L190_); trivial. % 9.95/10.19 apply (zenon_L453_); trivial. % 9.95/10.19 apply (zenon_L456_); trivial. % 9.95/10.19 apply (zenon_L458_); trivial. % 9.95/10.19 apply (zenon_L459_); trivial. % 9.95/10.19 apply (zenon_L463_); trivial. % 9.95/10.19 (* end of lemma zenon_L464_ *) % 9.95/10.19 assert (zenon_L465_ : ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (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)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (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) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H69 zenon_Haf zenon_H1de zenon_H1dd zenon_H67 zenon_H112 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_H58 zenon_H128 zenon_Hae zenon_H11d zenon_H132 zenon_H10b zenon_H12f zenon_H145 zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H16b zenon_H177 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H158 zenon_Hf8 zenon_H155 zenon_H108 zenon_H18e zenon_H1ef zenon_H195 zenon_H1ea zenon_H1f zenon_H1af zenon_H5e zenon_Hc5 zenon_Hc6 zenon_H42 zenon_H181 zenon_H7a zenon_H97 zenon_H44 zenon_Hd2 zenon_H56 zenon_H198 zenon_Hdd zenon_H53 zenon_H4c zenon_H95 zenon_Hda zenon_H159 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_H1b4 zenon_H3c zenon_H1bc zenon_H7e zenon_Hab zenon_H1e2 zenon_H18a zenon_H7d zenon_H86 zenon_H18d zenon_H187 zenon_H6f zenon_Hde zenon_Hce zenon_H114 zenon_H150 zenon_He3 zenon_H14d zenon_He7 zenon_H17a zenon_Hc0 zenon_H165 zenon_H64 zenon_Hb0 zenon_H200 zenon_H1cb zenon_H1b7 zenon_H156 zenon_H192 zenon_H191 zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_H168 zenon_H8c zenon_H103 zenon_Hec zenon_H16e zenon_H16f zenon_H157 zenon_H9a zenon_H35. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 9.95/10.19 apply (zenon_L17_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 9.95/10.19 exact (zenon_Haf zenon_Hb4). % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 9.95/10.19 apply (zenon_L464_); trivial. % 9.95/10.19 apply (zenon_L34_); trivial. % 9.95/10.19 (* end of lemma zenon_L465_ *) % 9.95/10.19 assert (zenon_L466_ : (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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). % 9.95/10.19 do 0 intro. intros zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H69 zenon_H192 zenon_Haf zenon_H191. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.19 apply (zenon_L191_); trivial. % 9.95/10.19 apply (zenon_L465_); trivial. % 9.95/10.19 (* end of lemma zenon_L466_ *) % 9.95/10.19 assert (zenon_L467_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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). % 9.95/10.19 do 0 intro. intros zenon_H1af zenon_H15a zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_Haf zenon_H191. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.19 apply (zenon_L191_); trivial. % 9.95/10.19 apply (zenon_L194_); trivial. % 9.95/10.19 (* end of lemma zenon_L467_ *) % 9.95/10.19 assert (zenon_L468_ : ((~((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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H198 zenon_H15a zenon_H1af. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.19 apply (zenon_L467_); trivial. % 9.95/10.19 apply (zenon_L123_); trivial. % 9.95/10.19 (* end of lemma zenon_L468_ *) % 9.95/10.19 assert (zenon_L469_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.19 do 0 intro. intros zenon_Hda zenon_H28 zenon_H53 zenon_H69 zenon_H76 zenon_Hf5 zenon_H4c zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.19 exact (zenon_H28 zenon_H31). % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.19 apply (zenon_L18_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.19 apply (zenon_L21_); trivial. % 9.95/10.19 apply (zenon_L329_); trivial. % 9.95/10.19 (* end of lemma zenon_L469_ *) % 9.95/10.19 assert (zenon_L470_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 9.95/10.19 do 0 intro. intros zenon_H10b zenon_H51 zenon_H106. % 9.95/10.19 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 9.95/10.19 intro zenon_D_pnotp. % 9.95/10.19 apply zenon_H10b. % 9.95/10.19 rewrite <- zenon_D_pnotp. % 9.95/10.19 exact zenon_H51. % 9.95/10.19 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 9.95/10.19 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 9.95/10.19 congruence. % 9.95/10.19 apply zenon_H134. apply refl_equal. % 9.95/10.19 apply zenon_H210. apply sym_equal. exact zenon_H106. % 9.95/10.19 (* end of lemma zenon_L470_ *) % 9.95/10.19 assert (zenon_L471_ : ((op (e3) (e2)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H135 zenon_Hd6 zenon_Hec. % 9.95/10.19 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 9.95/10.19 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 9.95/10.19 intro zenon_D_pnotp. % 9.95/10.19 apply zenon_Hec. % 9.95/10.19 rewrite <- zenon_D_pnotp. % 9.95/10.19 exact zenon_H10c. % 9.95/10.19 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.95/10.19 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 9.95/10.19 congruence. % 9.95/10.19 cut (((op (e3) (e2)) = (e2)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 9.95/10.19 intro zenon_D_pnotp. % 9.95/10.19 apply zenon_H211. % 9.95/10.19 rewrite <- zenon_D_pnotp. % 9.95/10.19 exact zenon_H135. % 9.95/10.19 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 9.95/10.19 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 9.95/10.19 congruence. % 9.95/10.19 apply zenon_H10d. apply refl_equal. % 9.95/10.19 apply zenon_H209. apply sym_equal. exact zenon_Hd6. % 9.95/10.19 apply zenon_H10d. apply refl_equal. % 9.95/10.19 apply zenon_H10d. apply refl_equal. % 9.95/10.19 (* end of lemma zenon_L471_ *) % 9.95/10.19 assert (zenon_L472_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (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)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 9.95/10.19 do 0 intro. intros zenon_H1de zenon_H69 zenon_H200 zenon_H25 zenon_H3c zenon_Hfd zenon_H144 zenon_H4c zenon_H10b zenon_Hb0 zenon_H181 zenon_H91 zenon_H12c zenon_Hc8 zenon_H17c zenon_H90 zenon_H1f8 zenon_H6f zenon_H155 zenon_H1e6 zenon_Hda zenon_H28 zenon_H198 zenon_Hf5 zenon_H1f0 zenon_H7e zenon_H56 zenon_H64 zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H128 zenon_H35 zenon_H95 zenon_H3a zenon_H1fb zenon_H97 zenon_Hd3 zenon_H187 zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_Hed. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 9.95/10.19 apply (zenon_L18_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 9.95/10.19 exact (zenon_Hc1 zenon_Hc4). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 9.95/10.19 apply (zenon_L282_); trivial. % 9.95/10.19 apply (zenon_L360_); trivial. % 9.95/10.19 (* end of lemma zenon_L472_ *) % 9.95/10.19 assert (zenon_L473_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (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)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H212 zenon_H51 zenon_Hec zenon_Hd6 zenon_H1de zenon_H69 zenon_H200 zenon_H25 zenon_H3c zenon_Hfd zenon_H144 zenon_H4c zenon_H10b zenon_Hb0 zenon_H181 zenon_H91 zenon_H12c zenon_Hc8 zenon_H17c zenon_H90 zenon_H1f8 zenon_H6f zenon_H155 zenon_H1e6 zenon_Hda zenon_H28 zenon_H198 zenon_Hf5 zenon_H1f0 zenon_H7e zenon_H56 zenon_H64 zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H128 zenon_H35 zenon_H95 zenon_H3a zenon_H1fb zenon_H97 zenon_Hd3 zenon_H187 zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H106 | zenon_intro zenon_H213 ]. % 9.95/10.19 apply (zenon_L470_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H214 ]. % 9.95/10.19 apply (zenon_L328_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H135 | zenon_intro zenon_Hed ]. % 9.95/10.19 apply (zenon_L471_); trivial. % 9.95/10.19 apply (zenon_L472_); trivial. % 9.95/10.19 (* end of lemma zenon_L473_ *) % 9.95/10.19 assert (zenon_L474_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((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)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H177 zenon_Hf0 zenon_H53 zenon_Hb1 zenon_H5e zenon_H100 zenon_H1cb zenon_H108 zenon_H187 zenon_Hd3 zenon_H97 zenon_H1fb zenon_H3a zenon_H95 zenon_H35 zenon_H128 zenon_H191 zenon_He8 zenon_H192 zenon_Hc1 zenon_H64 zenon_H56 zenon_H7e zenon_H1f0 zenon_Hf5 zenon_H198 zenon_H28 zenon_Hda zenon_H1e6 zenon_H155 zenon_H6f zenon_H1f8 zenon_H90 zenon_H17c zenon_H12c zenon_H181 zenon_Hb0 zenon_H10b zenon_H4c zenon_H144 zenon_Hfd zenon_H25 zenon_H200 zenon_H69 zenon_H1de zenon_Hec zenon_H212 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 9.95/10.19 apply (zenon_L211_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 9.95/10.19 apply (zenon_L473_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 9.95/10.19 apply (zenon_L367_); trivial. % 9.95/10.19 exact (zenon_H7f zenon_H85). % 9.95/10.19 (* end of lemma zenon_L474_ *) % 9.95/10.19 assert (zenon_L475_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 9.95/10.19 do 0 intro. intros zenon_Hda zenon_H28 zenon_H53 zenon_H69 zenon_H76 zenon_He7 zenon_H51 zenon_Hfd zenon_Hc1 zenon_H4b zenon_H192 zenon_He8 zenon_H191 zenon_Hf5 zenon_H4c zenon_H5e zenon_H100 zenon_H1e6 zenon_H7e. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.19 exact (zenon_H28 zenon_H31). % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.19 apply (zenon_L18_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.19 apply (zenon_L21_); trivial. % 9.95/10.19 apply (zenon_L365_); trivial. % 9.95/10.19 (* end of lemma zenon_L475_ *) % 9.95/10.19 assert (zenon_L476_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H212 zenon_H100 zenon_H1e6 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H52 zenon_H10b. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H106 | zenon_intro zenon_H213 ]. % 9.95/10.19 apply (zenon_L470_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H214 ]. % 9.95/10.19 apply (zenon_L328_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H135 | zenon_intro zenon_Hed ]. % 9.95/10.19 apply (zenon_L367_); trivial. % 9.95/10.19 apply (zenon_L75_); trivial. % 9.95/10.19 (* end of lemma zenon_L476_ *) % 9.95/10.19 assert (zenon_L477_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (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))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((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)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (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) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H1ea zenon_H195 zenon_H1af zenon_H1b4 zenon_H159 zenon_He7 zenon_H177 zenon_H53 zenon_Hb1 zenon_H5e zenon_H100 zenon_H1cb zenon_H108 zenon_H187 zenon_Hd3 zenon_H97 zenon_H1fb zenon_H3a zenon_H95 zenon_H35 zenon_H128 zenon_H191 zenon_He8 zenon_H192 zenon_Hc1 zenon_H64 zenon_H56 zenon_H7e zenon_H1f0 zenon_Hf5 zenon_H198 zenon_H28 zenon_Hda zenon_H1e6 zenon_H155 zenon_H6f zenon_H1f8 zenon_H90 zenon_H17c zenon_H12c zenon_H181 zenon_Hb0 zenon_H10b zenon_H4c zenon_H144 zenon_Hfd zenon_H25 zenon_H200 zenon_H69 zenon_H1de zenon_Hec zenon_H212 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.19 apply (zenon_L468_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.19 apply (zenon_L469_); trivial. % 9.95/10.19 apply (zenon_L474_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.19 apply (zenon_L228_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.19 apply (zenon_L123_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 9.95/10.19 exact (zenon_H28 zenon_H31). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 9.95/10.19 apply (zenon_L475_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 9.95/10.19 apply (zenon_L476_); trivial. % 9.95/10.19 apply (zenon_L13_); trivial. % 9.95/10.19 apply (zenon_L474_); trivial. % 9.95/10.19 (* end of lemma zenon_L477_ *) % 9.95/10.19 assert (zenon_L478_ : ((~((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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((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))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 9.95/10.19 do 0 intro. intros zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_Hb1 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_Hc8 zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H25 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.19 apply (zenon_L477_); trivial. % 9.95/10.19 apply (zenon_L472_); trivial. % 9.95/10.19 (* end of lemma zenon_L478_ *) % 9.95/10.19 assert (zenon_L479_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (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))) -> False). % 9.95/10.19 do 0 intro. intros zenon_Hd2 zenon_He7 zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H177 zenon_Hc5 zenon_H152 zenon_H158 zenon_H10b zenon_H51 zenon_Hec zenon_H1de zenon_H25 zenon_H144 zenon_H3a zenon_H3c zenon_H6f zenon_Hfd zenon_H95 zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H64 zenon_He8 zenon_Hb1 zenon_H90 zenon_H5e zenon_H91 zenon_Hd3 zenon_Hb0 zenon_H187 zenon_H97 zenon_H108 zenon_H1cb zenon_H200 zenon_Hc1 zenon_H212 zenon_H35 zenon_H1b4 zenon_H56 zenon_Hf8. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.19 apply (zenon_L478_); trivial. % 9.95/10.19 apply (zenon_L354_); trivial. % 9.95/10.19 (* end of lemma zenon_L479_ *) % 9.95/10.19 assert (zenon_L480_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((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))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H156 zenon_Hc6 zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H25 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7 zenon_Hd2. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.19 apply (zenon_L479_); trivial. % 9.95/10.19 apply (zenon_L321_); trivial. % 9.95/10.19 (* end of lemma zenon_L480_ *) % 9.95/10.19 assert (zenon_L481_ : (((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)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 9.95/10.19 do 0 intro. intros zenon_H90 zenon_H5e zenon_H73 zenon_Hd3 zenon_H1e zenon_H91 zenon_H17c zenon_H9a. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.19 apply (zenon_L165_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.19 apply (zenon_L196_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.19 exact (zenon_H91 zenon_H94). % 9.95/10.19 apply (zenon_L166_); trivial. % 9.95/10.19 (* end of lemma zenon_L481_ *) % 9.95/10.19 assert (zenon_L482_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.19 do 0 intro. intros zenon_H64 zenon_H56 zenon_H17c zenon_H91 zenon_Hd3 zenon_H73 zenon_H90 zenon_H5e zenon_H51 zenon_H9a zenon_H187. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.19 apply (zenon_L481_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.19 apply (zenon_L12_); trivial. % 9.95/10.19 apply (zenon_L202_); trivial. % 9.95/10.19 (* end of lemma zenon_L482_ *) % 9.95/10.19 assert (zenon_L483_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 9.95/10.19 do 0 intro. intros zenon_H90 zenon_H4c zenon_H74 zenon_H78 zenon_H5e zenon_H91 zenon_H17c zenon_H9a. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 9.95/10.19 apply (zenon_L21_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 9.95/10.19 apply (zenon_L22_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 9.95/10.19 exact (zenon_H91 zenon_H94). % 9.95/10.19 apply (zenon_L166_); trivial. % 9.95/10.19 (* end of lemma zenon_L483_ *) % 9.95/10.19 assert (zenon_L484_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> False). % 9.95/10.19 do 0 intro. intros zenon_Hb0 zenon_H187 zenon_H51 zenon_H56 zenon_H64 zenon_H9a zenon_H17c zenon_Hb1 zenon_H90 zenon_H4c zenon_H74 zenon_Hd3 zenon_H1e zenon_H91 zenon_H5e. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 9.95/10.19 apply (zenon_L482_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 9.95/10.19 apply (zenon_L483_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 9.95/10.19 exact (zenon_Hb1 zenon_Hb7). % 9.95/10.19 apply (zenon_L250_); trivial. % 9.95/10.19 (* end of lemma zenon_L484_ *) % 9.95/10.19 assert (zenon_L485_ : (((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)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 9.95/10.19 do 0 intro. intros zenon_Hda zenon_H28 zenon_H53 zenon_H69 zenon_H5e zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_Hb1 zenon_H17c zenon_H9a zenon_H64 zenon_H56 zenon_H51 zenon_H187 zenon_Hb0 zenon_H4c zenon_Hf0. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.19 exact (zenon_H28 zenon_H31). % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.19 apply (zenon_L18_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.19 apply (zenon_L484_); trivial. % 9.95/10.19 apply (zenon_L139_); trivial. % 9.95/10.19 (* end of lemma zenon_L485_ *) % 9.95/10.19 assert (zenon_L486_ : (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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 (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((~((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (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) = (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). % 9.95/10.19 do 0 intro. intros zenon_H4c zenon_Hb0 zenon_H187 zenon_H56 zenon_H64 zenon_H9a zenon_H17c zenon_Hb1 zenon_H90 zenon_Hd3 zenon_H91 zenon_H69 zenon_H53 zenon_H28 zenon_Hda zenon_Hf5 zenon_H1f0 zenon_H100 zenon_H1e6 zenon_H7e zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H198 zenon_H1af zenon_H1b4 zenon_H5e zenon_H51 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.19 apply (zenon_L468_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.19 apply (zenon_L469_); trivial. % 9.95/10.19 apply (zenon_L485_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.19 apply (zenon_L12_); trivial. % 9.95/10.19 apply (zenon_L87_); trivial. % 9.95/10.19 (* end of lemma zenon_L486_ *) % 9.95/10.19 assert (zenon_L487_ : (~((op (e3) (e0)) = (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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.19 do 0 intro. intros zenon_He3 zenon_H84 zenon_Hb0 zenon_H56 zenon_H64 zenon_H17c zenon_Hb1 zenon_H90 zenon_H4c zenon_Hd3 zenon_H91 zenon_H69 zenon_H53 zenon_H28 zenon_Hda zenon_H5e zenon_H51 zenon_H9a zenon_H187. % 9.95/10.19 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.19 exact (zenon_H56 zenon_H2c). % 9.95/10.19 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.19 exact (zenon_H28 zenon_H31). % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.19 apply (zenon_L18_); trivial. % 9.95/10.19 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.19 apply (zenon_L484_); trivial. % 9.95/10.20 apply (zenon_L266_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.20 apply (zenon_L12_); trivial. % 9.95/10.20 apply (zenon_L202_); trivial. % 9.95/10.20 (* end of lemma zenon_L487_ *) % 9.95/10.20 assert (zenon_L488_ : ((~((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 (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H156 zenon_H1b4 zenon_H192 zenon_H12c zenon_H205 zenon_H95 zenon_Hbb zenon_H1b1 zenon_H35 zenon_H198 zenon_Hce zenon_Hd2 zenon_H56 zenon_Hda zenon_H84 zenon_He3 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H4c zenon_Hb0 zenon_H69 zenon_H53 zenon_H28. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.20 apply (zenon_L487_); trivial. % 9.95/10.20 apply (zenon_L397_); trivial. % 9.95/10.20 (* end of lemma zenon_L488_ *) % 9.95/10.20 assert (zenon_L489_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((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))) -> (((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))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H18d zenon_He3 zenon_Hd2 zenon_Hce zenon_H35 zenon_H1b1 zenon_Hbb zenon_H95 zenon_H205 zenon_H12c zenon_H156 zenon_H56 zenon_H1b4 zenon_Hb0 zenon_Hb1 zenon_H90 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7f zenon_H7a zenon_H8d. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.20 apply (zenon_L486_); trivial. % 9.95/10.20 apply (zenon_L488_); trivial. % 9.95/10.20 (* end of lemma zenon_L489_ *) % 9.95/10.20 assert (zenon_L490_ : (((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) (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). % 9.95/10.20 do 0 intro. intros zenon_H1f8 zenon_H51 zenon_H6f zenon_H15a zenon_H159 zenon_H155 zenon_H3a zenon_Hed zenon_H1e6. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H101 | zenon_intro zenon_H1f9 ]. % 9.95/10.20 apply (zenon_L348_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H100 | zenon_intro zenon_H1fa ]. % 9.95/10.20 apply (zenon_L123_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H6e | zenon_intro zenon_H161 ]. % 9.95/10.20 apply (zenon_L223_); trivial. % 9.95/10.20 apply (zenon_L282_); trivial. % 9.95/10.20 (* end of lemma zenon_L490_ *) % 9.95/10.20 assert (zenon_L491_ : (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (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))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H4c zenon_Hb0 zenon_H56 zenon_H64 zenon_H17c zenon_Hb1 zenon_H90 zenon_Hd3 zenon_H91 zenon_H5e zenon_H69 zenon_H53 zenon_H28 zenon_Hda zenon_Hf5 zenon_H1f0 zenon_H100 zenon_H7e zenon_H159 zenon_H1b4 zenon_H1e6 zenon_Hed zenon_H3a zenon_H155 zenon_H6f zenon_H51 zenon_H1f8 zenon_H9a zenon_H187. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.20 exact (zenon_H56 zenon_H2c). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.20 exact (zenon_H56 zenon_H2c). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.20 apply (zenon_L490_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.20 apply (zenon_L469_); trivial. % 9.95/10.20 apply (zenon_L485_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.20 apply (zenon_L349_); trivial. % 9.95/10.20 apply (zenon_L202_); trivial. % 9.95/10.20 (* end of lemma zenon_L491_ *) % 9.95/10.20 assert (zenon_L492_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 9.95/10.20 do 0 intro. intros zenon_Hf8 zenon_H6f zenon_H155 zenon_H3a zenon_H1f8 zenon_H8d zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H56 zenon_H156 zenon_H12c zenon_H205 zenon_H95 zenon_Hbb zenon_H1b1 zenon_H35 zenon_Hce zenon_Hd2 zenon_He3 zenon_H18d. % 9.95/10.20 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.20 apply (zenon_L489_); trivial. % 9.95/10.20 apply (zenon_L491_); trivial. % 9.95/10.20 (* end of lemma zenon_L492_ *) % 9.95/10.20 assert (zenon_L493_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H1e6 zenon_H100 zenon_H1f0 zenon_H4c zenon_Hbc zenon_Hf5 zenon_H5e zenon_H51 zenon_H9a zenon_H187. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.20 exact (zenon_H56 zenon_H2c). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.20 apply (zenon_L329_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.20 apply (zenon_L12_); trivial. % 9.95/10.20 apply (zenon_L202_); trivial. % 9.95/10.20 (* end of lemma zenon_L493_ *) % 9.95/10.20 assert (zenon_L494_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H212 zenon_He8 zenon_H3a zenon_H25 zenon_H51 zenon_H28 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 9.95/10.20 apply (zenon_L466_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 9.95/10.20 apply (zenon_L480_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 9.95/10.20 apply (zenon_L492_); trivial. % 9.95/10.20 apply (zenon_L493_); trivial. % 9.95/10.20 apply (zenon_L435_); trivial. % 9.95/10.20 (* end of lemma zenon_L494_ *) % 9.95/10.20 assert (zenon_L495_ : ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H57 zenon_H25 zenon_H212 zenon_He8 zenon_H3a zenon_H51 zenon_H28 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H9a zenon_H7f. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.95/10.20 exact (zenon_H25 zenon_H2a). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.95/10.20 apply (zenon_L494_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.95/10.20 apply (zenon_L482_); trivial. % 9.95/10.20 apply (zenon_L56_); trivial. % 9.95/10.20 apply (zenon_L68_); trivial. % 9.95/10.20 (* end of lemma zenon_L495_ *) % 9.95/10.20 assert (zenon_L496_ : (((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)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 9.95/10.20 do 0 intro. intros zenon_H145 zenon_H53 zenon_H6c zenon_He8 zenon_H51 zenon_H6f zenon_H5e zenon_H9a. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 9.95/10.20 apply (zenon_L18_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 9.95/10.20 exact (zenon_He8 zenon_Heb). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 9.95/10.20 apply (zenon_L348_); trivial. % 9.95/10.20 apply (zenon_L192_); trivial. % 9.95/10.20 (* end of lemma zenon_L496_ *) % 9.95/10.20 assert (zenon_L497_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H1dd zenon_Hb0 zenon_H56 zenon_H64 zenon_H17c zenon_Hb1 zenon_H90 zenon_H4c zenon_Hd3 zenon_H91 zenon_H5e zenon_H145 zenon_H53 zenon_He8 zenon_H28 zenon_Hda zenon_H1e6 zenon_Hed zenon_H3a zenon_H155 zenon_H6f zenon_H51 zenon_H1f8 zenon_H9a zenon_H187. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.20 exact (zenon_H56 zenon_H2c). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 9.95/10.20 exact (zenon_H28 zenon_H31). % 9.95/10.20 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 9.95/10.20 apply (zenon_L496_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 9.95/10.20 apply (zenon_L484_); trivial. % 9.95/10.20 apply (zenon_L267_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.20 apply (zenon_L349_); trivial. % 9.95/10.20 apply (zenon_L202_); trivial. % 9.95/10.20 (* end of lemma zenon_L497_ *) % 9.95/10.20 assert (zenon_L498_ : (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> False). % 9.95/10.20 do 0 intro. intros zenon_Hb1 zenon_H9a zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H28 zenon_H51 zenon_H3a zenon_He8 zenon_H212 zenon_H25 zenon_H57. % 9.95/10.20 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 9.95/10.20 apply (zenon_L495_); trivial. % 9.95/10.20 apply (zenon_L497_); trivial. % 9.95/10.20 (* end of lemma zenon_L498_ *) % 9.95/10.20 assert (zenon_L499_ : (((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). % 9.95/10.20 do 0 intro. intros zenon_H12c zenon_H4c zenon_H76 zenon_H114 zenon_Hbd zenon_Hc8 zenon_H181 zenon_H57. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 9.95/10.20 apply (zenon_L21_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 9.95/10.20 apply (zenon_L80_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 9.95/10.20 exact (zenon_Hc8 zenon_Hcd). % 9.95/10.20 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H181. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_H57. % 9.95/10.20 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H215]. % 9.95/10.20 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 9.95/10.20 congruence. % 9.95/10.20 apply zenon_H5a. apply refl_equal. % 9.95/10.20 apply zenon_H215. apply sym_equal. exact zenon_H11f. % 9.95/10.20 (* end of lemma zenon_L499_ *) % 9.95/10.20 assert (zenon_L500_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H3a zenon_Hb8 zenon_H216. % 9.95/10.20 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 9.95/10.20 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e1)) = (op (e2) (e2)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H216. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_H3d. % 9.95/10.20 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.20 cut (((op (e2) (e2)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 9.95/10.20 congruence. % 9.95/10.20 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e1)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H217. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_H3a. % 9.95/10.20 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 9.95/10.20 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 9.95/10.20 congruence. % 9.95/10.20 apply zenon_H3e. apply refl_equal. % 9.95/10.20 apply zenon_H113. apply sym_equal. exact zenon_Hb8. % 9.95/10.20 apply zenon_H3e. apply refl_equal. % 9.95/10.20 apply zenon_H3e. apply refl_equal. % 9.95/10.20 (* end of lemma zenon_L500_ *) % 9.95/10.20 assert (zenon_L501_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H216 zenon_H151 zenon_H14a zenon_H174 zenon_H110 zenon_H118 zenon_H169 zenon_H57 zenon_H25 zenon_H212 zenon_He8 zenon_H3a zenon_H51 zenon_H28 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H9a zenon_Hb1. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 9.95/10.20 apply (zenon_L498_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 9.95/10.20 exact (zenon_H25 zenon_H2a). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 9.95/10.20 exact (zenon_H56 zenon_H2c). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 9.95/10.20 exact (zenon_H56 zenon_H2c). % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 9.95/10.20 apply (zenon_L194_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 9.95/10.20 apply (zenon_L499_); trivial. % 9.95/10.20 apply (zenon_L485_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 9.95/10.20 apply (zenon_L12_); trivial. % 9.95/10.20 apply (zenon_L202_); trivial. % 9.95/10.20 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 9.95/10.20 apply (zenon_L482_); trivial. % 9.95/10.20 apply (zenon_L160_); trivial. % 9.95/10.20 apply (zenon_L161_); trivial. % 9.95/10.20 apply (zenon_L354_); trivial. % 9.95/10.20 apply (zenon_L500_); trivial. % 9.95/10.20 (* end of lemma zenon_L501_ *) % 9.95/10.20 assert (zenon_L502_ : ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (op (op (e3) (e3)) (e3)))) -> False). % 9.95/10.20 do 0 intro. intros zenon_H8a zenon_H85 zenon_H1d5. % 9.95/10.20 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((e1) = (op (op (e3) (e3)) (e3)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H1d5. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_Ha9. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 9.95/10.20 congruence. % 9.95/10.20 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H1d8. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_H8a. % 9.95/10.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.20 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 9.95/10.20 congruence. % 9.95/10.20 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H1ff. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_Ha9. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 9.95/10.20 congruence. % 9.95/10.20 apply (zenon_L355_); trivial. % 9.95/10.20 apply zenon_Haa. apply refl_equal. % 9.95/10.20 apply zenon_Haa. apply refl_equal. % 9.95/10.20 apply zenon_H33. apply refl_equal. % 9.95/10.20 apply zenon_Haa. apply refl_equal. % 9.95/10.20 apply zenon_Haa. apply refl_equal. % 9.95/10.20 (* end of lemma zenon_L502_ *) % 9.95/10.20 assert (zenon_L503_ : ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 9.95/10.20 do 0 intro. intros zenon_H87 zenon_H8a zenon_H85. % 9.95/10.20 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H1fe | zenon_intro zenon_H218 ]. % 9.95/10.20 apply zenon_H1fe. apply sym_equal. exact zenon_H85. % 9.95/10.20 apply (zenon_notand_s _ _ zenon_H218); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H1d5 ]. % 9.95/10.20 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.20 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((e0) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_Ha1. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_Ha2. % 9.95/10.20 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.20 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 9.95/10.20 congruence. % 9.95/10.20 cut (((op (e1) (e3)) = (e0)) = ((op (op (op (e3) (e3)) (e3)) (e3)) = (e0))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_Ha4. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_H87. % 9.95/10.20 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 9.95/10.20 cut (((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 9.95/10.20 congruence. % 9.95/10.20 elim (classic ((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 9.95/10.20 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3))) = ((op (e1) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H1d6. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_Ha2. % 9.95/10.20 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (op (op (e3) (e3)) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 9.95/10.20 cut (((op (op (op (e3) (e3)) (e3)) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 9.95/10.20 congruence. % 9.95/10.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 9.95/10.20 congruence. % 9.95/10.20 cut (((op (e2) (e3)) = (e1)) = ((op (op (e3) (e3)) (e3)) = (e1))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H1d8. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_H8a. % 9.95/10.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 9.95/10.20 cut (((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 9.95/10.20 congruence. % 9.95/10.20 elim (classic ((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Haa ]. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3))) = ((op (e2) (e3)) = (op (op (e3) (e3)) (e3)))). % 9.95/10.20 intro zenon_D_pnotp. % 9.95/10.20 apply zenon_H1ff. % 9.95/10.20 rewrite <- zenon_D_pnotp. % 9.95/10.20 exact zenon_Ha9. % 9.95/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (op (e3) (e3)) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 10.04/10.20 cut (((op (op (e3) (e3)) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 10.04/10.20 congruence. % 10.04/10.20 apply (zenon_L355_); trivial. % 10.04/10.20 apply zenon_Haa. apply refl_equal. % 10.04/10.20 apply zenon_Haa. apply refl_equal. % 10.04/10.20 apply zenon_H33. apply refl_equal. % 10.04/10.20 apply zenon_H4e. apply refl_equal. % 10.04/10.20 apply zenon_Ha3. apply refl_equal. % 10.04/10.20 apply zenon_Ha3. apply refl_equal. % 10.04/10.20 apply zenon_H41. apply refl_equal. % 10.04/10.20 apply zenon_Ha3. apply refl_equal. % 10.04/10.20 apply zenon_Ha3. apply refl_equal. % 10.04/10.20 apply (zenon_L502_); trivial. % 10.04/10.20 (* end of lemma zenon_L503_ *) % 10.04/10.20 assert (zenon_L504_ : (((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) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> False). % 10.04/10.20 do 0 intro. intros zenon_H128 zenon_H95 zenon_H57 zenon_H44 zenon_H3a zenon_H1fb zenon_H87 zenon_H8a. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 10.04/10.20 apply (zenon_L54_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 10.04/10.20 apply (zenon_L92_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 10.04/10.20 apply (zenon_L354_); trivial. % 10.04/10.20 apply (zenon_L503_); trivial. % 10.04/10.20 (* end of lemma zenon_L504_ *) % 10.04/10.20 assert (zenon_L505_ : (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H145 zenon_H53 zenon_H6c zenon_He8 zenon_H51 zenon_H6f zenon_H90 zenon_H5e zenon_H73 zenon_Hd3 zenon_H1e zenon_H91 zenon_H128 zenon_H95 zenon_H57 zenon_H44 zenon_H3a zenon_H1fb. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.04/10.20 apply (zenon_L18_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.04/10.20 exact (zenon_He8 zenon_Heb). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.04/10.20 apply (zenon_L348_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.04/10.20 apply (zenon_L165_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.04/10.20 apply (zenon_L196_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.04/10.20 exact (zenon_H91 zenon_H94). % 10.04/10.20 apply (zenon_L504_); trivial. % 10.04/10.20 (* end of lemma zenon_L505_ *) % 10.04/10.20 assert (zenon_L506_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((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)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 10.04/10.20 do 0 intro. intros zenon_Hda zenon_H28 zenon_H1fb zenon_H3a zenon_H44 zenon_H57 zenon_H95 zenon_H128 zenon_H91 zenon_H1e zenon_Hd3 zenon_H5e zenon_H90 zenon_H6f zenon_H51 zenon_He8 zenon_H145 zenon_H53 zenon_H73 zenon_H4c zenon_Hf0. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.04/10.20 exact (zenon_H28 zenon_H31). % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.04/10.20 apply (zenon_L505_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.04/10.20 apply (zenon_L20_); trivial. % 10.04/10.20 apply (zenon_L139_); trivial. % 10.04/10.20 (* end of lemma zenon_L506_ *) % 10.04/10.20 assert (zenon_L507_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (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))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H64 zenon_H73 zenon_H53 zenon_H145 zenon_He8 zenon_H6f zenon_H90 zenon_Hd3 zenon_H91 zenon_H128 zenon_H95 zenon_H44 zenon_H3a zenon_H1fb zenon_H28 zenon_Hda zenon_H159 zenon_H100 zenon_H56 zenon_H1b4 zenon_H5e zenon_H51 zenon_H57 zenon_H4c. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.20 apply (zenon_L123_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.20 apply (zenon_L165_); trivial. % 10.04/10.20 apply (zenon_L506_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.20 apply (zenon_L12_); trivial. % 10.04/10.20 apply (zenon_L13_); trivial. % 10.04/10.20 (* end of lemma zenon_L507_ *) % 10.04/10.20 assert (zenon_L508_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.04/10.20 do 0 intro. intros zenon_Hf5 zenon_H5e zenon_He4 zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 10.04/10.20 apply (zenon_L62_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 10.04/10.20 apply (zenon_L327_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 10.04/10.20 apply (zenon_L328_); trivial. % 10.04/10.20 exact (zenon_H7e zenon_H83). % 10.04/10.20 (* end of lemma zenon_L508_ *) % 10.04/10.20 assert (zenon_L509_ : (((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 (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.04/10.20 do 0 intro. intros zenon_H108 zenon_H68 zenon_Hfd zenon_H100 zenon_H5e zenon_Hb1 zenon_H1dd zenon_He4. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 10.04/10.20 apply (zenon_L69_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 10.04/10.20 apply (zenon_L71_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 10.04/10.20 exact (zenon_Hb1 zenon_Hb7). % 10.04/10.20 apply (zenon_L442_); trivial. % 10.04/10.20 (* end of lemma zenon_L509_ *) % 10.04/10.20 assert (zenon_L510_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.04/10.20 do 0 intro. intros zenon_He7 zenon_H1dd zenon_Hb1 zenon_H5e zenon_H100 zenon_Hfd zenon_H108 zenon_Hc1 zenon_H4b zenon_H192 zenon_He8 zenon_H191 zenon_Hbb zenon_He4. % 10.04/10.20 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.04/10.20 apply (zenon_L509_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.04/10.20 exact (zenon_He8 zenon_Heb). % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.04/10.20 apply (zenon_L335_); trivial. % 10.04/10.20 apply (zenon_L58_); trivial. % 10.04/10.20 (* end of lemma zenon_L510_ *) % 10.04/10.20 assert (zenon_L511_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((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)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((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)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hf5 zenon_H51 zenon_H97 zenon_H28 zenon_He4 zenon_Hbb zenon_H191 zenon_He8 zenon_H192 zenon_Hc1 zenon_H108 zenon_Hfd zenon_H100 zenon_H5e zenon_Hb1 zenon_H1dd zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.20 apply (zenon_L508_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.20 apply (zenon_L12_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.04/10.20 exact (zenon_H28 zenon_H31). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.04/10.20 apply (zenon_L510_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.04/10.20 apply (zenon_L75_); trivial. % 10.04/10.20 apply (zenon_L13_); trivial. % 10.04/10.20 (* end of lemma zenon_L511_ *) % 10.04/10.20 assert (zenon_L512_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.04/10.20 do 0 intro. intros zenon_Hf8 zenon_H56 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_H5e zenon_H51 zenon_H97 zenon_H4c zenon_H10b zenon_H108 zenon_H1dd zenon_Hb1 zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_H192 zenon_Hbb zenon_He7 zenon_H28 zenon_H64 zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.20 apply (zenon_L56_); trivial. % 10.04/10.20 apply (zenon_L511_); trivial. % 10.04/10.20 (* end of lemma zenon_L512_ *) % 10.04/10.20 assert (zenon_L513_ : (((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 (e0) (e3)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H100 zenon_H159 zenon_H57 zenon_H181 zenon_Hc8 zenon_H114 zenon_H4c zenon_H12c zenon_H14d zenon_H5e zenon_H53 zenon_H7f zenon_H44 zenon_H95 zenon_Hbd zenon_H35 zenon_H177 zenon_H8d. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.20 apply (zenon_L123_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.20 apply (zenon_L499_); trivial. % 10.04/10.20 apply (zenon_L340_); trivial. % 10.04/10.20 (* end of lemma zenon_L513_ *) % 10.04/10.20 assert (zenon_L514_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (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 (e0) (e0)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H157 zenon_H216 zenon_H151 zenon_H8d zenon_H14d zenon_H114 zenon_H18e zenon_H7d zenon_He3 zenon_Hbb zenon_H1dd zenon_H145 zenon_H44 zenon_H57 zenon_He7 zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H177 zenon_Hc5 zenon_H152 zenon_H158 zenon_H10b zenon_H51 zenon_Hec zenon_H1de zenon_H144 zenon_H3a zenon_H3c zenon_H6f zenon_Hfd zenon_H95 zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H64 zenon_He8 zenon_Hb1 zenon_H90 zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H187 zenon_H97 zenon_H108 zenon_H1cb zenon_H200 zenon_Hc1 zenon_H212 zenon_H35 zenon_H1b4 zenon_H56 zenon_Hf8 zenon_H25 zenon_H7a zenon_H18d zenon_Hd2. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.20 exact (zenon_H25 zenon_H2a). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.20 apply (zenon_L478_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.20 apply (zenon_L507_); trivial. % 10.04/10.20 apply (zenon_L512_); trivial. % 10.04/10.20 apply (zenon_L68_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.20 apply (zenon_L513_); trivial. % 10.04/10.20 apply (zenon_L60_); trivial. % 10.04/10.20 apply (zenon_L354_); trivial. % 10.04/10.20 apply (zenon_L500_); trivial. % 10.04/10.20 (* end of lemma zenon_L514_ *) % 10.04/10.20 assert (zenon_L515_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H100 zenon_H1f0 zenon_He4 zenon_H5e zenon_Hf5 zenon_H1e6 zenon_Hed zenon_H3a zenon_H155 zenon_H6f zenon_H51 zenon_H1f8 zenon_H9a zenon_H187. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.20 apply (zenon_L508_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.20 apply (zenon_L349_); trivial. % 10.04/10.20 apply (zenon_L202_); trivial. % 10.04/10.20 (* end of lemma zenon_L515_ *) % 10.04/10.20 assert (zenon_L516_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.04/10.20 do 0 intro. intros zenon_Hf8 zenon_H1f8 zenon_H3a zenon_H155 zenon_H6f zenon_H18e zenon_He3 zenon_H56 zenon_H1b4 zenon_Hb0 zenon_Hb1 zenon_H90 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7a zenon_H8d zenon_H25 zenon_H57 zenon_H18d. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.20 exact (zenon_H25 zenon_H2a). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.20 apply (zenon_L486_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.20 apply (zenon_L482_); trivial. % 10.04/10.20 apply (zenon_L56_); trivial. % 10.04/10.20 apply (zenon_L68_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.20 exact (zenon_H25 zenon_H2a). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.20 apply (zenon_L491_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.20 apply (zenon_L482_); trivial. % 10.04/10.20 apply (zenon_L515_); trivial. % 10.04/10.20 (* end of lemma zenon_L516_ *) % 10.04/10.20 assert (zenon_L517_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (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))))) -> ((~((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H216 zenon_H17a zenon_H12c zenon_H181 zenon_H114 zenon_Hec zenon_H44 zenon_H95 zenon_H173 zenon_H16e zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hfd zenon_H174 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H35 zenon_H103 zenon_H168 zenon_H177 zenon_H18d zenon_H57 zenon_H25 zenon_H8d zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H17c zenon_H9a zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H56 zenon_He3 zenon_H18e zenon_H6f zenon_H155 zenon_H3a zenon_H1f8 zenon_Hf8 zenon_H1fb zenon_Hd2. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.20 apply (zenon_L516_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.20 exact (zenon_H25 zenon_H2a). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.20 exact (zenon_H56 zenon_H2c). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.20 apply (zenon_L123_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.20 apply (zenon_L499_); trivial. % 10.04/10.20 apply (zenon_L485_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.20 apply (zenon_L228_); trivial. % 10.04/10.20 apply (zenon_L87_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.20 apply (zenon_L482_); trivial. % 10.04/10.20 apply (zenon_L160_); trivial. % 10.04/10.20 apply (zenon_L161_); trivial. % 10.04/10.20 apply (zenon_L60_); trivial. % 10.04/10.20 apply (zenon_L354_); trivial. % 10.04/10.20 apply (zenon_L500_); trivial. % 10.04/10.20 (* end of lemma zenon_L517_ *) % 10.04/10.20 assert (zenon_L518_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H67 zenon_Hfd zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H95 zenon_H57 zenon_H42. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.20 apply (zenon_L178_); trivial. % 10.04/10.20 apply (zenon_L69_); trivial. % 10.04/10.20 (* end of lemma zenon_L518_ *) % 10.04/10.20 assert (zenon_L519_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((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 (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H184 zenon_H11b zenon_Hb1 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H212 zenon_H169 zenon_H118 zenon_H110 zenon_H174 zenon_H14a zenon_H151 zenon_H216 zenon_He8 zenon_H191 zenon_H8d zenon_H25 zenon_H58 zenon_H24 zenon_H57 zenon_H7a. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.20 exact (zenon_H25 zenon_H2a). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.20 apply (zenon_L15_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.20 apply (zenon_L189_); trivial. % 10.04/10.20 apply (zenon_L88_); trivial. % 10.04/10.20 apply (zenon_L149_); trivial. % 10.04/10.20 apply (zenon_L85_); trivial. % 10.04/10.20 apply (zenon_L69_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.20 apply (zenon_L11_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.20 apply (zenon_L190_); trivial. % 10.04/10.20 apply (zenon_L501_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.20 apply (zenon_L514_); trivial. % 10.04/10.20 apply (zenon_L517_); trivial. % 10.04/10.20 apply (zenon_L14_); trivial. % 10.04/10.20 apply (zenon_L343_); trivial. % 10.04/10.20 apply (zenon_L518_); trivial. % 10.04/10.20 apply (zenon_L68_); trivial. % 10.04/10.20 (* end of lemma zenon_L519_ *) % 10.04/10.20 assert (zenon_L520_ : (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((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 (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H28 zenon_H1e zenon_H51 zenon_H184 zenon_H11b zenon_Hb1 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H212 zenon_H169 zenon_H118 zenon_H110 zenon_H174 zenon_H14a zenon_H151 zenon_H216 zenon_He8 zenon_H191 zenon_H8d zenon_H25 zenon_H58 zenon_H24 zenon_H7a. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.04/10.20 exact (zenon_H28 zenon_H31). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.04/10.20 apply (zenon_L9_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.04/10.20 apply (zenon_L10_); trivial. % 10.04/10.20 apply (zenon_L519_); trivial. % 10.04/10.20 (* end of lemma zenon_L520_ *) % 10.04/10.20 assert (zenon_L521_ : (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H4c zenon_H1e zenon_H53 zenon_H51 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H216 zenon_H191 zenon_H67 zenon_H1f zenon_H5e zenon_H64 zenon_H58 zenon_H24 zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_He8 zenon_Hec zenon_Hf8 zenon_H44 zenon_Hdd zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H42 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H17a zenon_H1af zenon_H4a zenon_H25. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.20 apply (zenon_L520_); trivial. % 10.04/10.20 apply (zenon_L343_); trivial. % 10.04/10.20 (* end of lemma zenon_L521_ *) % 10.04/10.20 assert (zenon_L522_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H100 zenon_H161 zenon_H4c. % 10.04/10.20 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H4d | zenon_intro zenon_H4e ]. % 10.04/10.20 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.04/10.20 intro zenon_D_pnotp. % 10.04/10.20 apply zenon_H4c. % 10.04/10.20 rewrite <- zenon_D_pnotp. % 10.04/10.20 exact zenon_H4d. % 10.04/10.20 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 10.04/10.20 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 10.04/10.20 congruence. % 10.04/10.20 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 10.04/10.20 intro zenon_D_pnotp. % 10.04/10.20 apply zenon_H4f. % 10.04/10.20 rewrite <- zenon_D_pnotp. % 10.04/10.20 exact zenon_H100. % 10.04/10.20 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.04/10.20 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.04/10.20 congruence. % 10.04/10.20 exact (zenon_H1cd zenon_H161). % 10.04/10.20 apply zenon_H33. apply refl_equal. % 10.04/10.20 apply zenon_H4e. apply refl_equal. % 10.04/10.20 apply zenon_H4e. apply refl_equal. % 10.04/10.20 (* end of lemma zenon_L522_ *) % 10.04/10.20 assert (zenon_L523_ : (((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 (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.04/10.20 do 0 intro. intros zenon_H1de zenon_H53 zenon_H69 zenon_Hc1 zenon_H4c zenon_H100 zenon_H84 zenon_H86. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.04/10.20 apply (zenon_L18_); trivial. % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.04/10.20 exact (zenon_Hc1 zenon_Hc4). % 10.04/10.20 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.04/10.20 apply (zenon_L522_); trivial. % 10.04/10.20 apply (zenon_L252_); trivial. % 10.04/10.20 (* end of lemma zenon_L523_ *) % 10.04/10.20 assert (zenon_L524_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.04/10.21 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H76 zenon_Hf5 zenon_H35 zenon_H1f0 zenon_H1e zenon_H100 zenon_H1e6 zenon_H7e. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.21 exact (zenon_H27 zenon_H32). % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.21 apply (zenon_L17_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.21 apply (zenon_L47_); trivial. % 10.04/10.21 apply (zenon_L420_); trivial. % 10.04/10.21 (* end of lemma zenon_L524_ *) % 10.04/10.21 assert (zenon_L525_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H9a zenon_H17c zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_Hf0 zenon_H35. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.21 exact (zenon_H27 zenon_H32). % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.21 apply (zenon_L17_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.21 apply (zenon_L234_); trivial. % 10.04/10.21 apply (zenon_L211_); trivial. % 10.04/10.21 (* end of lemma zenon_L525_ *) % 10.04/10.21 assert (zenon_L526_ : (((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) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H198 zenon_H7e zenon_H1e6 zenon_H100 zenon_H1f0 zenon_Hf5 zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H9a zenon_H17c zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_H35. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.21 apply (zenon_L194_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.21 apply (zenon_L524_); trivial. % 10.04/10.21 apply (zenon_L525_); trivial. % 10.04/10.21 (* end of lemma zenon_L526_ *) % 10.04/10.21 assert (zenon_L527_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H64 zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H17c zenon_H69 zenon_H44 zenon_H27 zenon_Hdd zenon_Hf5 zenon_H1f0 zenon_H100 zenon_H1e6 zenon_H7e zenon_H198 zenon_H56 zenon_H1b4 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H9a zenon_H187. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.21 apply (zenon_L526_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.21 apply (zenon_L103_); trivial. % 10.04/10.21 apply (zenon_L202_); trivial. % 10.04/10.21 (* end of lemma zenon_L527_ *) % 10.04/10.21 assert (zenon_L528_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (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)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H64 zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H9a zenon_H69 zenon_H44 zenon_H27 zenon_Hdd zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H7e zenon_H198 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H18a zenon_H43 zenon_H187 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.21 apply (zenon_L426_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.21 apply (zenon_L524_); trivial. % 10.04/10.21 apply (zenon_L525_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.21 apply (zenon_L228_); trivial. % 10.04/10.21 apply (zenon_L411_); trivial. % 10.04/10.21 (* end of lemma zenon_L528_ *) % 10.04/10.21 assert (zenon_L529_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (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) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H187 zenon_H47 zenon_H17c zenon_H18a zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_Hf0 zenon_H35. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.21 exact (zenon_H27 zenon_H32). % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.21 apply (zenon_L17_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.21 apply (zenon_L414_); trivial. % 10.04/10.21 apply (zenon_L211_); trivial. % 10.04/10.21 (* end of lemma zenon_L529_ *) % 10.04/10.21 assert (zenon_L530_ : (((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (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)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (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)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (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 (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H9a zenon_H198 zenon_H1e6 zenon_H100 zenon_H1f0 zenon_Hf5 zenon_H42 zenon_H3c zenon_H3a zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H187 zenon_H17c zenon_H18a zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_H35. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.21 apply (zenon_L194_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.21 apply (zenon_L524_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.04/10.21 exact (zenon_H27 zenon_H32). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.04/10.21 apply (zenon_L4_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.04/10.21 apply (zenon_L5_); trivial. % 10.04/10.21 apply (zenon_L529_); trivial. % 10.04/10.21 (* end of lemma zenon_L530_ *) % 10.04/10.21 assert (zenon_L531_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((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)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (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)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H64 zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H18a zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d zenon_H69 zenon_H44 zenon_H27 zenon_Hdd zenon_H3a zenon_H3c zenon_H42 zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H198 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H9a zenon_H187. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.21 apply (zenon_L530_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.21 apply (zenon_L228_); trivial. % 10.04/10.21 apply (zenon_L202_); trivial. % 10.04/10.21 (* end of lemma zenon_L531_ *) % 10.04/10.21 assert (zenon_L532_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (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)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.04/10.21 do 0 intro. intros zenon_Hf8 zenon_H1cb zenon_H5e zenon_Hb1 zenon_H53 zenon_H108 zenon_H56 zenon_H1b4 zenon_H3c zenon_H3a zenon_Hd3 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H187 zenon_H90 zenon_H42 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H6f zenon_H64. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.21 apply (zenon_L531_); trivial. % 10.04/10.21 apply (zenon_L359_); trivial. % 10.04/10.21 (* end of lemma zenon_L532_ *) % 10.04/10.21 assert (zenon_L533_ : ((~((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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((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 (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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((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) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H158 zenon_H42 zenon_H18d zenon_H7a zenon_H7d zenon_H108 zenon_H53 zenon_H5e zenon_H1cb zenon_Hf8 zenon_H64 zenon_H187 zenon_Hb1 zenon_H3c zenon_Hc5 zenon_H198 zenon_H9a zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H35 zenon_H69 zenon_H44 zenon_H27 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4 zenon_H56 zenon_H6f zenon_H18a zenon_H84 zenon_H86 zenon_H43 zenon_Hd2. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.21 apply (zenon_L527_); trivial. % 10.04/10.21 apply (zenon_L528_); trivial. % 10.04/10.21 apply (zenon_L532_); trivial. % 10.04/10.21 (* end of lemma zenon_L533_ *) % 10.04/10.21 assert (zenon_L534_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H156 zenon_Hd2 zenon_H43 zenon_H86 zenon_H84 zenon_H18a zenon_H6f zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_Hc5 zenon_H3c zenon_H187 zenon_H64 zenon_Hf8 zenon_H1cb zenon_H5e zenon_H53 zenon_H108 zenon_H7d zenon_H7a zenon_H18d zenon_H42 zenon_H158. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.21 apply (zenon_L533_); trivial. % 10.04/10.21 apply (zenon_L235_); trivial. % 10.04/10.21 (* end of lemma zenon_L534_ *) % 10.04/10.21 assert (zenon_L535_ : ((op (e3) (e3)) = (e3)) -> ((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)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H84 zenon_H43 zenon_H27 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.21 apply (zenon_L466_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.21 apply (zenon_L523_); trivial. % 10.04/10.21 apply (zenon_L534_); trivial. % 10.04/10.21 (* end of lemma zenon_L535_ *) % 10.04/10.21 assert (zenon_L536_ : (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H27 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.21 apply (zenon_L24_); trivial. % 10.04/10.21 apply (zenon_L535_); trivial. % 10.04/10.21 (* end of lemma zenon_L536_ *) % 10.04/10.21 assert (zenon_L537_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H64 zenon_H56 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_He4 zenon_H5e zenon_Hf5 zenon_H6f zenon_H100 zenon_H9a zenon_H187. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.21 apply (zenon_L508_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.21 apply (zenon_L228_); trivial. % 10.04/10.21 apply (zenon_L202_); trivial. % 10.04/10.21 (* end of lemma zenon_L537_ *) % 10.04/10.21 assert (zenon_L538_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.04/10.21 do 0 intro. intros zenon_H90 zenon_H5e zenon_H73 zenon_H4c zenon_Hb9 zenon_H91 zenon_H17c zenon_H9a. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.04/10.21 apply (zenon_L165_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.04/10.21 apply (zenon_L48_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.04/10.21 exact (zenon_H91 zenon_H94). % 10.04/10.21 apply (zenon_L166_); trivial. % 10.04/10.21 (* end of lemma zenon_L538_ *) % 10.04/10.21 assert (zenon_L539_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> False). % 10.04/10.21 do 0 intro. intros zenon_He7 zenon_H44 zenon_He8 zenon_Hc0 zenon_H95 zenon_H34 zenon_H9a zenon_H17c zenon_H91 zenon_H4c zenon_H73 zenon_H5e zenon_H90 zenon_H53. % 10.04/10.21 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.04/10.21 apply (zenon_L16_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.04/10.21 exact (zenon_He8 zenon_Heb). % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.04/10.21 apply (zenon_L165_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.04/10.21 apply (zenon_L22_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.04/10.21 exact (zenon_H91 zenon_H94). % 10.04/10.21 apply (zenon_L166_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.04/10.21 apply (zenon_L184_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.04/10.21 apply (zenon_L199_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.04/10.21 apply (zenon_L538_); trivial. % 10.04/10.21 apply (zenon_L112_); trivial. % 10.04/10.21 (* end of lemma zenon_L539_ *) % 10.04/10.21 assert (zenon_L540_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H42 zenon_H27 zenon_H53 zenon_H90 zenon_H5e zenon_H73 zenon_H4c zenon_H91 zenon_H17c zenon_H9a zenon_H95 zenon_Hc0 zenon_He8 zenon_H44 zenon_He7 zenon_H35 zenon_H5d zenon_Hd0 zenon_H181. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.04/10.21 exact (zenon_H27 zenon_H32). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.04/10.21 apply (zenon_L539_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.04/10.21 apply (zenon_L70_); trivial. % 10.04/10.21 apply (zenon_L163_); trivial. % 10.04/10.21 (* end of lemma zenon_L540_ *) % 10.04/10.21 assert (zenon_L541_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H64 zenon_H56 zenon_Hd3 zenon_H181 zenon_H35 zenon_He7 zenon_H44 zenon_He8 zenon_Hc0 zenon_H95 zenon_H9a zenon_H91 zenon_H4c zenon_H73 zenon_H5e zenon_H90 zenon_H53 zenon_H27 zenon_H42 zenon_H18a zenon_H43 zenon_H187 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.21 exact (zenon_H56 zenon_H2c). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.21 apply (zenon_L481_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.21 apply (zenon_L540_); trivial. % 10.04/10.21 apply (zenon_L411_); trivial. % 10.04/10.21 (* end of lemma zenon_L541_ *) % 10.04/10.21 assert (zenon_L542_ : (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.04/10.21 do 0 intro. intros zenon_He8 zenon_Hb1 zenon_H25 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H27 zenon_H7a zenon_H43 zenon_H7d zenon_Hc7 zenon_H9a zenon_H100 zenon_H84 zenon_H151. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.21 exact (zenon_H25 zenon_H2a). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.21 apply (zenon_L536_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.21 apply (zenon_L43_); trivial. % 10.04/10.21 apply (zenon_L537_); trivial. % 10.04/10.21 apply (zenon_L254_); trivial. % 10.04/10.21 apply (zenon_L161_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.21 exact (zenon_H25 zenon_H2a). % 10.04/10.21 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.21 apply (zenon_L534_); trivial. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.21 apply (zenon_L541_); trivial. % 10.04/10.21 apply (zenon_L537_); trivial. % 10.04/10.21 apply (zenon_L161_); trivial. % 10.04/10.21 (* end of lemma zenon_L542_ *) % 10.04/10.21 assert (zenon_L543_ : ((op (e0) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> False). % 10.04/10.21 do 0 intro. intros zenon_H3b zenon_H151 zenon_H84 zenon_H100 zenon_H9a zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_Hb1 zenon_He8. % 10.04/10.21 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.21 apply (zenon_L542_); trivial. % 10.04/10.21 apply (zenon_L5_); trivial. % 10.04/10.21 (* end of lemma zenon_L543_ *) % 10.04/10.21 assert (zenon_L544_ : ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 10.04/10.21 do 0 intro. intros zenon_H101 zenon_Hf3 zenon_Hcd. % 10.04/10.21 apply (zenon_notand_s _ _ ax24); [ zenon_intro zenon_H20d | zenon_intro zenon_H219 ]. % 10.04/10.21 apply zenon_H20d. apply sym_equal. exact zenon_Hcd. % 10.04/10.21 apply (zenon_notand_s _ _ zenon_H219); [ zenon_intro zenon_H21a | zenon_intro zenon_H15e ]. % 10.04/10.21 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 10.04/10.21 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((e0) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 10.04/10.21 intro zenon_D_pnotp. % 10.04/10.21 apply zenon_H21a. % 10.04/10.21 rewrite <- zenon_D_pnotp. % 10.04/10.21 exact zenon_H13e. % 10.04/10.21 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.04/10.21 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 10.04/10.21 congruence. % 10.04/10.21 cut (((op (e1) (e2)) = (e0)) = ((op (op (op (e2) (e2)) (e2)) (e2)) = (e0))). % 10.04/10.21 intro zenon_D_pnotp. % 10.04/10.21 apply zenon_H21b. % 10.04/10.21 rewrite <- zenon_D_pnotp. % 10.04/10.21 exact zenon_H101. % 10.04/10.21 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 10.04/10.21 cut (((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 10.04/10.21 congruence. % 10.04/10.21 elim (classic ((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 10.04/10.22 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2))) = ((op (e1) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H163. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H13e. % 10.04/10.22 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (op (op (e2) (e2)) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.04/10.22 cut (((op (op (op (e2) (e2)) (e2)) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 10.04/10.22 congruence. % 10.04/10.22 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 10.04/10.22 congruence. % 10.04/10.22 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H15f. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_Hf3. % 10.04/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.04/10.22 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 10.04/10.22 congruence. % 10.04/10.22 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H20b. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H138. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 10.04/10.22 congruence. % 10.04/10.22 apply (zenon_L405_); trivial. % 10.04/10.22 apply zenon_H139. apply refl_equal. % 10.04/10.22 apply zenon_H139. apply refl_equal. % 10.04/10.22 apply zenon_H33. apply refl_equal. % 10.04/10.22 apply zenon_H37. apply refl_equal. % 10.04/10.22 apply zenon_H13f. apply refl_equal. % 10.04/10.22 apply zenon_H13f. apply refl_equal. % 10.04/10.22 apply zenon_H41. apply refl_equal. % 10.04/10.22 apply zenon_H13f. apply refl_equal. % 10.04/10.22 apply zenon_H13f. apply refl_equal. % 10.04/10.22 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((e1) = (op (op (e2) (e2)) (e2)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H15e. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H138. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 10.04/10.22 congruence. % 10.04/10.22 cut (((op (e3) (e2)) = (e1)) = ((op (op (e2) (e2)) (e2)) = (e1))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H15f. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_Hf3. % 10.04/10.22 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.04/10.22 cut (((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 10.04/10.22 congruence. % 10.04/10.22 elim (classic ((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [ zenon_intro zenon_H138 | zenon_intro zenon_H139 ]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2))) = ((op (e3) (e2)) = (op (op (e2) (e2)) (e2)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H20b. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H138. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (op (e2) (e2)) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 10.04/10.22 cut (((op (op (e2) (e2)) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 10.04/10.22 congruence. % 10.04/10.22 apply (zenon_L405_); trivial. % 10.04/10.22 apply zenon_H139. apply refl_equal. % 10.04/10.22 apply zenon_H139. apply refl_equal. % 10.04/10.22 apply zenon_H33. apply refl_equal. % 10.04/10.22 apply zenon_H139. apply refl_equal. % 10.04/10.22 apply zenon_H139. apply refl_equal. % 10.04/10.22 (* end of lemma zenon_L544_ *) % 10.04/10.22 assert (zenon_L545_ : ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.04/10.22 do 0 intro. intros zenon_H6a zenon_H4c zenon_H53 zenon_H3b zenon_H95 zenon_H165 zenon_H91 zenon_H151 zenon_H84 zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H42 zenon_H181 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_Hb1 zenon_He8 zenon_H5e zenon_H9a. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.04/10.22 apply (zenon_L17_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.04/10.22 exact (zenon_He8 zenon_Heb). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 10.04/10.22 apply (zenon_L70_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 10.04/10.22 apply (zenon_L543_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 10.04/10.22 exact (zenon_H91 zenon_H94). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H52 | zenon_intro zenon_H166 ]. % 10.04/10.22 apply (zenon_L32_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 10.04/10.22 apply (zenon_L441_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hed ]. % 10.04/10.22 apply (zenon_L544_); trivial. % 10.04/10.22 apply (zenon_L64_); trivial. % 10.04/10.22 apply (zenon_L192_); trivial. % 10.04/10.22 (* end of lemma zenon_L545_ *) % 10.04/10.22 assert (zenon_L546_ : ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H9a zenon_H5e zenon_He8 zenon_Hb1 zenon_H25 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H181 zenon_H42 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H27 zenon_H7a zenon_H43 zenon_H7d zenon_H84 zenon_H151 zenon_H91 zenon_H165 zenon_H95 zenon_H3b zenon_H53 zenon_H4c zenon_H76 zenon_H35 zenon_He4 zenon_H44. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.22 exact (zenon_H27 zenon_H32). % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.22 apply (zenon_L545_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.22 apply (zenon_L47_); trivial. % 10.04/10.22 apply (zenon_L99_); trivial. % 10.04/10.22 (* end of lemma zenon_L546_ *) % 10.04/10.22 assert (zenon_L547_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H67 zenon_Hfd zenon_H24 zenon_H1e zenon_H26 zenon_H25 zenon_H11b zenon_H68 zenon_H4a. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.22 apply (zenon_L2_); trivial. % 10.04/10.22 apply (zenon_L85_); trivial. % 10.04/10.22 apply (zenon_L69_); trivial. % 10.04/10.22 (* end of lemma zenon_L547_ *) % 10.04/10.22 assert (zenon_L548_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.04/10.22 do 0 intro. intros zenon_H181 zenon_H43 zenon_H89. % 10.04/10.22 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H181. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H43. % 10.04/10.22 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 10.04/10.22 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 10.04/10.22 congruence. % 10.04/10.22 apply zenon_H5a. apply refl_equal. % 10.04/10.22 apply zenon_H1e1. apply sym_equal. exact zenon_H89. % 10.04/10.22 (* end of lemma zenon_L548_ *) % 10.04/10.22 assert (zenon_L549_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H11f zenon_Hb9 zenon_H184. % 10.04/10.22 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 10.04/10.22 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H184. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H17d. % 10.04/10.22 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 10.04/10.22 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 10.04/10.22 congruence. % 10.04/10.22 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 10.04/10.22 intro zenon_D_pnotp. % 10.04/10.22 apply zenon_H21c. % 10.04/10.22 rewrite <- zenon_D_pnotp. % 10.04/10.22 exact zenon_H11f. % 10.04/10.22 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 10.04/10.22 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 10.04/10.22 congruence. % 10.04/10.22 apply zenon_H17e. apply refl_equal. % 10.04/10.22 apply zenon_H117. apply sym_equal. exact zenon_Hb9. % 10.04/10.22 apply zenon_H17e. apply refl_equal. % 10.04/10.22 apply zenon_H17e. apply refl_equal. % 10.04/10.22 (* end of lemma zenon_L549_ *) % 10.04/10.22 assert (zenon_L550_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (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) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H21d zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H187 zenon_H17c zenon_H18a zenon_H181 zenon_H47 zenon_Hb9 zenon_H184. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H89 | zenon_intro zenon_H21e ]. % 10.04/10.22 apply (zenon_L548_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_H8a | zenon_intro zenon_H21f ]. % 10.04/10.22 apply (zenon_L392_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H11f ]. % 10.04/10.22 apply (zenon_L163_); trivial. % 10.04/10.22 apply (zenon_L549_); trivial. % 10.04/10.22 (* end of lemma zenon_L550_ *) % 10.04/10.22 assert (zenon_L551_ : (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (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) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (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) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.04/10.22 do 0 intro. intros zenon_H44 zenon_H35 zenon_H76 zenon_H53 zenon_H95 zenon_H165 zenon_H151 zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H173 zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H42 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H156 zenon_H16e zenon_H1ea zenon_H17a zenon_H18e zenon_Hb1 zenon_He7 zenon_H4a zenon_H11b zenon_H25 zenon_H26 zenon_H1e zenon_H24 zenon_Hfd zenon_H67 zenon_He8 zenon_H84 zenon_H205 zenon_Hc8 zenon_H21d zenon_H7d zenon_H7f zenon_H7e zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H187 zenon_H17c zenon_H18a zenon_H181 zenon_H184 zenon_H90 zenon_H4c zenon_H5e zenon_H91 zenon_H9a zenon_H12c zenon_Hbb zenon_He4. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.04/10.22 exact (zenon_H27 zenon_H32). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.04/10.22 apply (zenon_L4_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.04/10.22 apply (zenon_L546_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.04/10.22 apply (zenon_L547_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.04/10.22 exact (zenon_He8 zenon_Heb). % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 10.04/10.22 apply (zenon_L483_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 10.04/10.22 apply (zenon_L550_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 10.04/10.22 exact (zenon_Hc8 zenon_Hcd). % 10.04/10.22 apply (zenon_L385_); trivial. % 10.04/10.22 apply (zenon_L58_); trivial. % 10.04/10.22 (* end of lemma zenon_L551_ *) % 10.04/10.22 assert (zenon_L552_ : ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H1e zenon_H44 zenon_He4 zenon_H35 zenon_H76 zenon_H4c zenon_H53 zenon_H95 zenon_H165 zenon_H91 zenon_H151 zenon_H84 zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H42 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H25 zenon_Hb1 zenon_He8 zenon_H5e zenon_H9a zenon_Hd0 zenon_H181. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.04/10.22 exact (zenon_H27 zenon_H32). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.04/10.22 apply (zenon_L4_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.04/10.22 apply (zenon_L546_); trivial. % 10.04/10.22 apply (zenon_L163_); trivial. % 10.04/10.22 (* end of lemma zenon_L552_ *) % 10.04/10.22 assert (zenon_L553_ : (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H25 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H42 zenon_H181 zenon_H53 zenon_Hc0 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_H205 zenon_H18e zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H90 zenon_He7 zenon_H43 zenon_H11b zenon_He8 zenon_H7e zenon_H4c zenon_Hed zenon_H35 zenon_H5e zenon_Hf5 zenon_H44 zenon_Haf zenon_H1e zenon_Hde zenon_Hbb. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.22 exact (zenon_H25 zenon_H2a). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.22 apply (zenon_L466_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.22 apply (zenon_L481_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.04/10.22 apply (zenon_L85_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.04/10.22 exact (zenon_He8 zenon_Heb). % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.04/10.22 apply (zenon_L4_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.04/10.22 exact (zenon_Haf zenon_Hb4). % 10.04/10.22 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.04/10.22 apply (zenon_L57_); trivial. % 10.04/10.22 apply (zenon_L65_); trivial. % 10.04/10.22 apply (zenon_L58_); trivial. % 10.04/10.22 (* end of lemma zenon_L553_ *) % 10.04/10.22 assert (zenon_L554_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H151 zenon_Hb1 zenon_H1e zenon_H9a zenon_Hd0 zenon_He8 zenon_H84 zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_H11b zenon_Haf. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.22 exact (zenon_H25 zenon_H2a). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.22 apply (zenon_L536_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.22 apply (zenon_L541_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.22 exact (zenon_H56 zenon_H2c). % 10.04/10.22 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.22 apply (zenon_L426_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.22 apply (zenon_L552_); trivial. % 10.04/10.22 apply (zenon_L62_); trivial. % 10.04/10.22 apply (zenon_L553_); trivial. % 10.04/10.22 apply (zenon_L161_); trivial. % 10.04/10.22 (* end of lemma zenon_L554_ *) % 10.04/10.22 assert (zenon_L555_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.04/10.22 do 0 intro. intros zenon_Hb0 zenon_H5e zenon_H76 zenon_Hb8 zenon_H44 zenon_Hb1 zenon_H181 zenon_H43. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.04/10.22 apply (zenon_L165_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.04/10.22 apply (zenon_L57_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.04/10.22 exact (zenon_Hb1 zenon_Hb7). % 10.04/10.22 apply (zenon_L548_); trivial. % 10.04/10.22 (* end of lemma zenon_L555_ *) % 10.04/10.22 assert (zenon_L556_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.04/10.22 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_Hb8 zenon_H112 zenon_Hf0 zenon_H35. % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.22 exact (zenon_H27 zenon_H32). % 10.04/10.22 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.22 apply (zenon_L17_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.22 apply (zenon_L79_); trivial. % 10.04/10.22 apply (zenon_L211_); trivial. % 10.04/10.22 (* end of lemma zenon_L556_ *) % 10.04/10.22 assert (zenon_L557_ : (((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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.04/10.22 do 0 intro. intros zenon_H12c zenon_H53 zenon_H73 zenon_H95 zenon_Hb8 zenon_Hc8 zenon_H205 zenon_H84. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 10.04/10.22 apply (zenon_L20_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 10.04/10.22 apply (zenon_L40_); trivial. % 10.04/10.22 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 10.04/10.22 exact (zenon_Hc8 zenon_Hcd). % 10.04/10.22 apply (zenon_L385_); trivial. % 10.04/10.22 (* end of lemma zenon_L557_ *) % 10.04/10.22 assert (zenon_L558_ : (((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)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.04/10.22 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H9a zenon_H198 zenon_H43 zenon_H181 zenon_Hb1 zenon_H44 zenon_Hb8 zenon_Hb0 zenon_He4 zenon_H5e. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.23 exact (zenon_H56 zenon_H2c). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.23 apply (zenon_L194_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.23 apply (zenon_L555_); trivial. % 10.04/10.23 apply (zenon_L62_); trivial. % 10.04/10.23 (* end of lemma zenon_L558_ *) % 10.04/10.23 assert (zenon_L559_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((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))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (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))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((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)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.04/10.23 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H25 zenon_H1b4 zenon_H27 zenon_H112 zenon_H35 zenon_Hdd zenon_H5e zenon_H44 zenon_Hb8 zenon_Hb1 zenon_H181 zenon_H43 zenon_Hb0 zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H56 zenon_H12c zenon_H84 zenon_H205 zenon_H95 zenon_H53 zenon_H9a zenon_H18e. % 10.04/10.23 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.23 exact (zenon_H25 zenon_H2a). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.23 exact (zenon_H56 zenon_H2c). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.23 apply (zenon_L468_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.23 apply (zenon_L555_); trivial. % 10.04/10.23 apply (zenon_L556_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.23 apply (zenon_L557_); trivial. % 10.04/10.23 apply (zenon_L558_); trivial. % 10.04/10.23 apply (zenon_L164_); trivial. % 10.04/10.23 (* end of lemma zenon_L559_ *) % 10.04/10.23 assert (zenon_L560_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.04/10.23 do 0 intro. intros zenon_H145 zenon_H86 zenon_H84 zenon_H4c zenon_Hc1 zenon_H53 zenon_H1de zenon_He8 zenon_H100 zenon_H5e zenon_H187 zenon_H43. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.04/10.23 apply (zenon_L523_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.04/10.23 exact (zenon_He8 zenon_Heb). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.04/10.23 apply (zenon_L71_); trivial. % 10.04/10.23 apply (zenon_L276_); trivial. % 10.04/10.23 (* end of lemma zenon_L560_ *) % 10.04/10.23 assert (zenon_L561_ : ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> False). % 10.04/10.23 do 0 intro. intros zenon_H1e zenon_H151 zenon_H84 zenon_H100 zenon_H9a zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_Hb1 zenon_He8. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.23 apply (zenon_L542_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.23 exact (zenon_H25 zenon_H2a). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.23 apply (zenon_L530_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.23 apply (zenon_L481_); trivial. % 10.04/10.23 apply (zenon_L537_); trivial. % 10.04/10.23 apply (zenon_L359_); trivial. % 10.04/10.23 apply (zenon_L161_); trivial. % 10.04/10.23 (* end of lemma zenon_L561_ *) % 10.04/10.23 assert (zenon_L562_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.04/10.23 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H18e zenon_H5e zenon_H53 zenon_H95 zenon_H205 zenon_H84 zenon_H12c zenon_H56 zenon_H1b4 zenon_H112 zenon_Hb8 zenon_H27 zenon_H44 zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H6f zenon_H187 zenon_H9a zenon_H64 zenon_H25 zenon_H17a zenon_H151. % 10.04/10.23 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.23 exact (zenon_H25 zenon_H2a). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.23 exact (zenon_H56 zenon_H2c). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.23 exact (zenon_H56 zenon_H2c). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.23 apply (zenon_L468_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.23 apply (zenon_L524_); trivial. % 10.04/10.23 apply (zenon_L556_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.23 apply (zenon_L228_); trivial. % 10.04/10.23 apply (zenon_L202_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.23 apply (zenon_L557_); trivial. % 10.04/10.23 apply (zenon_L537_); trivial. % 10.04/10.23 apply (zenon_L161_); trivial. % 10.04/10.23 apply (zenon_L164_); trivial. % 10.04/10.23 (* end of lemma zenon_L562_ *) % 10.04/10.23 assert (zenon_L563_ : ((op (e0) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (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 (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (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) (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (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) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (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 (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 10.04/10.23 do 0 intro. intros zenon_H1e zenon_H151 zenon_H7d zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H95 zenon_H42 zenon_H181 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_Hb1 zenon_H184 zenon_H1de zenon_H84 zenon_H86 zenon_H100 zenon_H4c zenon_H53 zenon_He8 zenon_H5e zenon_H187 zenon_H43 zenon_H145. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.23 apply (zenon_L560_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.23 apply (zenon_L561_); trivial. % 10.04/10.23 apply (zenon_L562_); trivial. % 10.04/10.23 (* end of lemma zenon_L563_ *) % 10.04/10.23 assert (zenon_L564_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((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 (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.23 do 0 intro. intros zenon_H191 zenon_He8 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H7a zenon_H7d zenon_Hb1 zenon_H84 zenon_H151 zenon_H21d zenon_H184 zenon_H11b zenon_H25 zenon_H26 zenon_H1e zenon_H27 zenon_H24. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.23 apply (zenon_L2_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.23 apply (zenon_L190_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.23 exact (zenon_H25 zenon_H2a). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.23 apply (zenon_L536_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.23 apply (zenon_L43_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.23 exact (zenon_H56 zenon_H2c). % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.23 apply (zenon_L194_); trivial. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.23 apply (zenon_L551_); trivial. % 10.04/10.23 apply (zenon_L62_); trivial. % 10.04/10.23 apply (zenon_L254_); trivial. % 10.04/10.23 apply (zenon_L161_); trivial. % 10.04/10.23 apply (zenon_L554_); trivial. % 10.04/10.23 apply (zenon_L7_); trivial. % 10.04/10.23 apply (zenon_L559_); trivial. % 10.04/10.23 apply (zenon_L563_); trivial. % 10.04/10.23 apply (zenon_L1_); trivial. % 10.04/10.23 (* end of lemma zenon_L564_ *) % 10.04/10.23 assert (zenon_L565_ : (~((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.04/10.23 do 0 intro. intros zenon_H220 zenon_H28 zenon_H4c zenon_H1e zenon_H53 zenon_H51 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H216 zenon_H191 zenon_H67 zenon_H1f zenon_H5e zenon_H64 zenon_H58 zenon_H24 zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_He8 zenon_Hec zenon_Hf8 zenon_H44 zenon_Hdd zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H42 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H17a zenon_H1af zenon_H4a zenon_H25. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.04/10.23 apply (zenon_L520_); trivial. % 10.04/10.23 exact (zenon_H220 zenon_Hbc). % 10.04/10.23 (* end of lemma zenon_L565_ *) % 10.04/10.23 assert (zenon_L566_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 10.04/10.23 do 0 intro. intros zenon_H25 zenon_H4a zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_Hb1 zenon_H8c zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_Hdd zenon_H44 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H24 zenon_H58 zenon_H64 zenon_H5e zenon_H1f zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H51 zenon_H53 zenon_H1e zenon_H4c zenon_H220. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.23 apply (zenon_L565_); trivial. % 10.04/10.23 apply (zenon_L343_); trivial. % 10.04/10.23 (* end of lemma zenon_L566_ *) % 10.04/10.23 assert (zenon_L567_ : (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.04/10.23 do 0 intro. intros zenon_H221 zenon_H28 zenon_H4c zenon_H1e zenon_H53 zenon_H51 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H216 zenon_H191 zenon_H67 zenon_H1f zenon_H5e zenon_H64 zenon_H58 zenon_H24 zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_He8 zenon_Hec zenon_Hf8 zenon_H44 zenon_Hdd zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H42 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H17a zenon_H1af zenon_H4a zenon_H25. % 10.04/10.23 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.23 apply (zenon_L520_); trivial. % 10.04/10.23 exact (zenon_H221 zenon_Hcf). % 10.04/10.23 (* end of lemma zenon_L567_ *) % 10.04/10.23 assert (zenon_L568_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H25 zenon_H4a zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_H8c zenon_H8d zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_Hdd zenon_H44 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H24 zenon_H58 zenon_H64 zenon_H5e zenon_H1f zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H51 zenon_H53 zenon_H1e zenon_H4c zenon_H221. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.24 apply (zenon_L567_); trivial. % 10.04/10.24 apply (zenon_L343_); trivial. % 10.04/10.24 (* end of lemma zenon_L568_ *) % 10.04/10.24 assert (zenon_L569_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (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))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.04/10.24 do 0 intro. intros zenon_H145 zenon_H44 zenon_H6a zenon_He8 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_Hc5 zenon_H187 zenon_H43. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.04/10.24 apply (zenon_L17_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.04/10.24 exact (zenon_He8 zenon_Heb). % 10.04/10.24 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.04/10.24 apply (zenon_L118_); trivial. % 10.04/10.24 apply (zenon_L276_); trivial. % 10.04/10.24 (* end of lemma zenon_L569_ *) % 10.04/10.24 assert (zenon_L570_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.04/10.24 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H43 zenon_H187 zenon_Hc5 zenon_H155 zenon_H91 zenon_Hc7 zenon_Hc8 zenon_He8 zenon_H145 zenon_H221 zenon_He4 zenon_H44. % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.24 exact (zenon_H27 zenon_H32). % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.24 apply (zenon_L569_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.24 exact (zenon_H221 zenon_Hcf). % 10.04/10.24 apply (zenon_L99_); trivial. % 10.04/10.24 (* end of lemma zenon_L570_ *) % 10.04/10.24 assert (zenon_L571_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e2))) -> (~((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 (e0) (e3)) = (e0)) -> (~((op (e0) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H151 zenon_H84 zenon_He8 zenon_H221 zenon_Hc7 zenon_Hc8 zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_Hb1. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.24 exact (zenon_H25 zenon_H2a). % 10.04/10.24 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.24 apply (zenon_L536_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.24 apply (zenon_L43_); trivial. % 10.04/10.24 apply (zenon_L570_); trivial. % 10.04/10.24 apply (zenon_L254_); trivial. % 10.04/10.24 apply (zenon_L161_); trivial. % 10.04/10.24 (* end of lemma zenon_L571_ *) % 10.04/10.24 assert (zenon_L572_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.04/10.24 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H221 zenon_Hf0 zenon_H35. % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.24 exact (zenon_H27 zenon_H32). % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.24 apply (zenon_L17_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.24 exact (zenon_H221 zenon_Hcf). % 10.04/10.24 apply (zenon_L211_); trivial. % 10.04/10.24 (* end of lemma zenon_L572_ *) % 10.04/10.24 assert (zenon_L573_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H43 zenon_H62 zenon_H5e. % 10.04/10.24 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H5f | zenon_intro zenon_H33 ]. % 10.04/10.24 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.04/10.24 intro zenon_D_pnotp. % 10.04/10.24 apply zenon_H5e. % 10.04/10.24 rewrite <- zenon_D_pnotp. % 10.04/10.24 exact zenon_H5f. % 10.04/10.24 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 10.04/10.24 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 10.04/10.24 congruence. % 10.04/10.24 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 10.04/10.24 intro zenon_D_pnotp. % 10.04/10.24 apply zenon_H60. % 10.04/10.24 rewrite <- zenon_D_pnotp. % 10.04/10.24 exact zenon_H43. % 10.04/10.24 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 10.04/10.24 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 10.04/10.24 congruence. % 10.04/10.24 exact (zenon_H222 zenon_H62). % 10.04/10.24 apply zenon_H41. apply refl_equal. % 10.04/10.24 apply zenon_H33. apply refl_equal. % 10.04/10.24 apply zenon_H33. apply refl_equal. % 10.04/10.24 (* end of lemma zenon_L573_ *) % 10.04/10.24 assert (zenon_L574_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.04/10.24 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H18e zenon_H187 zenon_H9a zenon_H53 zenon_H95 zenon_Hb8 zenon_H205 zenon_H84 zenon_H12c zenon_H56 zenon_H1b4 zenon_H221 zenon_H27 zenon_H44 zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H6f zenon_H5e zenon_H43 zenon_H64 zenon_H25 zenon_H17a zenon_H151. % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.24 exact (zenon_H25 zenon_H2a). % 10.04/10.24 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.24 exact (zenon_H56 zenon_H2c). % 10.04/10.24 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.24 exact (zenon_H56 zenon_H2c). % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.24 apply (zenon_L468_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.24 apply (zenon_L524_); trivial. % 10.04/10.24 apply (zenon_L572_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.24 apply (zenon_L228_); trivial. % 10.04/10.24 apply (zenon_L573_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.24 apply (zenon_L557_); trivial. % 10.04/10.24 apply (zenon_L537_); trivial. % 10.04/10.24 apply (zenon_L161_); trivial. % 10.04/10.24 apply (zenon_L164_); trivial. % 10.04/10.24 (* end of lemma zenon_L574_ *) % 10.04/10.24 assert (zenon_L575_ : (~((op (e2) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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) (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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (((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) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H221 zenon_H184 zenon_H25 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H181 zenon_H42 zenon_H95 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H27 zenon_H7a zenon_H7d zenon_H151 zenon_H1e zenon_H1de zenon_H84 zenon_H86 zenon_H100 zenon_H4c zenon_H53 zenon_He8 zenon_H5e zenon_H187 zenon_H43 zenon_H145. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.24 apply (zenon_L560_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.24 apply (zenon_L561_); trivial. % 10.04/10.24 apply (zenon_L574_); trivial. % 10.04/10.24 exact (zenon_H221 zenon_Hcf). % 10.04/10.24 (* end of lemma zenon_L575_ *) % 10.04/10.24 assert (zenon_L576_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H191 zenon_He8 zenon_H151 zenon_H84 zenon_H221 zenon_H7d zenon_H7a zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H11b zenon_H184 zenon_H25 zenon_H26 zenon_H1e zenon_H27 zenon_H24. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.24 apply (zenon_L2_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.24 apply (zenon_L190_); trivial. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.24 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.24 apply (zenon_L571_); trivial. % 10.04/10.24 apply (zenon_L554_); trivial. % 10.04/10.24 apply (zenon_L7_); trivial. % 10.04/10.24 apply (zenon_L559_); trivial. % 10.04/10.24 exact (zenon_H221 zenon_Hcf). % 10.04/10.24 apply (zenon_L575_); trivial. % 10.04/10.24 apply (zenon_L1_); trivial. % 10.04/10.24 (* end of lemma zenon_L576_ *) % 10.04/10.24 assert (zenon_L577_ : (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H221 zenon_H25 zenon_H4a zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_H8c zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_Hdd zenon_H44 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H24 zenon_H58 zenon_H64 zenon_H5e zenon_H1f zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H51 zenon_H53 zenon_H1e zenon_H4c zenon_H28 zenon_H220. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.24 apply (zenon_L565_); trivial. % 10.04/10.24 exact (zenon_H221 zenon_Hcf). % 10.04/10.24 (* end of lemma zenon_L577_ *) % 10.04/10.24 assert (zenon_L578_ : (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e0)) = (e2))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H220 zenon_H4c zenon_H1e zenon_H53 zenon_H51 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H216 zenon_H191 zenon_H67 zenon_H1f zenon_H5e zenon_H64 zenon_H58 zenon_H24 zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_He8 zenon_Hec zenon_Hf8 zenon_H44 zenon_Hdd zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H42 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H17a zenon_H1af zenon_H4a zenon_H25 zenon_H221. % 10.04/10.24 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.24 apply (zenon_L577_); trivial. % 10.04/10.24 apply (zenon_L343_); trivial. % 10.04/10.24 (* end of lemma zenon_L578_ *) % 10.04/10.24 assert (zenon_L579_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (e1))) -> False). % 10.04/10.24 do 0 intro. intros zenon_H25 zenon_H4a zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_Hb1 zenon_H8c zenon_H8d zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_Hdd zenon_H44 zenon_Hf8 zenon_Hec zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H24 zenon_H58 zenon_H64 zenon_H5e zenon_H1f zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H51 zenon_H53 zenon_H1e zenon_H4c zenon_H223. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.04/10.25 apply (zenon_L520_); trivial. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 apply (zenon_L343_); trivial. % 10.04/10.25 (* end of lemma zenon_L579_ *) % 10.04/10.25 assert (zenon_L580_ : (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.04/10.25 do 0 intro. intros zenon_H223 zenon_H24 zenon_H26 zenon_H11b zenon_Hc8 zenon_H184 zenon_H21d zenon_H151 zenon_H84 zenon_H43 zenon_Hb1 zenon_He8 zenon_H27 zenon_H1e zenon_H44 zenon_Haf zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H191 zenon_H192 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H9a zenon_H25. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.25 exact (zenon_H25 zenon_H2a). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.25 apply (zenon_L465_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.25 apply (zenon_L481_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.25 exact (zenon_H56 zenon_H2c). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.25 apply (zenon_L551_); trivial. % 10.04/10.25 apply (zenon_L62_); trivial. % 10.04/10.25 apply (zenon_L553_); trivial. % 10.04/10.25 apply (zenon_L161_); trivial. % 10.04/10.25 (* end of lemma zenon_L580_ *) % 10.04/10.25 assert (zenon_L581_ : (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> False). % 10.04/10.25 do 0 intro. intros zenon_H25 zenon_H9a zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_H192 zenon_H191 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_Haf zenon_H44 zenon_H1e zenon_H27 zenon_He8 zenon_Hb1 zenon_H43 zenon_H84 zenon_H151 zenon_H21d zenon_H184 zenon_H11b zenon_H26 zenon_H24 zenon_H223. % 10.04/10.25 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.25 apply (zenon_L580_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.25 exact (zenon_H25 zenon_H2a). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.25 apply (zenon_L536_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.25 apply (zenon_L541_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.25 exact (zenon_H56 zenon_H2c). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.25 apply (zenon_L552_); trivial. % 10.04/10.25 apply (zenon_L62_); trivial. % 10.04/10.25 apply (zenon_L553_); trivial. % 10.04/10.25 apply (zenon_L161_); trivial. % 10.04/10.25 (* end of lemma zenon_L581_ *) % 10.04/10.25 assert (zenon_L582_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.25 do 0 intro. intros zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_Hb1 zenon_H84 zenon_H151 zenon_H21d zenon_H184 zenon_H11b zenon_H223 zenon_H191 zenon_H25 zenon_H26 zenon_H1e zenon_H27 zenon_H24. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.25 apply (zenon_L2_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.25 apply (zenon_L190_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.25 apply (zenon_L581_); trivial. % 10.04/10.25 apply (zenon_L559_); trivial. % 10.04/10.25 apply (zenon_L563_); trivial. % 10.04/10.25 apply (zenon_L1_); trivial. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 (* end of lemma zenon_L582_ *) % 10.04/10.25 assert (zenon_L583_ : (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> False). % 10.04/10.25 do 0 intro. intros zenon_H220 zenon_H4c zenon_H1e zenon_H53 zenon_H51 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H216 zenon_H191 zenon_H67 zenon_H1f zenon_H5e zenon_H64 zenon_H58 zenon_H24 zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_Hec zenon_Hf8 zenon_H44 zenon_Hdd zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H42 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H17a zenon_H1af zenon_H4a zenon_H25 zenon_H223. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.04/10.25 apply (zenon_L565_); trivial. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 apply (zenon_L343_); trivial. % 10.04/10.25 (* end of lemma zenon_L583_ *) % 10.04/10.25 assert (zenon_L584_ : (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((~((op (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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((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) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> False). % 10.04/10.25 do 0 intro. intros zenon_H221 zenon_H4c zenon_H1e zenon_H53 zenon_H51 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H216 zenon_H191 zenon_H67 zenon_H1f zenon_H5e zenon_H64 zenon_H58 zenon_H24 zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_H17c zenon_H181 zenon_H108 zenon_H103 zenon_Hfd zenon_H10b zenon_H18e zenon_He3 zenon_Hf5 zenon_He7 zenon_Hec zenon_Hf8 zenon_H44 zenon_Hdd zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H42 zenon_H18d zenon_H177 zenon_H168 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H132 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H17a zenon_H1af zenon_H4a zenon_H25 zenon_H223. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.04/10.25 apply (zenon_L567_); trivial. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 apply (zenon_L343_); trivial. % 10.04/10.25 (* end of lemma zenon_L584_ *) % 10.04/10.25 assert (zenon_L585_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (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))))) -> (((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) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((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)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.04/10.25 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H25 zenon_H1b4 zenon_H27 zenon_H221 zenon_H35 zenon_Hdd zenon_H5e zenon_H44 zenon_Hb8 zenon_Hb1 zenon_H181 zenon_H43 zenon_Hb0 zenon_H191 zenon_Haf zenon_H192 zenon_H195 zenon_H198 zenon_H1af zenon_H56 zenon_H12c zenon_H84 zenon_H205 zenon_H95 zenon_H53 zenon_H9a zenon_H18e. % 10.04/10.25 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.25 exact (zenon_H25 zenon_H2a). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.25 exact (zenon_H56 zenon_H2c). % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.25 apply (zenon_L467_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.25 apply (zenon_L555_); trivial. % 10.04/10.25 apply (zenon_L572_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.25 apply (zenon_L557_); trivial. % 10.04/10.25 apply (zenon_L558_); trivial. % 10.04/10.25 apply (zenon_L164_); trivial. % 10.04/10.25 (* end of lemma zenon_L585_ *) % 10.04/10.25 assert (zenon_L586_ : (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.25 do 0 intro. intros zenon_H221 zenon_H223 zenon_H11b zenon_H184 zenon_H21d zenon_H151 zenon_H84 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H191 zenon_H25 zenon_H26 zenon_H1e zenon_H27 zenon_H24. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.25 apply (zenon_L2_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.25 apply (zenon_L190_); trivial. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.25 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.25 apply (zenon_L581_); trivial. % 10.04/10.25 apply (zenon_L585_); trivial. % 10.04/10.25 exact (zenon_H221 zenon_Hcf). % 10.04/10.25 apply (zenon_L575_); trivial. % 10.04/10.25 apply (zenon_L1_); trivial. % 10.04/10.25 exact (zenon_H223 zenon_H15a). % 10.04/10.25 (* end of lemma zenon_L586_ *) % 10.04/10.25 assert (zenon_L587_ : (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((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)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (e1))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H221 zenon_H25 zenon_H4a zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_H8c zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_Hdd zenon_H44 zenon_Hf8 zenon_Hec zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H24 zenon_H58 zenon_H64 zenon_H5e zenon_H1f zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H51 zenon_H53 zenon_H1e zenon_H4c zenon_H220 zenon_H223. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.04/10.26 apply (zenon_L577_); trivial. % 10.04/10.26 exact (zenon_H223 zenon_H15a). % 10.04/10.26 apply (zenon_L343_); trivial. % 10.04/10.26 (* end of lemma zenon_L587_ *) % 10.04/10.26 assert (zenon_L588_ : ((~((op (e1) (e1)) = (e0)))\/(~((op (e1) (e0)) = (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/(~((op (e3) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/(~((op (e2) (e0)) = (e2)))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H224 zenon_H225 zenon_H25 zenon_H1f zenon_H1e zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_Hab zenon_H8c zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_Hdd zenon_Hf8 zenon_Hec zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H58 zenon_H64 zenon_H5e zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H53 zenon_H4c zenon_H24 zenon_H26 zenon_H42 zenon_H44 zenon_H3c zenon_H35 zenon_H4a zenon_H21d zenon_H226. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_He8 | zenon_intro zenon_H223 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H221 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L521_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L564_); trivial. % 10.04/10.26 apply (zenon_L521_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L566_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L564_); trivial. % 10.04/10.26 apply (zenon_L566_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L568_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L576_); trivial. % 10.04/10.26 apply (zenon_L568_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L578_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L576_); trivial. % 10.04/10.26 apply (zenon_L578_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H221 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L579_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L582_); trivial. % 10.04/10.26 apply (zenon_L579_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L583_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L582_); trivial. % 10.04/10.26 apply (zenon_L583_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L584_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L586_); trivial. % 10.04/10.26 apply (zenon_L584_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L8_); trivial. % 10.04/10.26 apply (zenon_L587_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.26 apply (zenon_L586_); trivial. % 10.04/10.26 apply (zenon_L587_); trivial. % 10.04/10.26 apply (zenon_L547_); trivial. % 10.04/10.26 (* end of lemma zenon_L588_ *) % 10.04/10.26 assert (zenon_L589_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H24 zenon_H25 zenon_H56 zenon_H132 zenon_H3b zenon_H28. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 10.04/10.26 exact (zenon_H56 zenon_H2c). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 10.04/10.26 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H227 | zenon_intro zenon_H134 ]. % 10.04/10.26 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 10.04/10.26 intro zenon_D_pnotp. % 10.04/10.26 apply zenon_H132. % 10.04/10.26 rewrite <- zenon_D_pnotp. % 10.04/10.26 exact zenon_H227. % 10.04/10.26 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 10.04/10.26 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 10.04/10.26 congruence. % 10.04/10.26 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 10.04/10.26 intro zenon_D_pnotp. % 10.04/10.26 apply zenon_H228. % 10.04/10.26 rewrite <- zenon_D_pnotp. % 10.04/10.26 exact zenon_H3b. % 10.04/10.26 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 10.04/10.26 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 10.04/10.26 congruence. % 10.04/10.26 apply zenon_H134. apply refl_equal. % 10.04/10.26 apply zenon_H229. apply sym_equal. exact zenon_H32. % 10.04/10.26 apply zenon_H134. apply refl_equal. % 10.04/10.26 apply zenon_H134. apply refl_equal. % 10.04/10.26 exact (zenon_H28 zenon_H31). % 10.04/10.26 (* end of lemma zenon_L589_ *) % 10.04/10.26 assert (zenon_L590_ : (((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)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f zenon_H1d zenon_H35 zenon_H3b zenon_H43 zenon_H5e. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.26 exact (zenon_H56 zenon_H2c). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.26 apply (zenon_L1_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.26 apply (zenon_L70_); trivial. % 10.04/10.26 apply (zenon_L573_); trivial. % 10.04/10.26 (* end of lemma zenon_L590_ *) % 10.04/10.26 assert (zenon_L591_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((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 (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H4a zenon_H1f zenon_H1d zenon_H35 zenon_H5e zenon_H64 zenon_H25 zenon_H56 zenon_H132 zenon_H3b zenon_H24. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.26 apply (zenon_L589_); trivial. % 10.04/10.26 apply (zenon_L590_); trivial. % 10.04/10.26 (* end of lemma zenon_L591_ *) % 10.04/10.26 assert (zenon_L592_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H18e zenon_H25 zenon_Hae zenon_H6f zenon_Hb0 zenon_H8d zenon_H86 zenon_H7f zenon_H7a zenon_H8c zenon_H90 zenon_Hb1 zenon_Hab zenon_H3b zenon_H28 zenon_H97 zenon_Hda zenon_Hd3 zenon_Hd2 zenon_Hce zenon_H27 zenon_Hdd zenon_Hc8 zenon_Hc7 zenon_H91 zenon_Hc6 zenon_Hc5 zenon_Hf8 zenon_H44 zenon_H68 zenon_Haf zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_He3 zenon_H7e zenon_H80 zenon_H7d. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.26 apply (zenon_L53_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.26 apply (zenon_L43_); trivial. % 10.04/10.26 apply (zenon_L67_); trivial. % 10.04/10.26 (* end of lemma zenon_L592_ *) % 10.04/10.26 assert (zenon_L593_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_He7 zenon_Hbb zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_Haf zenon_H68 zenon_H44 zenon_Hf8. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.26 apply (zenon_L67_); trivial. % 10.04/10.26 apply (zenon_L160_); trivial. % 10.04/10.26 (* end of lemma zenon_L593_ *) % 10.04/10.26 assert (zenon_L594_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H18d zenon_H17a zenon_H25 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_Hb0 zenon_H97 zenon_H4c zenon_H95 zenon_H35 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hde zenon_H3b zenon_H6f zenon_Haf zenon_Hda zenon_Hd3 zenon_H68 zenon_H110 zenon_H1d zenon_H112 zenon_H114 zenon_Hbd zenon_H118 zenon_H44 zenon_H27 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_Hc6 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_He3 zenon_Hf5 zenon_He7 zenon_Hbb zenon_He8 zenon_Hc1 zenon_Hec zenon_Hc0 zenon_Hf8 zenon_H18e. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.26 apply (zenon_L84_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.26 apply (zenon_L43_); trivial. % 10.04/10.26 apply (zenon_L593_); trivial. % 10.04/10.26 apply (zenon_L161_); trivial. % 10.04/10.26 (* end of lemma zenon_L594_ *) % 10.04/10.26 assert (zenon_L595_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H173 zenon_H16e zenon_H64 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H118 zenon_H114 zenon_H112 zenon_H1d zenon_H110 zenon_H17a zenon_H18d zenon_H25 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H68 zenon_H95 zenon_H97 zenon_Hb0 zenon_H3b zenon_H6f zenon_Haf zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hc1 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H44 zenon_H27 zenon_Hc8 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H108 zenon_H103 zenon_Hfd. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_L592_); trivial. % 10.04/10.26 apply (zenon_L170_); trivial. % 10.04/10.26 apply (zenon_L74_); trivial. % 10.04/10.26 apply (zenon_L594_); trivial. % 10.04/10.26 (* end of lemma zenon_L595_ *) % 10.04/10.26 assert (zenon_L596_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((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) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H18e zenon_H25 zenon_Hae zenon_Haf zenon_H6f zenon_Hb0 zenon_Hb1 zenon_H3b zenon_H97 zenon_H27 zenon_Hdd zenon_H8d zenon_Hab zenon_H1d zenon_H11d zenon_H128 zenon_H7f zenon_H11b zenon_H68 zenon_H8c zenon_H12c zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He3 zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_H44 zenon_Hb8 zenon_Hbb zenon_He7 zenon_Hf8. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.26 exact (zenon_H25 zenon_H2a). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.26 apply (zenon_L181_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.26 apply (zenon_L182_); trivial. % 10.04/10.26 apply (zenon_L187_); trivial. % 10.04/10.26 (* end of lemma zenon_L596_ *) % 10.04/10.26 assert (zenon_L597_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.04/10.26 do 0 intro. intros zenon_H18e zenon_Hf8 zenon_He7 zenon_Hbb zenon_He8 zenon_Hec zenon_He3 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_Hc1 zenon_H12c zenon_H11b zenon_H128 zenon_H1d zenon_H11d zenon_H8d zenon_H7a zenon_H7d zenon_H8c zenon_Hc8 zenon_H114 zenon_Hc0 zenon_H27 zenon_H44 zenon_H112 zenon_Hb8 zenon_Hda zenon_Haf zenon_H6f zenon_H3b zenon_Hb0 zenon_H97 zenon_H4c zenon_H95 zenon_H68 zenon_H35 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hae zenon_H53 zenon_H28 zenon_Hdd zenon_H25 zenon_H18d. % 10.04/10.26 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.26 apply (zenon_L596_); trivial. % 10.04/10.26 apply (zenon_L170_); trivial. % 10.04/10.26 apply (zenon_L183_); trivial. % 10.04/10.26 (* end of lemma zenon_L597_ *) % 10.04/10.26 assert (zenon_L598_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.04/10.26 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H18d zenon_H25 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_Hb1 zenon_Hab zenon_H5e zenon_H35 zenon_H68 zenon_H95 zenon_H4c zenon_H97 zenon_Hb0 zenon_H3b zenon_H6f zenon_Haf zenon_Hda zenon_Hb8 zenon_H112 zenon_H44 zenon_H27 zenon_Hc0 zenon_H114 zenon_H8c zenon_H7d zenon_H7a zenon_H8d zenon_H11d zenon_H1d zenon_H128 zenon_H11b zenon_H12c zenon_Hc1 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_He3 zenon_Hec zenon_He8 zenon_Hbb zenon_He7 zenon_Hf8 zenon_H18e. % 10.04/10.26 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.26 apply (zenon_L597_); trivial. % 10.04/10.26 apply (zenon_L164_); trivial. % 10.04/10.26 (* end of lemma zenon_L598_ *) % 10.04/10.26 assert (zenon_L599_ : (((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) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.04/10.26 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H35 zenon_H15a zenon_Hd0 zenon_Hce zenon_He4 zenon_H44. % 10.04/10.26 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.26 exact (zenon_H27 zenon_H32). % 10.04/10.26 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.26 apply (zenon_L238_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.26 apply (zenon_L44_); trivial. % 10.04/10.26 apply (zenon_L99_); trivial. % 10.04/10.26 (* end of lemma zenon_L599_ *) % 10.04/10.26 assert (zenon_L600_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.04/10.26 do 0 intro. intros zenon_H145 zenon_H44 zenon_H6a zenon_He8 zenon_Hed zenon_H4c zenon_H91 zenon_H3b zenon_H35 zenon_H103 zenon_H5e zenon_H9a. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.04/10.26 apply (zenon_L17_); trivial. % 10.04/10.26 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.04/10.26 exact (zenon_He8 zenon_Heb). % 10.04/10.26 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.04/10.26 apply (zenon_L72_); trivial. % 10.04/10.26 apply (zenon_L192_); trivial. % 10.04/10.26 (* end of lemma zenon_L600_ *) % 10.04/10.26 assert (zenon_L601_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (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) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H25 zenon_H157 zenon_H16f zenon_H16e zenon_Hec zenon_H8c zenon_H168 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_H191 zenon_H192 zenon_H156 zenon_H1b7 zenon_H1cb zenon_H200 zenon_Hb0 zenon_H165 zenon_H17a zenon_H14d zenon_He3 zenon_H150 zenon_H114 zenon_Hce zenon_Hde zenon_H6f zenon_H18d zenon_H7d zenon_H1e2 zenon_Hab zenon_H7e zenon_H1bc zenon_H3c zenon_H1b4 zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_H159 zenon_Hda zenon_H198 zenon_Hd2 zenon_H97 zenon_H7a zenon_Hc6 zenon_Hc5 zenon_H1af zenon_H1f zenon_H1ea zenon_H195 zenon_H1ef zenon_H18e zenon_H108 zenon_H155 zenon_Hf8 zenon_H158 zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H177 zenon_H16b zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H12f zenon_H10b zenon_H132 zenon_H11d zenon_Hae zenon_H128 zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H112 zenon_H67 zenon_H1dd zenon_H1de zenon_Haf zenon_H42 zenon_H53 zenon_H95 zenon_Hc0 zenon_He7 zenon_H181 zenon_H64 zenon_H56 zenon_H44 zenon_H90 zenon_Hd3 zenon_H91 zenon_H9a zenon_H145 zenon_He8 zenon_Hed zenon_H4c zenon_H103 zenon_H5e zenon_H27 zenon_Hdd zenon_H35 zenon_H3b zenon_H18a zenon_H43 zenon_H187 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.27 exact (zenon_H25 zenon_H2a). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.27 apply (zenon_L465_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.27 apply (zenon_L541_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.04/10.27 exact (zenon_H56 zenon_H2c). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.27 exact (zenon_H27 zenon_H32). % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.27 apply (zenon_L600_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.27 apply (zenon_L234_); trivial. % 10.04/10.27 apply (zenon_L99_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.04/10.27 apply (zenon_L70_); trivial. % 10.04/10.27 apply (zenon_L411_); trivial. % 10.04/10.27 (* end of lemma zenon_L601_ *) % 10.04/10.27 assert (zenon_L602_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H4a zenon_H51 zenon_H1cb zenon_H25 zenon_H56 zenon_H132 zenon_H3b zenon_H24. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.27 apply (zenon_L589_); trivial. % 10.04/10.27 apply (zenon_L343_); trivial. % 10.04/10.27 (* end of lemma zenon_L602_ *) % 10.04/10.27 assert (zenon_L603_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (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))))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H4a zenon_H11b zenon_H53 zenon_H68 zenon_H95 zenon_H3b zenon_H7a zenon_H84 zenon_H97. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.27 apply (zenon_L170_); trivial. % 10.04/10.27 apply (zenon_L85_); trivial. % 10.04/10.27 (* end of lemma zenon_L603_ *) % 10.04/10.27 assert (zenon_L604_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H174 zenon_H11b zenon_H191 zenon_He8 zenon_H184 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H7a zenon_H7d zenon_H151 zenon_H84 zenon_Hb1 zenon_H25 zenon_H132 zenon_H3b zenon_H24. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.27 apply (zenon_L589_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.27 apply (zenon_L190_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.27 exact (zenon_H25 zenon_H2a). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.27 apply (zenon_L536_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.27 apply (zenon_L43_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.27 exact (zenon_H56 zenon_H2c). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.27 apply (zenon_L194_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.27 apply (zenon_L546_); trivial. % 10.04/10.27 apply (zenon_L62_); trivial. % 10.04/10.27 apply (zenon_L254_); trivial. % 10.04/10.27 apply (zenon_L161_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.27 exact (zenon_H25 zenon_H2a). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.27 apply (zenon_L536_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.27 apply (zenon_L541_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.27 exact (zenon_H56 zenon_H2c). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.27 apply (zenon_L599_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.27 apply (zenon_L546_); trivial. % 10.04/10.27 apply (zenon_L62_); trivial. % 10.04/10.27 apply (zenon_L601_); trivial. % 10.04/10.27 apply (zenon_L161_); trivial. % 10.04/10.27 apply (zenon_L5_); trivial. % 10.04/10.27 apply (zenon_L559_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.27 apply (zenon_L560_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.27 apply (zenon_L543_); trivial. % 10.04/10.27 apply (zenon_L562_); trivial. % 10.04/10.27 apply (zenon_L590_); trivial. % 10.04/10.27 apply (zenon_L602_); trivial. % 10.04/10.27 apply (zenon_L603_); trivial. % 10.04/10.27 (* end of lemma zenon_L604_ *) % 10.04/10.27 assert (zenon_L605_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> False). % 10.04/10.27 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H18e zenon_Hf8 zenon_He7 zenon_Hbb zenon_He8 zenon_Hec zenon_He3 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_Hc1 zenon_H12c zenon_H11b zenon_H128 zenon_H1d zenon_H11d zenon_H7a zenon_H7d zenon_H8c zenon_H114 zenon_Hc0 zenon_H27 zenon_H44 zenon_H112 zenon_Hb8 zenon_Hda zenon_Haf zenon_H6f zenon_H3b zenon_Hb0 zenon_H97 zenon_H4c zenon_H95 zenon_H68 zenon_H35 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hae zenon_H53 zenon_H28 zenon_Hdd zenon_H25 zenon_H18d zenon_H220. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.04/10.27 apply (zenon_L597_); trivial. % 10.04/10.27 exact (zenon_H220 zenon_Hbc). % 10.04/10.27 apply (zenon_L164_); trivial. % 10.04/10.27 (* end of lemma zenon_L605_ *) % 10.04/10.27 assert (zenon_L606_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> False). % 10.04/10.27 do 0 intro. intros zenon_H151 zenon_H84 zenon_He8 zenon_H221 zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H25 zenon_Hb1 zenon_Haf zenon_H9a zenon_H3b. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.04/10.27 apply (zenon_L571_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.04/10.27 exact (zenon_H25 zenon_H2a). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.04/10.27 apply (zenon_L466_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.04/10.27 apply (zenon_L541_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.04/10.27 exact (zenon_H27 zenon_H32). % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.04/10.27 apply (zenon_L545_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.04/10.27 exact (zenon_H221 zenon_Hcf). % 10.04/10.27 apply (zenon_L99_); trivial. % 10.04/10.27 apply (zenon_L161_); trivial. % 10.04/10.27 apply (zenon_L5_); trivial. % 10.04/10.27 (* end of lemma zenon_L606_ *) % 10.04/10.27 assert (zenon_L607_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H174 zenon_H11b zenon_H191 zenon_He8 zenon_H151 zenon_H84 zenon_H221 zenon_H7d zenon_H7a zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H184 zenon_H25 zenon_H132 zenon_H3b zenon_H24. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.04/10.27 apply (zenon_L589_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.27 apply (zenon_L190_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.27 apply (zenon_L606_); trivial. % 10.04/10.27 apply (zenon_L585_); trivial. % 10.04/10.27 exact (zenon_H221 zenon_Hcf). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.04/10.27 apply (zenon_L560_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.04/10.27 apply (zenon_L543_); trivial. % 10.04/10.27 apply (zenon_L574_); trivial. % 10.04/10.27 exact (zenon_H221 zenon_Hcf). % 10.04/10.27 apply (zenon_L590_); trivial. % 10.04/10.27 apply (zenon_L602_); trivial. % 10.04/10.27 apply (zenon_L603_); trivial. % 10.04/10.27 (* end of lemma zenon_L607_ *) % 10.04/10.27 assert (zenon_L608_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H169 zenon_H14a zenon_H118 zenon_H1d zenon_H110 zenon_H24 zenon_H132 zenon_H184 zenon_H205 zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H17c zenon_H103 zenon_H1cb zenon_H108 zenon_H158 zenon_H145 zenon_H155 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1af zenon_H181 zenon_H42 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H159 zenon_H198 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_H168 zenon_H67 zenon_H16f zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H128 zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_H195 zenon_H221 zenon_H151 zenon_H191 zenon_H11b zenon_H174 zenon_H25 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H68 zenon_H95 zenon_H97 zenon_Hb0 zenon_H3b zenon_H6f zenon_Haf zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hc1 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H44 zenon_H27 zenon_Hc8 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.04/10.27 apply (zenon_L592_); trivial. % 10.04/10.27 apply (zenon_L607_); trivial. % 10.04/10.27 apply (zenon_L254_); trivial. % 10.04/10.27 apply (zenon_L594_); trivial. % 10.04/10.27 (* end of lemma zenon_L608_ *) % 10.04/10.27 assert (zenon_L609_ : (~((op (e1) (e0)) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (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 (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.04/10.27 do 0 intro. intros zenon_H223 zenon_H44 zenon_H35 zenon_H4c zenon_H53 zenon_H3b zenon_H95 zenon_H165 zenon_H91 zenon_H151 zenon_H84 zenon_H7d zenon_H43 zenon_H7a zenon_H27 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H42 zenon_H181 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H25 zenon_Hb1 zenon_He8 zenon_H9a zenon_He4 zenon_H5e. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.04/10.27 exact (zenon_H56 zenon_H2c). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.04/10.27 exact (zenon_H223 zenon_H15a). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.04/10.27 apply (zenon_L546_); trivial. % 10.04/10.27 apply (zenon_L62_); trivial. % 10.04/10.27 (* end of lemma zenon_L609_ *) % 10.04/10.27 assert (zenon_L610_ : (((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). % 10.04/10.27 do 0 intro. intros zenon_H42 zenon_H27 zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H3c zenon_H3a zenon_H62 zenon_H35. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.04/10.27 exact (zenon_H27 zenon_H32). % 10.04/10.27 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.04/10.27 apply (zenon_L331_); trivial. % 10.04/10.27 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.04/10.27 apply (zenon_L5_); trivial. % 10.04/10.27 apply (zenon_L260_); trivial. % 10.04/10.27 (* end of lemma zenon_L610_ *) % 10.04/10.27 assert (zenon_L611_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H1f zenon_H27 zenon_H42 zenon_H44 zenon_Hdd zenon_Hc6 zenon_H158 zenon_H152 zenon_H3c zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H212 zenon_Hec zenon_H1de zenon_H69 zenon_H200 zenon_H25 zenon_Hfd zenon_H144 zenon_H4c zenon_H10b zenon_Hb0 zenon_H181 zenon_H12c zenon_H17c zenon_H90 zenon_H1f8 zenon_H6f zenon_H155 zenon_H1e6 zenon_Hda zenon_H28 zenon_H198 zenon_Hf5 zenon_H1f0 zenon_H56 zenon_H64 zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H128 zenon_H35 zenon_H95 zenon_H3a zenon_H1fb zenon_H97 zenon_Hd3 zenon_H187 zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_H177 zenon_He7 zenon_H159 zenon_H1b4 zenon_H1af zenon_H195 zenon_H1ea zenon_H7d zenon_H7a zenon_H7e zenon_H7f zenon_H80. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.28 exact (zenon_H25 zenon_H2a). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.28 exact (zenon_H56 zenon_H2c). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.28 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.13/10.28 exact (zenon_H27 zenon_H32). % 10.13/10.28 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.13/10.28 apply (zenon_L17_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.13/10.28 apply (zenon_L321_); trivial. % 10.13/10.28 apply (zenon_L420_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.28 apply (zenon_L342_); trivial. % 10.13/10.28 apply (zenon_L610_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.28 apply (zenon_L477_); trivial. % 10.13/10.28 apply (zenon_L24_); trivial. % 10.13/10.28 (* end of lemma zenon_L611_ *) % 10.13/10.28 assert (zenon_L612_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (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))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (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)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H200 zenon_H25 zenon_H97 zenon_H28 zenon_H53 zenon_H95 zenon_H42 zenon_H7a zenon_H181 zenon_H1cb zenon_H1b7 zenon_H64 zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H9a zenon_H69 zenon_H44 zenon_H27 zenon_Hdd zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H7e zenon_H198 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H18a zenon_H187 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.28 exact (zenon_H25 zenon_H2a). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.28 apply (zenon_L171_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.28 apply (zenon_L418_); trivial. % 10.13/10.28 apply (zenon_L528_); trivial. % 10.13/10.28 (* end of lemma zenon_L612_ *) % 10.13/10.28 assert (zenon_L613_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (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) (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 (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)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.13/10.28 do 0 intro. intros zenon_Hd2 zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H1b7 zenon_H1cb zenon_H6f zenon_H18a zenon_H86 zenon_H200 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H187 zenon_H64. % 10.13/10.28 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.28 apply (zenon_L527_); trivial. % 10.13/10.28 apply (zenon_L612_); trivial. % 10.13/10.28 (* end of lemma zenon_L613_ *) % 10.13/10.28 assert (zenon_L614_ : (((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 (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H62 zenon_H35. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.28 exact (zenon_H27 zenon_H32). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.28 apply (zenon_L16_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.28 apply (zenon_L5_); trivial. % 10.13/10.28 apply (zenon_L260_); trivial. % 10.13/10.28 (* end of lemma zenon_L614_ *) % 10.13/10.28 assert (zenon_L615_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (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)) -> (~((e1) = (e2))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H64 zenon_H90 zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H69 zenon_Hdd zenon_Hf5 zenon_H1f0 zenon_H100 zenon_H1e6 zenon_H7e zenon_H198 zenon_H56 zenon_H1b4 zenon_H95 zenon_H4c zenon_H53 zenon_H28 zenon_H97 zenon_H42 zenon_H27 zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H35. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.28 exact (zenon_H56 zenon_H2c). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.28 apply (zenon_L526_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.28 apply (zenon_L342_); trivial. % 10.13/10.28 apply (zenon_L614_); trivial. % 10.13/10.28 (* end of lemma zenon_L615_ *) % 10.13/10.28 assert (zenon_L616_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (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) (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.13/10.28 do 0 intro. intros zenon_H200 zenon_H25 zenon_H10b zenon_H3c zenon_Hfd zenon_H144 zenon_H187 zenon_H9a zenon_H1f8 zenon_H6f zenon_H155 zenon_H3a zenon_H1e6 zenon_H1b4 zenon_H159 zenon_H7e zenon_H1f0 zenon_Hf5 zenon_Hda zenon_H28 zenon_H69 zenon_H91 zenon_Hd3 zenon_H90 zenon_H17c zenon_H64 zenon_H56 zenon_Hb0 zenon_H4c zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_Hed. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.28 exact (zenon_H25 zenon_H2a). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.28 apply (zenon_L345_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.28 apply (zenon_L491_); trivial. % 10.13/10.28 apply (zenon_L359_); trivial. % 10.13/10.28 (* end of lemma zenon_L616_ *) % 10.13/10.28 assert (zenon_L617_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((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) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.13/10.28 do 0 intro. intros zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1f8 zenon_H155 zenon_H108 zenon_H1cb zenon_H25 zenon_H64 zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H4c zenon_H53 zenon_H28 zenon_H42 zenon_H198 zenon_H9a zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H35 zenon_H69 zenon_H44 zenon_H27 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4 zenon_H56 zenon_H18d zenon_He3 zenon_Hd2 zenon_Hce zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_H156 zenon_Hb0 zenon_Hb1 zenon_H5e zenon_H187 zenon_Hda zenon_H1af zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7a zenon_H8d zenon_H6f zenon_H86 zenon_H18a zenon_H200. % 10.13/10.28 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.28 exact (zenon_H25 zenon_H2a). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.28 apply (zenon_L615_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.28 apply (zenon_L489_); trivial. % 10.13/10.28 apply (zenon_L531_); trivial. % 10.13/10.28 apply (zenon_L616_); trivial. % 10.13/10.28 (* end of lemma zenon_L617_ *) % 10.13/10.28 assert (zenon_L618_ : (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((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) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H28 zenon_H51 zenon_H25 zenon_H3a zenon_H212. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.28 apply (zenon_L494_); trivial. % 10.13/10.28 apply (zenon_L468_); trivial. % 10.13/10.28 (* end of lemma zenon_L618_ *) % 10.13/10.28 assert (zenon_L619_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H212 zenon_H3a zenon_H25 zenon_H51 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.28 apply (zenon_L618_); trivial. % 10.13/10.28 apply (zenon_L343_); trivial. % 10.13/10.28 (* end of lemma zenon_L619_ *) % 10.13/10.28 assert (zenon_L620_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (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)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.28 do 0 intro. intros zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hce zenon_H1af zenon_Hd2 zenon_Hc0 zenon_He7 zenon_H181 zenon_H187 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H159 zenon_H6f zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H10b zenon_H18a zenon_H1e2 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H212 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H42 zenon_H28 zenon_H53 zenon_H4c zenon_H95 zenon_H97 zenon_H3a zenon_H3c zenon_H64 zenon_H25 zenon_Hbc. % 10.13/10.28 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.28 exact (zenon_H25 zenon_H2a). % 10.13/10.28 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.28 apply (zenon_L615_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.28 apply (zenon_L619_); trivial. % 10.13/10.28 apply (zenon_L24_); trivial. % 10.13/10.28 apply (zenon_L266_); trivial. % 10.13/10.28 apply (zenon_L267_); trivial. % 10.13/10.28 (* end of lemma zenon_L620_ *) % 10.13/10.28 assert (zenon_L621_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (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) (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 (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (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 (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (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 (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 (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((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 (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)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (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)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.28 do 0 intro. intros zenon_H212 zenon_Hec zenon_H1dd zenon_H1de zenon_H128 zenon_H8c zenon_H1e2 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H177 zenon_H1fb zenon_H173 zenon_H1b7 zenon_H58 zenon_H16b zenon_H14d zenon_H157 zenon_H181 zenon_He7 zenon_Hc0 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H145 zenon_H158 zenon_H103 zenon_H132 zenon_H16e zenon_H165 zenon_H17a zenon_H18e zenon_H200 zenon_H18a zenon_H86 zenon_H6f zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H1af zenon_Hda zenon_H187 zenon_H5e zenon_Hb1 zenon_Hb0 zenon_H156 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_Hce zenon_Hd2 zenon_He3 zenon_H18d zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H42 zenon_H28 zenon_H53 zenon_H4c zenon_H95 zenon_H97 zenon_H3a zenon_H3c zenon_H64 zenon_H25 zenon_H1cb zenon_H108 zenon_H155 zenon_H1f8 zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.28 apply (zenon_L617_); trivial. % 10.13/10.28 apply (zenon_L620_); trivial. % 10.13/10.28 (* end of lemma zenon_L621_ *) % 10.13/10.28 assert (zenon_L622_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((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 (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (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))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((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))))) -> False). % 10.13/10.28 do 0 intro. intros zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1f8 zenon_H155 zenon_H108 zenon_H18d zenon_He3 zenon_Hce zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_H156 zenon_Hb0 zenon_H5e zenon_Hda zenon_H1af zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H18e zenon_H17a zenon_H165 zenon_H16e zenon_H132 zenon_H103 zenon_H158 zenon_H145 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hc0 zenon_He7 zenon_H157 zenon_H14d zenon_H16b zenon_H58 zenon_H173 zenon_H1fb zenon_H177 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e2 zenon_H8c zenon_H128 zenon_H1dd zenon_Hec zenon_H212 zenon_H64 zenon_H187 zenon_H3c zenon_Hc5 zenon_H198 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H7e zenon_Hf5 zenon_H35 zenon_H44 zenon_H27 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4 zenon_H56 zenon_H200 zenon_H18a zenon_H6f zenon_H1cb zenon_H1b7 zenon_H97 zenon_H7a zenon_H95 zenon_H28 zenon_H181 zenon_H42 zenon_H25 zenon_Hd2 zenon_H53 zenon_H69 zenon_H4c zenon_H100 zenon_H86 zenon_H84 zenon_H1de. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.28 apply (zenon_L523_); trivial. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.28 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.28 apply (zenon_L613_); trivial. % 10.13/10.28 apply (zenon_L621_); trivial. % 10.13/10.28 apply (zenon_L235_); trivial. % 10.13/10.28 (* end of lemma zenon_L622_ *) % 10.13/10.28 assert (zenon_L623_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((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 (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)) = (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) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H1de zenon_H69 zenon_Hc1 zenon_Hed zenon_H173 zenon_H103 zenon_Hec zenon_H1b7 zenon_Hdd zenon_Hce zenon_H58 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1e2 zenon_H18a zenon_H112 zenon_Hab zenon_H67 zenon_H1dd zenon_He3 zenon_H168 zenon_Hae zenon_H191 zenon_H11d zenon_H192 zenon_Hd2 zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H187 zenon_H108 zenon_H200 zenon_H1cb zenon_H6f zenon_H56 zenon_H1b4 zenon_H3c zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_H53 zenon_H18d zenon_H7a zenon_H7d zenon_H8c zenon_H14d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hc0 zenon_H42 zenon_H4c zenon_Hf5 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H1f zenon_H159 zenon_H1ea zenon_H195 zenon_H1ef zenon_H97 zenon_H64 zenon_H1b1 zenon_H16b zenon_H114 zenon_H158 zenon_H152 zenon_Hc5 zenon_Hde zenon_He7 zenon_H150 zenon_Hc6 zenon_H156 zenon_H4a zenon_H132 zenon_H145 zenon_H12f zenon_H204 zenon_H86. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.13/10.29 apply (zenon_L18_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.13/10.29 exact (zenon_Hc1 zenon_Hc4). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.13/10.29 apply (zenon_L282_); trivial. % 10.13/10.29 apply (zenon_L379_); trivial. % 10.13/10.29 (* end of lemma zenon_L623_ *) % 10.13/10.29 assert (zenon_L624_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H43 zenon_H27 zenon_H3a zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.29 apply (zenon_L466_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.29 apply (zenon_L536_); trivial. % 10.13/10.29 apply (zenon_L623_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.29 apply (zenon_L532_); trivial. % 10.13/10.29 apply (zenon_L235_); trivial. % 10.13/10.29 (* end of lemma zenon_L624_ *) % 10.13/10.29 assert (zenon_L625_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((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))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H1af zenon_H28 zenon_Hb0 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_He3 zenon_Hda zenon_H56 zenon_Hd2 zenon_Hce zenon_H198 zenon_H35 zenon_H1b1 zenon_Hbb zenon_H95 zenon_H205 zenon_H12c zenon_H192 zenon_H1b4 zenon_H156 zenon_H53 zenon_H69 zenon_H4c zenon_H100 zenon_H86 zenon_H84 zenon_H1de. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.29 apply (zenon_L523_); trivial. % 10.13/10.29 apply (zenon_L488_); trivial. % 10.13/10.29 (* end of lemma zenon_L625_ *) % 10.13/10.29 assert (zenon_L626_ : (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> False). % 10.13/10.29 do 0 intro. intros zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H51 zenon_H84. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.29 apply (zenon_L466_); trivial. % 10.13/10.29 apply (zenon_L625_); trivial. % 10.13/10.29 apply (zenon_L343_); trivial. % 10.13/10.29 (* end of lemma zenon_L626_ *) % 10.13/10.29 assert (zenon_L627_ : (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H212. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.29 apply (zenon_L100_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.29 exact (zenon_H192 zenon_H1d). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.29 apply (zenon_L466_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.29 apply (zenon_L611_); trivial. % 10.13/10.29 apply (zenon_L622_); trivial. % 10.13/10.29 apply (zenon_L623_); trivial. % 10.13/10.29 apply (zenon_L354_); trivial. % 10.13/10.29 apply (zenon_L321_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.29 apply (zenon_L621_); trivial. % 10.13/10.29 apply (zenon_L321_); trivial. % 10.13/10.29 apply (zenon_L468_); trivial. % 10.13/10.29 apply (zenon_L624_); trivial. % 10.13/10.29 apply (zenon_L619_); trivial. % 10.13/10.29 apply (zenon_L100_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.29 apply (zenon_L466_); trivial. % 10.13/10.29 apply (zenon_L622_); trivial. % 10.13/10.29 apply (zenon_L535_); trivial. % 10.13/10.29 apply (zenon_L626_); trivial. % 10.13/10.29 apply (zenon_L100_); trivial. % 10.13/10.29 (* end of lemma zenon_L627_ *) % 10.13/10.29 assert (zenon_L628_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H223 zenon_H43 zenon_H181 zenon_Hb1 zenon_H44 zenon_Hb8 zenon_Hb0 zenon_He4 zenon_H5e. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.29 exact (zenon_H56 zenon_H2c). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.29 exact (zenon_H223 zenon_H15a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.29 apply (zenon_L555_); trivial. % 10.13/10.29 apply (zenon_L62_); trivial. % 10.13/10.29 (* end of lemma zenon_L628_ *) % 10.13/10.29 assert (zenon_L629_ : (((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)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H177 zenon_H35 zenon_Hf0 zenon_Hb8 zenon_H114 zenon_H10b zenon_H3b zenon_H7f. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.13/10.29 apply (zenon_L211_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.13/10.29 apply (zenon_L398_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.13/10.29 apply (zenon_L104_); trivial. % 10.13/10.29 exact (zenon_H7f zenon_H85). % 10.13/10.29 (* end of lemma zenon_L629_ *) % 10.13/10.29 assert (zenon_L630_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H223 zenon_H43 zenon_H181 zenon_Hb1 zenon_H44 zenon_H5e zenon_Hb0 zenon_H177 zenon_H35 zenon_Hb8 zenon_H114 zenon_H10b zenon_H3b zenon_H7f. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.29 exact (zenon_H56 zenon_H2c). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.29 exact (zenon_H223 zenon_H15a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.29 apply (zenon_L555_); trivial. % 10.13/10.29 apply (zenon_L629_); trivial. % 10.13/10.29 (* end of lemma zenon_L630_ *) % 10.13/10.29 assert (zenon_L631_ : (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> False). % 10.13/10.29 do 0 intro. intros zenon_H223 zenon_He8 zenon_Hb1 zenon_H25 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H27 zenon_H7a zenon_H43 zenon_H7d zenon_H9a zenon_H100 zenon_H84 zenon_H151 zenon_H3b. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.29 apply (zenon_L543_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.29 apply (zenon_L630_); trivial. % 10.13/10.29 apply (zenon_L359_); trivial. % 10.13/10.29 (* end of lemma zenon_L631_ *) % 10.13/10.29 assert (zenon_L632_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H174 zenon_H11b zenon_H223 zenon_Hb1 zenon_H84 zenon_H151 zenon_H7d zenon_H7a zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H212 zenon_H184 zenon_H191 zenon_H25 zenon_H132 zenon_H3b zenon_H24. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.29 apply (zenon_L589_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.29 apply (zenon_L190_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.29 exact (zenon_H25 zenon_H2a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.29 apply (zenon_L536_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.29 apply (zenon_L43_); trivial. % 10.13/10.29 apply (zenon_L609_); trivial. % 10.13/10.29 apply (zenon_L254_); trivial. % 10.13/10.29 apply (zenon_L161_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.29 exact (zenon_H25 zenon_H2a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.29 apply (zenon_L627_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.29 apply (zenon_L541_); trivial. % 10.13/10.29 apply (zenon_L609_); trivial. % 10.13/10.29 apply (zenon_L161_); trivial. % 10.13/10.29 apply (zenon_L5_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.29 exact (zenon_H25 zenon_H2a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.29 exact (zenon_H56 zenon_H2c). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.29 exact (zenon_H223 zenon_H15a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.29 apply (zenon_L555_); trivial. % 10.13/10.29 apply (zenon_L556_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.29 apply (zenon_L557_); trivial. % 10.13/10.29 apply (zenon_L628_); trivial. % 10.13/10.29 apply (zenon_L164_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.29 apply (zenon_L560_); trivial. % 10.13/10.29 apply (zenon_L631_); trivial. % 10.13/10.29 apply (zenon_L590_); trivial. % 10.13/10.29 exact (zenon_H223 zenon_H15a). % 10.13/10.29 apply (zenon_L602_); trivial. % 10.13/10.29 apply (zenon_L603_); trivial. % 10.13/10.29 (* end of lemma zenon_L632_ *) % 10.13/10.29 assert (zenon_L633_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (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 (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H169 zenon_H14a zenon_H118 zenon_H1d zenon_H110 zenon_H24 zenon_H132 zenon_H191 zenon_H184 zenon_H212 zenon_H205 zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H17c zenon_H103 zenon_H1cb zenon_H108 zenon_H158 zenon_H145 zenon_H155 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1af zenon_H181 zenon_H42 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H159 zenon_H198 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_H168 zenon_H67 zenon_H16f zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H128 zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_H195 zenon_H151 zenon_H223 zenon_H11b zenon_H174 zenon_H25 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H68 zenon_H95 zenon_H97 zenon_Hb0 zenon_H3b zenon_H6f zenon_Haf zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hc1 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H44 zenon_H27 zenon_Hc8 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.29 apply (zenon_L592_); trivial. % 10.13/10.29 apply (zenon_L632_); trivial. % 10.13/10.29 apply (zenon_L77_); trivial. % 10.13/10.29 apply (zenon_L594_); trivial. % 10.13/10.29 (* end of lemma zenon_L633_ *) % 10.13/10.29 assert (zenon_L634_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (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 (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (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 (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H18e zenon_Hf8 zenon_He7 zenon_Hbb zenon_He8 zenon_Hec zenon_He3 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_Hc1 zenon_H12c zenon_H11b zenon_H128 zenon_H1d zenon_H11d zenon_H8d zenon_H7a zenon_H7d zenon_H8c zenon_Hc8 zenon_H114 zenon_Hc0 zenon_H27 zenon_H44 zenon_H112 zenon_Hb8 zenon_Hda zenon_Haf zenon_H6f zenon_H3b zenon_Hb0 zenon_H97 zenon_H4c zenon_H95 zenon_H68 zenon_H35 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hae zenon_H53 zenon_H28 zenon_Hdd zenon_H25 zenon_H223 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H18a zenon_H1e6 zenon_Hde zenon_H67 zenon_Hc6 zenon_H4a zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H18d zenon_H1b7 zenon_H58 zenon_H198 zenon_H1b1 zenon_H187 zenon_H42 zenon_H181 zenon_Hd2 zenon_H1af zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H17c zenon_H90 zenon_H1ea zenon_H17a zenon_H205 zenon_H212 zenon_H184 zenon_H191 zenon_H24. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.29 apply (zenon_L596_); trivial. % 10.13/10.29 apply (zenon_L632_); trivial. % 10.13/10.29 apply (zenon_L183_); trivial. % 10.13/10.29 (* end of lemma zenon_L634_ *) % 10.13/10.29 assert (zenon_L635_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H169 zenon_H14a zenon_H118 zenon_H110 zenon_H8d zenon_H174 zenon_H11b zenon_H223 zenon_Hb1 zenon_H151 zenon_H7d zenon_H7a zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H212 zenon_H184 zenon_H191 zenon_H25 zenon_H132 zenon_H3b zenon_H24. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.29 exact (zenon_H25 zenon_H2a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.29 apply (zenon_L591_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.29 apply (zenon_L633_); trivial. % 10.13/10.29 apply (zenon_L176_); trivial. % 10.13/10.29 apply (zenon_L5_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.29 apply (zenon_L634_); trivial. % 10.13/10.29 apply (zenon_L164_); trivial. % 10.13/10.29 apply (zenon_L88_); trivial. % 10.13/10.29 apply (zenon_L149_); trivial. % 10.13/10.29 exact (zenon_H223 zenon_H15a). % 10.13/10.29 apply (zenon_L85_); trivial. % 10.13/10.29 apply (zenon_L69_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.29 apply (zenon_L5_); trivial. % 10.13/10.29 apply (zenon_L632_); trivial. % 10.13/10.29 (* end of lemma zenon_L635_ *) % 10.13/10.29 assert (zenon_L636_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H223 zenon_H43 zenon_H181 zenon_Hb1 zenon_H1e2 zenon_Hc7 zenon_H17c zenon_H5e zenon_Hb0 zenon_H3b zenon_H6f zenon_Haf zenon_Hae zenon_Hdd zenon_H27 zenon_H44 zenon_H69 zenon_H221 zenon_H35. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.29 exact (zenon_H56 zenon_H2c). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.29 exact (zenon_H223 zenon_H15a). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.13/10.29 apply (zenon_L17_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.13/10.29 exact (zenon_Haf zenon_Hb4). % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.13/10.29 apply (zenon_L19_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.13/10.29 apply (zenon_L165_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 10.13/10.29 exact (zenon_H221 zenon_Hcf). % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 10.13/10.29 apply (zenon_L57_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 10.13/10.29 exact (zenon_Hc7 zenon_H3a). % 10.13/10.29 apply (zenon_L162_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.13/10.29 exact (zenon_Hb1 zenon_Hb7). % 10.13/10.29 apply (zenon_L548_); trivial. % 10.13/10.29 apply (zenon_L572_); trivial. % 10.13/10.29 (* end of lemma zenon_L636_ *) % 10.13/10.29 assert (zenon_L637_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.29 do 0 intro. intros zenon_H18a zenon_H43 zenon_H187 zenon_H1d zenon_H11d zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 10.13/10.29 apply (zenon_L276_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 10.13/10.29 apply (zenon_L88_); trivial. % 10.13/10.29 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 10.13/10.29 apply (zenon_L162_); trivial. % 10.13/10.29 apply (zenon_L252_); trivial. % 10.13/10.29 (* end of lemma zenon_L637_ *) % 10.13/10.29 assert (zenon_L638_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 10.13/10.29 do 0 intro. intros zenon_Hd2 zenon_H187 zenon_H43 zenon_H11d zenon_H1d zenon_H17c zenon_H86 zenon_H84 zenon_H18a zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.13/10.29 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_L43_); trivial. % 10.13/10.30 apply (zenon_L637_); trivial. % 10.13/10.30 (* end of lemma zenon_L638_ *) % 10.13/10.30 assert (zenon_L639_ : (((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))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1de zenon_H53 zenon_H69 zenon_Hc1 zenon_H1e6 zenon_Hed zenon_H84 zenon_H86. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.13/10.30 apply (zenon_L18_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.13/10.30 exact (zenon_Hc1 zenon_Hc4). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.13/10.30 apply (zenon_L282_); trivial. % 10.13/10.30 apply (zenon_L252_); trivial. % 10.13/10.30 (* end of lemma zenon_L639_ *) % 10.13/10.30 assert (zenon_L640_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H18e zenon_H25 zenon_H86 zenon_H1e6 zenon_H1de zenon_H84 zenon_H205 zenon_Hc8 zenon_H12c zenon_Hc0 zenon_Hbb zenon_H44 zenon_He8 zenon_H53 zenon_He7 zenon_Hc1 zenon_H95 zenon_Hb8 zenon_Hec zenon_Hed. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_L639_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L557_); trivial. % 10.13/10.30 apply (zenon_L61_); trivial. % 10.13/10.30 (* end of lemma zenon_L640_ *) % 10.13/10.30 assert (zenon_L641_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (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))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (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 (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((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 (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H1b4 zenon_H35 zenon_H114 zenon_H10b zenon_H3b zenon_H177 zenon_H5e zenon_H44 zenon_Hb8 zenon_Hb1 zenon_H181 zenon_H43 zenon_Hb0 zenon_H223 zenon_H56 zenon_H18e zenon_He7 zenon_Hbb zenon_He8 zenon_Hec zenon_Hc0 zenon_H95 zenon_H205 zenon_H12c zenon_H53 zenon_Hc1 zenon_H1e6 zenon_H86 zenon_H84 zenon_H1de zenon_H25 zenon_Hf8. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_L630_); trivial. % 10.13/10.30 apply (zenon_L640_); trivial. % 10.13/10.30 apply (zenon_L164_); trivial. % 10.13/10.30 (* end of lemma zenon_L641_ *) % 10.13/10.30 assert (zenon_L642_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((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)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H174 zenon_H11b zenon_H184 zenon_H223 zenon_H216 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H7a zenon_H7d zenon_H221 zenon_H84 zenon_H151 zenon_H191 zenon_H25 zenon_H132 zenon_H3b zenon_H24. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_L589_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_L190_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_L606_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_L636_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L557_); trivial. % 10.13/10.30 apply (zenon_L628_); trivial. % 10.13/10.30 apply (zenon_L164_); trivial. % 10.13/10.30 apply (zenon_L500_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_L560_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_L631_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_L636_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L638_); trivial. % 10.13/10.30 apply (zenon_L570_); trivial. % 10.13/10.30 apply (zenon_L637_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L641_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 exact (zenon_H223 zenon_H15a). % 10.13/10.30 apply (zenon_L602_); trivial. % 10.13/10.30 apply (zenon_L603_); trivial. % 10.13/10.30 (* end of lemma zenon_L642_ *) % 10.13/10.30 assert (zenon_L643_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((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))) -> (~((e0) = (e1))) -> (~((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)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H221 zenon_Hda zenon_Hbd zenon_Hb0 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H3b zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_Haf zenon_Hde zenon_H6f zenon_H69 zenon_Hae zenon_H95. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.13/10.30 exact (zenon_H27 zenon_H32). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.13/10.30 apply (zenon_L17_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_L83_); trivial. % 10.13/10.30 (* end of lemma zenon_L643_ *) % 10.13/10.30 assert (zenon_L644_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((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 (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1ea zenon_H1d zenon_Hf8 zenon_H44 zenon_H68 zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_H173 zenon_H16e zenon_H64 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_L593_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 (* end of lemma zenon_L644_ *) % 10.13/10.30 assert (zenon_L645_ : ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (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) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (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))))) -> (((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1d zenon_H169 zenon_H118 zenon_H110 zenon_H14a zenon_H24 zenon_H132 zenon_H191 zenon_H151 zenon_H221 zenon_H195 zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_H128 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_H16f zenon_H67 zenon_H168 zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H198 zenon_H159 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H42 zenon_H181 zenon_H1af zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_H155 zenon_H145 zenon_H158 zenon_H108 zenon_H1cb zenon_H103 zenon_H17c zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_H205 zenon_H216 zenon_H223 zenon_H184 zenon_H11b zenon_H174 zenon_H25 zenon_Hdd zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H68 zenon_H95 zenon_H97 zenon_Hb0 zenon_H3b zenon_H6f zenon_Haf zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hc1 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H44 zenon_H27 zenon_Hc8 zenon_Hf8 zenon_Hec zenon_He8 zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L592_); trivial. % 10.13/10.30 apply (zenon_L642_); trivial. % 10.13/10.30 apply (zenon_L77_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_L643_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L98_); trivial. % 10.13/10.30 apply (zenon_L644_); trivial. % 10.13/10.30 apply (zenon_L161_); trivial. % 10.13/10.30 apply (zenon_L60_); trivial. % 10.13/10.30 (* end of lemma zenon_L645_ *) % 10.13/10.30 assert (zenon_L646_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((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) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H18e zenon_Hf8 zenon_He7 zenon_Hbb zenon_He8 zenon_Hec zenon_He3 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_Hc1 zenon_H12c zenon_H11b zenon_H128 zenon_H1d zenon_H11d zenon_H8d zenon_H7a zenon_H7d zenon_H8c zenon_Hc8 zenon_H114 zenon_Hc0 zenon_H27 zenon_H44 zenon_H112 zenon_Hb8 zenon_Hda zenon_Haf zenon_H6f zenon_H3b zenon_Hb0 zenon_H97 zenon_H4c zenon_H95 zenon_H68 zenon_H35 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hae zenon_H53 zenon_H28 zenon_Hdd zenon_H25 zenon_H184 zenon_H223 zenon_H216 zenon_H205 zenon_H17a zenon_H1ea zenon_H90 zenon_H17c zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_H1af zenon_Hd2 zenon_H181 zenon_H42 zenon_H187 zenon_H1b1 zenon_H198 zenon_H58 zenon_H1b7 zenon_H18d zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H4a zenon_Hc6 zenon_H67 zenon_Hde zenon_H1e6 zenon_H18a zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H221 zenon_H191 zenon_H24. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L596_); trivial. % 10.13/10.30 apply (zenon_L642_); trivial. % 10.13/10.30 apply (zenon_L183_); trivial. % 10.13/10.30 (* end of lemma zenon_L646_ *) % 10.13/10.30 assert (zenon_L647_ : ((~((op (e1) (e1)) = (e0)))\/(~((op (e1) (e0)) = (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/(~((op (e3) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (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 (e1) (e0)) = (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 (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/(~((op (e2) (e0)) = (e2)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H224 zenon_H212 zenon_H216 zenon_H225 zenon_H25 zenon_H1af zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H17a zenon_H18d zenon_Hdd zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_H4c zenon_Hab zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Hde zenon_Hd3 zenon_Hc5 zenon_Hc6 zenon_Hce zenon_Hd2 zenon_Hbb zenon_Hc0 zenon_Hda zenon_H44 zenon_Hf8 zenon_Hec zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H108 zenon_H103 zenon_Hfd zenon_H42 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H11d zenon_H128 zenon_H11b zenon_H12c zenon_H1ea zenon_H67 zenon_H24 zenon_H3b zenon_H132 zenon_H64 zenon_H5e zenon_H35 zenon_H1f zenon_H4a zenon_H191 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H1b1 zenon_H198 zenon_H58 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H226. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_He8 | zenon_intro zenon_H223 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H221 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_L595_); trivial. % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L598_); trivial. % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L604_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L595_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L605_); trivial. % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L604_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_L608_); trivial. % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L598_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L607_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L608_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L605_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L607_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H221 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.30 apply (zenon_L635_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L633_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L634_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L164_); trivial. % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 exact (zenon_H223 zenon_H15a). % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L632_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_L645_); trivial. % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_L646_); trivial. % 10.13/10.30 apply (zenon_L164_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 exact (zenon_H223 zenon_H15a). % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L642_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.30 apply (zenon_L591_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L645_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L646_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L164_); trivial. % 10.13/10.30 exact (zenon_H221 zenon_Hcf). % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 exact (zenon_H223 zenon_H15a). % 10.13/10.30 apply (zenon_L85_); trivial. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L5_); trivial. % 10.13/10.30 apply (zenon_L642_); trivial. % 10.13/10.30 (* end of lemma zenon_L647_ *) % 10.13/10.30 assert (zenon_L648_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_He7 zenon_He8 zenon_H44 zenon_Hc0 zenon_H34 zenon_H95 zenon_Hb8 zenon_H53. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.13/10.30 apply (zenon_L16_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.13/10.30 exact (zenon_He8 zenon_Heb). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.13/10.30 apply (zenon_L57_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.13/10.30 apply (zenon_L184_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.13/10.30 apply (zenon_L199_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.13/10.30 apply (zenon_L40_); trivial. % 10.13/10.30 apply (zenon_L112_); trivial. % 10.13/10.30 (* end of lemma zenon_L648_ *) % 10.13/10.30 assert (zenon_L649_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H42 zenon_H27 zenon_Hc0 zenon_He8 zenon_He7 zenon_H220 zenon_Hae zenon_H69 zenon_Haf zenon_H6f zenon_Hb0 zenon_Hb8 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_Hda zenon_H57 zenon_H95. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.30 exact (zenon_H27 zenon_H32). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.30 apply (zenon_L648_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.30 exact (zenon_H28 zenon_H31). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.30 apply (zenon_L18_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L179_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L54_); trivial. % 10.13/10.30 (* end of lemma zenon_L649_ *) % 10.13/10.30 assert (zenon_L650_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (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)) = (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (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 (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H18e zenon_H25 zenon_H57 zenon_H97 zenon_Hb1 zenon_Hb0 zenon_H6f zenon_Haf zenon_Hae zenon_H220 zenon_H27 zenon_H42 zenon_H8d zenon_Hab zenon_H1d zenon_H11d zenon_H128 zenon_H7f zenon_H11b zenon_H68 zenon_H8c zenon_Hbd zenon_H12c zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He3 zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_H44 zenon_Hb8 zenon_Hbb zenon_He7 zenon_Hf8. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_L649_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L98_); trivial. % 10.13/10.30 apply (zenon_L187_); trivial. % 10.13/10.30 (* end of lemma zenon_L650_ *) % 10.13/10.30 assert (zenon_L651_ : (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (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)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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 (e3) (e0)) = (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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hde zenon_Hf8 zenon_He7 zenon_Hbb zenon_H44 zenon_He8 zenon_H53 zenon_Hc1 zenon_Hec zenon_Hc0 zenon_He3 zenon_H80 zenon_H7d zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177 zenon_H12c zenon_H8c zenon_H68 zenon_H11b zenon_H7f zenon_H128 zenon_H11d zenon_H1d zenon_Hab zenon_H8d zenon_H42 zenon_H27 zenon_H220 zenon_Hae zenon_Haf zenon_H6f zenon_Hb0 zenon_Hb1 zenon_H97 zenon_H57 zenon_H25 zenon_H18e zenon_H95 zenon_Hbd. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.13/10.30 apply (zenon_L16_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.13/10.30 exact (zenon_Haf zenon_Hb4). % 10.13/10.30 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.13/10.30 apply (zenon_L650_); trivial. % 10.13/10.30 apply (zenon_L50_); trivial. % 10.13/10.30 (* end of lemma zenon_L651_ *) % 10.13/10.30 assert (zenon_L652_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H18a zenon_H187 zenon_H184 zenon_Hd2 zenon_H17c zenon_H181 zenon_H17a zenon_H173 zenon_H16e zenon_H64 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H114 zenon_H11d zenon_H1d zenon_H128 zenon_H11b zenon_H12c zenon_H18d zenon_H25 zenon_H42 zenon_H57 zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Haf zenon_H220 zenon_Hda zenon_H68 zenon_H44 zenon_H27 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_Hf8 zenon_Hc0 zenon_Hec zenon_Hc1 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_Hde zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.30 exact (zenon_H27 zenon_H32). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.30 apply (zenon_L16_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.30 exact (zenon_H28 zenon_H31). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.30 apply (zenon_L18_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_L39_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L54_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L43_); trivial. % 10.13/10.30 apply (zenon_L67_); trivial. % 10.13/10.30 apply (zenon_L68_); trivial. % 10.13/10.30 apply (zenon_L77_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L651_); trivial. % 10.13/10.30 apply (zenon_L161_); trivial. % 10.13/10.30 apply (zenon_L60_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L176_); trivial. % 10.13/10.30 (* end of lemma zenon_L652_ *) % 10.13/10.30 assert (zenon_L653_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> ((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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (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 (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hd2 zenon_H184 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hbb zenon_H18d zenon_H17a zenon_H25 zenon_H42 zenon_H57 zenon_H28 zenon_Hae zenon_Hb1 zenon_Hab zenon_H5e zenon_H35 zenon_H68 zenon_H4c zenon_H97 zenon_Hb0 zenon_H6f zenon_Haf zenon_H220 zenon_Hda zenon_H44 zenon_He8 zenon_Hb8 zenon_Hc0 zenon_H53 zenon_H95 zenon_He7 zenon_H27 zenon_H114 zenon_H8c zenon_H7d zenon_H7a zenon_H11d zenon_H1d zenon_H128 zenon_H11b zenon_H12c zenon_Hc1 zenon_He3 zenon_H18e zenon_Hec zenon_Hf8. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.30 exact (zenon_H25 zenon_H2a). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.30 apply (zenon_L649_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.30 apply (zenon_L182_); trivial. % 10.13/10.30 apply (zenon_L56_); trivial. % 10.13/10.30 apply (zenon_L173_); trivial. % 10.13/10.30 apply (zenon_L183_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.30 apply (zenon_L650_); trivial. % 10.13/10.30 apply (zenon_L173_); trivial. % 10.13/10.30 apply (zenon_L60_); trivial. % 10.13/10.30 exact (zenon_H220 zenon_Hbc). % 10.13/10.30 apply (zenon_L164_); trivial. % 10.13/10.30 (* end of lemma zenon_L653_ *) % 10.13/10.30 assert (zenon_L654_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H18a zenon_H187 zenon_H184 zenon_Hd2 zenon_H17c zenon_H181 zenon_H17a zenon_H173 zenon_H16e zenon_H64 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H114 zenon_H11d zenon_H1d zenon_H128 zenon_H11b zenon_H12c zenon_H18d zenon_H25 zenon_H42 zenon_H57 zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_Haf zenon_H220 zenon_Hda zenon_H68 zenon_H44 zenon_H27 zenon_Hc5 zenon_Hc6 zenon_Hf8 zenon_Hc0 zenon_Hec zenon_Hc1 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_Hde zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.30 apply (zenon_L652_); trivial. % 10.13/10.30 apply (zenon_L178_); trivial. % 10.13/10.30 apply (zenon_L653_); trivial. % 10.13/10.30 (* end of lemma zenon_L654_ *) % 10.13/10.30 assert (zenon_L655_ : ((~((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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1ea zenon_H18a zenon_H187 zenon_H184 zenon_Hd2 zenon_H17c zenon_H181 zenon_H17a zenon_H173 zenon_H16e zenon_H64 zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H114 zenon_H11d zenon_H1d zenon_H128 zenon_H11b zenon_H12c zenon_H18d zenon_H25 zenon_H42 zenon_H57 zenon_H28 zenon_H53 zenon_Hae zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H8c zenon_H5e zenon_H4c zenon_Hb1 zenon_Hab zenon_H35 zenon_H95 zenon_H97 zenon_Hb0 zenon_H6f zenon_H220 zenon_Hda zenon_H68 zenon_H44 zenon_H27 zenon_Hc5 zenon_Hc6 zenon_Hf8 zenon_Hc0 zenon_Hec zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_Hde zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H1af. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.30 apply (zenon_L654_); trivial. % 10.13/10.30 apply (zenon_L88_); trivial. % 10.13/10.30 apply (zenon_L149_); trivial. % 10.13/10.30 (* end of lemma zenon_L655_ *) % 10.13/10.30 assert (zenon_L656_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hda zenon_H28 zenon_H6f zenon_He8 zenon_H53 zenon_H145 zenon_H5e zenon_H91 zenon_H1e zenon_Hd3 zenon_H4c zenon_H90 zenon_Hb1 zenon_H17c zenon_H9a zenon_H64 zenon_H56 zenon_H51 zenon_H187 zenon_Hb0 zenon_H220. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.31 exact (zenon_H28 zenon_H31). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.31 apply (zenon_L496_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.31 apply (zenon_L484_); trivial. % 10.13/10.31 exact (zenon_H220 zenon_Hbc). % 10.13/10.31 (* end of lemma zenon_L656_ *) % 10.13/10.31 assert (zenon_L657_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H157 zenon_H3a zenon_H216 zenon_H56 zenon_Hda zenon_H220 zenon_H64 zenon_H187 zenon_Hd3 zenon_H17c zenon_H90 zenon_H4c zenon_Hb1 zenon_Hb0 zenon_H53 zenon_He8 zenon_H6f zenon_H51 zenon_H5e zenon_H9a zenon_H145 zenon_H28. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.31 apply (zenon_L656_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.31 apply (zenon_L12_); trivial. % 10.13/10.31 apply (zenon_L202_); trivial. % 10.13/10.31 apply (zenon_L500_); trivial. % 10.13/10.31 (* end of lemma zenon_L657_ *) % 10.13/10.31 assert (zenon_L658_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((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)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hda zenon_H28 zenon_H1fb zenon_H3a zenon_H44 zenon_H57 zenon_H95 zenon_H128 zenon_H91 zenon_H1e zenon_Hd3 zenon_H5e zenon_H90 zenon_H6f zenon_H51 zenon_He8 zenon_H145 zenon_H53 zenon_H73 zenon_H220. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.31 exact (zenon_H28 zenon_H31). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.31 apply (zenon_L505_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.31 apply (zenon_L20_); trivial. % 10.13/10.31 exact (zenon_H220 zenon_Hbc). % 10.13/10.31 (* end of lemma zenon_L658_ *) % 10.13/10.31 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) (e0)) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((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) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H64 zenon_H56 zenon_H220 zenon_H73 zenon_H53 zenon_H145 zenon_He8 zenon_H51 zenon_H90 zenon_H5e zenon_Hd3 zenon_H91 zenon_H128 zenon_H95 zenon_H57 zenon_H44 zenon_H3a zenon_H1fb zenon_H28 zenon_Hda zenon_H6f zenon_H100 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.31 apply (zenon_L658_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.31 apply (zenon_L228_); trivial. % 10.13/10.31 apply (zenon_L87_); trivial. % 10.13/10.31 (* end of lemma zenon_L659_ *) % 10.13/10.31 assert (zenon_L660_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hbb zenon_H1dd zenon_Hc8 zenon_H18e zenon_He3 zenon_H220 zenon_H57 zenon_H44 zenon_H145 zenon_H7d zenon_H7a zenon_H8d zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_Hb1 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7 zenon_Hd2 zenon_H25 zenon_H18d. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.31 exact (zenon_H25 zenon_H2a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.31 apply (zenon_L479_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.31 apply (zenon_L659_); trivial. % 10.13/10.31 apply (zenon_L56_); trivial. % 10.13/10.31 apply (zenon_L68_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.31 exact (zenon_H25 zenon_H2a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.31 apply (zenon_L472_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.31 apply (zenon_L658_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.31 apply (zenon_L349_); trivial. % 10.13/10.31 apply (zenon_L13_); trivial. % 10.13/10.31 apply (zenon_L512_); trivial. % 10.13/10.31 apply (zenon_L68_); trivial. % 10.13/10.31 (* end of lemma zenon_L660_ *) % 10.13/10.31 assert (zenon_L661_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e3) (e0)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hda zenon_H28 zenon_H53 zenon_H69 zenon_H4c zenon_H76 zenon_H220. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.31 exact (zenon_H28 zenon_H31). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.31 apply (zenon_L18_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.31 apply (zenon_L21_); trivial. % 10.13/10.31 exact (zenon_H220 zenon_Hbc). % 10.13/10.31 (* end of lemma zenon_L661_ *) % 10.13/10.31 assert (zenon_L662_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H28 zenon_He7 zenon_Hbb zenon_H192 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hfd zenon_Hb1 zenon_H1dd zenon_H108 zenon_H10b zenon_H4c zenon_H97 zenon_H51 zenon_H5e zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H56 zenon_Hf8. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.31 apply (zenon_L512_); trivial. % 10.13/10.31 apply (zenon_L160_); trivial. % 10.13/10.31 (* end of lemma zenon_L662_ *) % 10.13/10.31 assert (zenon_L663_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H216 zenon_Hbb zenon_H1dd zenon_H18e zenon_He3 zenon_H220 zenon_H57 zenon_H44 zenon_H145 zenon_H7d zenon_H7a zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H5e zenon_H90 zenon_Hb1 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7 zenon_Hd2 zenon_H25 zenon_H18d zenon_H173 zenon_H16e zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H174 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H132 zenon_H86 zenon_H14a zenon_H151 zenon_H165 zenon_H103 zenon_H168 zenon_H14d. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.31 apply (zenon_L660_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.31 exact (zenon_H25 zenon_H2a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.31 apply (zenon_L123_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.31 apply (zenon_L661_); trivial. % 10.13/10.31 apply (zenon_L340_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.31 apply (zenon_L659_); trivial. % 10.13/10.31 apply (zenon_L662_); trivial. % 10.13/10.31 apply (zenon_L68_); trivial. % 10.13/10.31 apply (zenon_L60_); trivial. % 10.13/10.31 exact (zenon_H220 zenon_Hbc). % 10.13/10.31 apply (zenon_L354_); trivial. % 10.13/10.31 apply (zenon_L500_); trivial. % 10.13/10.31 (* end of lemma zenon_L663_ *) % 10.13/10.31 assert (zenon_L664_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hf8 zenon_Hec zenon_H56 zenon_H223 zenon_H12c zenon_H57 zenon_H181 zenon_Hc8 zenon_Hbd zenon_H114 zenon_H4c zenon_H14d zenon_H8d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_H53 zenon_H5e zenon_H1b4. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.31 exact (zenon_H223 zenon_H15a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.31 apply (zenon_L499_); trivial. % 10.13/10.31 apply (zenon_L340_); trivial. % 10.13/10.31 apply (zenon_L60_); trivial. % 10.13/10.31 (* end of lemma zenon_L664_ *) % 10.13/10.31 assert (zenon_L665_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H216 zenon_H151 zenon_H8d zenon_H223 zenon_H57 zenon_H25 zenon_H212 zenon_He8 zenon_H3a zenon_H51 zenon_H28 zenon_H191 zenon_H192 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H9a zenon_Hb1. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.31 apply (zenon_L498_); trivial. % 10.13/10.31 apply (zenon_L664_); trivial. % 10.13/10.31 apply (zenon_L354_); trivial. % 10.13/10.31 apply (zenon_L500_); trivial. % 10.13/10.31 (* end of lemma zenon_L665_ *) % 10.13/10.31 assert (zenon_L666_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H64 zenon_H73 zenon_H53 zenon_H145 zenon_He8 zenon_H51 zenon_H90 zenon_H5e zenon_Hd3 zenon_H91 zenon_H128 zenon_H95 zenon_H44 zenon_H3a zenon_H1fb zenon_H28 zenon_Hda zenon_H223 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H57 zenon_H4c. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.31 exact (zenon_H223 zenon_H15a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.31 apply (zenon_L165_); trivial. % 10.13/10.31 apply (zenon_L506_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.31 apply (zenon_L228_); trivial. % 10.13/10.31 apply (zenon_L13_); trivial. % 10.13/10.31 (* end of lemma zenon_L666_ *) % 10.13/10.31 assert (zenon_L667_ : (((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 (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_Haf zenon_H78 zenon_H44 zenon_Hf5 zenon_H5e zenon_He4 zenon_H35 zenon_Hed zenon_H4c zenon_H7e. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.13/10.31 apply (zenon_L331_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.13/10.31 exact (zenon_Haf zenon_Hb4). % 10.13/10.31 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.13/10.31 apply (zenon_L57_); trivial. % 10.13/10.31 apply (zenon_L65_); trivial. % 10.13/10.31 (* end of lemma zenon_L667_ *) % 10.13/10.31 assert (zenon_L668_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H191 zenon_H1f zenon_H192 zenon_H44 zenon_Haf zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_Hf8. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_L56_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.13/10.31 apply (zenon_L66_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.13/10.31 exact (zenon_He8 zenon_Heb). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.13/10.31 apply (zenon_L667_); trivial. % 10.13/10.31 apply (zenon_L58_); trivial. % 10.13/10.31 apply (zenon_L160_); trivial. % 10.13/10.31 (* end of lemma zenon_L668_ *) % 10.13/10.31 assert (zenon_L669_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H158 zenon_Hcf zenon_Hc6 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.31 apply (zenon_L129_); trivial. % 10.13/10.31 apply (zenon_L321_); trivial. % 10.13/10.31 (* end of lemma zenon_L669_ *) % 10.13/10.31 assert (zenon_L670_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H157 zenon_H112 zenon_Hc5 zenon_Hc8 zenon_H51 zenon_H3c zenon_Hc6 zenon_Hcf zenon_H158. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.31 apply (zenon_L669_); trivial. % 10.13/10.31 apply (zenon_L79_); trivial. % 10.13/10.31 (* end of lemma zenon_L670_ *) % 10.13/10.31 assert (zenon_L671_ : (((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). % 10.13/10.31 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f zenon_H1d zenon_H5e zenon_H51 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.31 exact (zenon_H56 zenon_H2c). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.31 apply (zenon_L1_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.31 apply (zenon_L12_); trivial. % 10.13/10.31 apply (zenon_L87_); trivial. % 10.13/10.31 (* end of lemma zenon_L671_ *) % 10.13/10.31 assert (zenon_L672_ : (((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). % 10.13/10.31 do 0 intro. intros zenon_H1f8 zenon_H51 zenon_H6f zenon_H1d zenon_H16e zenon_H155 zenon_H3a zenon_Hed zenon_H1e6. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_H101 | zenon_intro zenon_H1f9 ]. % 10.13/10.31 apply (zenon_L348_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1f9); [ zenon_intro zenon_H100 | zenon_intro zenon_H1fa ]. % 10.13/10.31 apply (zenon_L149_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H6e | zenon_intro zenon_H161 ]. % 10.13/10.31 apply (zenon_L223_); trivial. % 10.13/10.31 apply (zenon_L282_); trivial. % 10.13/10.31 (* end of lemma zenon_L672_ *) % 10.13/10.31 assert (zenon_L673_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hf8 zenon_Hbc zenon_H1dd zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_L56_); trivial. % 10.13/10.31 apply (zenon_L267_); trivial. % 10.13/10.31 (* end of lemma zenon_L673_ *) % 10.13/10.31 assert (zenon_L674_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H151 zenon_Hbb zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1dd zenon_Hbc zenon_Hf8. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.31 apply (zenon_L673_); trivial. % 10.13/10.31 apply (zenon_L41_); trivial. % 10.13/10.31 (* end of lemma zenon_L674_ *) % 10.13/10.31 assert (zenon_L675_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (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 (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H150 zenon_H1dd zenon_He3 zenon_He4 zenon_Hbb zenon_H151 zenon_H64 zenon_H7a zenon_H80 zenon_H7d zenon_H51 zenon_H5e zenon_H1d zenon_H1f zenon_H56 zenon_H1f8 zenon_H1e6 zenon_H3a zenon_H155 zenon_H16e zenon_H6f zenon_Hf8. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_L671_); trivial. % 10.13/10.31 apply (zenon_L672_); trivial. % 10.13/10.31 apply (zenon_L674_); trivial. % 10.13/10.31 (* end of lemma zenon_L675_ *) % 10.13/10.31 assert (zenon_L676_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((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 (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1ef zenon_H6f zenon_H3a zenon_H1f8 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H191 zenon_H1f zenon_H44 zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_Hf8 zenon_Hc6 zenon_H56 zenon_H1e6 zenon_H1f0 zenon_H51 zenon_H97 zenon_H1dd zenon_H1ea. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.31 apply (zenon_L668_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.31 apply (zenon_L662_); trivial. % 10.13/10.31 apply (zenon_L670_); trivial. % 10.13/10.31 apply (zenon_L675_); trivial. % 10.13/10.31 (* end of lemma zenon_L676_ *) % 10.13/10.31 assert (zenon_L677_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H216 zenon_H8d zenon_H18d zenon_H7a zenon_H25 zenon_H156 zenon_Hc6 zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H5e zenon_H90 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7 zenon_Hd2 zenon_H223 zenon_H57 zenon_H44 zenon_H145 zenon_H7d zenon_He3 zenon_H18e zenon_Hb1 zenon_H1ef zenon_H168 zenon_H103 zenon_H165 zenon_H151 zenon_H14a zenon_H14d zenon_H86 zenon_H132 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H174 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H16b zenon_H169 zenon_H16e zenon_H173 zenon_H1f zenon_Hc0 zenon_Hbb zenon_Hde zenon_H1dd. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.31 exact (zenon_H25 zenon_H2a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.31 apply (zenon_L480_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.31 apply (zenon_L666_); trivial. % 10.13/10.31 apply (zenon_L56_); trivial. % 10.13/10.31 apply (zenon_L68_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.31 exact (zenon_H25 zenon_H2a). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.31 apply (zenon_L472_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.31 apply (zenon_L666_); trivial. % 10.13/10.31 apply (zenon_L676_); trivial. % 10.13/10.31 apply (zenon_L68_); trivial. % 10.13/10.31 apply (zenon_L664_); trivial. % 10.13/10.31 apply (zenon_L354_); trivial. % 10.13/10.31 apply (zenon_L500_); trivial. % 10.13/10.31 (* end of lemma zenon_L677_ *) % 10.13/10.31 assert (zenon_L678_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (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))))) -> ((~((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 (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H157 zenon_H216 zenon_H151 zenon_H177 zenon_H44 zenon_H95 zenon_H35 zenon_H14d zenon_H114 zenon_H181 zenon_H12c zenon_H223 zenon_Hec zenon_H18d zenon_H57 zenon_H25 zenon_H8d zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H17c zenon_H9a zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H56 zenon_He3 zenon_H18e zenon_H6f zenon_H155 zenon_H3a zenon_H1f8 zenon_Hf8 zenon_H1fb zenon_Hd2. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.32 apply (zenon_L516_); trivial. % 10.13/10.32 apply (zenon_L664_); trivial. % 10.13/10.32 apply (zenon_L354_); trivial. % 10.13/10.32 apply (zenon_L500_); trivial. % 10.13/10.32 (* end of lemma zenon_L678_ *) % 10.13/10.32 assert (zenon_L679_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (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)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H24 zenon_H57 zenon_H58 zenon_H25 zenon_Hb1 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H3a zenon_H212 zenon_H223 zenon_H8d zenon_H151 zenon_H216 zenon_H191 zenon_H169 zenon_H118 zenon_H110 zenon_H174 zenon_H14a. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.32 apply (zenon_L11_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.32 apply (zenon_L190_); trivial. % 10.13/10.32 apply (zenon_L665_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.32 apply (zenon_L677_); trivial. % 10.13/10.32 apply (zenon_L678_); trivial. % 10.13/10.32 apply (zenon_L14_); trivial. % 10.13/10.32 exact (zenon_H223 zenon_H15a). % 10.13/10.32 apply (zenon_L343_); trivial. % 10.13/10.32 apply (zenon_L518_); trivial. % 10.13/10.32 (* end of lemma zenon_L679_ *) % 10.13/10.32 assert (zenon_L680_ : (~((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H220 zenon_Hb0 zenon_H56 zenon_H64 zenon_H17c zenon_Hb1 zenon_H90 zenon_H4c zenon_Hd3 zenon_H91 zenon_H5e zenon_H145 zenon_H53 zenon_He8 zenon_H28 zenon_Hda zenon_H1e6 zenon_Hed zenon_H3a zenon_H155 zenon_H6f zenon_H51 zenon_H1f8 zenon_H9a zenon_H187. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.32 exact (zenon_H56 zenon_H2c). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.32 apply (zenon_L656_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.32 apply (zenon_L349_); trivial. % 10.13/10.32 apply (zenon_L202_); trivial. % 10.13/10.32 (* end of lemma zenon_L680_ *) % 10.13/10.32 assert (zenon_L681_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H223 zenon_H220 zenon_H4c zenon_H69 zenon_H28 zenon_Hda zenon_H14d zenon_H5e zenon_H53 zenon_H7f zenon_H44 zenon_H95 zenon_Hbd zenon_H35 zenon_H177 zenon_H8d. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.32 exact (zenon_H56 zenon_H2c). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.32 exact (zenon_H223 zenon_H15a). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.32 apply (zenon_L661_); trivial. % 10.13/10.32 apply (zenon_L340_); trivial. % 10.13/10.32 (* end of lemma zenon_L681_ *) % 10.13/10.32 assert (zenon_L682_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H223 zenon_H73 zenon_H14d zenon_H5e zenon_H53 zenon_H7f zenon_H44 zenon_H95 zenon_Hbd zenon_H35 zenon_H177 zenon_H8d. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.32 exact (zenon_H56 zenon_H2c). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.32 exact (zenon_H223 zenon_H15a). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.32 apply (zenon_L165_); trivial. % 10.13/10.32 apply (zenon_L340_); trivial. % 10.13/10.32 (* end of lemma zenon_L682_ *) % 10.13/10.32 assert (zenon_L683_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H18e zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hec zenon_H56 zenon_H223 zenon_Hda zenon_H220 zenon_H4c zenon_H53 zenon_H28 zenon_H14d zenon_H8d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hbd zenon_H5e zenon_H1b4 zenon_H25 zenon_H17a zenon_H18d. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.32 exact (zenon_H25 zenon_H2a). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.32 apply (zenon_L681_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.32 apply (zenon_L682_); trivial. % 10.13/10.32 apply (zenon_L160_); trivial. % 10.13/10.32 apply (zenon_L161_); trivial. % 10.13/10.32 apply (zenon_L60_); trivial. % 10.13/10.32 (* end of lemma zenon_L683_ *) % 10.13/10.32 assert (zenon_L684_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (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) (e0)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H216 zenon_H220 zenon_Hb1 zenon_H9a zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H192 zenon_H191 zenon_H28 zenon_H51 zenon_H3a zenon_He8 zenon_H212 zenon_H25 zenon_H57 zenon_H151 zenon_H14a zenon_H174 zenon_H110 zenon_H118 zenon_H169 zenon_H223. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.32 apply (zenon_L495_); trivial. % 10.13/10.32 apply (zenon_L680_); trivial. % 10.13/10.32 apply (zenon_L683_); trivial. % 10.13/10.32 exact (zenon_H220 zenon_Hbc). % 10.13/10.32 apply (zenon_L354_); trivial. % 10.13/10.32 apply (zenon_L500_); trivial. % 10.13/10.32 (* end of lemma zenon_L684_ *) % 10.13/10.32 assert (zenon_L685_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H216 zenon_Hbb zenon_H1dd zenon_H18e zenon_He3 zenon_H220 zenon_H57 zenon_H44 zenon_H145 zenon_H7d zenon_H7a zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H5e zenon_H90 zenon_Hb1 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7 zenon_Hd2 zenon_H25 zenon_H18d zenon_H173 zenon_H16e zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H174 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H132 zenon_H86 zenon_H14a zenon_H151 zenon_H165 zenon_H103 zenon_H168 zenon_H223 zenon_H14d zenon_H17a. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.32 apply (zenon_L660_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.32 exact (zenon_H25 zenon_H2a). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.32 apply (zenon_L681_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.32 apply (zenon_L682_); trivial. % 10.13/10.32 apply (zenon_L662_); trivial. % 10.13/10.32 apply (zenon_L161_); trivial. % 10.13/10.32 apply (zenon_L60_); trivial. % 10.13/10.32 exact (zenon_H220 zenon_Hbc). % 10.13/10.32 apply (zenon_L354_); trivial. % 10.13/10.32 apply (zenon_L500_); trivial. % 10.13/10.32 (* end of lemma zenon_L685_ *) % 10.13/10.32 assert (zenon_L686_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e3) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H216 zenon_Hf8 zenon_H1f8 zenon_H3a zenon_H155 zenon_H6f zenon_H18e zenon_He3 zenon_H56 zenon_H1b4 zenon_Hb0 zenon_Hb1 zenon_H90 zenon_H9a zenon_H17c zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7a zenon_H25 zenon_H57 zenon_H18d zenon_H17a zenon_H223 zenon_H220 zenon_Hec zenon_H44 zenon_H95 zenon_H173 zenon_H16e zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hfd zenon_H174 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H35 zenon_H103 zenon_H168 zenon_H177 zenon_H1fb zenon_Hd2. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.32 apply (zenon_L516_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.32 exact (zenon_H25 zenon_H2a). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.32 exact (zenon_H56 zenon_H2c). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.13/10.32 exact (zenon_H56 zenon_H2c). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.13/10.32 exact (zenon_H223 zenon_H15a). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.13/10.32 apply (zenon_L661_); trivial. % 10.13/10.32 apply (zenon_L485_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.32 apply (zenon_L228_); trivial. % 10.13/10.32 apply (zenon_L202_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.32 apply (zenon_L482_); trivial. % 10.13/10.32 apply (zenon_L160_); trivial. % 10.13/10.32 apply (zenon_L161_); trivial. % 10.13/10.32 exact (zenon_H220 zenon_Hbc). % 10.13/10.32 apply (zenon_L354_); trivial. % 10.13/10.32 apply (zenon_L500_); trivial. % 10.13/10.32 (* end of lemma zenon_L686_ *) % 10.13/10.32 assert (zenon_L687_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (e1))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H24 zenon_H57 zenon_H58 zenon_H25 zenon_H216 zenon_H151 zenon_H8d zenon_H223 zenon_H212 zenon_H3a zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H221 zenon_H191 zenon_H14a zenon_H174 zenon_H110 zenon_H118 zenon_H169. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.32 apply (zenon_L11_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.32 apply (zenon_L190_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.32 apply (zenon_L665_); trivial. % 10.13/10.32 exact (zenon_H221 zenon_Hcf). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.32 apply (zenon_L677_); trivial. % 10.13/10.32 exact (zenon_H221 zenon_Hcf). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.32 apply (zenon_L678_); trivial. % 10.13/10.32 exact (zenon_H221 zenon_Hcf). % 10.13/10.32 apply (zenon_L14_); trivial. % 10.13/10.32 exact (zenon_H223 zenon_H15a). % 10.13/10.32 apply (zenon_L343_); trivial. % 10.13/10.32 apply (zenon_L518_); trivial. % 10.13/10.32 (* end of lemma zenon_L687_ *) % 10.13/10.32 assert (zenon_L688_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((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))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H42 zenon_Hc0 zenon_He8 zenon_He7 zenon_Hae zenon_H69 zenon_Haf zenon_H6f zenon_Hb0 zenon_Hb8 zenon_H44 zenon_Hb1 zenon_Hab zenon_H4c zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H35 zenon_H5e zenon_Hda zenon_H221 zenon_H27 zenon_Hdd zenon_H57 zenon_H95. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.32 exact (zenon_H27 zenon_H32). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.32 apply (zenon_L648_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.13/10.32 exact (zenon_H27 zenon_H32). % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.13/10.32 apply (zenon_L17_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.13/10.32 exact (zenon_H221 zenon_Hcf). % 10.13/10.32 apply (zenon_L180_); trivial. % 10.13/10.32 apply (zenon_L54_); trivial. % 10.13/10.32 (* end of lemma zenon_L688_ *) % 10.13/10.32 assert (zenon_L689_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (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))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H191 zenon_H205 zenon_H1cb zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_H1af zenon_H1b1 zenon_H198 zenon_H1b7 zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1ef zenon_H204 zenon_H4a zenon_H1e6 zenon_H1e2 zenon_H1de zenon_H1dd zenon_H195 zenon_H212 zenon_H223 zenon_H216 zenon_H17a zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H114 zenon_H1ea zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_H221 zenon_Hda zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_H8c zenon_H8d zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_H53 zenon_Hdd zenon_H44 zenon_Hc5 zenon_Hc6 zenon_Hf8 zenon_Hc0 zenon_Hec zenon_Hbb zenon_He7 zenon_Hf5 zenon_Hde zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_Hd2 zenon_H184 zenon_H187 zenon_H18a zenon_H24 zenon_H57 zenon_H58 zenon_H25 zenon_H64 zenon_H4c zenon_H5e zenon_H1d zenon_H1f zenon_H67. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.32 apply (zenon_L15_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.33 exact (zenon_H27 zenon_H32). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.33 apply (zenon_L16_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.13/10.33 exact (zenon_H27 zenon_H32). % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.13/10.33 apply (zenon_L17_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L52_); trivial. % 10.13/10.33 apply (zenon_L54_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.33 apply (zenon_L43_); trivial. % 10.13/10.33 apply (zenon_L67_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_L77_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.33 exact (zenon_H27 zenon_H32). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.33 apply (zenon_L16_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.33 apply (zenon_L643_); trivial. % 10.13/10.33 apply (zenon_L54_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.33 apply (zenon_L98_); trivial. % 10.13/10.33 apply (zenon_L644_); trivial. % 10.13/10.33 apply (zenon_L161_); trivial. % 10.13/10.33 apply (zenon_L60_); trivial. % 10.13/10.33 apply (zenon_L176_); trivial. % 10.13/10.33 apply (zenon_L687_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.33 apply (zenon_L688_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.33 apply (zenon_L182_); trivial. % 10.13/10.33 apply (zenon_L186_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_L183_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.13/10.33 apply (zenon_L688_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.13/10.33 apply (zenon_L182_); trivial. % 10.13/10.33 apply (zenon_L159_); trivial. % 10.13/10.33 apply (zenon_L161_); trivial. % 10.13/10.33 apply (zenon_L60_); trivial. % 10.13/10.33 apply (zenon_L164_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L88_); trivial. % 10.13/10.33 apply (zenon_L149_); trivial. % 10.13/10.33 exact (zenon_H223 zenon_H15a). % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 (* end of lemma zenon_L689_ *) % 10.13/10.33 assert (zenon_L690_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e0) (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 (e0) (e3)) = (op (e3) (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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H150 zenon_H220 zenon_H18d zenon_H57 zenon_H56 zenon_H1f zenon_H1d zenon_H5e zenon_H51 zenon_H7d zenon_H7a zenon_H64 zenon_H1f8 zenon_H1e6 zenon_H3a zenon_H155 zenon_H16e zenon_H6f zenon_Hf8. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_L671_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_L672_); trivial. % 10.13/10.33 exact (zenon_H220 zenon_Hbc). % 10.13/10.33 (* end of lemma zenon_L690_ *) % 10.13/10.33 assert (zenon_L691_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H24 zenon_H57 zenon_H58 zenon_H25 zenon_H216 zenon_H220 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H3a zenon_H212 zenon_H151 zenon_H14a zenon_H174 zenon_H110 zenon_H118 zenon_H169 zenon_H223 zenon_H221 zenon_H191. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_L11_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L190_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L684_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L685_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L686_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L690_); trivial. % 10.13/10.33 exact (zenon_H223 zenon_H15a). % 10.13/10.33 apply (zenon_L343_); trivial. % 10.13/10.33 apply (zenon_L518_); trivial. % 10.13/10.33 (* end of lemma zenon_L691_ *) % 10.13/10.33 assert (zenon_L692_ : ((~((op (e1) (e1)) = (e0)))\/(~((op (e1) (e0)) = (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/(~((op (e3) (e0)) = (e3)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((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)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (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) (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)) = (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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/(~((op (e2) (e0)) = (e2)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H224 zenon_H225 zenon_H25 zenon_H4a zenon_H1af zenon_H17a zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_H12c zenon_H11b zenon_H128 zenon_H11d zenon_H173 zenon_H16e zenon_H169 zenon_H16b zenon_H16f zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_H132 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H168 zenon_H177 zenon_H18d zenon_H42 zenon_Hda zenon_Hc0 zenon_Hbb zenon_Hd2 zenon_Hce zenon_Hc6 zenon_Hc5 zenon_Hd3 zenon_Hde zenon_H6f zenon_Hb0 zenon_H97 zenon_H95 zenon_H35 zenon_Hab zenon_H8c zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hae zenon_H53 zenon_Hdd zenon_H44 zenon_Hf8 zenon_Hec zenon_He7 zenon_Hf5 zenon_He3 zenon_H18e zenon_H10b zenon_Hfd zenon_H103 zenon_H108 zenon_H181 zenon_H17c zenon_H184 zenon_H187 zenon_H18a zenon_H1ea zenon_H24 zenon_H57 zenon_H58 zenon_H64 zenon_H4c zenon_H5e zenon_H1f zenon_H67 zenon_H191 zenon_H216 zenon_H212 zenon_H195 zenon_H1dd zenon_H1de zenon_H1e2 zenon_H1e6 zenon_H204 zenon_H1ef zenon_H1f0 zenon_H200 zenon_H1f8 zenon_H1fb zenon_H1b7 zenon_H198 zenon_H1b1 zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H1cb zenon_H205 zenon_H226. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_He8 | zenon_intro zenon_H223 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H221 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.33 apply (zenon_L519_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_L655_); trivial. % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_L11_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L190_); trivial. % 10.13/10.33 apply (zenon_L657_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L663_); trivial. % 10.13/10.33 apply (zenon_L501_); trivial. % 10.13/10.33 apply (zenon_L14_); trivial. % 10.13/10.33 apply (zenon_L343_); trivial. % 10.13/10.33 apply (zenon_L518_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L189_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L88_); trivial. % 10.13/10.33 apply (zenon_L149_); trivial. % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_L11_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L190_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L501_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L514_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L517_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L14_); trivial. % 10.13/10.33 apply (zenon_L343_); trivial. % 10.13/10.33 apply (zenon_L518_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L654_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L88_); trivial. % 10.13/10.33 apply (zenon_L149_); trivial. % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_L11_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L190_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L657_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_L663_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.33 exact (zenon_H56 zenon_H2c). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.33 apply (zenon_L656_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.33 apply (zenon_L228_); trivial. % 10.13/10.33 apply (zenon_L202_); trivial. % 10.13/10.33 apply (zenon_L500_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L14_); trivial. % 10.13/10.33 apply (zenon_L343_); trivial. % 10.13/10.33 apply (zenon_L518_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H221 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.33 apply (zenon_L177_); trivial. % 10.13/10.33 apply (zenon_L679_); trivial. % 10.13/10.33 apply (zenon_L188_); trivial. % 10.13/10.33 apply (zenon_L88_); trivial. % 10.13/10.33 apply (zenon_L149_); trivial. % 10.13/10.33 exact (zenon_H223 zenon_H15a). % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_L679_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.33 apply (zenon_L655_); trivial. % 10.13/10.33 exact (zenon_H223 zenon_H15a). % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_L11_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L190_); trivial. % 10.13/10.33 apply (zenon_L684_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L685_); trivial. % 10.13/10.33 apply (zenon_L686_); trivial. % 10.13/10.33 apply (zenon_L14_); trivial. % 10.13/10.33 exact (zenon_H223 zenon_H15a). % 10.13/10.33 apply (zenon_L343_); trivial. % 10.13/10.33 apply (zenon_L518_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H8d | zenon_intro zenon_H220 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_L689_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_L687_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.33 exact (zenon_H25 zenon_H2a). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.33 apply (zenon_L652_); trivial. % 10.13/10.33 apply (zenon_L691_); trivial. % 10.13/10.33 apply (zenon_L653_); trivial. % 10.13/10.33 exact (zenon_H221 zenon_Hcf). % 10.13/10.33 apply (zenon_L88_); trivial. % 10.13/10.33 apply (zenon_L149_); trivial. % 10.13/10.33 exact (zenon_H223 zenon_H15a). % 10.13/10.33 apply (zenon_L85_); trivial. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.33 apply (zenon_L691_); trivial. % 10.13/10.33 apply (zenon_L68_); trivial. % 10.13/10.33 (* end of lemma zenon_L692_ *) % 10.13/10.33 assert (zenon_L693_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H44 zenon_H69 zenon_Haf zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H191 zenon_H192 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H9a. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.33 apply (zenon_L465_); trivial. % 10.13/10.33 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.33 (* end of lemma zenon_L693_ *) % 10.13/10.33 assert (zenon_L694_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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). % 10.13/10.33 do 0 intro. intros zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H1b0 zenon_H151 zenon_H195 zenon_H69 zenon_H192 zenon_Haf zenon_H191. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.33 apply (zenon_L191_); trivial. % 10.13/10.33 apply (zenon_L693_); trivial. % 10.13/10.33 (* end of lemma zenon_L694_ *) % 10.13/10.33 assert (zenon_L695_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H187 zenon_H64. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.33 apply (zenon_L527_); trivial. % 10.13/10.33 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.33 (* end of lemma zenon_L695_ *) % 10.13/10.33 assert (zenon_L696_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H25 zenon_H42 zenon_Hd0 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H44 zenon_H27 zenon_H1b7 zenon_H9a zenon_H187 zenon_H1cb zenon_H64 zenon_H6f zenon_H18a zenon_H86 zenon_H17c zenon_H198 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H35 zenon_H69 zenon_Hd3 zenon_H91 zenon_H90 zenon_H1b4 zenon_H56 zenon_H200. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.33 apply (zenon_L612_); trivial. % 10.13/10.33 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.33 (* end of lemma zenon_L696_ *) % 10.13/10.33 assert (zenon_L697_ : ((~((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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((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) (e0)) = (e1))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hd2 zenon_H200 zenon_H86 zenon_H18a zenon_H6f zenon_H1cb zenon_H1b7 zenon_H97 zenon_H84 zenon_H7a zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H25 zenon_H64 zenon_H187 zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H198 zenon_H9a zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H35 zenon_H69 zenon_H44 zenon_H27 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4 zenon_H56 zenon_H1b0 zenon_H151. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.33 apply (zenon_L695_); trivial. % 10.13/10.33 apply (zenon_L696_); trivial. % 10.13/10.33 (* end of lemma zenon_L697_ *) % 10.13/10.33 assert (zenon_L698_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (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 (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 (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((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 (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)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (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)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H200 zenon_H18a zenon_H86 zenon_H6f zenon_H8d zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H1af zenon_Hda zenon_H187 zenon_H5e zenon_Hb1 zenon_Hb0 zenon_H156 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_Hce zenon_Hd2 zenon_He3 zenon_H18d zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H42 zenon_H28 zenon_H53 zenon_H4c zenon_H95 zenon_H97 zenon_H3a zenon_H3c zenon_H64 zenon_H25 zenon_H1cb zenon_H108 zenon_H155 zenon_H1f8 zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_L617_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 (* end of lemma zenon_L698_ *) % 10.13/10.34 assert (zenon_L699_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((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 (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((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))))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H158 zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H195 zenon_H1af zenon_Hda zenon_H5e zenon_Hb0 zenon_H156 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_Hce zenon_He3 zenon_H18d zenon_H108 zenon_H155 zenon_H1f8 zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8 zenon_H150 zenon_H151 zenon_H1b0 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H35 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H198 zenon_Hc5 zenon_H3c zenon_H187 zenon_H64 zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H95 zenon_H7a zenon_H97 zenon_H1b7 zenon_H1cb zenon_H6f zenon_H18a zenon_H200 zenon_Hd2 zenon_H53 zenon_H69 zenon_H4c zenon_H100 zenon_H86 zenon_H84 zenon_H1de. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.34 apply (zenon_L523_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.34 apply (zenon_L697_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.34 apply (zenon_L698_); trivial. % 10.13/10.34 apply (zenon_L266_); trivial. % 10.13/10.34 apply (zenon_L397_); trivial. % 10.13/10.34 (* end of lemma zenon_L699_ *) % 10.13/10.34 assert (zenon_L700_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((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) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (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) (e2)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H64 zenon_H6f zenon_H198 zenon_H9a zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H35 zenon_H69 zenon_H44 zenon_H27 zenon_H42 zenon_H90 zenon_H187 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H91 zenon_Hd3 zenon_H3a zenon_H3c zenon_H1b4 zenon_H56 zenon_H108 zenon_H53 zenon_Hb1 zenon_H5e zenon_H1cb zenon_Hf8. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_L532_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 (* end of lemma zenon_L700_ *) % 10.13/10.34 assert (zenon_L701_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (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)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H158 zenon_Hf8 zenon_H1cb zenon_H5e zenon_H53 zenon_H108 zenon_H7d zenon_H7a zenon_H18d zenon_H42 zenon_H151 zenon_H1b0 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_Hc5 zenon_H3c zenon_Hb1 zenon_H187 zenon_H64 zenon_H43 zenon_H86 zenon_H84 zenon_H18a zenon_H6f zenon_Hd2. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.34 apply (zenon_L695_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_L528_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 apply (zenon_L700_); trivial. % 10.13/10.34 (* end of lemma zenon_L701_ *) % 10.13/10.34 assert (zenon_L702_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((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))))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H1af zenon_H158 zenon_Hf8 zenon_H1cb zenon_H5e zenon_H108 zenon_H7d zenon_H7a zenon_H18d zenon_H42 zenon_H151 zenon_H1b0 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H35 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H198 zenon_Hc5 zenon_H3c zenon_H187 zenon_H64 zenon_H43 zenon_H18a zenon_H6f zenon_Hd2 zenon_H156 zenon_H53 zenon_H69 zenon_H4c zenon_H100 zenon_H86 zenon_H84 zenon_H1de. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.34 apply (zenon_L523_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.34 apply (zenon_L701_); trivial. % 10.13/10.34 apply (zenon_L235_); trivial. % 10.13/10.34 (* end of lemma zenon_L702_ *) % 10.13/10.34 assert (zenon_L703_ : (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H27 zenon_H43 zenon_H3a zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H151 zenon_H1b0 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.34 apply (zenon_L694_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.34 apply (zenon_L24_); trivial. % 10.13/10.34 apply (zenon_L702_); trivial. % 10.13/10.34 apply (zenon_L623_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.34 apply (zenon_L700_); trivial. % 10.13/10.34 apply (zenon_L235_); trivial. % 10.13/10.34 (* end of lemma zenon_L703_ *) % 10.13/10.34 assert (zenon_L704_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (((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)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((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))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_Hd2 zenon_Hf8 zenon_H56 zenon_H1b4 zenon_H35 zenon_H212 zenon_Hc1 zenon_H200 zenon_H1cb zenon_H108 zenon_H97 zenon_H187 zenon_Hb0 zenon_Hd3 zenon_H91 zenon_H5e zenon_H90 zenon_Hb1 zenon_He8 zenon_H64 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H95 zenon_Hfd zenon_H6f zenon_H3c zenon_H3a zenon_H144 zenon_H25 zenon_H1de zenon_Hec zenon_H51 zenon_H10b zenon_H158 zenon_H152 zenon_Hc5 zenon_H177 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_He7 zenon_H1b0 zenon_H151. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_L478_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 apply (zenon_L354_); trivial. % 10.13/10.34 (* end of lemma zenon_L704_ *) % 10.13/10.34 assert (zenon_L705_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H56 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hbc zenon_H4c zenon_H5e zenon_H51 zenon_H187 zenon_H9a zenon_H64. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_L493_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 (* end of lemma zenon_L705_ *) % 10.13/10.34 assert (zenon_L706_ : (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H28 zenon_H51 zenon_H25 zenon_H3a zenon_He8 zenon_H212 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H151 zenon_H1b0 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.34 apply (zenon_L694_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.34 apply (zenon_L704_); trivial. % 10.13/10.34 apply (zenon_L321_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.34 apply (zenon_L492_); trivial. % 10.13/10.34 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.34 apply (zenon_L705_); trivial. % 10.13/10.34 apply (zenon_L435_); trivial. % 10.13/10.34 (* end of lemma zenon_L706_ *) % 10.13/10.34 assert (zenon_L707_ : ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H51 zenon_H25 zenon_H3a zenon_H212 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H151 zenon_H1b0 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.34 apply (zenon_L706_); trivial. % 10.13/10.34 apply (zenon_L468_); trivial. % 10.13/10.34 apply (zenon_L343_); trivial. % 10.13/10.34 (* end of lemma zenon_L707_ *) % 10.13/10.34 assert (zenon_L708_ : ((op (e3) (e3)) = (e3)) -> ((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)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H84 zenon_H43 zenon_H27 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H151 zenon_H1b0 zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.34 apply (zenon_L694_); trivial. % 10.13/10.34 apply (zenon_L702_); trivial. % 10.13/10.34 (* end of lemma zenon_L708_ *) % 10.13/10.34 assert (zenon_L709_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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). % 10.13/10.34 do 0 intro. intros zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H1ae zenon_H195 zenon_H69 zenon_H192 zenon_Haf zenon_H191. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.34 apply (zenon_L191_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.34 apply (zenon_L465_); trivial. % 10.13/10.34 exact (zenon_H1ae zenon_Hb8). % 10.13/10.34 (* end of lemma zenon_L709_ *) % 10.13/10.34 assert (zenon_L710_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H10b zenon_H5d zenon_Hf3. % 10.13/10.35 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_H10b. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H5d. % 10.13/10.35 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 10.13/10.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 10.13/10.35 congruence. % 10.13/10.35 apply zenon_H134. apply refl_equal. % 10.13/10.35 apply zenon_H1da. apply sym_equal. exact zenon_Hf3. % 10.13/10.35 (* end of lemma zenon_L710_ *) % 10.13/10.35 assert (zenon_L711_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H1b1 zenon_H10b zenon_H1f0 zenon_Hbc zenon_Hf5 zenon_H192 zenon_H7e zenon_H198 zenon_H15a zenon_H47 zenon_Hab zenon_Hc8 zenon_H1e2 zenon_Hc7 zenon_H181 zenon_H12c zenon_Hde zenon_H188 zenon_H187 zenon_H5d zenon_H4c zenon_H95 zenon_H28 zenon_H97 zenon_Haf zenon_H1ae zenon_H35. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 10.13/10.35 apply (zenon_L139_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 10.13/10.35 apply (zenon_L327_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 10.13/10.35 apply (zenon_L710_); trivial. % 10.13/10.35 exact (zenon_H7e zenon_H83). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.13/10.35 exact (zenon_H192 zenon_H1d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.13/10.35 apply (zenon_L292_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.13/10.35 apply (zenon_L317_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.13/10.35 exact (zenon_Haf zenon_Hb4). % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L63_); trivial. % 10.13/10.35 (* end of lemma zenon_L711_ *) % 10.13/10.35 assert (zenon_L712_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H42 zenon_H27 zenon_Hda zenon_Hcf zenon_H1b1 zenon_H10b zenon_H1f0 zenon_Hf5 zenon_H192 zenon_H7e zenon_H198 zenon_H15a zenon_Hab zenon_Hc8 zenon_H1e2 zenon_Hc7 zenon_H181 zenon_H12c zenon_Hde zenon_H188 zenon_H187 zenon_H5d zenon_H4c zenon_H95 zenon_H28 zenon_H97 zenon_Haf zenon_H1ae zenon_H35. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.35 exact (zenon_H27 zenon_H32). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.35 apply (zenon_L317_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.35 apply (zenon_L70_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.35 exact (zenon_H28 zenon_H31). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.35 apply (zenon_L236_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.35 apply (zenon_L155_); trivial. % 10.13/10.35 apply (zenon_L711_); trivial. % 10.13/10.35 (* end of lemma zenon_L712_ *) % 10.13/10.35 assert (zenon_L713_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((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 (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((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)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (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) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.13/10.35 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H64 zenon_H53 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H97 zenon_H4c zenon_H28 zenon_H1b1 zenon_Haf zenon_H1ae zenon_Hde zenon_H1e2 zenon_H181 zenon_Hc7 zenon_Hc8 zenon_Hab zenon_H198 zenon_H12c zenon_H192 zenon_H1f0 zenon_H10b zenon_Hf5 zenon_H42 zenon_H35 zenon_Hcf zenon_Hd3 zenon_H91 zenon_H8c zenon_H1b7 zenon_H188 zenon_H187 zenon_H7a zenon_Hdd zenon_H95 zenon_Hce zenon_H1ba zenon_H1bc zenon_H15a zenon_H1c0 zenon_Hbc zenon_H1c3 zenon_H27 zenon_H128 zenon_H5e zenon_H86 zenon_H7e zenon_H7d zenon_H2a zenon_H58 zenon_H90 zenon_H56 zenon_He3 zenon_H18d. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.35 exact (zenon_H56 zenon_H2c). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.35 apply (zenon_L246_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.13/10.35 exact (zenon_H27 zenon_H32). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.13/10.35 apply (zenon_L317_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.13/10.35 apply (zenon_L70_); trivial. % 10.13/10.35 apply (zenon_L711_); trivial. % 10.13/10.35 apply (zenon_L265_); trivial. % 10.13/10.35 apply (zenon_L266_); trivial. % 10.13/10.35 apply (zenon_L267_); trivial. % 10.13/10.35 (* end of lemma zenon_L713_ *) % 10.13/10.35 assert (zenon_L714_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e1) (e0)) = (op (e1) (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)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H67 zenon_Hc6 zenon_Hde zenon_Hab zenon_H1f0 zenon_Hf5 zenon_Hae zenon_H168 zenon_H150 zenon_He3 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H12c zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H58 zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H64 zenon_H17c zenon_H1e2 zenon_H18a zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H198 zenon_H1dd zenon_Hda zenon_H56 zenon_H158 zenon_H144 zenon_H6f zenon_Hf8 zenon_Hc5 zenon_H3c zenon_H155 zenon_H53 zenon_H108 zenon_H145 zenon_H86 zenon_H7e zenon_H7d zenon_H5e zenon_H2a zenon_H12f zenon_H18d zenon_H97 zenon_H187 zenon_H10b zenon_H95 zenon_H35 zenon_H4c zenon_H103 zenon_H132 zenon_H181 zenon_H42 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H1ea zenon_H4a. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.35 apply (zenon_L297_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_L305_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L309_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_L316_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.35 exact (zenon_H56 zenon_H2c). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.35 apply (zenon_L248_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.35 apply (zenon_L712_); trivial. % 10.13/10.35 apply (zenon_L87_); trivial. % 10.13/10.35 apply (zenon_L296_); trivial. % 10.13/10.35 apply (zenon_L306_); trivial. % 10.13/10.35 apply (zenon_L713_); trivial. % 10.13/10.35 apply (zenon_L44_); trivial. % 10.13/10.35 apply (zenon_L321_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L123_); trivial. % 10.13/10.35 apply (zenon_L213_); trivial. % 10.13/10.35 apply (zenon_L101_); trivial. % 10.13/10.35 (* end of lemma zenon_L714_ *) % 10.13/10.35 assert (zenon_L715_ : (((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 (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (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) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H64 zenon_H56 zenon_H97 zenon_H28 zenon_H7e zenon_H1e6 zenon_H100 zenon_H5e zenon_Hbc zenon_Hf5 zenon_H1b1 zenon_H1f0 zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H177 zenon_H80 zenon_H10b zenon_H114 zenon_H95 zenon_H16b zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f zenon_Hc1 zenon_Hc0 zenon_H1ae zenon_H35 zenon_Hfd zenon_He7 zenon_H4c. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.35 exact (zenon_H56 zenon_H2c). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.35 apply (zenon_L329_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.35 apply (zenon_L12_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.13/10.35 exact (zenon_H28 zenon_H31). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.13/10.35 apply (zenon_L365_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.13/10.35 apply (zenon_L69_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.13/10.35 exact (zenon_He8 zenon_Heb). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.13/10.35 apply (zenon_L329_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.13/10.35 exact (zenon_H192 zenon_H1d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.13/10.35 apply (zenon_L22_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.13/10.35 apply (zenon_L331_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.13/10.35 apply (zenon_L369_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L63_); trivial. % 10.13/10.35 apply (zenon_L364_); trivial. % 10.13/10.35 apply (zenon_L13_); trivial. % 10.13/10.35 (* end of lemma zenon_L715_ *) % 10.13/10.35 assert (zenon_L716_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((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 (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H4a zenon_H156 zenon_Hc6 zenon_Hd2 zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H187 zenon_H108 zenon_H200 zenon_H1cb zenon_H6f zenon_H56 zenon_H1b4 zenon_H27 zenon_H3c zenon_H3a zenon_Hb0 zenon_Hd3 zenon_H5e zenon_H90 zenon_H53 zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H8c zenon_H14d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hc0 zenon_H42 zenon_H4c zenon_Hf5 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H1f zenon_H159 zenon_H1ea zenon_H195 zenon_H1ef zenon_H97 zenon_H64 zenon_H25 zenon_H1b1 zenon_H16b zenon_H114 zenon_H158 zenon_H152 zenon_Hc5 zenon_H1ae zenon_Hde zenon_He7 zenon_H150 zenon_H157 zenon_H192 zenon_H11d zenon_H188 zenon_H191 zenon_Hae zenon_H168. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.35 apply (zenon_L297_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.35 apply (zenon_L361_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.35 exact (zenon_H25 zenon_H2a). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.35 apply (zenon_L363_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.35 apply (zenon_L715_); trivial. % 10.13/10.35 apply (zenon_L24_); trivial. % 10.13/10.35 apply (zenon_L252_); trivial. % 10.13/10.35 apply (zenon_L360_); trivial. % 10.13/10.35 apply (zenon_L354_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L321_); trivial. % 10.13/10.35 apply (zenon_L373_); trivial. % 10.13/10.35 apply (zenon_L314_); trivial. % 10.13/10.35 apply (zenon_L375_); trivial. % 10.13/10.35 (* end of lemma zenon_L716_ *) % 10.13/10.35 assert (zenon_L717_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H18d zenon_He3 zenon_H56 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hbc zenon_H4c zenon_H5e zenon_H51 zenon_H97 zenon_H1b1 zenon_H1f zenon_Hc0 zenon_H16b zenon_H10b zenon_H114 zenon_H95 zenon_H35 zenon_H158 zenon_H152 zenon_H3c zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H7f zenon_H177 zenon_H1ae zenon_Hde zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_H192 zenon_He7 zenon_H28 zenon_H64. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.35 apply (zenon_L715_); trivial. % 10.13/10.35 apply (zenon_L266_); trivial. % 10.13/10.35 (* end of lemma zenon_L717_ *) % 10.13/10.35 assert (zenon_L718_ : (((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))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H8c zenon_H51 zenon_H1cb zenon_H44 zenon_H5e zenon_H8a zenon_H1b7 zenon_H7a zenon_H9b zenon_H187 zenon_H188. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.13/10.35 apply (zenon_L343_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.13/10.35 apply (zenon_L92_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.13/10.35 apply (zenon_L27_); trivial. % 10.13/10.35 apply (zenon_L244_); trivial. % 10.13/10.35 (* end of lemma zenon_L718_ *) % 10.13/10.35 assert (zenon_L719_ : (((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)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (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)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H90 zenon_H17c zenon_Hc8 zenon_H4c zenon_H73 zenon_H53 zenon_H12c zenon_H91 zenon_H8c zenon_H51 zenon_H1cb zenon_H44 zenon_H5e zenon_H1b7 zenon_H7a zenon_H9b zenon_H187 zenon_H188. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.13/10.35 apply (zenon_L165_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.13/10.35 apply (zenon_L351_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.13/10.35 exact (zenon_H91 zenon_H94). % 10.13/10.35 apply (zenon_L718_); trivial. % 10.13/10.35 (* end of lemma zenon_L719_ *) % 10.13/10.35 assert (zenon_L720_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (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)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H90 zenon_H15a zenon_H1bc zenon_H78 zenon_H91 zenon_H8c zenon_H51 zenon_H1cb zenon_H44 zenon_H5e zenon_H1b7 zenon_H7a zenon_H9b zenon_H187 zenon_H188. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.13/10.35 apply (zenon_L217_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.13/10.35 apply (zenon_L22_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.13/10.35 exact (zenon_H91 zenon_H94). % 10.13/10.35 apply (zenon_L718_); trivial. % 10.13/10.35 (* end of lemma zenon_L720_ *) % 10.13/10.35 assert (zenon_L721_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e0)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H12c zenon_H1c0 zenon_Hbc zenon_H4c zenon_H77 zenon_Hc8 zenon_H53 zenon_H89. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 10.13/10.35 apply (zenon_L219_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 10.13/10.35 apply (zenon_L48_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 10.13/10.35 exact (zenon_Hc8 zenon_Hcd). % 10.13/10.35 apply (zenon_L96_); trivial. % 10.13/10.35 (* end of lemma zenon_L721_ *) % 10.13/10.35 assert (zenon_L722_ : (((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)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H90 zenon_H15a zenon_H1bc zenon_H53 zenon_Hc8 zenon_H4c zenon_Hbc zenon_H1c0 zenon_H12c zenon_H91 zenon_H89 zenon_H5e. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.13/10.35 apply (zenon_L217_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.13/10.35 apply (zenon_L721_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.13/10.35 exact (zenon_H91 zenon_H94). % 10.13/10.35 apply (zenon_L27_); trivial. % 10.13/10.35 (* end of lemma zenon_L722_ *) % 10.13/10.35 assert (zenon_L723_ : (((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 (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (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))))) -> (~((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 (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> False). % 10.13/10.35 do 0 intro. intros zenon_Hae zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_Hb0 zenon_H17c zenon_H188 zenon_H187 zenon_H7a zenon_H1b7 zenon_H44 zenon_H1cb zenon_H51 zenon_H8c zenon_Hb1 zenon_H90 zenon_H15a zenon_H1bc zenon_H53 zenon_Hc8 zenon_H4c zenon_Hbc zenon_H1c0 zenon_H12c zenon_H91 zenon_H5e. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.13/10.35 apply (zenon_L238_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.13/10.35 exact (zenon_Haf zenon_Hb4). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.13/10.35 apply (zenon_L223_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.13/10.35 apply (zenon_L719_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.13/10.35 apply (zenon_L720_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.13/10.35 exact (zenon_Hb1 zenon_Hb7). % 10.13/10.35 apply (zenon_L722_); trivial. % 10.13/10.35 (* end of lemma zenon_L723_ *) % 10.13/10.35 assert (zenon_L724_ : (((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 (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.35 do 0 intro. intros zenon_Hae zenon_H35 zenon_H15a zenon_Haf zenon_H155 zenon_H3a zenon_Hd0 zenon_H17c. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.13/10.35 apply (zenon_L238_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.13/10.35 exact (zenon_Haf zenon_Hb4). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.13/10.35 apply (zenon_L223_); trivial. % 10.13/10.35 apply (zenon_L162_); trivial. % 10.13/10.35 (* end of lemma zenon_L724_ *) % 10.13/10.35 assert (zenon_L725_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (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 (e2) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((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) (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H1ea zenon_H157 zenon_H1ae zenon_H150 zenon_H18d zenon_H86 zenon_H56 zenon_Hda zenon_H1c0 zenon_H35 zenon_H155 zenon_H3a zenon_Hb0 zenon_Hd3 zenon_H1bc zenon_H5e zenon_H12c zenon_H188 zenon_H17c zenon_H53 zenon_H8c zenon_H7a zenon_H187 zenon_H1b7 zenon_H44 zenon_H51 zenon_H1cb zenon_H90 zenon_Hae zenon_H15a zenon_H4c zenon_H28 zenon_H7d zenon_H64 zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H6f zenon_Hf8 zenon_Hd2 zenon_Hc6 zenon_H156. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.13/10.35 exact (zenon_H56 zenon_H2c). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.13/10.35 exact (zenon_H28 zenon_H31). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.13/10.35 apply (zenon_L236_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.13/10.35 apply (zenon_L238_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.13/10.35 exact (zenon_Haf zenon_Hb4). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.13/10.35 apply (zenon_L223_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.13/10.35 apply (zenon_L719_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.13/10.35 apply (zenon_L720_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.13/10.35 exact (zenon_Hb1 zenon_Hb7). % 10.13/10.35 apply (zenon_L250_); trivial. % 10.13/10.35 apply (zenon_L723_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.13/10.35 apply (zenon_L12_); trivial. % 10.13/10.35 apply (zenon_L87_); trivial. % 10.13/10.35 apply (zenon_L252_); trivial. % 10.13/10.35 apply (zenon_L490_); trivial. % 10.13/10.35 apply (zenon_L723_); trivial. % 10.13/10.35 apply (zenon_L724_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L321_); trivial. % 10.13/10.35 apply (zenon_L123_); trivial. % 10.13/10.35 (* end of lemma zenon_L725_ *) % 10.13/10.35 assert (zenon_L726_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (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))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H173 zenon_H103 zenon_H18a zenon_H1e2 zenon_H1c3 zenon_H1ba zenon_H58 zenon_Hce zenon_Hdd zenon_Hec zenon_Hab zenon_H67 zenon_H1b7 zenon_H1bc zenon_H1c0 zenon_He3 zenon_H1dd zenon_H168 zenon_Hae zenon_H191 zenon_H11d zenon_H192 zenon_H157 zenon_H150 zenon_He7 zenon_Hde zenon_H1ae zenon_Hc5 zenon_H152 zenon_H158 zenon_H114 zenon_H16b zenon_H1b1 zenon_H64 zenon_H97 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H7e zenon_Hf5 zenon_H4c zenon_H42 zenon_Hc0 zenon_H177 zenon_H44 zenon_H95 zenon_H35 zenon_H14d zenon_H8c zenon_H7d zenon_H7a zenon_H18d zenon_H53 zenon_H90 zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H3c zenon_H1b4 zenon_H56 zenon_H6f zenon_H1cb zenon_H200 zenon_H108 zenon_H187 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8 zenon_Hd2 zenon_Hc6 zenon_H156 zenon_H4a zenon_H132 zenon_H145 zenon_H12f zenon_H204 zenon_H188 zenon_H86. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.13/10.35 apply (zenon_L714_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.13/10.35 exact (zenon_H192 zenon_H1d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.35 apply (zenon_L716_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.35 apply (zenon_L297_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.35 apply (zenon_L377_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.35 apply (zenon_L717_); trivial. % 10.13/10.35 apply (zenon_L267_); trivial. % 10.13/10.35 apply (zenon_L354_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 apply (zenon_L321_); trivial. % 10.13/10.35 apply (zenon_L373_); trivial. % 10.13/10.35 apply (zenon_L725_); trivial. % 10.13/10.35 apply (zenon_L375_); trivial. % 10.13/10.35 apply (zenon_L315_); trivial. % 10.13/10.35 apply (zenon_L252_); trivial. % 10.13/10.35 (* end of lemma zenon_L726_ *) % 10.13/10.35 assert (zenon_L727_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (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))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H1de zenon_H69 zenon_Hc1 zenon_H100 zenon_H173 zenon_H103 zenon_H18a zenon_H1e2 zenon_H1c3 zenon_H1ba zenon_H58 zenon_Hce zenon_Hdd zenon_Hec zenon_Hab zenon_H67 zenon_H1b7 zenon_H1bc zenon_H1c0 zenon_He3 zenon_H1dd zenon_H168 zenon_Hae zenon_H191 zenon_H11d zenon_H192 zenon_H157 zenon_H150 zenon_He7 zenon_Hde zenon_H1ae zenon_Hc5 zenon_H152 zenon_H158 zenon_H114 zenon_H16b zenon_H1b1 zenon_H64 zenon_H97 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H7e zenon_Hf5 zenon_H4c zenon_H42 zenon_Hc0 zenon_H177 zenon_H44 zenon_H95 zenon_H35 zenon_H14d zenon_H8c zenon_H7d zenon_H7a zenon_H18d zenon_H53 zenon_H90 zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H3c zenon_H1b4 zenon_H56 zenon_H6f zenon_H1cb zenon_H200 zenon_H108 zenon_H187 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8 zenon_Hd2 zenon_Hc6 zenon_H156 zenon_H4a zenon_H132 zenon_H145 zenon_H12f zenon_H204 zenon_H86. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.13/10.35 apply (zenon_L18_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.13/10.35 exact (zenon_Hc1 zenon_Hc4). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.13/10.35 apply (zenon_L522_); trivial. % 10.13/10.35 apply (zenon_L726_); trivial. % 10.13/10.35 (* end of lemma zenon_L727_ *) % 10.13/10.35 assert (zenon_L728_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H157 zenon_H1ae zenon_H56 zenon_Hda zenon_H84 zenon_He3 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H17c zenon_H9a zenon_H90 zenon_H4c zenon_Hb1 zenon_Hb0 zenon_H69 zenon_H53 zenon_H28. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.35 apply (zenon_L487_); trivial. % 10.13/10.35 exact (zenon_H1ae zenon_Hb8). % 10.13/10.35 (* end of lemma zenon_L728_ *) % 10.13/10.35 assert (zenon_L729_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((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))) -> (((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))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H18d zenon_He3 zenon_H1ae zenon_H157 zenon_H56 zenon_H1b4 zenon_Hb0 zenon_Hb1 zenon_H90 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7f zenon_H7a zenon_H8d. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.36 apply (zenon_L486_); trivial. % 10.13/10.36 apply (zenon_L728_); trivial. % 10.13/10.36 (* end of lemma zenon_L729_ *) % 10.13/10.36 assert (zenon_L730_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (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))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((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) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hf8 zenon_H144 zenon_H10b zenon_Hfd zenon_H1f8 zenon_H155 zenon_H108 zenon_H1cb zenon_H25 zenon_H64 zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H4c zenon_H53 zenon_H28 zenon_H42 zenon_H198 zenon_H9a zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H35 zenon_H69 zenon_H44 zenon_H27 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4 zenon_H56 zenon_H18d zenon_He3 zenon_H1ae zenon_H157 zenon_Hb0 zenon_Hb1 zenon_H5e zenon_H187 zenon_Hda zenon_H1af zenon_H195 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7a zenon_H8d zenon_H6f zenon_H86 zenon_H18a zenon_H200. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.36 exact (zenon_H25 zenon_H2a). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.36 apply (zenon_L615_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.36 apply (zenon_L729_); trivial. % 10.13/10.36 apply (zenon_L531_); trivial. % 10.13/10.36 apply (zenon_L616_); trivial. % 10.13/10.36 (* end of lemma zenon_L730_ *) % 10.13/10.36 assert (zenon_L731_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((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) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hf8 zenon_H6f zenon_H155 zenon_H3a zenon_H1f8 zenon_H8d zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H56 zenon_H157 zenon_H1ae zenon_He3 zenon_H18d. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.36 apply (zenon_L729_); trivial. % 10.13/10.36 apply (zenon_L491_); trivial. % 10.13/10.36 (* end of lemma zenon_L731_ *) % 10.13/10.36 assert (zenon_L732_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H157 zenon_H1ae zenon_Hd2 zenon_Hcf zenon_Hce zenon_H3c zenon_H51 zenon_Hc5 zenon_Hc6 zenon_H158. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.36 apply (zenon_L435_); trivial. % 10.13/10.36 exact (zenon_H1ae zenon_Hb8). % 10.13/10.36 (* end of lemma zenon_L732_ *) % 10.13/10.36 assert (zenon_L733_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((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 (e0) (e2)) = (e0)) -> False). % 10.13/10.36 do 0 intro. intros zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7e zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H1ae zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H3a zenon_H51. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.36 apply (zenon_L709_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.36 apply (zenon_L727_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.13/10.36 apply (zenon_L731_); trivial. % 10.13/10.36 apply (zenon_L493_); trivial. % 10.13/10.36 exact (zenon_H1ae zenon_Hb8). % 10.13/10.36 apply (zenon_L732_); trivial. % 10.13/10.36 apply (zenon_L343_); trivial. % 10.13/10.36 (* end of lemma zenon_L733_ *) % 10.13/10.36 assert (zenon_L734_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> ((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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H25 zenon_H27 zenon_H28 zenon_H100 zenon_H9a zenon_H91 zenon_H3a zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H1ae zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H7d zenon_H7a zenon_H7e zenon_H7f zenon_H80. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.36 exact (zenon_H25 zenon_H2a). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.36 apply (zenon_L615_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.36 apply (zenon_L733_); trivial. % 10.13/10.36 apply (zenon_L24_); trivial. % 10.13/10.36 (* end of lemma zenon_L734_ *) % 10.13/10.36 assert (zenon_L735_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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 (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (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 (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (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)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (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)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H191 zenon_H192 zenon_H195 zenon_H1ae zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hce zenon_H1af zenon_Hd2 zenon_Hc0 zenon_He7 zenon_H181 zenon_H187 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H159 zenon_H6f zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H10b zenon_H18a zenon_H1e2 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H42 zenon_H28 zenon_H53 zenon_H4c zenon_H95 zenon_H97 zenon_H3a zenon_H3c zenon_H64 zenon_H25 zenon_Hbc. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.13/10.36 apply (zenon_L734_); trivial. % 10.13/10.36 apply (zenon_L266_); trivial. % 10.13/10.36 apply (zenon_L267_); trivial. % 10.13/10.36 (* end of lemma zenon_L735_ *) % 10.13/10.36 assert (zenon_L736_ : ((op (e2) (e2)) = (e2)) -> ((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)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H3a zenon_H43 zenon_H27 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H1ae zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.36 apply (zenon_L709_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.36 apply (zenon_L727_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.36 apply (zenon_L532_); trivial. % 10.13/10.36 exact (zenon_H1ae zenon_Hb8). % 10.13/10.36 apply (zenon_L321_); trivial. % 10.13/10.36 (* end of lemma zenon_L736_ *) % 10.13/10.36 assert (zenon_L737_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((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)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H157 zenon_H1ae zenon_H1b4 zenon_H90 zenon_H17c zenon_Hd3 zenon_H192 zenon_H12c zenon_H84 zenon_H205 zenon_H4c zenon_H95 zenon_Hbb zenon_H1b1 zenon_Hcf zenon_H35 zenon_H9a zenon_H198 zenon_H56 zenon_Hce zenon_Hd2. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.36 apply (zenon_L397_); trivial. % 10.13/10.36 exact (zenon_H1ae zenon_Hb8). % 10.13/10.36 (* end of lemma zenon_L737_ *) % 10.13/10.36 assert (zenon_L738_ : (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H27 zenon_H84 zenon_H43 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H1ae zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H7e zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.36 apply (zenon_L709_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.36 apply (zenon_L727_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.36 apply (zenon_L533_); trivial. % 10.13/10.36 exact (zenon_H1ae zenon_Hb8). % 10.13/10.36 apply (zenon_L737_); trivial. % 10.13/10.36 (* end of lemma zenon_L738_ *) % 10.13/10.36 assert (zenon_L739_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (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 (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H156 zenon_Hd2 zenon_Hce zenon_H198 zenon_H35 zenon_H1b1 zenon_Hbb zenon_H95 zenon_H205 zenon_H12c zenon_H192 zenon_H1b4 zenon_H28 zenon_H53 zenon_H69 zenon_Hb0 zenon_H4c zenon_H90 zenon_H9a zenon_H17c zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_He3 zenon_H84 zenon_Hda zenon_H56 zenon_H1ae zenon_H157. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.36 apply (zenon_L728_); trivial. % 10.13/10.36 apply (zenon_L737_); trivial. % 10.13/10.36 (* end of lemma zenon_L739_ *) % 10.13/10.36 assert (zenon_L740_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((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))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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). % 10.13/10.36 do 0 intro. intros zenon_H1af zenon_H157 zenon_H1ae zenon_H56 zenon_Hda zenon_H84 zenon_He3 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H17c zenon_H90 zenon_H4c zenon_Hb0 zenon_H53 zenon_H28 zenon_H1b4 zenon_H12c zenon_H205 zenon_H95 zenon_Hbb zenon_H1b1 zenon_H35 zenon_H198 zenon_Hce zenon_Hd2 zenon_H156 zenon_H195 zenon_H69 zenon_H192 zenon_Haf zenon_H191. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.36 apply (zenon_L191_); trivial. % 10.13/10.36 apply (zenon_L739_); trivial. % 10.13/10.36 (* end of lemma zenon_L740_ *) % 10.13/10.36 assert (zenon_L741_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((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))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (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 (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H1af zenon_H157 zenon_H1ae zenon_H56 zenon_Hda zenon_H84 zenon_He3 zenon_H64 zenon_H187 zenon_H51 zenon_H5e zenon_Hd3 zenon_H17c zenon_H90 zenon_H4c zenon_Hb0 zenon_H53 zenon_H1b4 zenon_H12c zenon_H205 zenon_H95 zenon_Hbb zenon_H1b1 zenon_H35 zenon_H198 zenon_Hce zenon_Hd2 zenon_H156 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H173 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H1f zenon_H1e6 zenon_Hc0 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H10b zenon_H97 zenon_H18d zenon_H12f zenon_H7d zenon_H7e zenon_H86 zenon_H145 zenon_H108 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_H6f zenon_H144 zenon_H158 zenon_H1dd zenon_H11d zenon_H18a zenon_H1e2 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H58 zenon_H128 zenon_Hdd zenon_H7a zenon_H1b7 zenon_H8c zenon_Hec zenon_H159 zenon_H1cb zenon_H150 zenon_H168 zenon_Hae zenon_Hf5 zenon_H1f0 zenon_Hab zenon_Hde zenon_Hc6 zenon_H67 zenon_H1de. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.37 apply (zenon_L740_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.37 apply (zenon_L727_); trivial. % 10.13/10.37 apply (zenon_L739_); trivial. % 10.13/10.37 apply (zenon_L343_); trivial. % 10.13/10.37 (* end of lemma zenon_L741_ *) % 10.13/10.37 assert (zenon_L742_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H44 zenon_H69 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H1ae zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.37 apply (zenon_L190_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.37 apply (zenon_L693_); trivial. % 10.13/10.37 exact (zenon_H1ae zenon_Hb8). % 10.13/10.37 (* end of lemma zenon_L742_ *) % 10.13/10.37 assert (zenon_L743_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H53 zenon_H69 zenon_Hc1 zenon_H4c zenon_H100 zenon_H173 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1f zenon_H1af zenon_H1e6 zenon_Hc0 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H157 zenon_H1ae zenon_Hd2 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H35 zenon_H95 zenon_H10b zenon_H187 zenon_H97 zenon_H18d zenon_H12f zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H108 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_H6f zenon_H144 zenon_H158 zenon_H56 zenon_Hda zenon_H1dd zenon_H198 zenon_H1b4 zenon_H156 zenon_H192 zenon_H11d zenon_H191 zenon_H18a zenon_H1e2 zenon_H17c zenon_H64 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H58 zenon_H128 zenon_Hce zenon_Hdd zenon_H7a zenon_H1b7 zenon_H8c zenon_Hd3 zenon_Hb0 zenon_H12c zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_He3 zenon_H150 zenon_H168 zenon_Hae zenon_Hf5 zenon_H1f0 zenon_Hab zenon_Hde zenon_Hc6 zenon_H67 zenon_H1de. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.37 apply (zenon_L727_); trivial. % 10.13/10.37 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.37 (* end of lemma zenon_L743_ *) % 10.13/10.37 assert (zenon_L744_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H84 zenon_H51 zenon_H191 zenon_H192 zenon_H1ae zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H69 zenon_H44 zenon_H1b0 zenon_H151. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.37 apply (zenon_L742_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.37 apply (zenon_L523_); trivial. % 10.13/10.37 apply (zenon_L739_); trivial. % 10.13/10.37 apply (zenon_L468_); trivial. % 10.13/10.37 apply (zenon_L343_); trivial. % 10.13/10.37 (* end of lemma zenon_L744_ *) % 10.13/10.37 assert (zenon_L745_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e1) (e0)) = (op (e1) (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)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H84 zenon_H43 zenon_H27 zenon_H205 zenon_Hbb zenon_H1de zenon_H67 zenon_Hc6 zenon_Hde zenon_Hab zenon_H1f0 zenon_Hf5 zenon_Hae zenon_H168 zenon_H150 zenon_He3 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H12c zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H58 zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H64 zenon_H17c zenon_H1e2 zenon_H18a zenon_H191 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H198 zenon_H1dd zenon_Hda zenon_H56 zenon_H158 zenon_H144 zenon_H6f zenon_Hf8 zenon_Hc5 zenon_H3c zenon_H155 zenon_H108 zenon_H145 zenon_H86 zenon_H7d zenon_H5e zenon_H12f zenon_H18d zenon_H97 zenon_H187 zenon_H10b zenon_H95 zenon_H35 zenon_H103 zenon_H132 zenon_H181 zenon_H42 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H1ea zenon_H4a zenon_H204 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H44 zenon_H177 zenon_Hc0 zenon_H1e6 zenon_H1af zenon_H1f zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_He7 zenon_H173 zenon_H100 zenon_H4c zenon_H69 zenon_H53 zenon_H1b0 zenon_H151. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.37 apply (zenon_L743_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.37 apply (zenon_L701_); trivial. % 10.13/10.37 exact (zenon_H1ae zenon_Hb8). % 10.13/10.37 apply (zenon_L737_); trivial. % 10.13/10.37 (* end of lemma zenon_L745_ *) % 10.13/10.37 assert (zenon_L746_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H44 zenon_H69 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H1ae zenon_H192 zenon_H191 zenon_H84 zenon_H43 zenon_H27. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.37 apply (zenon_L742_); trivial. % 10.13/10.37 apply (zenon_L745_); trivial. % 10.13/10.37 apply (zenon_L468_); trivial. % 10.13/10.37 (* end of lemma zenon_L746_ *) % 10.13/10.37 assert (zenon_L747_ : ((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 (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H84 zenon_H191 zenon_H192 zenon_H1ae zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H69 zenon_H44 zenon_H1b0 zenon_H151. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.37 apply (zenon_L742_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.37 apply (zenon_L523_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.13/10.37 apply (zenon_L697_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.13/10.37 exact (zenon_H25 zenon_H2a). % 10.13/10.37 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.13/10.37 apply (zenon_L615_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.13/10.37 apply (zenon_L744_); trivial. % 10.13/10.37 apply (zenon_L746_); trivial. % 10.13/10.37 exact (zenon_H1b0 zenon_Hbd). % 10.13/10.37 exact (zenon_H1ae zenon_Hb8). % 10.13/10.37 apply (zenon_L737_); trivial. % 10.13/10.37 apply (zenon_L468_); trivial. % 10.13/10.37 apply (zenon_L746_); trivial. % 10.13/10.37 apply (zenon_L744_); trivial. % 10.13/10.37 apply (zenon_L100_); trivial. % 10.13/10.37 (* end of lemma zenon_L747_ *) % 10.13/10.37 assert (zenon_L748_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (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)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H157 zenon_H1ae zenon_Hf8 zenon_H1cb zenon_H5e zenon_Hb1 zenon_H53 zenon_H108 zenon_H56 zenon_H1b4 zenon_H3c zenon_H3a zenon_Hd3 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H187 zenon_H90 zenon_H42 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H6f zenon_H64 zenon_H1b0 zenon_H151. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.13/10.37 apply (zenon_L700_); trivial. % 10.13/10.37 exact (zenon_H1ae zenon_Hb8). % 10.13/10.37 (* end of lemma zenon_L748_ *) % 10.13/10.37 assert (zenon_L749_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (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 (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H44 zenon_H69 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H1ae zenon_H192 zenon_H191 zenon_H3a zenon_H43 zenon_H27. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.13/10.37 apply (zenon_L742_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.13/10.37 apply (zenon_L743_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.13/10.37 apply (zenon_L748_); trivial. % 10.13/10.37 apply (zenon_L321_); trivial. % 10.13/10.37 apply (zenon_L468_); trivial. % 10.13/10.37 (* end of lemma zenon_L749_ *) % 10.13/10.37 assert (zenon_L750_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.23/10.37 do 0 intro. intros zenon_H3a zenon_H51 zenon_H191 zenon_H192 zenon_H1ae zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H69 zenon_H44 zenon_H1b0 zenon_H151. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.37 apply (zenon_L742_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.37 apply (zenon_L743_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.37 apply (zenon_L731_); trivial. % 10.23/10.37 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.37 apply (zenon_L705_); trivial. % 10.23/10.37 exact (zenon_H1ae zenon_Hb8). % 10.23/10.37 apply (zenon_L732_); trivial. % 10.23/10.37 apply (zenon_L468_); trivial. % 10.23/10.37 apply (zenon_L343_); trivial. % 10.23/10.37 (* end of lemma zenon_L750_ *) % 10.23/10.37 assert (zenon_L751_ : ((~((op (e2) (e2)) = (e1)))\/(~((op (e2) (e1)) = (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> False). % 10.23/10.37 do 0 intro. intros zenon_H22a zenon_H44 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H195 zenon_H191 zenon_H212 zenon_H192 zenon_H69 zenon_H12f zenon_H151 zenon_H22b. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H91 | zenon_intro zenon_H1ae ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.23/10.37 apply (zenon_L627_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.23/10.37 apply (zenon_L100_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.23/10.37 exact (zenon_H192 zenon_H1d). % 10.23/10.37 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.37 apply (zenon_L694_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.23/10.37 apply (zenon_L611_); trivial. % 10.23/10.37 apply (zenon_L699_); trivial. % 10.23/10.37 apply (zenon_L472_); trivial. % 10.23/10.37 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.37 apply (zenon_L354_); trivial. % 10.23/10.37 apply (zenon_L321_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.37 apply (zenon_L698_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.37 apply (zenon_L620_); trivial. % 10.23/10.37 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.37 apply (zenon_L321_); trivial. % 10.23/10.37 apply (zenon_L468_); trivial. % 10.23/10.37 apply (zenon_L703_); trivial. % 10.23/10.37 apply (zenon_L707_); trivial. % 10.23/10.37 apply (zenon_L100_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.37 apply (zenon_L694_); trivial. % 10.23/10.37 apply (zenon_L699_); trivial. % 10.23/10.37 apply (zenon_L708_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.37 apply (zenon_L694_); trivial. % 10.23/10.37 apply (zenon_L625_); trivial. % 10.23/10.37 apply (zenon_L343_); trivial. % 10.23/10.37 apply (zenon_L100_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.23/10.37 apply (zenon_L100_); trivial. % 10.23/10.37 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.23/10.38 exact (zenon_H192 zenon_H1d). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.38 apply (zenon_L709_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.38 apply (zenon_L727_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_L730_); trivial. % 10.23/10.38 apply (zenon_L735_); trivial. % 10.23/10.38 exact (zenon_H1ae zenon_Hb8). % 10.23/10.38 apply (zenon_L321_); trivial. % 10.23/10.38 apply (zenon_L736_); trivial. % 10.23/10.38 apply (zenon_L733_); trivial. % 10.23/10.38 apply (zenon_L100_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.38 apply (zenon_L709_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.38 apply (zenon_L727_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.23/10.38 apply (zenon_L613_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_L730_); trivial. % 10.23/10.38 apply (zenon_L266_); trivial. % 10.23/10.38 exact (zenon_H1ae zenon_Hb8). % 10.23/10.38 apply (zenon_L737_); trivial. % 10.23/10.38 apply (zenon_L738_); trivial. % 10.23/10.38 apply (zenon_L741_); trivial. % 10.23/10.38 apply (zenon_L100_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.23/10.38 apply (zenon_L100_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.23/10.38 exact (zenon_H192 zenon_H1d). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.38 apply (zenon_L742_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.38 apply (zenon_L743_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.23/10.38 apply (zenon_L734_); trivial. % 10.23/10.38 apply (zenon_L747_); trivial. % 10.23/10.38 apply (zenon_L616_); trivial. % 10.23/10.38 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.38 exact (zenon_H1ae zenon_Hb8). % 10.23/10.38 apply (zenon_L321_); trivial. % 10.23/10.38 apply (zenon_L468_); trivial. % 10.23/10.38 apply (zenon_L749_); trivial. % 10.23/10.38 apply (zenon_L750_); trivial. % 10.23/10.38 apply (zenon_L100_); trivial. % 10.23/10.38 apply (zenon_L747_); trivial. % 10.23/10.38 (* end of lemma zenon_L751_ *) % 10.23/10.38 assert (zenon_L752_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (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) (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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.23/10.38 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H187 zenon_H9a zenon_H1f8 zenon_H6f zenon_H155 zenon_H3a zenon_H1e6 zenon_H1b4 zenon_H159 zenon_H7e zenon_H1f0 zenon_Hf5 zenon_Hda zenon_H28 zenon_H69 zenon_H91 zenon_Hd3 zenon_H90 zenon_H17c zenon_H64 zenon_H56 zenon_Hb0 zenon_H4c zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_Hed. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L491_); trivial. % 10.23/10.38 apply (zenon_L359_); trivial. % 10.23/10.38 (* end of lemma zenon_L752_ *) % 10.23/10.38 assert (zenon_L753_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H187 zenon_H9a zenon_H5e zenon_Hf5 zenon_Hbc zenon_H4c zenon_H1f0 zenon_H100 zenon_H1e6 zenon_H56 zenon_H64 zenon_H7d zenon_H7a zenon_H7e zenon_H7f zenon_H80. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L493_); trivial. % 10.23/10.38 apply (zenon_L24_); trivial. % 10.23/10.38 (* end of lemma zenon_L753_ *) % 10.23/10.38 assert (zenon_L754_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (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 (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.23/10.38 do 0 intro. intros zenon_Hf8 zenon_H1f8 zenon_H3a zenon_H155 zenon_H159 zenon_H6f zenon_Hda zenon_H69 zenon_H53 zenon_H28 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H108 zenon_H1cb zenon_H200 zenon_H7a zenon_H7d zenon_H56 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hbc zenon_H4c zenon_H5e zenon_H187 zenon_H9a zenon_H64 zenon_H22c zenon_H25 zenon_He3 zenon_H18d. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.23/10.38 apply (zenon_L753_); trivial. % 10.23/10.38 apply (zenon_L266_); trivial. % 10.23/10.38 apply (zenon_L752_); trivial. % 10.23/10.38 (* end of lemma zenon_L754_ *) % 10.23/10.38 assert (zenon_L755_ : ((~((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 (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (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 (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H150 zenon_H200 zenon_H3c zenon_H3a zenon_H18a zenon_H86 zenon_H42 zenon_H27 zenon_H44 zenon_Hdd zenon_H6f zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H64 zenon_H187 zenon_H5e zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H56 zenon_H156 zenon_H12c zenon_H205 zenon_H95 zenon_Hbb zenon_H1b1 zenon_H35 zenon_Hce zenon_Hd2 zenon_He3 zenon_H18d zenon_H22c zenon_H25 zenon_H1cb zenon_H108 zenon_H155 zenon_H1f8 zenon_Hf8. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L489_); trivial. % 10.23/10.38 apply (zenon_L531_); trivial. % 10.23/10.38 apply (zenon_L752_); trivial. % 10.23/10.38 apply (zenon_L754_); trivial. % 10.23/10.38 (* end of lemma zenon_L755_ *) % 10.23/10.38 assert (zenon_L756_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (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)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H7a zenon_H181 zenon_H1cb zenon_H1b7 zenon_H64 zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H9a zenon_H69 zenon_H44 zenon_H27 zenon_Hdd zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H7e zenon_H198 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H18a zenon_H187 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L418_); trivial. % 10.23/10.38 apply (zenon_L528_); trivial. % 10.23/10.38 (* end of lemma zenon_L756_ *) % 10.23/10.38 assert (zenon_L757_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (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) (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 (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)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((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)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_Hd2 zenon_H25 zenon_H22c zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H1cb zenon_H6f zenon_H18a zenon_H86 zenon_H200 zenon_H56 zenon_H1b4 zenon_H90 zenon_H17c zenon_H91 zenon_Hd3 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H187 zenon_H64. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.38 apply (zenon_L527_); trivial. % 10.23/10.38 apply (zenon_L756_); trivial. % 10.23/10.38 (* end of lemma zenon_L757_ *) % 10.23/10.38 assert (zenon_L758_ : (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (e1) (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e0))) -> (~((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)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H22c zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H58 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H1b0 zenon_H151 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H212 zenon_He8 zenon_H3a zenon_H25 zenon_H28 zenon_H7d zenon_H7a zenon_H7e zenon_H7f zenon_H80. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L706_); trivial. % 10.23/10.38 apply (zenon_L24_); trivial. % 10.23/10.38 (* end of lemma zenon_L758_ *) % 10.23/10.38 assert (zenon_L759_ : (((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 (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (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))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H8c zenon_H51 zenon_H1cb zenon_H7a zenon_H84 zenon_Hd0 zenon_H181 zenon_H187 zenon_H1b7 zenon_H5e zenon_H8a zenon_H8d. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.23/10.38 apply (zenon_L343_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.23/10.38 apply (zenon_L277_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.23/10.38 apply (zenon_L27_); trivial. % 10.23/10.38 exact (zenon_H8d zenon_H7b). % 10.23/10.38 (* end of lemma zenon_L759_ *) % 10.23/10.38 assert (zenon_L760_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (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 (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_He3 zenon_H18a zenon_H198 zenon_H17c zenon_H86 zenon_H7e zenon_H1e6 zenon_H100 zenon_H1f0 zenon_Hf5 zenon_Hda zenon_H28 zenon_H69 zenon_H5e zenon_H91 zenon_H1e zenon_Hd3 zenon_H90 zenon_Hb1 zenon_H8c zenon_H51 zenon_H1cb zenon_H7a zenon_H84 zenon_Hd0 zenon_H181 zenon_H187 zenon_H1b7 zenon_H8d zenon_H53 zenon_Hb0 zenon_H4c. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.23/10.38 exact (zenon_H56 zenon_H2c). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.23/10.38 apply (zenon_L428_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.23/10.38 apply (zenon_L469_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.23/10.38 exact (zenon_H28 zenon_H31). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.23/10.38 apply (zenon_L18_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.23/10.38 apply (zenon_L20_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.23/10.38 apply (zenon_L21_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.23/10.38 apply (zenon_L22_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.23/10.38 exact (zenon_H91 zenon_H94). % 10.23/10.38 apply (zenon_L759_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.23/10.38 exact (zenon_Hb1 zenon_Hb7). % 10.23/10.38 apply (zenon_L250_); trivial. % 10.23/10.38 apply (zenon_L139_); trivial. % 10.23/10.38 (* end of lemma zenon_L760_ *) % 10.23/10.38 assert (zenon_L761_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.23/10.38 do 0 intro. intros zenon_H90 zenon_H4c zenon_H74 zenon_H78 zenon_H5e zenon_H91 zenon_H181 zenon_H62. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.23/10.38 apply (zenon_L21_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.23/10.38 apply (zenon_L22_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.23/10.38 exact (zenon_H91 zenon_H94). % 10.23/10.38 apply (zenon_L258_); trivial. % 10.23/10.38 (* end of lemma zenon_L761_ *) % 10.23/10.38 assert (zenon_L762_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H18d zenon_H25 zenon_H22c zenon_H64 zenon_H7a zenon_H6f zenon_H28 zenon_H198 zenon_H188 zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H4c zenon_H5e zenon_H91 zenon_H8c zenon_H8d zenon_H86 zenon_H7e zenon_H7f zenon_H7d zenon_H1cb zenon_H90 zenon_H53 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H56 zenon_H200. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L344_); trivial. % 10.23/10.38 apply (zenon_L24_); trivial. % 10.23/10.38 apply (zenon_L252_); trivial. % 10.23/10.38 (* end of lemma zenon_L762_ *) % 10.23/10.38 assert (zenon_L763_ : (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_Hc1 zenon_H4b zenon_H192 zenon_He8 zenon_H191 zenon_H18a zenon_Hc5 zenon_H51 zenon_H3c zenon_H1b7 zenon_H84 zenon_H181 zenon_H187 zenon_Hd2 zenon_H17c zenon_Hc7 zenon_H77 zenon_H35 zenon_H74 zenon_H95 zenon_H1e2 zenon_H18d zenon_H25 zenon_H22c zenon_H64 zenon_H7a zenon_H6f zenon_H28 zenon_H198 zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H4c zenon_H5e zenon_H91 zenon_H8c zenon_H8d zenon_H86 zenon_H7e zenon_H7f zenon_H7d zenon_H1cb zenon_H90 zenon_H53 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H56 zenon_H200. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.23/10.38 apply (zenon_L20_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.23/10.38 apply (zenon_L335_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.23/10.38 exact (zenon_Hb1 zenon_Hb7). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H87 | zenon_intro zenon_H18b ]. % 10.23/10.38 apply (zenon_L270_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H9a | zenon_intro zenon_H18c ]. % 10.23/10.38 apply (zenon_L424_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H9b | zenon_intro zenon_H188 ]. % 10.23/10.38 apply (zenon_L271_); trivial. % 10.23/10.38 apply (zenon_L762_); trivial. % 10.23/10.38 (* end of lemma zenon_L763_ *) % 10.23/10.38 assert (zenon_L764_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (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 (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> False). % 10.23/10.38 do 0 intro. intros zenon_He7 zenon_H1b1 zenon_H62 zenon_H1b0 zenon_H4c zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H18a zenon_Hc5 zenon_H51 zenon_H3c zenon_H1b7 zenon_H84 zenon_H181 zenon_H187 zenon_Hd2 zenon_H17c zenon_Hc7 zenon_H35 zenon_H74 zenon_H95 zenon_H1e2 zenon_H18d zenon_H25 zenon_H22c zenon_H64 zenon_H7a zenon_H6f zenon_H28 zenon_H198 zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H91 zenon_H8c zenon_H8d zenon_H86 zenon_H7e zenon_H7f zenon_H7d zenon_H1cb zenon_H90 zenon_H53 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H56 zenon_H200 zenon_Hc0 zenon_H5e. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.23/10.38 exact (zenon_He8 zenon_Heb). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.23/10.38 apply (zenon_L761_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.23/10.38 apply (zenon_L20_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.23/10.38 apply (zenon_L761_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.23/10.38 exact (zenon_Hb1 zenon_Hb7). % 10.23/10.38 apply (zenon_L250_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.23/10.38 exact (zenon_H192 zenon_H1d). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.23/10.38 apply (zenon_L763_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.23/10.38 exact (zenon_Hc1 zenon_Hc4). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.23/10.38 apply (zenon_L48_); trivial. % 10.23/10.38 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.38 apply (zenon_L206_); trivial. % 10.23/10.38 (* end of lemma zenon_L764_ *) % 10.23/10.38 assert (zenon_L765_ : (((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 (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.23/10.38 do 0 intro. intros zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H4b zenon_H78 zenon_H44 zenon_Hf2 zenon_H35. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.23/10.38 apply (zenon_L331_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.23/10.38 apply (zenon_L334_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.23/10.38 apply (zenon_L57_); trivial. % 10.23/10.38 apply (zenon_L63_); trivial. % 10.23/10.38 (* end of lemma zenon_L765_ *) % 10.23/10.38 assert (zenon_L766_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((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 (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H22d zenon_H22c zenon_H1f0 zenon_Hb4 zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H78 zenon_H44 zenon_Hf2 zenon_H35. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H68 | zenon_intro zenon_H22e ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1e | zenon_intro zenon_H22f ]. % 10.23/10.38 apply (zenon_L327_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H34 | zenon_intro zenon_H4b ]. % 10.23/10.38 apply (zenon_L330_); trivial. % 10.23/10.38 apply (zenon_L765_); trivial. % 10.23/10.38 (* end of lemma zenon_L766_ *) % 10.23/10.38 assert (zenon_L767_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (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 (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.23/10.38 do 0 intro. intros zenon_He7 zenon_H35 zenon_H44 zenon_H22d zenon_H22c zenon_H1f0 zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H1b1 zenon_Hf5 zenon_Hbc zenon_H4c zenon_H5e zenon_H100 zenon_H1e6 zenon_H7e. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.23/10.38 exact (zenon_He8 zenon_Heb). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.23/10.38 apply (zenon_L329_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.23/10.38 exact (zenon_H192 zenon_H1d). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.23/10.38 apply (zenon_L22_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.23/10.38 apply (zenon_L331_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.23/10.38 apply (zenon_L766_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.23/10.38 apply (zenon_L57_); trivial. % 10.23/10.38 apply (zenon_L63_); trivial. % 10.23/10.38 apply (zenon_L364_); trivial. % 10.23/10.38 (* end of lemma zenon_L767_ *) % 10.23/10.38 assert (zenon_L768_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (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 (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((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)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((~((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) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((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). % 10.23/10.38 do 0 intro. intros zenon_Hbb zenon_H205 zenon_H212 zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H14d zenon_H177 zenon_H1af zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H1ea zenon_H158 zenon_H144 zenon_Hf8 zenon_H155 zenon_H108 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_H42 zenon_H1dd zenon_H156 zenon_H11d zenon_Hae zenon_H168 zenon_H150 zenon_H159 zenon_Hec zenon_H12c zenon_Hdd zenon_Hce zenon_H128 zenon_H58 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hc6 zenon_H112 zenon_Hab zenon_H67 zenon_H1de zenon_H56 zenon_H1b4 zenon_H1cb zenon_H69 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_H28 zenon_H4c zenon_Hb0 zenon_Hd3 zenon_H5e zenon_H8c zenon_H181 zenon_H7a zenon_H1b7 zenon_H187 zenon_H198 zenon_H17c zenon_H86 zenon_H84 zenon_H18a zenon_H90 zenon_H53 zenon_He3 zenon_Hda zenon_H1f zenon_H22d zenon_H44 zenon_Hde zenon_H22c zenon_He8 zenon_H1b1 zenon_Hd2 zenon_H1e2 zenon_H35 zenon_H95 zenon_H18d zenon_H25 zenon_H64 zenon_H6f zenon_H7d zenon_H200 zenon_H191 zenon_H1b0 zenon_Hc0 zenon_H192 zenon_He7 zenon_H151. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.38 apply (zenon_L129_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.23/10.38 exact (zenon_H56 zenon_H2c). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.23/10.38 apply (zenon_L760_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.23/10.38 apply (zenon_L12_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.23/10.38 exact (zenon_H28 zenon_H31). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.23/10.38 apply (zenon_L18_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_L764_); trivial. % 10.23/10.38 apply (zenon_L767_); trivial. % 10.23/10.38 apply (zenon_L623_); trivial. % 10.23/10.38 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.38 apply (zenon_L266_); trivial. % 10.23/10.38 apply (zenon_L704_); trivial. % 10.23/10.38 apply (zenon_L435_); trivial. % 10.23/10.38 apply (zenon_L488_); trivial. % 10.23/10.38 (* end of lemma zenon_L768_ *) % 10.23/10.38 assert (zenon_L769_ : ((~((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 (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e3) (e0)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((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 (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 (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((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) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H151 zenon_He7 zenon_H192 zenon_Hc0 zenon_H1b0 zenon_H191 zenon_H200 zenon_H25 zenon_H95 zenon_H1e2 zenon_H1b1 zenon_He8 zenon_H22c zenon_Hde zenon_H22d zenon_H1f zenon_Hda zenon_He3 zenon_H1b7 zenon_H181 zenon_H8c zenon_Hb0 zenon_H4c zenon_H28 zenon_H1de zenon_H67 zenon_Hab zenon_H112 zenon_Hc6 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H58 zenon_H128 zenon_Hce zenon_H12c zenon_Hec zenon_H159 zenon_H150 zenon_H168 zenon_Hae zenon_H11d zenon_H156 zenon_H1dd zenon_H132 zenon_H103 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H155 zenon_H144 zenon_H1ea zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1af zenon_H177 zenon_H14d zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H212 zenon_H205 zenon_Hbb zenon_H158 zenon_H42 zenon_H18d zenon_H7a zenon_H7d zenon_H108 zenon_H53 zenon_H5e zenon_H1cb zenon_Hf8 zenon_H64 zenon_H187 zenon_Hb1 zenon_H3c zenon_Hc5 zenon_H198 zenon_H9a zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H35 zenon_H69 zenon_H44 zenon_H27 zenon_Hd3 zenon_H91 zenon_H17c zenon_H90 zenon_H1b4 zenon_H56 zenon_H6f zenon_H18a zenon_H84 zenon_H86 zenon_Hd2. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L768_); trivial. % 10.23/10.38 apply (zenon_L533_); trivial. % 10.23/10.38 (* end of lemma zenon_L769_ *) % 10.23/10.38 assert (zenon_L770_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((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) (e2)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (((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))) -> (((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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_Hf8 zenon_H1f8 zenon_H155 zenon_H108 zenon_H1cb zenon_H25 zenon_H22c zenon_H18d zenon_He3 zenon_H1ae zenon_H157 zenon_H56 zenon_H1b4 zenon_Hb0 zenon_Hb1 zenon_H90 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H5e zenon_H187 zenon_H64 zenon_H28 zenon_H53 zenon_H4c zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H1af zenon_H198 zenon_H195 zenon_H69 zenon_H192 zenon_H191 zenon_H159 zenon_H1ea zenon_H7d zenon_H7a zenon_H8d zenon_H6f zenon_Hdd zenon_H35 zenon_H44 zenon_H27 zenon_H42 zenon_H86 zenon_H18a zenon_H3a zenon_H3c zenon_H200. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L729_); trivial. % 10.23/10.38 apply (zenon_L531_); trivial. % 10.23/10.38 apply (zenon_L752_); trivial. % 10.23/10.38 (* end of lemma zenon_L770_ *) % 10.23/10.38 assert (zenon_L771_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (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 (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H150 zenon_H84 zenon_H200 zenon_H3c zenon_H3a zenon_H18a zenon_H86 zenon_H42 zenon_H27 zenon_H44 zenon_H35 zenon_Hdd zenon_H6f zenon_H7a zenon_H7d zenon_H1ea zenon_H159 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H4c zenon_H53 zenon_H28 zenon_H64 zenon_H187 zenon_H5e zenon_Hd3 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_Hb1 zenon_Hb0 zenon_H1b4 zenon_H56 zenon_H157 zenon_H1ae zenon_He3 zenon_H18d zenon_H22c zenon_H25 zenon_H1cb zenon_H108 zenon_H155 zenon_H1f8 zenon_Hf8. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_L770_); trivial. % 10.23/10.38 apply (zenon_L266_); trivial. % 10.23/10.38 (* end of lemma zenon_L771_ *) % 10.23/10.38 assert (zenon_L772_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H44 zenon_H78 zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hc1 zenon_Hde zenon_H1f0 zenon_H22c zenon_H22d zenon_H1ae zenon_Hf2 zenon_H35. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.23/10.38 apply (zenon_L331_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.23/10.38 apply (zenon_L766_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.23/10.38 exact (zenon_H1ae zenon_Hb8). % 10.23/10.38 apply (zenon_L63_); trivial. % 10.23/10.38 (* end of lemma zenon_L772_ *) % 10.23/10.38 assert (zenon_L773_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (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))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.23/10.38 do 0 intro. intros zenon_He7 zenon_H35 zenon_H1ae zenon_H22d zenon_H22c zenon_H1f0 zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H44 zenon_H1b1 zenon_Hf5 zenon_Hbc zenon_H4c zenon_H5e zenon_H100 zenon_H1e6 zenon_H7e. % 10.23/10.38 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.23/10.38 exact (zenon_He8 zenon_Heb). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.23/10.38 apply (zenon_L329_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.23/10.38 exact (zenon_H192 zenon_H1d). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.23/10.38 apply (zenon_L22_); trivial. % 10.23/10.38 apply (zenon_L772_); trivial. % 10.23/10.38 apply (zenon_L364_); trivial. % 10.23/10.38 (* end of lemma zenon_L773_ *) % 10.23/10.38 assert (zenon_L774_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H22c zenon_He8 zenon_H1b1 zenon_H191 zenon_Hc1 zenon_H1f zenon_H22d zenon_H44 zenon_H35 zenon_Hde zenon_H1ae zenon_H5e zenon_H192 zenon_H4c zenon_Hbc zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_He7. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.38 apply (zenon_L773_); trivial. % 10.23/10.38 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.38 (* end of lemma zenon_L774_ *) % 10.23/10.38 assert (zenon_L775_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (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)) = (op (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((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) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((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)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (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 (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H212 zenon_Hc5 zenon_H3c zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H14d zenon_H177 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H1ea zenon_H158 zenon_H144 zenon_Hf8 zenon_H155 zenon_H108 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_H42 zenon_H1dd zenon_H11d zenon_Hae zenon_H168 zenon_H150 zenon_H159 zenon_Hec zenon_Hdd zenon_H128 zenon_H58 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hc6 zenon_H112 zenon_Hab zenon_H67 zenon_H1de zenon_H1cb zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_H8c zenon_H181 zenon_H7a zenon_H1b7 zenon_H86 zenon_H18a zenon_H6f zenon_H1f zenon_H22d zenon_H44 zenon_Hde zenon_H22c zenon_He8 zenon_H1e2 zenon_H18d zenon_H25 zenon_H7d zenon_H200 zenon_H1b0 zenon_Hc0 zenon_He7 zenon_H151 zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H156 zenon_Hd2 zenon_Hce zenon_H198 zenon_H35 zenon_H1b1 zenon_Hbb zenon_H95 zenon_H205 zenon_H12c zenon_H1b4 zenon_H28 zenon_H53 zenon_Hb0 zenon_H4c zenon_H90 zenon_H17c zenon_Hd3 zenon_H5e zenon_H51 zenon_H187 zenon_H64 zenon_He3 zenon_H84 zenon_Hda zenon_H56 zenon_H1ae zenon_H157 zenon_H1af. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.23/10.38 apply (zenon_L740_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.38 apply (zenon_L129_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.23/10.38 exact (zenon_H56 zenon_H2c). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.23/10.38 apply (zenon_L760_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.23/10.38 apply (zenon_L228_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.23/10.38 exact (zenon_H28 zenon_H31). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.23/10.38 apply (zenon_L18_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_L764_); trivial. % 10.23/10.38 apply (zenon_L773_); trivial. % 10.23/10.38 apply (zenon_L623_); trivial. % 10.23/10.38 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.38 apply (zenon_L774_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.23/10.38 exact (zenon_H56 zenon_H2c). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.23/10.38 apply (zenon_L123_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.23/10.38 exact (zenon_H28 zenon_H31). % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.23/10.38 apply (zenon_L18_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.23/10.38 apply (zenon_L21_); trivial. % 10.23/10.38 apply (zenon_L717_); trivial. % 10.23/10.38 apply (zenon_L474_); trivial. % 10.23/10.38 apply (zenon_L472_); trivial. % 10.23/10.38 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.38 apply (zenon_L354_); trivial. % 10.23/10.38 exact (zenon_H1ae zenon_Hb8). % 10.23/10.38 apply (zenon_L732_); trivial. % 10.23/10.38 apply (zenon_L739_); trivial. % 10.23/10.38 (* end of lemma zenon_L775_ *) % 10.23/10.38 assert (zenon_L776_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (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)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((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)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (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)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H1af zenon_H157 zenon_H1ae zenon_Hda zenon_H84 zenon_He3 zenon_H4c zenon_Hb0 zenon_H28 zenon_H12c zenon_H205 zenon_H95 zenon_Hbb zenon_H1b1 zenon_Hce zenon_Hd2 zenon_H156 zenon_H195 zenon_H192 zenon_H191 zenon_H151 zenon_He7 zenon_Hc0 zenon_H1b0 zenon_H200 zenon_H25 zenon_H1e2 zenon_He8 zenon_H22c zenon_Hde zenon_H22d zenon_H1f zenon_H1b7 zenon_H181 zenon_H8c zenon_H1de zenon_H67 zenon_Hab zenon_H112 zenon_Hc6 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H58 zenon_H128 zenon_Hec zenon_H159 zenon_H150 zenon_H168 zenon_Hae zenon_H11d zenon_H1dd zenon_H132 zenon_H103 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H155 zenon_H144 zenon_H158 zenon_H1ea zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H177 zenon_H14d zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_Hc5 zenon_H212 zenon_Hf8 zenon_H1cb zenon_H5e zenon_Hb1 zenon_H53 zenon_H108 zenon_H56 zenon_H1b4 zenon_H3c zenon_H3a zenon_Hd3 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H187 zenon_H90 zenon_H42 zenon_H27 zenon_H44 zenon_H69 zenon_H35 zenon_Hf5 zenon_H7e zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H9a zenon_H198 zenon_H6f zenon_H64. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.38 exact (zenon_H25 zenon_H2a). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.38 exact (zenon_H22c zenon_H68). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.38 apply (zenon_L775_); trivial. % 10.23/10.38 apply (zenon_L532_); trivial. % 10.23/10.38 (* end of lemma zenon_L776_ *) % 10.23/10.38 assert (zenon_L777_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H1e2 zenon_H76 zenon_H1ae zenon_Hc7 zenon_H150 zenon_He3 zenon_H56 zenon_H42 zenon_H181 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H43 zenon_H187 zenon_H64. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 10.23/10.38 apply (zenon_L47_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 10.23/10.38 exact (zenon_H1ae zenon_Hb8). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 10.23/10.38 exact (zenon_Hc7 zenon_H3a). % 10.23/10.38 apply (zenon_L412_); trivial. % 10.23/10.38 (* end of lemma zenon_L777_ *) % 10.23/10.38 assert (zenon_L778_ : (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (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))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.23/10.38 do 0 intro. intros zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H18a zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_H6f zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H42 zenon_H1e2 zenon_H1ae zenon_H150 zenon_He3 zenon_H56 zenon_H181 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_H53 zenon_H165 zenon_H64 zenon_H198 zenon_H1b4 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H9a zenon_H187. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.23/10.38 exact (zenon_H56 zenon_H2c). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.23/10.38 exact (zenon_H56 zenon_H2c). % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.23/10.38 apply (zenon_L194_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.23/10.38 apply (zenon_L777_); trivial. % 10.23/10.38 apply (zenon_L415_); trivial. % 10.23/10.38 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.23/10.38 apply (zenon_L103_); trivial. % 10.23/10.38 apply (zenon_L202_); trivial. % 10.23/10.38 (* end of lemma zenon_L778_ *) % 10.23/10.38 assert (zenon_L779_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> False). % 10.23/10.38 do 0 intro. intros zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7e zenon_H7a zenon_H18d zenon_H35 zenon_H1ae zenon_Hc7 zenon_H150 zenon_He3 zenon_H42 zenon_H181 zenon_H6e zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H43 zenon_H187 zenon_H64 zenon_H1e2 zenon_H9a zenon_H198 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_Hb1. % 10.23/10.38 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.38 apply (zenon_L778_); trivial. % 10.23/10.38 apply (zenon_L254_); trivial. % 10.23/10.38 (* end of lemma zenon_L779_ *) % 10.23/10.38 assert (zenon_L780_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((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))))) -> (((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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 (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). % 10.23/10.39 do 0 intro. intros zenon_H157 zenon_Hd2 zenon_H56 zenon_H198 zenon_H9a zenon_H1e2 zenon_H64 zenon_H187 zenon_H43 zenon_H86 zenon_H18a zenon_H165 zenon_H53 zenon_H159 zenon_H90 zenon_H17c zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_He7 zenon_Hdd zenon_H191 zenon_H1f zenon_H192 zenon_H14d zenon_H95 zenon_H4c zenon_H27 zenon_H6f zenon_H6e zenon_H181 zenon_H42 zenon_He3 zenon_H150 zenon_H1ae zenon_H35 zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_Hcf zenon_Hd3 zenon_H1b4 zenon_Hc6 zenon_H158. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.23/10.39 exact (zenon_H56 zenon_H2c). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.23/10.39 apply (zenon_L194_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.23/10.39 apply (zenon_L777_); trivial. % 10.23/10.39 apply (zenon_L388_); trivial. % 10.23/10.39 apply (zenon_L412_); trivial. % 10.23/10.39 apply (zenon_L321_); trivial. % 10.23/10.39 exact (zenon_H1ae zenon_Hb8). % 10.23/10.39 (* end of lemma zenon_L780_ *) % 10.23/10.39 assert (zenon_L781_ : ((~((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 (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) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((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))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((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))))) -> (~((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))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (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))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H1af zenon_H157 zenon_Hd2 zenon_H3c zenon_Hc5 zenon_H198 zenon_H1e2 zenon_H64 zenon_H187 zenon_H43 zenon_H86 zenon_H18a zenon_H165 zenon_H53 zenon_H159 zenon_H90 zenon_H17c zenon_H44 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_He7 zenon_Hdd zenon_H1f zenon_H14d zenon_H95 zenon_H4c zenon_H27 zenon_H6f zenon_H181 zenon_H42 zenon_He3 zenon_H150 zenon_H1ae zenon_H35 zenon_H18d zenon_H7a zenon_H7e zenon_H7d zenon_Hd3 zenon_H1b4 zenon_H56 zenon_H108 zenon_H155 zenon_Hf8 zenon_H158 zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_Hc6 zenon_H156 zenon_He8 zenon_H192 zenon_H16e zenon_H6e zenon_H191. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.39 apply (zenon_L224_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.39 apply (zenon_L779_); trivial. % 10.23/10.39 apply (zenon_L412_); trivial. % 10.23/10.39 apply (zenon_L223_); trivial. % 10.23/10.39 exact (zenon_H1ae zenon_Hb8). % 10.23/10.39 apply (zenon_L780_); trivial. % 10.23/10.39 (* end of lemma zenon_L781_ *) % 10.23/10.39 assert (zenon_L782_ : (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H21d zenon_H43 zenon_H181 zenon_H9a zenon_H17c zenon_H9b zenon_Hb9 zenon_H184. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H89 | zenon_intro zenon_H21e ]. % 10.23/10.39 apply (zenon_L548_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_H8a | zenon_intro zenon_H21f ]. % 10.23/10.39 apply (zenon_L166_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H11f ]. % 10.23/10.39 apply (zenon_L162_); trivial. % 10.23/10.39 apply (zenon_L549_); trivial. % 10.23/10.39 (* end of lemma zenon_L782_ *) % 10.23/10.39 assert (zenon_L783_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H18d zenon_H11f zenon_H205 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.23/10.39 apply (zenon_L24_); trivial. % 10.23/10.39 apply (zenon_L385_); trivial. % 10.23/10.39 (* end of lemma zenon_L783_ *) % 10.23/10.39 assert (zenon_L784_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H12c zenon_H91 zenon_H5e zenon_H78 zenon_H4c zenon_H90 zenon_H184 zenon_H9b zenon_H17c zenon_H9a zenon_H181 zenon_H21d zenon_Hc8 zenon_H18d zenon_H205 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 10.23/10.39 apply (zenon_L483_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 10.23/10.39 apply (zenon_L782_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 10.23/10.39 exact (zenon_Hc8 zenon_Hcd). % 10.23/10.39 apply (zenon_L783_); trivial. % 10.23/10.39 (* end of lemma zenon_L784_ *) % 10.23/10.39 assert (zenon_L785_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (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)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_Hae zenon_H69 zenon_Haf zenon_H191 zenon_H16e zenon_H192 zenon_He8 zenon_H156 zenon_Hc6 zenon_Hbb zenon_H1b1 zenon_H158 zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H35 zenon_H1ae zenon_H150 zenon_He3 zenon_H42 zenon_H6f zenon_H27 zenon_H95 zenon_H14d zenon_H1f zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H44 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H187 zenon_H64 zenon_H1e2 zenon_H198 zenon_Hc5 zenon_H3c zenon_Hd2 zenon_H157 zenon_H1af zenon_H12c zenon_H91 zenon_H5e zenon_H78 zenon_H4c zenon_H90 zenon_H184 zenon_H17c zenon_H9a zenon_H181 zenon_H21d zenon_Hc8 zenon_H18d zenon_H205 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.23/10.39 apply (zenon_L17_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.23/10.39 exact (zenon_Haf zenon_Hb4). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.23/10.39 apply (zenon_L781_); trivial. % 10.23/10.39 apply (zenon_L784_); trivial. % 10.23/10.39 (* end of lemma zenon_L785_ *) % 10.23/10.39 assert (zenon_L786_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H7a zenon_H1cb zenon_H1b7 zenon_H150 zenon_He3 zenon_H56 zenon_H42 zenon_Hd0 zenon_H181 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H187 zenon_H64. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.23/10.39 exact (zenon_H25 zenon_H2a). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.23/10.39 exact (zenon_H22c zenon_H68). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.23/10.39 apply (zenon_L418_); trivial. % 10.23/10.39 apply (zenon_L412_); trivial. % 10.23/10.39 (* end of lemma zenon_L786_ *) % 10.23/10.39 assert (zenon_L787_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H1e2 zenon_Hbb zenon_H12c zenon_Hc8 zenon_H205 zenon_Hd3 zenon_H1b1 zenon_H198 zenon_H1b4 zenon_Hd6 zenon_H114 zenon_Hc7 zenon_H200 zenon_H25 zenon_H22c zenon_H7a zenon_H1cb zenon_H1b7 zenon_H150 zenon_He3 zenon_H56 zenon_H42 zenon_H181 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H187 zenon_H64. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 10.23/10.39 apply (zenon_L396_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 10.23/10.39 apply (zenon_L398_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 10.23/10.39 exact (zenon_Hc7 zenon_H3a). % 10.23/10.39 apply (zenon_L786_); trivial. % 10.23/10.39 (* end of lemma zenon_L787_ *) % 10.23/10.39 assert (zenon_L788_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (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 (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.23/10.39 do 0 intro. intros zenon_Hde zenon_He5 zenon_Haf zenon_H1e zenon_Hb1 zenon_H76 zenon_Hb0 zenon_H1e2 zenon_Hbb zenon_H12c zenon_Hc8 zenon_H205 zenon_Hd3 zenon_H1b1 zenon_H198 zenon_H1b4 zenon_H114 zenon_Hc7 zenon_H200 zenon_H25 zenon_H22c zenon_H7a zenon_H1cb zenon_H1b7 zenon_H150 zenon_He3 zenon_H56 zenon_H42 zenon_H181 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H187 zenon_H64. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.23/10.39 apply (zenon_L404_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.23/10.39 exact (zenon_Haf zenon_Hb4). % 10.23/10.39 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.23/10.39 apply (zenon_L395_); trivial. % 10.23/10.39 apply (zenon_L787_); trivial. % 10.23/10.39 (* end of lemma zenon_L788_ *) % 10.23/10.39 assert (zenon_L789_ : (((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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.23/10.39 do 0 intro. intros zenon_Hae zenon_H44 zenon_H69 zenon_Haf zenon_H181 zenon_H6f zenon_H1e zenon_H35 zenon_H27 zenon_H42 zenon_Hd0 zenon_H17c. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.23/10.39 apply (zenon_L17_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.23/10.39 exact (zenon_Haf zenon_Hb4). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.23/10.39 apply (zenon_L227_); trivial. % 10.23/10.39 apply (zenon_L162_); trivial. % 10.23/10.39 (* end of lemma zenon_L789_ *) % 10.23/10.39 assert (zenon_L790_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (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)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 10.23/10.39 do 0 intro. intros zenon_Hae zenon_H69 zenon_H158 zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_Haf zenon_Hb0 zenon_Hd3 zenon_H53 zenon_H44 zenon_H5e zenon_H64 zenon_H165 zenon_H159 zenon_He8 zenon_Hc0 zenon_H17a zenon_He7 zenon_Hdd zenon_H191 zenon_H1f zenon_H14d zenon_He3 zenon_H150 zenon_H114 zenon_H1b4 zenon_H192 zenon_H84 zenon_H205 zenon_Hbb zenon_H1b1 zenon_H9a zenon_Hce zenon_Hd2 zenon_Hde zenon_H27 zenon_H35 zenon_H6f zenon_H90 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H91 zenon_H1e2 zenon_H181 zenon_H95 zenon_H4c zenon_Hab zenon_H7e zenon_H198 zenon_H12c zenon_H1bc zenon_H42 zenon_Hc5 zenon_H3c zenon_H156 zenon_H187 zenon_H47. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.23/10.39 apply (zenon_L17_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.23/10.39 exact (zenon_Haf zenon_Hb4). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.23/10.39 apply (zenon_L453_); trivial. % 10.23/10.39 apply (zenon_L243_); trivial. % 10.23/10.39 (* end of lemma zenon_L790_ *) % 10.23/10.39 assert (zenon_L791_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H156 zenon_H3c zenon_Hc5 zenon_H42 zenon_H1bc zenon_H12c zenon_H198 zenon_H7e zenon_Hab zenon_H4c zenon_H95 zenon_H181 zenon_H1e2 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H90 zenon_H6f zenon_H35 zenon_H27 zenon_Hde zenon_Hd2 zenon_Hce zenon_H1b1 zenon_Hbb zenon_H205 zenon_H84 zenon_H192 zenon_H1b4 zenon_H114 zenon_H150 zenon_He3 zenon_H14d zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_Hc0 zenon_He8 zenon_H159 zenon_H165 zenon_H64 zenon_H5e zenon_H44 zenon_H53 zenon_Hd3 zenon_Hb0 zenon_Haf zenon_H56 zenon_H108 zenon_H155 zenon_Hf8 zenon_H158 zenon_H69 zenon_Hae zenon_H8d zenon_Hd0 zenon_H9a zenon_H187. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.23/10.39 exact (zenon_H56 zenon_H2c). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.23/10.39 apply (zenon_L789_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.23/10.39 exact (zenon_H27 zenon_H32). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.23/10.39 apply (zenon_L17_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.23/10.39 exact (zenon_Haf zenon_Hb4). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.23/10.39 apply (zenon_L410_); trivial. % 10.23/10.39 apply (zenon_L162_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.23/10.39 apply (zenon_L70_); trivial. % 10.23/10.39 apply (zenon_L790_); trivial. % 10.23/10.39 apply (zenon_L202_); trivial. % 10.23/10.39 (* end of lemma zenon_L791_ *) % 10.23/10.39 assert (zenon_L792_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H14d zenon_H44 zenon_Hd8 zenon_Hf2 zenon_H5e zenon_Hed zenon_H53 zenon_H8d. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 10.23/10.39 apply (zenon_L99_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 10.23/10.39 apply (zenon_L206_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 10.23/10.39 apply (zenon_L73_); trivial. % 10.23/10.39 exact (zenon_H8d zenon_H7b). % 10.23/10.39 (* end of lemma zenon_L792_ *) % 10.23/10.39 assert (zenon_L793_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> False). % 10.23/10.39 do 0 intro. intros zenon_H1b1 zenon_H35 zenon_H192 zenon_H17a zenon_H84 zenon_H4c zenon_H34 zenon_H95 zenon_Hc0 zenon_H5e zenon_He5. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.23/10.39 apply (zenon_L4_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.23/10.39 exact (zenon_H192 zenon_H1d). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.23/10.39 apply (zenon_L399_); trivial. % 10.23/10.39 apply (zenon_L206_); trivial. % 10.23/10.39 (* end of lemma zenon_L793_ *) % 10.23/10.39 assert (zenon_L794_ : (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (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 (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 (e2) (e1)) = (e2))) -> ((~((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)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> False). % 10.23/10.39 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H69 zenon_Hd2 zenon_Hce zenon_H56 zenon_H198 zenon_H9a zenon_Hbb zenon_H205 zenon_H12c zenon_Hd3 zenon_H17c zenon_H90 zenon_H1b4 zenon_H1ae zenon_H157 zenon_He7 zenon_H22c zenon_He8 zenon_H8d zenon_H53 zenon_Hed zenon_H44 zenon_H14d zenon_H1b1 zenon_H35 zenon_H192 zenon_H17a zenon_H84 zenon_H4c zenon_H34 zenon_H95 zenon_Hc0 zenon_H5e. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.23/10.39 exact (zenon_H27 zenon_H32). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.23/10.39 apply (zenon_L17_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.23/10.39 apply (zenon_L737_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.23/10.39 exact (zenon_H22c zenon_H68). % 10.23/10.39 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.23/10.39 exact (zenon_He8 zenon_Heb). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.23/10.39 apply (zenon_L4_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.23/10.39 exact (zenon_H192 zenon_H1d). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.23/10.39 apply (zenon_L22_); trivial. % 10.23/10.39 apply (zenon_L792_); trivial. % 10.23/10.39 apply (zenon_L793_); trivial. % 10.23/10.39 (* end of lemma zenon_L794_ *) % 10.23/10.39 assert (zenon_L795_ : ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e0)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (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)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.23/10.39 do 0 intro. intros zenon_Hed zenon_H8d zenon_H22c zenon_H157 zenon_H1ae zenon_H3a zenon_Hae zenon_H69 zenon_H158 zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_Haf zenon_Hb0 zenon_Hd3 zenon_H53 zenon_H44 zenon_H5e zenon_H64 zenon_H165 zenon_H159 zenon_He8 zenon_Hc0 zenon_H17a zenon_He7 zenon_Hdd zenon_H191 zenon_H1f zenon_H14d zenon_He3 zenon_H150 zenon_H114 zenon_H1b4 zenon_H192 zenon_H84 zenon_H205 zenon_Hbb zenon_H1b1 zenon_H9a zenon_Hce zenon_Hd2 zenon_Hde zenon_H27 zenon_H35 zenon_H6f zenon_H90 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H91 zenon_H1e2 zenon_H181 zenon_H95 zenon_H4c zenon_Hab zenon_H7e zenon_H198 zenon_H12c zenon_H1bc zenon_H42 zenon_Hc5 zenon_H3c zenon_H156 zenon_H187. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.23/10.39 exact (zenon_H27 zenon_H32). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.23/10.39 apply (zenon_L794_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.23/10.39 apply (zenon_L5_); trivial. % 10.23/10.39 apply (zenon_L790_); trivial. % 10.23/10.39 (* end of lemma zenon_L795_ *) % 10.23/10.39 assert (zenon_L796_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((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 (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (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). % 10.23/10.39 do 0 intro. intros zenon_H1bc zenon_Hab zenon_Hce zenon_H56 zenon_H22c zenon_He8 zenon_Hae zenon_H21d zenon_H184 zenon_H16e zenon_H156 zenon_Hc6 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_H158 zenon_Hf8 zenon_H155 zenon_H108 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7a zenon_H18d zenon_H35 zenon_H1ae zenon_H150 zenon_He3 zenon_H42 zenon_H181 zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H1f zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H43 zenon_H187 zenon_H64 zenon_H1e2 zenon_Hc5 zenon_H3c zenon_Hd2 zenon_H157 zenon_H1af zenon_H44 zenon_Hb0 zenon_H25 zenon_H1b7 zenon_H1cb zenon_H200 zenon_H114 zenon_Hde zenon_H198 zenon_H1b0 zenon_H151 zenon_H1fb zenon_H195 zenon_H69 zenon_H192 zenon_Haf zenon_H191. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.23/10.39 apply (zenon_L191_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.23/10.39 exact (zenon_H56 zenon_H2c). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.23/10.39 exact (zenon_H56 zenon_H2c). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.23/10.39 apply (zenon_L194_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.23/10.39 exact (zenon_H22c zenon_H68). % 10.23/10.39 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.23/10.39 exact (zenon_He8 zenon_Heb). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.23/10.39 apply (zenon_L785_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.23/10.39 apply (zenon_L17_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.23/10.39 exact (zenon_Haf zenon_Hb4). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.23/10.39 apply (zenon_L788_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.23/10.39 apply (zenon_L43_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.23/10.39 apply (zenon_L784_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.23/10.39 exact (zenon_Hb1 zenon_Hb7). % 10.23/10.39 apply (zenon_L548_); trivial. % 10.23/10.39 apply (zenon_L525_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.23/10.39 apply (zenon_L103_); trivial. % 10.23/10.39 apply (zenon_L202_); trivial. % 10.23/10.39 apply (zenon_L254_); trivial. % 10.23/10.39 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.39 apply (zenon_L791_); trivial. % 10.23/10.39 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.39 apply (zenon_L266_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.23/10.39 exact (zenon_H27 zenon_H32). % 10.23/10.39 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.23/10.39 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.23/10.39 exact (zenon_H22c zenon_H68). % 10.23/10.39 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.23/10.39 exact (zenon_He8 zenon_Heb). % 10.23/10.39 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.23/10.39 apply (zenon_L785_); trivial. % 10.23/10.39 apply (zenon_L404_); trivial. % 10.23/10.39 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.23/10.39 apply (zenon_L5_); trivial. % 10.23/10.39 apply (zenon_L790_); trivial. % 10.23/10.39 apply (zenon_L795_); trivial. % 10.23/10.39 exact (zenon_H1b0 zenon_Hbd). % 10.23/10.39 apply (zenon_L266_); trivial. % 10.23/10.39 apply (zenon_L354_); trivial. % 10.23/10.39 exact (zenon_H1ae zenon_Hb8). % 10.23/10.39 apply (zenon_L737_); trivial. % 10.23/10.39 (* end of lemma zenon_L796_ *) % 10.23/10.39 assert (zenon_L797_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (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 (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (((op (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 (e1) (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 (e1) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((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)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (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) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (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) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 10.23/10.39 do 0 intro. intros zenon_H1fb zenon_H151 zenon_H1b0 zenon_Hde zenon_H114 zenon_H200 zenon_H1cb zenon_H1b7 zenon_H44 zenon_H3c zenon_Hc5 zenon_H1e2 zenon_H86 zenon_H18a zenon_H165 zenon_H159 zenon_Hc0 zenon_H17a zenon_He7 zenon_Hdd zenon_H1f zenon_H14d zenon_H6f zenon_H181 zenon_H42 zenon_H150 zenon_H18d zenon_H7a zenon_H7d zenon_H108 zenon_H155 zenon_Hf8 zenon_H158 zenon_Hc6 zenon_H16e zenon_H184 zenon_H21d zenon_Hae zenon_Hab zenon_H1bc zenon_H191 zenon_H192 zenon_H69 zenon_H195 zenon_H156 zenon_Hd2 zenon_Hce zenon_H198 zenon_H35 zenon_H1b1 zenon_Hbb zenon_H95 zenon_H205 zenon_H12c zenon_H1b4 zenon_H53 zenon_Hb0 zenon_H4c zenon_H90 zenon_H17c zenon_Hd3 zenon_H5e zenon_H187 zenon_H64 zenon_He3 zenon_H84 zenon_Hda zenon_H1ae zenon_H157 zenon_H1af zenon_H22c zenon_H212 zenon_H112 zenon_H22d zenon_H1de zenon_H67 zenon_H1f0 zenon_Hf5 zenon_H168 zenon_Hec zenon_H8c zenon_H128 zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H11d zenon_H1dd zenon_H144 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_H1ea zenon_H4a zenon_H204 zenon_Hfd zenon_H1f8 zenon_H177 zenon_H1e6 zenon_H1ef zenon_H16b zenon_H152 zenon_H173 zenon_H174. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.26/10.40 exact (zenon_H25 zenon_H2a). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_L740_); trivial. % 10.26/10.40 apply (zenon_L796_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_L743_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.40 apply (zenon_L695_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L756_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L776_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 exact (zenon_H1ae zenon_Hb8). % 10.26/10.40 apply (zenon_L737_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L796_); trivial. % 10.26/10.40 apply (zenon_L745_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_L775_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_L343_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 (* end of lemma zenon_L797_ *) % 10.26/10.40 assert (zenon_L798_ : ((~((op (e2) (e2)) = (e1)))\/(~((op (e2) (e1)) = (e2)))) -> (((op (e2) (e3)) = (e0))\/(((op (e2) (e3)) = (e1))\/(((op (e2) (e3)) = (e2))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((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) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (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) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H22a zenon_H21d zenon_H184 zenon_H174 zenon_H212 zenon_H22c zenon_H191 zenon_H195 zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H165 zenon_H17a zenon_Hbb zenon_H205 zenon_H18e zenon_H44 zenon_H192 zenon_H69 zenon_H12f zenon_H22d zenon_H151 zenon_H22b. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H91 | zenon_intro zenon_H1ae ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.26/10.40 exact (zenon_H192 zenon_H1d). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L466_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.26/10.40 exact (zenon_H25 zenon_H2a). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_L618_); trivial. % 10.26/10.40 apply (zenon_L24_); trivial. % 10.26/10.40 apply (zenon_L523_); trivial. % 10.26/10.40 apply (zenon_L472_); trivial. % 10.26/10.40 apply (zenon_L354_); trivial. % 10.26/10.40 apply (zenon_L321_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_L755_); trivial. % 10.26/10.40 apply (zenon_L235_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_L624_); trivial. % 10.26/10.40 apply (zenon_L619_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L466_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_L523_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_L757_); trivial. % 10.26/10.40 apply (zenon_L755_); trivial. % 10.26/10.40 apply (zenon_L235_); trivial. % 10.26/10.40 apply (zenon_L535_); trivial. % 10.26/10.40 apply (zenon_L626_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.26/10.40 exact (zenon_H192 zenon_H1d). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L694_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_L758_); trivial. % 10.26/10.40 apply (zenon_L523_); trivial. % 10.26/10.40 apply (zenon_L623_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_L758_); trivial. % 10.26/10.40 apply (zenon_L769_); trivial. % 10.26/10.40 apply (zenon_L752_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_L235_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_L703_); trivial. % 10.26/10.40 apply (zenon_L707_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L694_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_L523_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L769_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_L235_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_L708_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L694_); trivial. % 10.26/10.40 apply (zenon_L768_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_L343_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.26/10.40 exact (zenon_H192 zenon_H1d). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L709_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_L727_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.40 apply (zenon_L770_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_L753_); trivial. % 10.26/10.40 apply (zenon_L771_); trivial. % 10.26/10.40 apply (zenon_L267_); trivial. % 10.26/10.40 exact (zenon_H1ae zenon_Hb8). % 10.26/10.40 apply (zenon_L321_); trivial. % 10.26/10.40 apply (zenon_L736_); trivial. % 10.26/10.40 apply (zenon_L733_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L709_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_L727_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_L757_); trivial. % 10.26/10.40 apply (zenon_L771_); trivial. % 10.26/10.40 exact (zenon_H1ae zenon_Hb8). % 10.26/10.40 apply (zenon_L737_); trivial. % 10.26/10.40 apply (zenon_L738_); trivial. % 10.26/10.40 apply (zenon_L741_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.26/10.40 exact (zenon_H192 zenon_H1d). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L742_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_L743_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.26/10.40 exact (zenon_H25 zenon_H2a). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.26/10.40 apply (zenon_L486_); trivial. % 10.26/10.40 apply (zenon_L748_); trivial. % 10.26/10.40 apply (zenon_L776_); trivial. % 10.26/10.40 apply (zenon_L752_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_L753_); trivial. % 10.26/10.40 apply (zenon_L776_); trivial. % 10.26/10.40 apply (zenon_L267_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 exact (zenon_H1ae zenon_Hb8). % 10.26/10.40 apply (zenon_L321_); trivial. % 10.26/10.40 apply (zenon_L468_); trivial. % 10.26/10.40 apply (zenon_L749_); trivial. % 10.26/10.40 apply (zenon_L750_); trivial. % 10.26/10.40 exact (zenon_H22c zenon_H68). % 10.26/10.40 apply (zenon_L100_); trivial. % 10.26/10.40 apply (zenon_L797_); trivial. % 10.26/10.40 (* end of lemma zenon_L798_ *) % 10.26/10.40 assert (zenon_L799_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (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 (e0) (e2)) = (op (e2) (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))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_H56 zenon_Hb0 zenon_Hb1 zenon_H8d zenon_H4c zenon_H53 zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_Hd3 zenon_H91 zenon_H8c zenon_H1b7 zenon_H187 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H5e zenon_H86 zenon_H7d zenon_H58 zenon_H90 zenon_H1ba zenon_H2a zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H15a zenon_H35 zenon_H27 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_H64 zenon_H108 zenon_H155 zenon_Hf8. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L310_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 (* end of lemma zenon_L799_ *) % 10.26/10.40 assert (zenon_L800_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (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)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_He3 zenon_H56 zenon_H42 zenon_H1bc zenon_H15a zenon_Hd3 zenon_H91 zenon_H8c zenon_H5e zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1c0 zenon_Hbc zenon_H4c zenon_H95 zenon_H128 zenon_H53 zenon_H2a zenon_H58 zenon_H12c zenon_H192 zenon_H181 zenon_H64 zenon_H1dd zenon_Hf8. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L268_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 (* end of lemma zenon_L800_ *) % 10.26/10.40 assert (zenon_L801_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (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 (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (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)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((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 (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) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H150 zenon_Hf8 zenon_Hc1 zenon_H1e6 zenon_H1de zenon_H10b zenon_H108 zenon_H132 zenon_H28 zenon_H4c zenon_H90 zenon_H86 zenon_H8c zenon_H91 zenon_H56 zenon_Hd3 zenon_H42 zenon_H181 zenon_H95 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_Hdd zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H187 zenon_Hc7 zenon_H1e2 zenon_H198 zenon_H17c zenon_Hb0 zenon_H97 zenon_H7d zenon_H7a zenon_H64 zenon_Hd0 zenon_Hce zenon_H15a zenon_H35 zenon_H27 zenon_H192 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_H1b7 zenon_H58 zenon_H18d zenon_H1b0 zenon_H151. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L287_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_L221_); trivial. % 10.26/10.40 (* end of lemma zenon_L801_ *) % 10.26/10.40 assert (zenon_L802_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((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 (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (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 (e1) (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((~((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) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H168 zenon_H156 zenon_H97 zenon_H17c zenon_H1e2 zenon_H18a zenon_H132 zenon_H10b zenon_H1e6 zenon_H1de zenon_Hf8 zenon_H108 zenon_H64 zenon_H3c zenon_H27 zenon_H35 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H7d zenon_H86 zenon_H128 zenon_Hce zenon_Hdd zenon_H8c zenon_Hd3 zenon_H198 zenon_H28 zenon_H53 zenon_Hb0 zenon_H56 zenon_H18d zenon_H1b0 zenon_H151 zenon_H95 zenon_H4c zenon_He3 zenon_H42 zenon_H6f zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H12c zenon_H1dd zenon_H150 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H1af. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_L461_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.26/10.40 apply (zenon_L236_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.26/10.40 exact (zenon_Hc1 zenon_Hc4). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.26/10.40 apply (zenon_L237_); trivial. % 10.26/10.40 apply (zenon_L799_); trivial. % 10.26/10.40 apply (zenon_L800_); trivial. % 10.26/10.40 apply (zenon_L801_); trivial. % 10.26/10.40 apply (zenon_L223_); trivial. % 10.26/10.40 apply (zenon_L296_); trivial. % 10.26/10.40 apply (zenon_L194_); trivial. % 10.26/10.40 (* end of lemma zenon_L802_ *) % 10.26/10.40 assert (zenon_L803_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((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))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H158 zenon_H145 zenon_H9a zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H151 zenon_H1b0 zenon_H18d zenon_H58 zenon_H187 zenon_H181 zenon_H7a zenon_H1b7 zenon_H100 zenon_H7d zenon_H86 zenon_H64 zenon_H132 zenon_H103 zenon_H4c zenon_H1cb zenon_Hb1 zenon_H53 zenon_H108 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H42 zenon_H56 zenon_Hf8 zenon_Hd2. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.40 apply (zenon_L193_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L232_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_L223_); trivial. % 10.26/10.40 (* end of lemma zenon_L803_ *) % 10.26/10.40 assert (zenon_L804_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((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)) = (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 (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H157 zenon_H112 zenon_H145 zenon_H9a zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_Hce zenon_Hcf zenon_Hd2. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.40 apply (zenon_L193_); trivial. % 10.26/10.40 apply (zenon_L44_); trivial. % 10.26/10.40 apply (zenon_L79_); trivial. % 10.26/10.40 (* end of lemma zenon_L804_ *) % 10.26/10.40 assert (zenon_L805_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((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) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H158 zenon_Hc6 zenon_Hd2 zenon_Hcf zenon_Hce zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_H155 zenon_H5e zenon_H9a zenon_H145 zenon_H112 zenon_H157. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_L804_); trivial. % 10.26/10.40 apply (zenon_L321_); trivial. % 10.26/10.40 (* end of lemma zenon_L805_ *) % 10.26/10.40 assert (zenon_L806_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_H188 zenon_H12f zenon_H2a zenon_He8 zenon_H5e zenon_H100 zenon_H7d zenon_H86 zenon_H145 zenon_H144 zenon_H10b zenon_H3a zenon_H3c zenon_H6f zenon_H132 zenon_Hf8. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L304_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 (* end of lemma zenon_L806_ *) % 10.26/10.40 assert (zenon_L807_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.26/10.40 do 0 intro. intros zenon_H97 zenon_H28 zenon_H1b0 zenon_H16b zenon_Hd8 zenon_H95 zenon_H114 zenon_H10b zenon_H80 zenon_Hc1 zenon_H34 zenon_Hc0 zenon_H187 zenon_H188. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.26/10.40 exact (zenon_H28 zenon_H31). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.26/10.40 apply (zenon_L184_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.26/10.40 apply (zenon_L184_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.26/10.40 exact (zenon_Hc1 zenon_Hc4). % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L366_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_L167_); trivial. % 10.26/10.40 (* end of lemma zenon_L807_ *) % 10.26/10.40 assert (zenon_L808_ : (((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). % 10.26/10.40 do 0 intro. intros zenon_Hae zenon_H35 zenon_H15a zenon_Haf zenon_H155 zenon_H3a zenon_H187 zenon_H47. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.26/10.40 apply (zenon_L238_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.26/10.40 exact (zenon_Haf zenon_Hb4). % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.26/10.40 apply (zenon_L223_); trivial. % 10.26/10.40 apply (zenon_L243_); trivial. % 10.26/10.40 (* end of lemma zenon_L808_ *) % 10.26/10.40 assert (zenon_L809_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (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)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (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 (e3) (e3)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H1af zenon_H198 zenon_H42 zenon_Haf zenon_H155 zenon_Hae zenon_H3c zenon_H35 zenon_H15a zenon_Hc6 zenon_H3a zenon_H97 zenon_H188 zenon_H187 zenon_H16b zenon_H10b zenon_H114 zenon_H1b0 zenon_Hc0 zenon_H95 zenon_H28 zenon_Hdd zenon_H27 zenon_H86 zenon_H18d. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.26/10.40 exact (zenon_H27 zenon_H32). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.26/10.40 exact (zenon_H27 zenon_H32). % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.26/10.40 apply (zenon_L238_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.26/10.40 apply (zenon_L321_); trivial. % 10.26/10.40 apply (zenon_L807_); trivial. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.26/10.40 apply (zenon_L5_); trivial. % 10.26/10.40 apply (zenon_L808_); trivial. % 10.26/10.40 apply (zenon_L252_); trivial. % 10.26/10.40 apply (zenon_L194_); trivial. % 10.26/10.40 (* end of lemma zenon_L809_ *) % 10.26/10.40 assert (zenon_L810_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H1ea zenon_H159 zenon_H18d zenon_H86 zenon_H27 zenon_Hdd zenon_H28 zenon_H95 zenon_Hc0 zenon_H1b0 zenon_H114 zenon_H10b zenon_H16b zenon_H187 zenon_H188 zenon_H97 zenon_H3a zenon_Hc6 zenon_H15a zenon_H35 zenon_H3c zenon_Hae zenon_H155 zenon_H42 zenon_H198 zenon_H1af. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L809_); trivial. % 10.26/10.40 apply (zenon_L123_); trivial. % 10.26/10.40 (* end of lemma zenon_L810_ *) % 10.26/10.40 assert (zenon_L811_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H168 zenon_H1af zenon_H198 zenon_H42 zenon_H155 zenon_Hae zenon_H35 zenon_Hc6 zenon_H97 zenon_H187 zenon_H16b zenon_H114 zenon_Hc0 zenon_H95 zenon_H28 zenon_Hdd zenon_H27 zenon_H159 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H151 zenon_H1b0 zenon_H18d zenon_H12f zenon_H2a zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H144 zenon_H10b zenon_H3a zenon_H3c zenon_H6f zenon_H132 zenon_Hf8 zenon_H1ea. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.40 apply (zenon_L297_); trivial. % 10.26/10.40 apply (zenon_L806_); trivial. % 10.26/10.40 apply (zenon_L810_); trivial. % 10.26/10.40 (* end of lemma zenon_L811_ *) % 10.26/10.40 assert (zenon_L812_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H158 zenon_H1ea zenon_H6f zenon_H144 zenon_H192 zenon_H11d zenon_H191 zenon_H159 zenon_Hdd zenon_Hc0 zenon_H114 zenon_H16b zenon_Hc6 zenon_Hae zenon_H198 zenon_H1af zenon_H168 zenon_H151 zenon_H1b0 zenon_H18d zenon_H188 zenon_H12f zenon_H2a zenon_He8 zenon_H5e zenon_H100 zenon_H7d zenon_H86 zenon_H145 zenon_H108 zenon_H53 zenon_Hb1 zenon_H155 zenon_H3c zenon_H91 zenon_Hc5 zenon_Hf8 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H4c zenon_H35 zenon_H28 zenon_H95 zenon_H10b zenon_H187 zenon_H97 zenon_H27 zenon_Hd2. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L299_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L302_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 apply (zenon_L811_); trivial. % 10.26/10.40 (* end of lemma zenon_L812_ *) % 10.26/10.40 assert (zenon_L813_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (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)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_H188 zenon_H12f zenon_H2a zenon_He8 zenon_H5e zenon_H100 zenon_H7d zenon_H86 zenon_H145 zenon_H1b4 zenon_H198 zenon_H35 zenon_H28 zenon_H4c zenon_H95 zenon_Hcf zenon_H1dd zenon_Hda zenon_H56 zenon_Hf8. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L309_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 (* end of lemma zenon_L813_ *) % 10.26/10.40 assert (zenon_L814_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (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)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.26/10.40 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_He3 zenon_H56 zenon_H35 zenon_Hd3 zenon_H91 zenon_H8c zenon_H1b7 zenon_H188 zenon_H187 zenon_H7a zenon_Hdd zenon_H95 zenon_Hce zenon_H128 zenon_H5e zenon_H86 zenon_H7d zenon_H58 zenon_H90 zenon_H1ba zenon_H2a zenon_H1bc zenon_H15a zenon_H1c0 zenon_Hbc zenon_H1c3 zenon_H27 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H4c zenon_H53 zenon_H12c zenon_H192 zenon_H181 zenon_H64 zenon_H1dd zenon_Hf8. % 10.26/10.40 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.40 apply (zenon_L311_); trivial. % 10.26/10.40 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.40 (* end of lemma zenon_L814_ *) % 10.26/10.40 assert (zenon_L815_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (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)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H150 zenon_Hf8 zenon_H10b zenon_H108 zenon_H103 zenon_H132 zenon_H28 zenon_H4c zenon_H90 zenon_H86 zenon_H8c zenon_H91 zenon_H56 zenon_Hd3 zenon_H42 zenon_H181 zenon_H95 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_Hdd zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H187 zenon_Hc7 zenon_H1e2 zenon_H198 zenon_H17c zenon_Hb0 zenon_H97 zenon_H7d zenon_H7a zenon_H64 zenon_Hd0 zenon_Hce zenon_H15a zenon_H35 zenon_H27 zenon_H188 zenon_H18d zenon_H1b0 zenon_H151. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L312_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_L221_); trivial. % 10.26/10.41 (* end of lemma zenon_L815_ *) % 10.26/10.41 assert (zenon_L816_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((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 (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (op (e2) (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 (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H67 zenon_H112 zenon_Hde zenon_Hab zenon_H17c zenon_H1e2 zenon_H18a zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_H7a zenon_Hce zenon_H128 zenon_H58 zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H64 zenon_He3 zenon_H1b1 zenon_H1cb zenon_Hec zenon_H12c zenon_H150 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H56 zenon_Hda zenon_H1dd zenon_H1b4 zenon_Hd2 zenon_H97 zenon_H187 zenon_H10b zenon_H95 zenon_H35 zenon_H4c zenon_H103 zenon_H132 zenon_H181 zenon_H42 zenon_Hf8 zenon_Hc5 zenon_H91 zenon_H3c zenon_H155 zenon_H53 zenon_H108 zenon_H145 zenon_H86 zenon_H7d zenon_H5e zenon_H2a zenon_H12f zenon_H18d zenon_H1b0 zenon_H151 zenon_H168 zenon_H1af zenon_H198 zenon_Hae zenon_Hc6 zenon_H16b zenon_H114 zenon_Hc0 zenon_Hdd zenon_H159 zenon_H144 zenon_H6f zenon_H1ea zenon_H158 zenon_H4a. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.41 apply (zenon_L297_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.41 apply (zenon_L812_); trivial. % 10.26/10.41 apply (zenon_L813_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.41 apply (zenon_L799_); trivial. % 10.26/10.41 apply (zenon_L814_); trivial. % 10.26/10.41 apply (zenon_L815_); trivial. % 10.26/10.41 apply (zenon_L811_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L319_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L320_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_L44_); trivial. % 10.26/10.41 apply (zenon_L321_); trivial. % 10.26/10.41 apply (zenon_L123_); trivial. % 10.26/10.41 apply (zenon_L213_); trivial. % 10.26/10.41 apply (zenon_L101_); trivial. % 10.26/10.41 (* end of lemma zenon_L816_ *) % 10.26/10.41 assert (zenon_L817_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (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)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H168 zenon_Hae zenon_H95 zenon_H155 zenon_H35 zenon_H159 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H3a zenon_Hc6 zenon_Hf8 zenon_H1cb zenon_H5e zenon_H53 zenon_H108 zenon_H7d zenon_H43 zenon_H7a zenon_H86 zenon_H18d zenon_H1b0 zenon_H151 zenon_H1ea. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.41 apply (zenon_L297_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L374_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_L321_); trivial. % 10.26/10.41 apply (zenon_L314_); trivial. % 10.26/10.41 (* end of lemma zenon_L817_ *) % 10.26/10.41 assert (zenon_L818_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (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))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_H56 zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H53 zenon_H90 zenon_H1cb zenon_H51 zenon_H7d zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hd3 zenon_Hb0 zenon_H188 zenon_H198 zenon_H28 zenon_H6f zenon_H7a zenon_H64 zenon_H35 zenon_H95 zenon_H1fb zenon_H128 zenon_H1f8 zenon_H3a zenon_H155 zenon_H181 zenon_Hc8 zenon_H17c zenon_H12c zenon_H191 zenon_Hc1 zenon_H192 zenon_He8 zenon_H10b zenon_H187 zenon_H97 zenon_Hf8. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L377_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 (* end of lemma zenon_L818_ *) % 10.26/10.41 assert (zenon_L819_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H67 zenon_H168 zenon_H1af zenon_H198 zenon_H42 zenon_H155 zenon_Hae zenon_H35 zenon_Hc6 zenon_H97 zenon_H187 zenon_H16b zenon_H114 zenon_Hc0 zenon_H95 zenon_Hdd zenon_H159 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H151 zenon_H1b0 zenon_H18d zenon_H12f zenon_H2a zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H144 zenon_H10b zenon_H3a zenon_H3c zenon_H6f zenon_H132 zenon_Hf8 zenon_H1ea zenon_H58 zenon_H4a. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.41 apply (zenon_L811_); trivial. % 10.26/10.41 apply (zenon_L213_); trivial. % 10.26/10.41 apply (zenon_L101_); trivial. % 10.26/10.41 (* end of lemma zenon_L819_ *) % 10.26/10.41 assert (zenon_L820_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (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) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H173 zenon_H103 zenon_Hec zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_Hce zenon_H1b7 zenon_H18a zenon_H1e2 zenon_Hab zenon_H112 zenon_H67 zenon_He3 zenon_H1dd zenon_H168 zenon_Hae zenon_Hdd zenon_H191 zenon_H11d zenon_H192 zenon_Hd2 zenon_H151 zenon_H1b0 zenon_H64 zenon_H97 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_H4c zenon_H42 zenon_Hc0 zenon_H177 zenon_H44 zenon_H95 zenon_H35 zenon_H14d zenon_H8c zenon_H7d zenon_H7a zenon_H18d zenon_H53 zenon_H90 zenon_H5e zenon_H91 zenon_Hd3 zenon_Hb0 zenon_H3c zenon_H1b4 zenon_H56 zenon_H6f zenon_H1cb zenon_H200 zenon_H108 zenon_H187 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8 zenon_He7 zenon_Hde zenon_Hc5 zenon_H152 zenon_H158 zenon_H114 zenon_H16b zenon_H1b1 zenon_H150 zenon_Hc6 zenon_H156 zenon_H4a zenon_H12f zenon_H145 zenon_H132 zenon_H58 zenon_H204 zenon_H188 zenon_H86. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.26/10.41 apply (zenon_L816_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.26/10.41 exact (zenon_H192 zenon_H1d). % 10.26/10.41 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.41 apply (zenon_L297_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L361_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L372_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_L354_); trivial. % 10.26/10.41 apply (zenon_L321_); trivial. % 10.26/10.41 apply (zenon_L373_); trivial. % 10.26/10.41 apply (zenon_L810_); trivial. % 10.26/10.41 apply (zenon_L817_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.41 apply (zenon_L297_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.41 apply (zenon_L818_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L378_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 apply (zenon_L354_); trivial. % 10.26/10.41 apply (zenon_L321_); trivial. % 10.26/10.41 apply (zenon_L373_); trivial. % 10.26/10.41 apply (zenon_L314_); trivial. % 10.26/10.41 apply (zenon_L343_); trivial. % 10.26/10.41 apply (zenon_L819_); trivial. % 10.26/10.41 apply (zenon_L252_); trivial. % 10.26/10.41 (* end of lemma zenon_L820_ *) % 10.26/10.41 assert (zenon_L821_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (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) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H1de zenon_H15a zenon_Hc1 zenon_H6e zenon_H173 zenon_H103 zenon_Hec zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_Hce zenon_H1b7 zenon_H18a zenon_H1e2 zenon_Hab zenon_H112 zenon_H67 zenon_He3 zenon_H1dd zenon_H168 zenon_Hae zenon_Hdd zenon_H191 zenon_H11d zenon_H192 zenon_Hd2 zenon_H151 zenon_H1b0 zenon_H64 zenon_H97 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_H4c zenon_H42 zenon_Hc0 zenon_H177 zenon_H44 zenon_H95 zenon_H35 zenon_H14d zenon_H8c zenon_H7d zenon_H7a zenon_H18d zenon_H53 zenon_H90 zenon_H5e zenon_H91 zenon_Hd3 zenon_Hb0 zenon_H3c zenon_H1b4 zenon_H56 zenon_H6f zenon_H1cb zenon_H200 zenon_H108 zenon_H187 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8 zenon_He7 zenon_Hde zenon_Hc5 zenon_H152 zenon_H158 zenon_H114 zenon_H16b zenon_H1b1 zenon_H150 zenon_Hc6 zenon_H156 zenon_H4a zenon_H12f zenon_H145 zenon_H132 zenon_H58 zenon_H204 zenon_H86. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.26/10.41 apply (zenon_L236_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.26/10.41 exact (zenon_Hc1 zenon_Hc4). % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.26/10.41 apply (zenon_L237_); trivial. % 10.26/10.41 apply (zenon_L820_); trivial. % 10.26/10.41 (* end of lemma zenon_L821_ *) % 10.26/10.41 assert (zenon_L822_ : (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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 (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H4c zenon_H15a zenon_H95 zenon_H6e zenon_H173 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_He7 zenon_H152 zenon_H204 zenon_H4a zenon_H158 zenon_H1ea zenon_H6f zenon_H144 zenon_H159 zenon_Hdd zenon_Hc0 zenon_H114 zenon_H16b zenon_Hc6 zenon_Hae zenon_H198 zenon_H1af zenon_H168 zenon_H151 zenon_H1b0 zenon_H18d zenon_H12f zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_H91 zenon_Hc5 zenon_Hf8 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H35 zenon_H10b zenon_H187 zenon_H97 zenon_Hd2 zenon_H1b4 zenon_H1dd zenon_Hda zenon_H56 zenon_H156 zenon_H192 zenon_H11d zenon_H191 zenon_H150 zenon_H12c zenon_Hec zenon_H1cb zenon_H1b1 zenon_He3 zenon_H64 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H58 zenon_H128 zenon_Hce zenon_H7a zenon_H1b7 zenon_H8c zenon_Hd3 zenon_Hb0 zenon_H18a zenon_H1e2 zenon_H17c zenon_Hab zenon_Hde zenon_H112 zenon_H67 zenon_H1de. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.41 apply (zenon_L821_); trivial. % 10.26/10.41 apply (zenon_L194_); trivial. % 10.26/10.41 (* end of lemma zenon_L822_ *) % 10.26/10.41 assert (zenon_L823_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (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 (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (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) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H67 zenon_Hde zenon_Hab zenon_H11d zenon_Hae zenon_H114 zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H173 zenon_H58 zenon_H7a zenon_H1b7 zenon_H158 zenon_H150 zenon_H1dd zenon_H12c zenon_H103 zenon_Hec zenon_H1cb zenon_He3 zenon_H151 zenon_H1b0 zenon_H18d zenon_Hb0 zenon_H8c zenon_H128 zenon_H86 zenon_H7d zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H3c zenon_H108 zenon_Hf8 zenon_H1de zenon_H1e6 zenon_H10b zenon_H132 zenon_H18a zenon_H1e2 zenon_H17c zenon_H97 zenon_H156 zenon_H168 zenon_H56 zenon_H198 zenon_H6f zenon_H159 zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H12f zenon_H2a zenon_Hc5 zenon_H91 zenon_H155 zenon_H5e zenon_H145 zenon_H192 zenon_H16e zenon_H6e zenon_H191 zenon_Hc6 zenon_H112 zenon_H1ea. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.41 apply (zenon_L224_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.26/10.41 apply (zenon_L193_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.26/10.41 apply (zenon_L212_); trivial. % 10.26/10.41 apply (zenon_L802_); trivial. % 10.26/10.41 apply (zenon_L222_); trivial. % 10.26/10.41 apply (zenon_L223_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.26/10.41 apply (zenon_L224_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.26/10.41 apply (zenon_L803_); trivial. % 10.26/10.41 apply (zenon_L805_); trivial. % 10.26/10.41 apply (zenon_L822_); trivial. % 10.26/10.41 apply (zenon_L213_); trivial. % 10.26/10.41 apply (zenon_L101_); trivial. % 10.26/10.41 (* end of lemma zenon_L823_ *) % 10.26/10.41 assert (zenon_L824_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (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) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((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))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H200 zenon_H25 zenon_H97 zenon_H28 zenon_Hd0 zenon_H1cb zenon_H1b7 zenon_H156 zenon_H205 zenon_Hbb zenon_H1b1 zenon_Hce zenon_Hd2 zenon_H165 zenon_H191 zenon_H1f zenon_H192 zenon_H14d zenon_He3 zenon_H150 zenon_H64 zenon_H3c zenon_Hc5 zenon_H42 zenon_H1bc zenon_H12c zenon_H198 zenon_H7e zenon_Hab zenon_H4c zenon_H95 zenon_H181 zenon_H1e2 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H187 zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H159 zenon_Hd3 zenon_H9a zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_He7 zenon_H1b4 zenon_H56 zenon_H108 zenon_H53 zenon_H155 zenon_Hf8 zenon_H158. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.26/10.41 exact (zenon_H25 zenon_H2a). % 10.26/10.41 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.26/10.41 apply (zenon_L171_); trivial. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.26/10.41 apply (zenon_L418_); trivial. % 10.26/10.41 apply (zenon_L455_); trivial. % 10.26/10.41 (* end of lemma zenon_L824_ *) % 10.26/10.41 assert (zenon_L825_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.26/10.41 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H25 zenon_H42 zenon_Hd0 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H44 zenon_H27 zenon_H1b7 zenon_H9a zenon_H187 zenon_H1cb zenon_H156 zenon_H205 zenon_Hbb zenon_H1b1 zenon_Hce zenon_Hd2 zenon_H165 zenon_H191 zenon_H1f zenon_H192 zenon_H14d zenon_He3 zenon_H150 zenon_H64 zenon_H3c zenon_Hc5 zenon_H1bc zenon_H12c zenon_H198 zenon_Hab zenon_H4c zenon_H1e2 zenon_H91 zenon_H18a zenon_H7d zenon_H86 zenon_H18d zenon_H17c zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H159 zenon_Hd3 zenon_He8 zenon_H5e zenon_Hc0 zenon_H17a zenon_He7 zenon_H1b4 zenon_H56 zenon_H108 zenon_H155 zenon_Hf8 zenon_H158 zenon_H200. % 10.26/10.41 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.26/10.41 apply (zenon_L824_); trivial. % 10.26/10.41 exact (zenon_H1b0 zenon_Hbd). % 10.26/10.41 (* end of lemma zenon_L825_ *) % 10.26/10.41 assert (zenon_L826_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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 (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((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))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H64 zenon_Hb1 zenon_H3c zenon_Hc5 zenon_H42 zenon_H1bc zenon_H12c zenon_H198 zenon_Hab zenon_Hc8 zenon_H4c zenon_H95 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_H91 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H187 zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H159 zenon_Hd3 zenon_H9a zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_He7 zenon_H1b4 zenon_H56 zenon_H108 zenon_H53 zenon_H155 zenon_Hf8. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.42 apply (zenon_L454_); trivial. % 10.28/10.42 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.42 (* end of lemma zenon_L826_ *) % 10.28/10.42 assert (zenon_L827_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H42 zenon_H35 zenon_Hf0 zenon_H90 zenon_H17a zenon_H84 zenon_H4c zenon_H95 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_He7 zenon_H91 zenon_H17c zenon_H9a zenon_H159 zenon_H27 zenon_Hdd zenon_H6f zenon_H6e zenon_Hd0 zenon_H181. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.42 exact (zenon_H27 zenon_H32). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.42 apply (zenon_L413_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.42 apply (zenon_L19_); trivial. % 10.28/10.42 apply (zenon_L163_); trivial. % 10.28/10.42 (* end of lemma zenon_L827_ *) % 10.28/10.42 assert (zenon_L828_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (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 (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H64 zenon_H181 zenon_Hd0 zenon_H6e zenon_Hdd zenon_H27 zenon_H159 zenon_H17c zenon_H91 zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H90 zenon_H35 zenon_H42 zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H7e zenon_H18a zenon_H43 zenon_H198 zenon_H86 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H9a zenon_H187. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.42 exact (zenon_H56 zenon_H2c). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.28/10.42 exact (zenon_H56 zenon_H2c). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.28/10.42 apply (zenon_L426_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.28/10.42 apply (zenon_L421_); trivial. % 10.28/10.42 apply (zenon_L827_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.42 apply (zenon_L228_); trivial. % 10.28/10.42 apply (zenon_L202_); trivial. % 10.28/10.42 (* end of lemma zenon_L828_ *) % 10.28/10.42 assert (zenon_L829_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H56 zenon_H1b4 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H9a zenon_H90 zenon_H6f zenon_H181 zenon_H42 zenon_H27 zenon_H159 zenon_H6e zenon_H35 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hdd zenon_H187 zenon_H43 zenon_H198 zenon_H17c zenon_Hd0 zenon_H86 zenon_H84 zenon_H18a zenon_H64. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.42 apply (zenon_L828_); trivial. % 10.28/10.42 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.42 (* end of lemma zenon_L829_ *) % 10.28/10.42 assert (zenon_L830_ : ((~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (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) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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 (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 (e1) (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) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (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) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (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 (e3) (e0)) = (op (e3) (e2)))) -> ((~((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) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H67 zenon_H168 zenon_H156 zenon_H97 zenon_H17c zenon_H1e2 zenon_H18a zenon_H132 zenon_H10b zenon_H1e6 zenon_H1de zenon_Hf8 zenon_H108 zenon_H64 zenon_H3c zenon_H35 zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H7d zenon_H86 zenon_H128 zenon_Hce zenon_Hdd zenon_H8c zenon_Hd3 zenon_H198 zenon_H53 zenon_Hb0 zenon_H56 zenon_H18d zenon_H1b0 zenon_H151 zenon_H95 zenon_H4c zenon_He3 zenon_H42 zenon_H6f zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H12c zenon_H1dd zenon_H150 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_H91 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H1af zenon_H4a. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.42 apply (zenon_L802_); trivial. % 10.28/10.42 apply (zenon_L213_); trivial. % 10.28/10.42 apply (zenon_L101_); trivial. % 10.28/10.42 (* end of lemma zenon_L830_ *) % 10.28/10.42 assert (zenon_L831_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.28/10.42 do 0 intro. intros zenon_Hb0 zenon_Hd8 zenon_H53 zenon_H5e zenon_Hb1 zenon_H1e2 zenon_He3 zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H35 zenon_H77 zenon_Hc7 zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_H84 zenon_H86. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.28/10.42 apply (zenon_L249_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.28/10.42 apply (zenon_L22_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.28/10.42 exact (zenon_Hb1 zenon_Hb7). % 10.28/10.42 apply (zenon_L430_); trivial. % 10.28/10.42 (* end of lemma zenon_L831_ *) % 10.28/10.42 assert (zenon_L832_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (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) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.28/10.42 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f0 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H103 zenon_H1cb zenon_H15a zenon_H159 zenon_H91 zenon_Hec zenon_Hf2. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.42 exact (zenon_H56 zenon_H2c). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.42 apply (zenon_L327_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.42 apply (zenon_L103_); trivial. % 10.28/10.42 apply (zenon_L264_); trivial. % 10.28/10.42 (* end of lemma zenon_L832_ *) % 10.28/10.42 assert (zenon_L833_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.28/10.42 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H1b1 zenon_H62 zenon_H181 zenon_Hd3 zenon_H1bc zenon_H90 zenon_H192 zenon_H86 zenon_H84 zenon_H17c zenon_H198 zenon_H18a zenon_H35 zenon_Hda zenon_H28 zenon_H4c zenon_H95 zenon_He3 zenon_H1e2 zenon_H5e zenon_H53 zenon_Hb0 zenon_H64 zenon_H56 zenon_H1f0 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H103 zenon_H1cb zenon_H15a zenon_H159 zenon_H91 zenon_Hec. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.28/10.42 exact (zenon_H27 zenon_H32). % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.28/10.42 apply (zenon_L238_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.28/10.42 apply (zenon_L296_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.28/10.42 apply (zenon_L259_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.28/10.42 exact (zenon_H192 zenon_H1d). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.28/10.42 apply (zenon_L831_); trivial. % 10.28/10.42 apply (zenon_L832_); trivial. % 10.28/10.42 (* end of lemma zenon_L833_ *) % 10.28/10.42 assert (zenon_L834_ : (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (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) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H8d zenon_H1b7 zenon_H187 zenon_H7a zenon_H58 zenon_H2a zenon_H8c zenon_H1ae zenon_Hdd zenon_H27 zenon_H1b1 zenon_H181 zenon_Hd3 zenon_H1bc zenon_H90 zenon_H192 zenon_H86 zenon_H84 zenon_H17c zenon_H198 zenon_H18a zenon_H35 zenon_Hda zenon_H28 zenon_H4c zenon_H95 zenon_He3 zenon_H1e2 zenon_H5e zenon_H53 zenon_Hb0 zenon_H64 zenon_H56 zenon_H1f0 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H103 zenon_H1cb zenon_H15a zenon_H159 zenon_H91 zenon_Hec. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.42 exact (zenon_H56 zenon_H2c). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.28/10.42 exact (zenon_H28 zenon_H31). % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.28/10.42 apply (zenon_L236_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.28/10.42 apply (zenon_L20_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.28/10.42 apply (zenon_L21_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.28/10.42 apply (zenon_L22_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.28/10.42 exact (zenon_H91 zenon_H94). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 10.28/10.42 apply (zenon_L155_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 10.28/10.42 exact (zenon_H1ae zenon_Hb8). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 10.28/10.42 exact (zenon_Hc7 zenon_H3a). % 10.28/10.42 apply (zenon_L278_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.28/10.42 exact (zenon_Hb1 zenon_Hb7). % 10.28/10.42 apply (zenon_L250_); trivial. % 10.28/10.42 apply (zenon_L266_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.42 apply (zenon_L103_); trivial. % 10.28/10.42 apply (zenon_L833_); trivial. % 10.28/10.42 (* end of lemma zenon_L834_ *) % 10.28/10.42 assert (zenon_L835_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (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)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((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) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H168 zenon_H97 zenon_H42 zenon_Hce zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H27 zenon_H35 zenon_H1b1 zenon_H1f0 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H64 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H1bc zenon_Hdd zenon_H3c zenon_H28 zenon_H4c zenon_Hb0 zenon_Hd3 zenon_H1e2 zenon_H8c zenon_H95 zenon_H90 zenon_H53 zenon_He3 zenon_Hda zenon_H56 zenon_H150 zenon_H156 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H157 zenon_H1ae zenon_Hd2 zenon_H58 zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H12f zenon_H2a zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_H1af. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.42 apply (zenon_L224_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.42 apply (zenon_L460_); trivial. % 10.28/10.42 exact (zenon_H1ae zenon_Hb8). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.42 apply (zenon_L834_); trivial. % 10.28/10.42 apply (zenon_L266_); trivial. % 10.28/10.42 apply (zenon_L462_); trivial. % 10.28/10.42 apply (zenon_L223_); trivial. % 10.28/10.42 exact (zenon_H1ae zenon_Hb8). % 10.28/10.42 apply (zenon_L296_); trivial. % 10.28/10.42 (* end of lemma zenon_L835_ *) % 10.28/10.42 assert (zenon_L836_ : (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (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) (e1)) = (op (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b4 zenon_Hce zenon_H27 zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H6e zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H168 zenon_H97 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H1f0 zenon_H103 zenon_Hec zenon_H1cb zenon_H17c zenon_H86 zenon_H18a zenon_H1bc zenon_H3c zenon_H28 zenon_Hb0 zenon_H1e2 zenon_H8c zenon_H90 zenon_He3 zenon_Hda zenon_H150 zenon_H156 zenon_H16e zenon_H1ae zenon_H58 zenon_H7a zenon_H1b7 zenon_H158 zenon_H18d zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.42 apply (zenon_L190_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.42 apply (zenon_L193_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.42 apply (zenon_L212_); trivial. % 10.28/10.42 apply (zenon_L835_); trivial. % 10.28/10.42 apply (zenon_L222_); trivial. % 10.28/10.42 apply (zenon_L223_); trivial. % 10.28/10.42 exact (zenon_H1ae zenon_Hb8). % 10.28/10.42 (* end of lemma zenon_L836_ *) % 10.28/10.42 assert (zenon_L837_ : (((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 (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (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))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H1de zenon_H15a zenon_Hc1 zenon_Hed zenon_H173 zenon_H103 zenon_H18a zenon_H1e2 zenon_H1c3 zenon_H1ba zenon_H58 zenon_Hce zenon_Hdd zenon_Hec zenon_Hab zenon_H67 zenon_H1b7 zenon_H1bc zenon_H1c0 zenon_He3 zenon_H1dd zenon_H168 zenon_Hae zenon_H191 zenon_H11d zenon_H192 zenon_H157 zenon_H150 zenon_He7 zenon_Hde zenon_H1ae zenon_Hc5 zenon_H152 zenon_H158 zenon_H114 zenon_H16b zenon_H1b1 zenon_H64 zenon_H97 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H198 zenon_H1af zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H7e zenon_Hf5 zenon_H4c zenon_H42 zenon_Hc0 zenon_H177 zenon_H44 zenon_H95 zenon_H35 zenon_H14d zenon_H8c zenon_H7d zenon_H7a zenon_H18d zenon_H53 zenon_H90 zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H3c zenon_H1b4 zenon_H56 zenon_H6f zenon_H1cb zenon_H200 zenon_H108 zenon_H187 zenon_H12c zenon_H17c zenon_H181 zenon_H155 zenon_H1f8 zenon_H128 zenon_H1fb zenon_Hfd zenon_H10b zenon_H144 zenon_Hf8 zenon_Hd2 zenon_Hc6 zenon_H156 zenon_H4a zenon_H132 zenon_H145 zenon_H12f zenon_H204 zenon_H86. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.28/10.42 apply (zenon_L236_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.28/10.42 exact (zenon_Hc1 zenon_Hc4). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.28/10.42 apply (zenon_L282_); trivial. % 10.28/10.42 apply (zenon_L726_); trivial. % 10.28/10.42 (* end of lemma zenon_L837_ *) % 10.28/10.42 assert (zenon_L838_ : (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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) (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 (e0) (e2)) = (e0))) -> (((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 (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 (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.42 do 0 intro. intros zenon_Hc1 zenon_H1e6 zenon_H173 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1f zenon_H1af zenon_Hc0 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H157 zenon_Hd2 zenon_H132 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H108 zenon_H155 zenon_Hf8 zenon_H144 zenon_H158 zenon_H1dd zenon_H1b4 zenon_H156 zenon_H11d zenon_H191 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_H128 zenon_Hce zenon_H12c zenon_H150 zenon_H168 zenon_Hae zenon_Hf5 zenon_Hab zenon_Hde zenon_Hc6 zenon_H67 zenon_H1de zenon_H64 zenon_H8d zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H5e zenon_H8c zenon_H91 zenon_Hd3 zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_H1b1 zenon_H1f0 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H17c zenon_H198 zenon_H18a zenon_H192 zenon_Hdd zenon_H28 zenon_H4c zenon_Hb0 zenon_H1e2 zenon_H58 zenon_H2a zenon_H1b7 zenon_H181 zenon_H187 zenon_H1ae zenon_H95 zenon_H53 zenon_He3 zenon_Hda zenon_H18d. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.42 exact (zenon_H56 zenon_H2c). % 10.28/10.42 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.42 apply (zenon_L257_); trivial. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.42 apply (zenon_L103_); trivial. % 10.28/10.42 apply (zenon_L87_); trivial. % 10.28/10.42 apply (zenon_L834_); trivial. % 10.28/10.42 apply (zenon_L837_); trivial. % 10.28/10.42 (* end of lemma zenon_L838_ *) % 10.28/10.42 assert (zenon_L839_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 10.28/10.42 do 0 intro. intros zenon_H4a zenon_H1af zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H192 zenon_H16e zenon_H6e zenon_H191 zenon_H156 zenon_H150 zenon_H56 zenon_Hda zenon_He3 zenon_H53 zenon_H90 zenon_H95 zenon_H8c zenon_H1e2 zenon_Hd3 zenon_Hb0 zenon_H4c zenon_H3c zenon_Hdd zenon_H1bc zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H64 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1f0 zenon_H1b1 zenon_H35 zenon_H27 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_Hce zenon_H42 zenon_H97 zenon_H168. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.42 apply (zenon_L835_); trivial. % 10.28/10.42 apply (zenon_L213_); trivial. % 10.28/10.42 (* end of lemma zenon_L839_ *) % 10.28/10.42 assert (zenon_L840_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (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 (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.42 do 0 intro. intros zenon_Hf8 zenon_H1dd zenon_H64 zenon_H8d zenon_H97 zenon_Hcf zenon_H1de zenon_H187 zenon_Hc1 zenon_H16f zenon_Hda zenon_H4c zenon_H95 zenon_H28 zenon_H192 zenon_H12c zenon_H198 zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_H112 zenon_Haf zenon_H1b1 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H5e zenon_H8c zenon_H91 zenon_Hd3 zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_H4a zenon_H1af zenon_H158 zenon_H145 zenon_H155 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b7 zenon_H58 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H16e zenon_H191 zenon_H156 zenon_H150 zenon_He3 zenon_H53 zenon_Hb0 zenon_H3c zenon_Hdd zenon_H18a zenon_H17c zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1f0 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_Hce zenon_H168 zenon_H18d. % 10.28/10.42 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.42 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.42 apply (zenon_L295_); trivial. % 10.28/10.42 apply (zenon_L839_); trivial. % 10.28/10.42 apply (zenon_L306_); trivial. % 10.28/10.42 (* end of lemma zenon_L840_ *) % 10.28/10.42 assert (zenon_L841_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H1e6 zenon_H173 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1f zenon_H1af zenon_Hc0 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H157 zenon_H1ae zenon_Hd2 zenon_H132 zenon_H10b zenon_H12f zenon_H145 zenon_H108 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_H144 zenon_H158 zenon_Hda zenon_H1dd zenon_H1b4 zenon_H156 zenon_H11d zenon_H191 zenon_H18a zenon_H17c zenon_H1c3 zenon_H1ba zenon_Hce zenon_Hdd zenon_H1b7 zenon_Hb0 zenon_H150 zenon_H168 zenon_Hae zenon_Hf5 zenon_H1f0 zenon_Hc6 zenon_H67 zenon_H64 zenon_H58 zenon_H2a zenon_H53 zenon_H128 zenon_H1c0 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H97 zenon_H16f zenon_Hbc zenon_Hc1 zenon_H187 zenon_H1de zenon_H4c zenon_H95 zenon_H28 zenon_H192 zenon_H12c zenon_H198 zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_Hcf zenon_H112 zenon_Haf zenon_H1b1 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H5e zenon_H8c zenon_H91 zenon_Hd3 zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_He3 zenon_H18d. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.43 apply (zenon_L381_); trivial. % 10.28/10.43 apply (zenon_L837_); trivial. % 10.28/10.43 (* end of lemma zenon_L841_ *) % 10.28/10.43 assert (zenon_L842_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (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 (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (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) (e1)) = (op (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H1e6 zenon_H173 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H10b zenon_H144 zenon_H1dd zenon_H11d zenon_H128 zenon_H12c zenon_Hae zenon_Hf5 zenon_Hab zenon_Hde zenon_H67 zenon_H1de zenon_H16f zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H6e zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H168 zenon_H97 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H1f0 zenon_H103 zenon_Hec zenon_H1cb zenon_H17c zenon_H86 zenon_H18a zenon_H1bc zenon_H3c zenon_Hb0 zenon_H1e2 zenon_H8c zenon_H90 zenon_He3 zenon_Hda zenon_H150 zenon_H156 zenon_H16e zenon_H1ae zenon_H58 zenon_H7a zenon_H1b7 zenon_H158 zenon_H18d zenon_H192 zenon_H191 zenon_H7d zenon_H7e zenon_H132 zenon_H108 zenon_Hf8 zenon_Hc6 zenon_H112 zenon_H1ea. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.43 apply (zenon_L836_); trivial. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.43 apply (zenon_L224_); trivial. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_L233_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_L805_); trivial. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.43 apply (zenon_L838_); trivial. % 10.28/10.43 apply (zenon_L268_); trivial. % 10.28/10.43 apply (zenon_L288_); trivial. % 10.28/10.43 apply (zenon_L223_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.43 apply (zenon_L840_); trivial. % 10.28/10.43 apply (zenon_L841_); trivial. % 10.28/10.43 apply (zenon_L44_); trivial. % 10.28/10.43 apply (zenon_L321_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_L194_); trivial. % 10.28/10.43 apply (zenon_L123_); trivial. % 10.28/10.43 apply (zenon_L213_); trivial. % 10.28/10.43 apply (zenon_L101_); trivial. % 10.28/10.43 (* end of lemma zenon_L842_ *) % 10.28/10.43 assert (zenon_L843_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H157 zenon_H1ae zenon_Hd2 zenon_H1cb zenon_H187 zenon_H9a zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H3c zenon_H51 zenon_Hc5 zenon_H155 zenon_H6e zenon_H158. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_L425_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 (* end of lemma zenon_L843_ *) % 10.28/10.43 assert (zenon_L844_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H1af zenon_H158 zenon_H155 zenon_Hc5 zenon_H51 zenon_H3c zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H1cb zenon_Hd2 zenon_H1ae zenon_H157 zenon_He8 zenon_H192 zenon_H16e zenon_H6e zenon_H191. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.43 apply (zenon_L224_); trivial. % 10.28/10.43 apply (zenon_L843_); trivial. % 10.28/10.43 (* end of lemma zenon_L844_ *) % 10.28/10.43 assert (zenon_L845_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H4a zenon_H1af zenon_H158 zenon_H155 zenon_Hc5 zenon_H51 zenon_H3c zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H1cb zenon_Hd2 zenon_H1ae zenon_H157 zenon_H192 zenon_H16e zenon_H6e zenon_H191 zenon_H156 zenon_H150 zenon_H56 zenon_Hda zenon_He3 zenon_H53 zenon_H90 zenon_H18a zenon_H86 zenon_H17c zenon_H198 zenon_H8c zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H4c zenon_H95 zenon_H35 zenon_H1e2 zenon_H1bc zenon_H103 zenon_Hec zenon_H159 zenon_H1b1 zenon_H64 zenon_H168. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.43 apply (zenon_L844_); trivial. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_L433_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_L296_); trivial. % 10.28/10.43 apply (zenon_L343_); trivial. % 10.28/10.43 (* end of lemma zenon_L845_ *) % 10.28/10.43 assert (zenon_L846_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((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)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (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 (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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 (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.28/10.43 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H25 zenon_H64 zenon_H44 zenon_H97 zenon_H7a zenon_H53 zenon_H28 zenon_H42 zenon_H1ef zenon_H195 zenon_H1ea zenon_H159 zenon_H1f zenon_H191 zenon_H198 zenon_H1af zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_H7e zenon_Hf5 zenon_H35 zenon_H6e zenon_H27 zenon_H90 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H192 zenon_H12c zenon_H84 zenon_H205 zenon_Hc8 zenon_H4c zenon_H95 zenon_Hbb zenon_H1b1 zenon_H1b4 zenon_H56 zenon_H4a zenon_H158 zenon_H155 zenon_Hc5 zenon_H3c zenon_H1b7 zenon_H181 zenon_H187 zenon_H1cb zenon_Hd2 zenon_H1ae zenon_H157 zenon_H16e zenon_H156 zenon_H150 zenon_Hda zenon_He3 zenon_H18a zenon_H86 zenon_H8c zenon_H5e zenon_Hb0 zenon_H1e2 zenon_H1bc zenon_H103 zenon_Hec zenon_H168 zenon_Hb1 zenon_Hab zenon_Hc7 zenon_H7d zenon_H18d zenon_H6f zenon_He8 zenon_Hc0 zenon_H17a zenon_He7 zenon_H200. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.43 exact (zenon_H25 zenon_H2a). % 10.28/10.43 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.43 apply (zenon_L423_); trivial. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.43 apply (zenon_L845_); trivial. % 10.28/10.43 apply (zenon_L437_); trivial. % 10.28/10.43 apply (zenon_L254_); trivial. % 10.28/10.43 (* end of lemma zenon_L846_ *) % 10.28/10.43 assert (zenon_L847_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 10.28/10.43 do 0 intro. intros zenon_Hd2 zenon_H187 zenon_H43 zenon_H198 zenon_H15a zenon_H17c zenon_H86 zenon_H84 zenon_H18a zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.43 apply (zenon_L43_); trivial. % 10.28/10.43 apply (zenon_L426_); trivial. % 10.28/10.43 (* end of lemma zenon_L847_ *) % 10.28/10.43 assert (zenon_L848_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H157 zenon_Hcf zenon_H112 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H18a zenon_H84 zenon_H86 zenon_H17c zenon_H15a zenon_H198 zenon_H43 zenon_H187 zenon_Hd2. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_L847_); trivial. % 10.28/10.43 apply (zenon_L79_); trivial. % 10.28/10.43 (* end of lemma zenon_L848_ *) % 10.28/10.43 assert (zenon_L849_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H157 zenon_H1ae zenon_Hd2 zenon_H18e zenon_H56 zenon_H42 zenon_H1bc zenon_H15a zenon_H12c zenon_H198 zenon_Hab zenon_H4c zenon_H181 zenon_H1e2 zenon_H18a zenon_H17c zenon_H187 zenon_H90 zenon_H6f zenon_H35 zenon_H27 zenon_H5e zenon_H1dd zenon_H108 zenon_Hdd zenon_H44 zenon_H84 zenon_H205 zenon_H64 zenon_Hc6 zenon_Hc5 zenon_H53 zenon_H95 zenon_H6e zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7d zenon_H1de zenon_H25 zenon_H155 zenon_H3c zenon_Hf8 zenon_H158 zenon_H112 zenon_H67 zenon_Hde zenon_H1f0 zenon_Hf5 zenon_Hae zenon_H168 zenon_H150 zenon_He3 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_Hce zenon_H128 zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H191 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_Hda zenon_H144 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_H1ea zenon_H4a zenon_H204 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H177 zenon_Hc0 zenon_H1af zenon_H1f zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_He7 zenon_H173 zenon_H1e6. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_L457_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.28/10.43 exact (zenon_H25 zenon_H2a). % 10.28/10.43 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.28/10.43 apply (zenon_L440_); trivial. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.28/10.43 apply (zenon_L848_); trivial. % 10.28/10.43 apply (zenon_L447_); trivial. % 10.28/10.43 apply (zenon_L837_); trivial. % 10.28/10.43 apply (zenon_L426_); trivial. % 10.28/10.43 apply (zenon_L321_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_L194_); trivial. % 10.28/10.43 (* end of lemma zenon_L849_ *) % 10.28/10.43 assert (zenon_L850_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (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)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H1e6 zenon_H173 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H132 zenon_H103 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H144 zenon_Hda zenon_H11d zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_H58 zenon_H128 zenon_Hce zenon_H1b7 zenon_H8c zenon_Hb0 zenon_Hec zenon_H1cb zenon_H168 zenon_Hae zenon_Hf5 zenon_H1f0 zenon_Hde zenon_H67 zenon_H112 zenon_H25 zenon_H1de zenon_H1dd zenon_Hab zenon_H1bc zenon_H18e zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H156 zenon_Hc6 zenon_H12c zenon_H205 zenon_Hbb zenon_H1b1 zenon_H158 zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7e zenon_H7a zenon_H18d zenon_H35 zenon_H1ae zenon_H150 zenon_He3 zenon_H42 zenon_H181 zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H1f zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H44 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H43 zenon_H187 zenon_H64 zenon_H1e2 zenon_H198 zenon_Hc5 zenon_H3c zenon_Hd2 zenon_H157 zenon_H1af. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.43 apply (zenon_L781_); trivial. % 10.28/10.43 apply (zenon_L849_); trivial. % 10.28/10.43 (* end of lemma zenon_L850_ *) % 10.28/10.43 assert (zenon_L851_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (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))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((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) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H67 zenon_H132 zenon_H168 zenon_H97 zenon_H42 zenon_Hce zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H35 zenon_H1b1 zenon_H1f0 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H64 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H1bc zenon_Hdd zenon_H3c zenon_H4c zenon_Hb0 zenon_Hd3 zenon_H1e2 zenon_H8c zenon_H95 zenon_H90 zenon_H53 zenon_He3 zenon_Hda zenon_H56 zenon_H150 zenon_H156 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H157 zenon_H1ae zenon_Hd2 zenon_H58 zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H12f zenon_H2a zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_H1af zenon_H4a. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.43 apply (zenon_L839_); trivial. % 10.28/10.43 apply (zenon_L101_); trivial. % 10.28/10.43 (* end of lemma zenon_L851_ *) % 10.28/10.43 assert (zenon_L852_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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) (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 (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((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 (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (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 (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H16f zenon_H112 zenon_H16e zenon_H1e6 zenon_H173 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1f zenon_H1af zenon_Hc0 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H157 zenon_Hd2 zenon_H132 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H108 zenon_H155 zenon_Hf8 zenon_H144 zenon_H158 zenon_H1dd zenon_H1b4 zenon_H156 zenon_H11d zenon_H191 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_H128 zenon_Hce zenon_H12c zenon_H150 zenon_H168 zenon_Hae zenon_Hf5 zenon_Hab zenon_Hde zenon_Hc6 zenon_H67 zenon_H1de zenon_H64 zenon_H3c zenon_Hc5 zenon_H27 zenon_H35 zenon_H6f zenon_H6e zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H5e zenon_H8c zenon_Hd3 zenon_H15a zenon_H1bc zenon_H42 zenon_H56 zenon_H1b1 zenon_H1f0 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_H17c zenon_H198 zenon_H18a zenon_H192 zenon_Hdd zenon_H28 zenon_H4c zenon_Hb0 zenon_H1e2 zenon_H58 zenon_H2a zenon_H1b7 zenon_H181 zenon_H187 zenon_H1ae zenon_H95 zenon_H53 zenon_He3 zenon_Hda zenon_H18d zenon_H1b0 zenon_H151. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.43 apply (zenon_L838_); trivial. % 10.28/10.43 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.43 apply (zenon_L800_); trivial. % 10.28/10.43 apply (zenon_L801_); trivial. % 10.28/10.43 apply (zenon_L223_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.43 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.43 apply (zenon_L840_); trivial. % 10.28/10.43 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.43 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.43 apply (zenon_L841_); trivial. % 10.28/10.43 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.43 apply (zenon_L44_); trivial. % 10.28/10.43 apply (zenon_L321_); trivial. % 10.28/10.43 exact (zenon_H1ae zenon_Hb8). % 10.28/10.43 apply (zenon_L194_); trivial. % 10.28/10.43 apply (zenon_L123_); trivial. % 10.28/10.43 (* end of lemma zenon_L852_ *) % 10.28/10.43 assert (zenon_L853_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (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 (e2) (e0)) = (op (e2) (e3)))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (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) (e1)) = (op (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) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.28/10.43 do 0 intro. intros zenon_H1de zenon_H67 zenon_Hde zenon_Hab zenon_Hf5 zenon_Hae zenon_H12c zenon_H128 zenon_H11d zenon_H1dd zenon_H144 zenon_H10b zenon_H4a zenon_H204 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H173 zenon_H1e6 zenon_H16f zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H6e zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H168 zenon_H97 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H1f0 zenon_H103 zenon_Hec zenon_H1cb zenon_H17c zenon_H86 zenon_H18a zenon_H1bc zenon_H3c zenon_Hb0 zenon_H1e2 zenon_H8c zenon_H90 zenon_He3 zenon_Hda zenon_H150 zenon_H156 zenon_H16e zenon_H1ae zenon_H58 zenon_H7a zenon_H1b7 zenon_H158 zenon_H18d zenon_H192 zenon_H191 zenon_Hf8 zenon_H108 zenon_H132 zenon_H7d zenon_H1b0 zenon_H151 zenon_Hc6 zenon_H112 zenon_H1ea. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.44 apply (zenon_L836_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.44 apply (zenon_L224_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_L803_); trivial. % 10.28/10.44 exact (zenon_H1ae zenon_Hb8). % 10.28/10.44 apply (zenon_L805_); trivial. % 10.28/10.44 apply (zenon_L852_); trivial. % 10.28/10.44 apply (zenon_L213_); trivial. % 10.28/10.44 apply (zenon_L101_); trivial. % 10.28/10.44 (* end of lemma zenon_L853_ *) % 10.28/10.44 assert (zenon_L854_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((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 (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (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 (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 10.28/10.44 do 0 intro. intros zenon_H1de zenon_H67 zenon_H112 zenon_Hde zenon_Hab zenon_H17c zenon_H1e2 zenon_H18a zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_H7a zenon_Hce zenon_H128 zenon_H58 zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H64 zenon_He3 zenon_H1b1 zenon_H1cb zenon_Hec zenon_H12c zenon_H150 zenon_H191 zenon_H11d zenon_H192 zenon_H156 zenon_H56 zenon_Hda zenon_H1dd zenon_H1b4 zenon_Hd2 zenon_H97 zenon_H187 zenon_H10b zenon_H35 zenon_H103 zenon_H132 zenon_H181 zenon_H42 zenon_Hf8 zenon_Hc5 zenon_H3c zenon_H155 zenon_H53 zenon_H108 zenon_H145 zenon_H86 zenon_H7d zenon_H5e zenon_H12f zenon_H18d zenon_H1b0 zenon_H151 zenon_H168 zenon_H1af zenon_H198 zenon_Hae zenon_Hc6 zenon_H16b zenon_H114 zenon_Hc0 zenon_Hdd zenon_H159 zenon_H144 zenon_H6f zenon_H1ea zenon_H158 zenon_H4a zenon_H204 zenon_H152 zenon_He7 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H44 zenon_H177 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H173 zenon_H6e zenon_H95 zenon_H15a zenon_H4c zenon_H1ae zenon_H157. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_L821_); trivial. % 10.28/10.44 exact (zenon_H1ae zenon_Hb8). % 10.28/10.44 apply (zenon_L194_); trivial. % 10.28/10.44 (* end of lemma zenon_L854_ *) % 10.28/10.44 assert (zenon_L855_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e3) (e1)) = (e3))) -> False). % 10.28/10.44 do 0 intro. intros zenon_Hc0 zenon_H95 zenon_H34 zenon_Hc1 zenon_H4c zenon_H77 zenon_H1b0. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.28/10.44 apply (zenon_L184_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.28/10.44 exact (zenon_Hc1 zenon_Hc4). % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.28/10.44 apply (zenon_L48_); trivial. % 10.28/10.44 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.44 (* end of lemma zenon_L855_ *) % 10.28/10.44 assert (zenon_L856_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((e0) = (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 (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.28/10.44 do 0 intro. intros zenon_H128 zenon_H7d zenon_H7e zenon_H43 zenon_H18d zenon_H6e zenon_H230 zenon_H8d zenon_H8a zenon_H5e zenon_H1b7 zenon_H187 zenon_H181 zenon_H84 zenon_H7a zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_H86 zenon_H8c zenon_H7f. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 10.28/10.44 apply (zenon_L392_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 10.28/10.44 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 10.28/10.44 intro zenon_D_pnotp. % 10.28/10.44 apply zenon_H230. % 10.28/10.44 rewrite <- zenon_D_pnotp. % 10.28/10.44 exact zenon_H6e. % 10.28/10.44 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 10.28/10.44 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 10.28/10.44 congruence. % 10.28/10.44 apply zenon_H71. apply refl_equal. % 10.28/10.44 apply zenon_H180. apply sym_equal. exact zenon_H9b. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 10.28/10.44 apply (zenon_L427_); trivial. % 10.28/10.44 exact (zenon_H7f zenon_H85). % 10.28/10.44 (* end of lemma zenon_L856_ *) % 10.28/10.44 assert (zenon_L857_ : ((~((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 10.28/10.44 do 0 intro. intros zenon_Hf8 zenon_Hc5 zenon_H3c zenon_H155 zenon_Hb1 zenon_H53 zenon_H108 zenon_H27 zenon_H90 zenon_H18a zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H43 zenon_H187 zenon_H230 zenon_H6e zenon_H8c zenon_H8d zenon_H5e zenon_H181 zenon_H1b7 zenon_H198 zenon_H84 zenon_H128 zenon_H91 zenon_H95 zenon_Hc1 zenon_H4c zenon_H1b0 zenon_Hc0 zenon_H15a zenon_H1bc zenon_H6f zenon_H1e2 zenon_Hc7 zenon_H35 zenon_Hc8 zenon_Hab zenon_H12c zenon_H42. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.44 exact (zenon_H27 zenon_H32). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.28/10.44 apply (zenon_L217_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.28/10.44 apply (zenon_L855_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.28/10.44 exact (zenon_H91 zenon_H94). % 10.28/10.44 apply (zenon_L856_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.44 apply (zenon_L19_); trivial. % 10.28/10.44 apply (zenon_L393_); trivial. % 10.28/10.44 apply (zenon_L254_); trivial. % 10.28/10.44 (* end of lemma zenon_L857_ *) % 10.28/10.44 assert (zenon_L858_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 10.28/10.44 do 0 intro. intros zenon_Hc0 zenon_H95 zenon_H34 zenon_Hc1 zenon_H7f zenon_H8c zenon_H86 zenon_H17c zenon_H198 zenon_H15a zenon_H18a zenon_H7a zenon_H84 zenon_H181 zenon_H187 zenon_H1b7 zenon_H5e zenon_H8d zenon_H230 zenon_H6e zenon_H18d zenon_H43 zenon_H7e zenon_H7d zenon_H128 zenon_H91 zenon_H4c zenon_H35 zenon_Hcf zenon_H90 zenon_H1b0. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.28/10.44 apply (zenon_L184_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.28/10.44 exact (zenon_Hc1 zenon_Hc4). % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.28/10.44 apply (zenon_L47_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.28/10.44 apply (zenon_L48_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.28/10.44 exact (zenon_H91 zenon_H94). % 10.28/10.44 apply (zenon_L856_); trivial. % 10.28/10.44 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.44 (* end of lemma zenon_L858_ *) % 10.28/10.44 assert (zenon_L859_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((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 (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (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)) = (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.28/10.44 do 0 intro. intros zenon_H157 zenon_H1ae zenon_Hd2 zenon_H151 zenon_H42 zenon_H12c zenon_Hab zenon_H35 zenon_H1e2 zenon_H6f zenon_H1bc zenon_H15a zenon_Hc0 zenon_H1b0 zenon_H4c zenon_H95 zenon_H128 zenon_H84 zenon_H198 zenon_H1b7 zenon_H181 zenon_H5e zenon_H8c zenon_H6e zenon_H230 zenon_H187 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H90 zenon_H27 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_He3 zenon_H150 zenon_H158 zenon_H1de zenon_H67 zenon_Hc6 zenon_Hde zenon_H1f0 zenon_Hf5 zenon_Hae zenon_H168 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_Hb0 zenon_Hd3 zenon_Hdd zenon_Hce zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H64 zenon_H191 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H1dd zenon_Hda zenon_H56 zenon_H144 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_H1ea zenon_H4a zenon_H204 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H44 zenon_H177 zenon_H1af zenon_H1f zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_He7 zenon_H173 zenon_H1e6. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.44 apply (zenon_L857_); trivial. % 10.28/10.44 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.44 apply (zenon_L266_); trivial. % 10.28/10.44 apply (zenon_L426_); trivial. % 10.28/10.44 apply (zenon_L223_); trivial. % 10.28/10.44 exact (zenon_H1ae zenon_Hb8). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.44 exact (zenon_H27 zenon_H32). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.44 apply (zenon_L858_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.44 apply (zenon_L19_); trivial. % 10.28/10.44 apply (zenon_L393_); trivial. % 10.28/10.44 apply (zenon_L837_); trivial. % 10.28/10.44 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.44 apply (zenon_L266_); trivial. % 10.28/10.44 apply (zenon_L44_); trivial. % 10.28/10.44 apply (zenon_L321_); trivial. % 10.28/10.44 exact (zenon_H1ae zenon_Hb8). % 10.28/10.44 apply (zenon_L194_); trivial. % 10.28/10.44 (* end of lemma zenon_L859_ *) % 10.28/10.44 assert (zenon_L860_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((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 (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((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 (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.28/10.44 do 0 intro. intros zenon_H1e6 zenon_H173 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1f zenon_H1af zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H132 zenon_H103 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H144 zenon_H56 zenon_Hda zenon_H1dd zenon_H1b4 zenon_H156 zenon_H11d zenon_H191 zenon_H64 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_H58 zenon_Hce zenon_Hdd zenon_Hb0 zenon_Hec zenon_H159 zenon_H1cb zenon_H168 zenon_Hae zenon_Hf5 zenon_H1f0 zenon_Hde zenon_Hc6 zenon_H67 zenon_H1de zenon_H158 zenon_H150 zenon_He3 zenon_Hf8 zenon_Hc5 zenon_H3c zenon_H155 zenon_H53 zenon_H108 zenon_H27 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H43 zenon_H187 zenon_H230 zenon_H6e zenon_H8c zenon_H5e zenon_H181 zenon_H1b7 zenon_H198 zenon_H128 zenon_H1b0 zenon_Hc0 zenon_H1bc zenon_H6f zenon_H1e2 zenon_Hab zenon_H42 zenon_H151 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H1b1 zenon_H9a zenon_H17c zenon_H91 zenon_Hd3 zenon_H35 zenon_H90 zenon_H192 zenon_H84 zenon_H205 zenon_Hc8 zenon_H4c zenon_Hcf zenon_H95 zenon_H12c zenon_Hbb. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.28/10.44 exact (zenon_H56 zenon_H2c). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.28/10.44 apply (zenon_L859_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.28/10.44 apply (zenon_L47_); trivial. % 10.28/10.44 apply (zenon_L388_); trivial. % 10.28/10.44 (* end of lemma zenon_L860_ *) % 10.28/10.44 assert (zenon_L861_ : (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((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 (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (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 (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (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)) = (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 (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (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) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.28/10.44 do 0 intro. intros zenon_H56 zenon_H157 zenon_H1ae zenon_Hd2 zenon_H151 zenon_H42 zenon_H12c zenon_Hab zenon_H35 zenon_H1e2 zenon_H6f zenon_H1bc zenon_Hc0 zenon_H1b0 zenon_H4c zenon_H95 zenon_H128 zenon_H84 zenon_H198 zenon_H1b7 zenon_H181 zenon_H5e zenon_H8c zenon_H6e zenon_H230 zenon_H187 zenon_H43 zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H7d zenon_H18a zenon_H90 zenon_H27 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_He3 zenon_H150 zenon_H158 zenon_H1de zenon_H67 zenon_Hc6 zenon_Hde zenon_H1f0 zenon_Hf5 zenon_Hae zenon_H168 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_Hb0 zenon_Hd3 zenon_Hdd zenon_Hce zenon_H58 zenon_H1ba zenon_H1c0 zenon_H1c3 zenon_H64 zenon_H191 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H1dd zenon_Hda zenon_H144 zenon_H145 zenon_H12f zenon_H97 zenon_H10b zenon_H103 zenon_H132 zenon_H1ea zenon_H4a zenon_H204 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H44 zenon_H177 zenon_H1af zenon_H1f zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_He7 zenon_H173 zenon_H1e6 zenon_Hcf zenon_Hbb zenon_H205 zenon_H91 zenon_H9a. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.44 apply (zenon_L860_); trivial. % 10.28/10.44 apply (zenon_L44_); trivial. % 10.28/10.44 (* end of lemma zenon_L861_ *) % 10.28/10.44 assert (zenon_L862_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 10.28/10.44 do 0 intro. intros zenon_H144 zenon_Hb7 zenon_H3c zenon_H100 zenon_H6f zenon_H6e zenon_Hed zenon_H10b. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_H51 | zenon_intro zenon_H148 ]. % 10.28/10.44 apply (zenon_L128_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H5d | zenon_intro zenon_H149 ]. % 10.28/10.44 apply (zenon_L228_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H149); [ zenon_intro zenon_H3b | zenon_intro zenon_H52 ]. % 10.28/10.44 apply (zenon_L19_); trivial. % 10.28/10.44 apply (zenon_L75_); trivial. % 10.28/10.44 (* end of lemma zenon_L862_ *) % 10.28/10.44 assert (zenon_L863_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((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 (e3) (e2)) = (e3)) -> False). % 10.28/10.44 do 0 intro. intros zenon_H108 zenon_H191 zenon_H16e zenon_H192 zenon_He8 zenon_H157 zenon_H1ae zenon_Hd2 zenon_H1cb zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_Hc5 zenon_H155 zenon_H158 zenon_H1af zenon_H5e zenon_H10b zenon_H6e zenon_H6f zenon_H100 zenon_H3c zenon_H144 zenon_H53 zenon_Hed. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 10.28/10.44 apply (zenon_L844_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 10.28/10.44 apply (zenon_L71_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 10.28/10.44 apply (zenon_L862_); trivial. % 10.28/10.44 apply (zenon_L73_); trivial. % 10.28/10.44 (* end of lemma zenon_L863_ *) % 10.28/10.44 assert (zenon_L864_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (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 (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.28/10.44 do 0 intro. intros zenon_Hf8 zenon_H1af zenon_H158 zenon_H155 zenon_Hc5 zenon_H3c zenon_H1b7 zenon_H181 zenon_H1cb zenon_Hd2 zenon_H1ae zenon_H157 zenon_H192 zenon_H16e zenon_H191 zenon_H144 zenon_H10b zenon_H53 zenon_H108 zenon_H56 zenon_H42 zenon_Hd3 zenon_H18a zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H18d zenon_H43 zenon_H187 zenon_H6e zenon_H6f zenon_H35 zenon_Hcf zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H27 zenon_H100 zenon_H64. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.44 exact (zenon_H56 zenon_H2c). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.44 exact (zenon_H27 zenon_H32). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.44 apply (zenon_L401_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.44 apply (zenon_L19_); trivial. % 10.28/10.44 apply (zenon_L414_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.44 apply (zenon_L228_); trivial. % 10.28/10.44 apply (zenon_L202_); trivial. % 10.28/10.44 apply (zenon_L863_); trivial. % 10.28/10.44 (* end of lemma zenon_L864_ *) % 10.28/10.44 assert (zenon_L865_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (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)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (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 (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (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 (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 10.28/10.44 do 0 intro. intros zenon_H157 zenon_Hd2 zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7a zenon_H18d zenon_H35 zenon_H1ae zenon_H150 zenon_He3 zenon_H42 zenon_H181 zenon_H6e zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H1f zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H44 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H43 zenon_H187 zenon_H64 zenon_H1e2 zenon_H198 zenon_Hc5 zenon_H3c zenon_H1b0 zenon_H151 zenon_H158 zenon_H205 zenon_Hbb zenon_H1e6 zenon_H173 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1af zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H204 zenon_H4a zenon_H1ea zenon_H132 zenon_H103 zenon_H10b zenon_H97 zenon_H12f zenon_H145 zenon_H144 zenon_Hda zenon_H1dd zenon_H156 zenon_H11d zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_H58 zenon_Hce zenon_Hb0 zenon_Hec zenon_H1cb zenon_H1b1 zenon_H168 zenon_Hae zenon_Hf5 zenon_H1f0 zenon_Hde zenon_Hc6 zenon_H67 zenon_H1de zenon_H230 zenon_H8c zenon_H1b7 zenon_H128 zenon_H1bc zenon_Hab zenon_H12c zenon_H192 zenon_H191 zenon_H16e. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.44 apply (zenon_L190_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.44 apply (zenon_L779_); trivial. % 10.28/10.44 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.44 apply (zenon_L412_); trivial. % 10.28/10.44 apply (zenon_L223_); trivial. % 10.28/10.44 exact (zenon_H1ae zenon_Hb8). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_L861_); trivial. % 10.28/10.44 exact (zenon_H1ae zenon_Hb8). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.44 apply (zenon_L224_); trivial. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.44 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.44 exact (zenon_H56 zenon_H2c). % 10.28/10.44 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.28/10.45 exact (zenon_H56 zenon_H2c). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.28/10.45 apply (zenon_L859_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.28/10.45 apply (zenon_L421_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.45 exact (zenon_H27 zenon_H32). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.45 apply (zenon_L413_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.45 apply (zenon_L19_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.28/10.45 exact (zenon_H27 zenon_H32). % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.28/10.45 apply (zenon_L195_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.28/10.45 apply (zenon_L414_); trivial. % 10.28/10.45 apply (zenon_L420_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.45 apply (zenon_L103_); trivial. % 10.28/10.45 apply (zenon_L202_); trivial. % 10.28/10.45 apply (zenon_L254_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L829_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L864_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L859_); trivial. % 10.28/10.45 (* end of lemma zenon_L865_ *) % 10.28/10.45 assert (zenon_L866_ : ((~((op (e2) (e2)) = (e1)))\/(~((op (e2) (e1)) = (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H22a zenon_H230 zenon_H18e zenon_H205 zenon_Hbb zenon_H17a zenon_H165 zenon_H1ea zenon_H16e zenon_H156 zenon_H90 zenon_H17c zenon_H7d zenon_H86 zenon_H132 zenon_H103 zenon_H1cb zenon_H108 zenon_Hf8 zenon_H191 zenon_H192 zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H12f zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_Hce zenon_Hdd zenon_H1af zenon_Hd2 zenon_Hd3 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H187 zenon_H64 zenon_H157 zenon_H14d zenon_H16b zenon_H1b1 zenon_H35 zenon_H6e zenon_H159 zenon_H6f zenon_H198 zenon_H56 zenon_H58 zenon_H7a zenon_H1b7 zenon_H18d zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H177 zenon_Hf5 zenon_H1f0 zenon_H1f zenon_H195 zenon_H1ef zenon_H114 zenon_H152 zenon_H204 zenon_H4a zenon_H144 zenon_H11d zenon_Hae zenon_H168 zenon_Hc6 zenon_H67 zenon_H16f zenon_Hab zenon_Hde zenon_H112 zenon_H1e6 zenon_H10b zenon_H18a zenon_H1e2 zenon_H97 zenon_Hb0 zenon_H8c zenon_H128 zenon_Hda zenon_H3c zenon_H1de zenon_H1dd zenon_H12c zenon_Hec zenon_He3 zenon_H151 zenon_H22b. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H91 | zenon_intro zenon_H1ae ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.45 apply (zenon_L464_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_L823_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L417_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L419_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L397_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L438_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L825_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L235_); trivial. % 10.28/10.45 apply (zenon_L822_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L452_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L412_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L397_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L826_); trivial. % 10.28/10.45 apply (zenon_L829_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L235_); trivial. % 10.28/10.45 apply (zenon_L822_); trivial. % 10.28/10.45 apply (zenon_L459_); trivial. % 10.28/10.45 apply (zenon_L830_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_L842_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 apply (zenon_L391_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L129_); trivial. % 10.28/10.45 apply (zenon_L779_); trivial. % 10.28/10.45 apply (zenon_L419_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L737_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L846_); trivial. % 10.28/10.45 apply (zenon_L824_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L737_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 apply (zenon_L323_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 apply (zenon_L850_); trivial. % 10.28/10.45 apply (zenon_L194_); trivial. % 10.28/10.45 apply (zenon_L123_); trivial. % 10.28/10.45 apply (zenon_L850_); trivial. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 apply (zenon_L851_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_L853_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H2a | zenon_intro zenon_H18f ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H69 | zenon_intro zenon_H190 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.28/10.45 exact (zenon_H56 zenon_H2c). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.28/10.45 apply (zenon_L854_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.28/10.45 apply (zenon_L384_); trivial. % 10.28/10.45 apply (zenon_L389_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H73 | zenon_intro zenon_He4 ]. % 10.28/10.45 apply (zenon_L43_); trivial. % 10.28/10.45 apply (zenon_L390_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 apply (zenon_L778_); trivial. % 10.28/10.45 apply (zenon_L254_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L419_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L737_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L846_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L825_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L737_); trivial. % 10.28/10.45 apply (zenon_L854_); trivial. % 10.28/10.45 apply (zenon_L865_); trivial. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 apply (zenon_L851_); trivial. % 10.28/10.45 (* end of lemma zenon_L866_ *) % 10.28/10.45 assert (zenon_L867_ : (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (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))))) -> (((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H35 zenon_H90 zenon_Hd3 zenon_H91 zenon_H18a zenon_H17c zenon_H18d zenon_H86 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d zenon_H6e zenon_H159 zenon_H27 zenon_Hdd zenon_H6f zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H42 zenon_Hde zenon_Haf zenon_Hb0 zenon_H1e2 zenon_Hbb zenon_H12c zenon_H205 zenon_H1b1 zenon_H198 zenon_H1b4 zenon_H114 zenon_H200 zenon_H25 zenon_H22c zenon_H1cb zenon_H1b7 zenon_H150 zenon_He3 zenon_H56 zenon_H181 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_H53 zenon_H165 zenon_H64 zenon_H1bc zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H9a zenon_H187. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.45 exact (zenon_H56 zenon_H2c). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.28/10.45 exact (zenon_H56 zenon_H2c). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.28/10.45 apply (zenon_L394_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.28/10.45 exact (zenon_He8 zenon_Heb). % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.28/10.45 apply (zenon_L4_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.28/10.45 exact (zenon_Haf zenon_Hb4). % 10.28/10.45 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.28/10.45 apply (zenon_L57_); trivial. % 10.28/10.45 apply (zenon_L787_); trivial. % 10.28/10.45 apply (zenon_L788_); trivial. % 10.28/10.45 apply (zenon_L415_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.45 apply (zenon_L103_); trivial. % 10.28/10.45 apply (zenon_L202_); trivial. % 10.28/10.45 (* end of lemma zenon_L867_ *) % 10.28/10.45 assert (zenon_L868_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e0))) -> (~((op (e0) (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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.28/10.45 do 0 intro. intros zenon_Hf8 zenon_H155 zenon_H108 zenon_H25 zenon_H22c zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H3c zenon_H42 zenon_H1bc zenon_H12c zenon_H198 zenon_H7e zenon_Hab zenon_H4c zenon_H95 zenon_H181 zenon_H1e2 zenon_H18a zenon_H7d zenon_H7a zenon_H86 zenon_H18d zenon_H17c zenon_H187 zenon_H90 zenon_H6e zenon_H6f zenon_H35 zenon_H27 zenon_Hb0 zenon_Hb1 zenon_Haf zenon_H44 zenon_H1b7 zenon_H1cb zenon_H150 zenon_He3 zenon_H14d zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_Hc0 zenon_H5e zenon_H159 zenon_H53 zenon_H165 zenon_H64 zenon_H200 zenon_H114 zenon_H9a zenon_H1b1 zenon_Hbb zenon_H205 zenon_H84 zenon_H192 zenon_Hd3 zenon_H1b4 zenon_Hde zenon_He8 zenon_H56. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L129_); trivial. % 10.28/10.45 apply (zenon_L867_); trivial. % 10.28/10.45 apply (zenon_L254_); trivial. % 10.28/10.45 (* end of lemma zenon_L868_ *) % 10.28/10.45 assert (zenon_L869_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((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) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((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) (e2)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (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 (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H25 zenon_H22c zenon_H168 zenon_H150 zenon_H56 zenon_Hda zenon_He3 zenon_H53 zenon_H90 zenon_H18a zenon_H86 zenon_H17c zenon_H198 zenon_H8c zenon_H5e zenon_Hd3 zenon_Hb0 zenon_H4c zenon_H28 zenon_H95 zenon_H35 zenon_H1e2 zenon_H1bc zenon_H103 zenon_Hec zenon_H159 zenon_H1b1 zenon_H64 zenon_Hc6 zenon_Hce zenon_H156 zenon_H191 zenon_H6e zenon_H16e zenon_H192 zenon_H158 zenon_H155 zenon_Hc5 zenon_H91 zenon_H3c zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H1cb zenon_Hd2 zenon_H1af zenon_Hb1 zenon_H42 zenon_H12c zenon_H7e zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H7d zenon_H18d zenon_H6f zenon_H27 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H9a zenon_H44 zenon_He8 zenon_Hc0 zenon_H17a zenon_He7 zenon_H1b4 zenon_H200. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L436_); trivial. % 10.28/10.45 apply (zenon_L437_); trivial. % 10.28/10.45 apply (zenon_L254_); trivial. % 10.28/10.45 (* end of lemma zenon_L869_ *) % 10.28/10.45 assert (zenon_L870_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (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 (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H150 zenon_H25 zenon_H22c zenon_H64 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1bc zenon_H1e2 zenon_Hc7 zenon_H35 zenon_H95 zenon_H192 zenon_H28 zenon_H4c zenon_H15a zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H5e zenon_H91 zenon_H8c zenon_H181 zenon_H7a zenon_H1b7 zenon_H187 zenon_H198 zenon_H17c zenon_Hd0 zenon_H86 zenon_H84 zenon_H18a zenon_H90 zenon_H53 zenon_He3 zenon_Hda zenon_H56 zenon_H200. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L432_); trivial. % 10.28/10.45 apply (zenon_L426_); trivial. % 10.28/10.45 apply (zenon_L266_); trivial. % 10.28/10.45 (* end of lemma zenon_L870_ *) % 10.28/10.45 assert (zenon_L871_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H200 zenon_H18e zenon_H42 zenon_H12c zenon_Hab zenon_H6f zenon_H27 zenon_H1dd zenon_H108 zenon_Hdd zenon_H44 zenon_H205 zenon_Hc6 zenon_Hc1 zenon_H18d zenon_H7e zenon_H7d zenon_H1de zenon_Hf8 zenon_Hd2 zenon_H64 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1bc zenon_H1e2 zenon_H35 zenon_H95 zenon_H192 zenon_H28 zenon_H4c zenon_H15a zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H5e zenon_H8c zenon_H181 zenon_H7a zenon_H1b7 zenon_H187 zenon_H198 zenon_H17c zenon_H86 zenon_H84 zenon_H18a zenon_H90 zenon_H53 zenon_He3 zenon_Hda zenon_H56 zenon_H150 zenon_H3c zenon_H91 zenon_Hc5 zenon_H155 zenon_H6e zenon_H158 zenon_H22c zenon_H25. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L433_); trivial. % 10.28/10.45 apply (zenon_L449_); trivial. % 10.28/10.45 apply (zenon_L870_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 (* end of lemma zenon_L871_ *) % 10.28/10.45 assert (zenon_L872_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (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 (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) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (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) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H7a zenon_H1cb zenon_H1b7 zenon_H64 zenon_H181 zenon_Hd0 zenon_H6e zenon_Hdd zenon_H27 zenon_H159 zenon_H17c zenon_H91 zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H84 zenon_H17a zenon_H90 zenon_H35 zenon_H42 zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H7e zenon_H18a zenon_H198 zenon_H86 zenon_H56 zenon_H1b4 zenon_H6f zenon_H100 zenon_H9a zenon_H187. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L418_); trivial. % 10.28/10.45 apply (zenon_L828_); trivial. % 10.28/10.45 (* end of lemma zenon_L872_ *) % 10.28/10.45 assert (zenon_L873_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H25 zenon_H22c zenon_H1b7 zenon_H84 zenon_H7a zenon_Hd0 zenon_H181 zenon_H9a zenon_H187 zenon_H1cb zenon_H64 zenon_H18a zenon_H86 zenon_H17c zenon_H198 zenon_Hdd zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H35 zenon_H6e zenon_H159 zenon_H27 zenon_H42 zenon_H6f zenon_H90 zenon_H91 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H1b4 zenon_H56 zenon_H200. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L872_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 (* end of lemma zenon_L873_ *) % 10.28/10.45 assert (zenon_L874_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H158 zenon_H1b7 zenon_H1cb zenon_Hd2 zenon_H157 zenon_Hf8 zenon_H155 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7e zenon_H7a zenon_H18d zenon_H35 zenon_H1ae zenon_Hc7 zenon_H150 zenon_He3 zenon_H42 zenon_H181 zenon_H6e zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H187 zenon_H64 zenon_H1e2 zenon_H9a zenon_H198 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_Hb1. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L843_); trivial. % 10.28/10.45 apply (zenon_L779_); trivial. % 10.28/10.45 (* end of lemma zenon_L874_ *) % 10.28/10.45 assert (zenon_L875_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (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) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H43 zenon_H25 zenon_H22c zenon_H157 zenon_H1ae zenon_Hd2 zenon_H1cb zenon_H187 zenon_H9a zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H3c zenon_Hc5 zenon_H155 zenon_H6e zenon_H158 zenon_Hf8 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7e zenon_H18d zenon_H35 zenon_H150 zenon_He3 zenon_H42 zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H64 zenon_H1e2 zenon_H198 zenon_Hb1 zenon_H200. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L874_); trivial. % 10.28/10.45 apply (zenon_L412_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 (* end of lemma zenon_L875_ *) % 10.28/10.45 assert (zenon_L876_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (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) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (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))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H1af zenon_H43 zenon_H25 zenon_H22c zenon_H157 zenon_H1ae zenon_Hd2 zenon_H1cb zenon_H187 zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H3c zenon_Hc5 zenon_H155 zenon_H6e zenon_H158 zenon_Hf8 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H7e zenon_H18d zenon_H35 zenon_H150 zenon_He3 zenon_H42 zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H1f zenon_Hdd zenon_He7 zenon_H17a zenon_Hc0 zenon_H5e zenon_H44 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H64 zenon_H1e2 zenon_H198 zenon_H200 zenon_H1b1 zenon_Hbb zenon_H205 zenon_H12c zenon_Hc6 zenon_H156 zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_L875_); trivial. % 10.28/10.45 apply (zenon_L780_); trivial. % 10.28/10.45 (* end of lemma zenon_L876_ *) % 10.28/10.45 assert (zenon_L877_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (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 (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_Hc8 zenon_Hc7 zenon_Hf8 zenon_H1af zenon_H158 zenon_H155 zenon_Hc5 zenon_H3c zenon_H1b7 zenon_H181 zenon_H1cb zenon_Hd2 zenon_H1ae zenon_H157 zenon_H192 zenon_H16e zenon_H191 zenon_H144 zenon_H10b zenon_H53 zenon_H108 zenon_H56 zenon_H42 zenon_Hd3 zenon_H18a zenon_H7d zenon_H7e zenon_H7a zenon_H86 zenon_H18d zenon_H187 zenon_H6e zenon_H6f zenon_H35 zenon_Hcf zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H9a zenon_H90 zenon_H27 zenon_H100 zenon_H64. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L129_); trivial. % 10.28/10.45 apply (zenon_L864_); trivial. % 10.28/10.45 (* end of lemma zenon_L877_ *) % 10.28/10.45 assert (zenon_L878_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H174 zenon_H22c zenon_H4a zenon_H1af zenon_H158 zenon_H145 zenon_H5e zenon_H155 zenon_Hc5 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H192 zenon_H16e zenon_H6e zenon_H191 zenon_H156 zenon_H150 zenon_Hda zenon_He3 zenon_H53 zenon_H90 zenon_H95 zenon_H8c zenon_H1e2 zenon_Hd3 zenon_Hb0 zenon_H4c zenon_H3c zenon_Hdd zenon_H1bc zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H64 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H1f0 zenon_H1b1 zenon_H35 zenon_H1c3 zenon_H1c0 zenon_H1ba zenon_Hce zenon_H42 zenon_H97 zenon_H168 zenon_H132 zenon_H67. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L851_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 (* end of lemma zenon_L878_ *) % 10.28/10.45 assert (zenon_L879_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (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) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H25 zenon_H22c zenon_H157 zenon_H1ae zenon_Hd2 zenon_H1cb zenon_H187 zenon_H9a zenon_H181 zenon_H7a zenon_H84 zenon_H1b7 zenon_H3c zenon_Hc5 zenon_H155 zenon_H6e zenon_H158 zenon_Hf8 zenon_H108 zenon_H56 zenon_H1b4 zenon_Hd3 zenon_H7d zenon_H18d zenon_H35 zenon_Hc7 zenon_H150 zenon_He3 zenon_H42 zenon_H6f zenon_H27 zenon_H4c zenon_H95 zenon_H14d zenon_H192 zenon_H1f zenon_H191 zenon_Hdd zenon_He7 zenon_H17a zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H91 zenon_H17c zenon_H90 zenon_H159 zenon_H53 zenon_H165 zenon_H18a zenon_H86 zenon_H64 zenon_H1e2 zenon_H198 zenon_Hc8 zenon_Hb1 zenon_H200. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L874_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 (* end of lemma zenon_L879_ *) % 10.28/10.45 assert (zenon_L880_ : ((~((op (e2) (e2)) = (e1)))\/(~((op (e2) (e1)) = (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (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 (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (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 (e0) (e0)) = (op (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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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)) = (op (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 (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 (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H22a zenon_H230 zenon_H205 zenon_Hbb zenon_H165 zenon_H17a zenon_H18e zenon_He3 zenon_Hec zenon_H12c zenon_H1dd zenon_H1de zenon_H3c zenon_Hda zenon_H128 zenon_H8c zenon_Hb0 zenon_H97 zenon_H1e2 zenon_H18a zenon_H10b zenon_H1e6 zenon_H112 zenon_Hde zenon_Hab zenon_H16f zenon_H67 zenon_Hc6 zenon_H168 zenon_Hae zenon_H11d zenon_H144 zenon_H4a zenon_H204 zenon_H152 zenon_H114 zenon_H1ef zenon_H195 zenon_H1f zenon_H1f0 zenon_Hf5 zenon_H177 zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173 zenon_H18d zenon_H1b7 zenon_H7a zenon_H58 zenon_H198 zenon_H6f zenon_H159 zenon_H6e zenon_H35 zenon_H1b1 zenon_H16b zenon_H14d zenon_H157 zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_Hdd zenon_Hce zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H12f zenon_Hc5 zenon_H155 zenon_H5e zenon_H145 zenon_H158 zenon_H192 zenon_H191 zenon_Hf8 zenon_H108 zenon_H1cb zenon_H103 zenon_H132 zenon_H86 zenon_H7d zenon_H17c zenon_H90 zenon_H156 zenon_H16e zenon_H1ea zenon_H22c zenon_H174 zenon_H151 zenon_H22b. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H91 | zenon_intro zenon_H1ae ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L382_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L868_); trivial. % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L397_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L869_); trivial. % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L235_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_L871_); trivial. % 10.28/10.45 apply (zenon_L296_); trivial. % 10.28/10.45 apply (zenon_L194_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L868_); trivial. % 10.28/10.45 apply (zenon_L412_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L397_); trivial. % 10.28/10.45 apply (zenon_L456_); trivial. % 10.28/10.45 apply (zenon_L458_); trivial. % 10.28/10.45 apply (zenon_L459_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L463_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L823_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L868_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L397_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L869_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L873_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L235_); trivial. % 10.28/10.45 apply (zenon_L822_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.45 apply (zenon_L867_); trivial. % 10.28/10.45 apply (zenon_L254_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L397_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L826_); trivial. % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_L235_); trivial. % 10.28/10.45 apply (zenon_L822_); trivial. % 10.28/10.45 apply (zenon_L459_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L830_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L842_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L874_); trivial. % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L669_); trivial. % 10.28/10.45 apply (zenon_L876_); trivial. % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L874_); trivial. % 10.28/10.45 apply (zenon_L872_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L877_); trivial. % 10.28/10.45 apply (zenon_L872_); trivial. % 10.28/10.45 apply (zenon_L321_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_L871_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L296_); trivial. % 10.28/10.45 apply (zenon_L194_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_L876_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_L875_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_L864_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L849_); trivial. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_L878_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_L853_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.45 exact (zenon_H192 zenon_H1d). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L190_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L879_); trivial. % 10.28/10.45 apply (zenon_L786_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L129_); trivial. % 10.28/10.45 apply (zenon_L861_); trivial. % 10.28/10.45 apply (zenon_L44_); trivial. % 10.28/10.45 apply (zenon_L321_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_L224_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L879_); trivial. % 10.28/10.45 apply (zenon_L873_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L877_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L44_); trivial. % 10.28/10.45 apply (zenon_L321_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.45 exact (zenon_H25 zenon_H2a). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 apply (zenon_L857_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L266_); trivial. % 10.28/10.45 apply (zenon_L870_); trivial. % 10.28/10.45 apply (zenon_L223_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L296_); trivial. % 10.28/10.45 apply (zenon_L194_); trivial. % 10.28/10.45 apply (zenon_L865_); trivial. % 10.28/10.45 apply (zenon_L845_); trivial. % 10.28/10.45 exact (zenon_H22c zenon_H68). % 10.28/10.45 apply (zenon_L878_); trivial. % 10.28/10.45 (* end of lemma zenon_L880_ *) % 10.28/10.45 assert (zenon_L881_ : ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e1) (e0)) = (op (e1) (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)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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 (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H22b zenon_H151 zenon_H67 zenon_Hab zenon_Hde zenon_H112 zenon_Hc6 zenon_H18a zenon_H1e2 zenon_H17c zenon_H64 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H58 zenon_H128 zenon_Hce zenon_Hdd zenon_H7a zenon_H1b7 zenon_H8c zenon_Hd3 zenon_Hb0 zenon_H12c zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_He3 zenon_H150 zenon_H168 zenon_Hae zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H198 zenon_H1dd zenon_Hda zenon_H56 zenon_Hd2 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H4c zenon_H35 zenon_H95 zenon_H10b zenon_H187 zenon_H97 zenon_H18d zenon_H12f zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_H91 zenon_Hc5 zenon_Hf8 zenon_H6f zenon_H144 zenon_H158 zenon_H1ea zenon_H4a zenon_H204 zenon_He7 zenon_H152 zenon_H114 zenon_H16b zenon_H1ef zenon_H195 zenon_H1f zenon_H1af zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_Hc0 zenon_H177 zenon_H44 zenon_H14d zenon_H200 zenon_H1f8 zenon_H1fb zenon_Hfd zenon_H173. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.45 apply (zenon_L379_); trivial. % 10.28/10.45 apply (zenon_L820_); trivial. % 10.28/10.45 (* end of lemma zenon_L881_ *) % 10.28/10.45 assert (zenon_L882_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((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). % 10.28/10.45 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H18d zenon_He3 zenon_H56 zenon_H90 zenon_H58 zenon_H2a zenon_H7d zenon_H86 zenon_H5e zenon_H128 zenon_H27 zenon_H1c3 zenon_Hbc zenon_H1c0 zenon_H15a zenon_H1bc zenon_H1ba zenon_Hce zenon_H95 zenon_Hdd zenon_H7a zenon_H187 zenon_H188 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_Hcf zenon_H35 zenon_H42 zenon_Hf5 zenon_H10b zenon_H1f0 zenon_H192 zenon_H12c zenon_H198 zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_H1ae zenon_Haf zenon_H1b1 zenon_H28 zenon_H4c zenon_H97 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H53 zenon_H64 zenon_H1dd zenon_Hf8. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L713_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 (* end of lemma zenon_L882_ *) % 10.28/10.45 assert (zenon_L883_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((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). % 10.28/10.45 do 0 intro. intros zenon_Hda zenon_H151 zenon_H1b0 zenon_H18d zenon_He3 zenon_H56 zenon_H90 zenon_H58 zenon_H2a zenon_H7d zenon_H86 zenon_H5e zenon_H128 zenon_H27 zenon_H1c3 zenon_H1c0 zenon_H15a zenon_H1bc zenon_H1ba zenon_Hce zenon_H95 zenon_Hdd zenon_H7a zenon_H187 zenon_H188 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_Hcf zenon_H35 zenon_H42 zenon_Hf5 zenon_H10b zenon_H1f0 zenon_H192 zenon_H12c zenon_H198 zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_H1ae zenon_Haf zenon_H1b1 zenon_H28 zenon_H4c zenon_H97 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H53 zenon_H64 zenon_H1dd zenon_Hf8. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.28/10.45 exact (zenon_H28 zenon_H31). % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.28/10.45 apply (zenon_L239_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.28/10.45 apply (zenon_L155_); trivial. % 10.28/10.45 apply (zenon_L882_); trivial. % 10.28/10.45 (* end of lemma zenon_L883_ *) % 10.28/10.45 assert (zenon_L884_ : (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((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) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (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 (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> (((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))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H56 zenon_Hb0 zenon_Hb1 zenon_H8d zenon_H7e zenon_H7f zenon_H28 zenon_H198 zenon_H188 zenon_H95 zenon_H151 zenon_H1b0 zenon_H18d zenon_He3 zenon_H90 zenon_H58 zenon_H2a zenon_H7d zenon_H86 zenon_H5e zenon_H128 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_Hce zenon_Hdd zenon_H7a zenon_H187 zenon_H1b7 zenon_H8c zenon_H91 zenon_Hd3 zenon_H42 zenon_Hf5 zenon_H10b zenon_H1f0 zenon_H192 zenon_H12c zenon_Hab zenon_Hc8 zenon_Hc7 zenon_H181 zenon_H1e2 zenon_Hde zenon_H1ae zenon_Haf zenon_H1b1 zenon_H4c zenon_H97 zenon_H1cb zenon_H159 zenon_Hec zenon_H103 zenon_H53 zenon_H64 zenon_H1dd zenon_Hf8 zenon_Hda zenon_H15a zenon_H35 zenon_H27 zenon_Hc5 zenon_H3c. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.45 exact (zenon_H56 zenon_H2c). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.28/10.45 exact (zenon_H27 zenon_H32). % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.28/10.45 apply (zenon_L238_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.28/10.45 apply (zenon_L883_); trivial. % 10.28/10.45 apply (zenon_L251_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.45 apply (zenon_L103_); trivial. % 10.28/10.45 apply (zenon_L87_); trivial. % 10.28/10.45 apply (zenon_L252_); trivial. % 10.28/10.45 (* end of lemma zenon_L884_ *) % 10.28/10.45 assert (zenon_L885_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((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 (e3) (e1)) = (op (e3) (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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((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 (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (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) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.28/10.45 do 0 intro. intros zenon_H67 zenon_H150 zenon_H64 zenon_Hec zenon_H1cb zenon_H1b1 zenon_Hde zenon_H1e2 zenon_Hab zenon_H12c zenon_H1f0 zenon_Hf5 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_H7a zenon_Hce zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H128 zenon_H58 zenon_H90 zenon_He3 zenon_Hb0 zenon_H18a zenon_H17c zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H56 zenon_Hda zenon_H1dd zenon_H1b4 zenon_H158 zenon_H1ea zenon_H6f zenon_H144 zenon_H159 zenon_Hdd zenon_Hc0 zenon_H114 zenon_H16b zenon_Hc6 zenon_Hae zenon_H198 zenon_H1af zenon_H168 zenon_H151 zenon_H1b0 zenon_H18d zenon_H12f zenon_H2a zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H4c zenon_H35 zenon_H95 zenon_H10b zenon_H187 zenon_H97 zenon_Hd2 zenon_H1ae zenon_H157 zenon_H4a. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_L297_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_L812_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L813_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.45 apply (zenon_L884_); trivial. % 10.28/10.45 apply (zenon_L254_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 apply (zenon_L814_); trivial. % 10.28/10.45 apply (zenon_L815_); trivial. % 10.28/10.45 apply (zenon_L811_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.45 apply (zenon_L883_); trivial. % 10.28/10.45 apply (zenon_L44_); trivial. % 10.28/10.45 apply (zenon_L321_); trivial. % 10.28/10.45 exact (zenon_H1ae zenon_Hb8). % 10.28/10.45 apply (zenon_L123_); trivial. % 10.28/10.45 apply (zenon_L213_); trivial. % 10.28/10.45 apply (zenon_L101_); trivial. % 10.28/10.45 (* end of lemma zenon_L885_ *) % 10.28/10.45 assert (zenon_L886_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 10.28/10.45 do 0 intro. intros zenon_Hc0 zenon_Hb4 zenon_H78 zenon_Hc1 zenon_H7f zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_Hf2 zenon_H35 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H52 zenon_H80 zenon_H177 zenon_H1b0. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.28/10.45 apply (zenon_L334_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.28/10.45 exact (zenon_Hc1 zenon_Hc4). % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.28/10.45 apply (zenon_L368_); trivial. % 10.28/10.45 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.45 (* end of lemma zenon_L886_ *) % 10.28/10.45 assert (zenon_L887_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.28/10.45 do 0 intro. intros zenon_Hf5 zenon_Hbc zenon_H4c zenon_H35 zenon_Hd6 zenon_H100 zenon_H1e6 zenon_H7e. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 10.28/10.45 apply (zenon_L139_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 10.28/10.45 apply (zenon_L63_); trivial. % 10.28/10.45 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 10.28/10.45 apply (zenon_L328_); trivial. % 10.28/10.45 exact (zenon_H7e zenon_H83). % 10.28/10.45 (* end of lemma zenon_L887_ *) % 10.28/10.45 assert (zenon_L888_ : (((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 (e0) (e0)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e1)) = (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) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H64 zenon_H56 zenon_H97 zenon_H28 zenon_H7e zenon_H1e6 zenon_H100 zenon_H5e zenon_Hbc zenon_Hf5 zenon_H1b1 zenon_H1f0 zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H1b0 zenon_H177 zenon_H80 zenon_H10b zenon_H114 zenon_H95 zenon_H16b zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f zenon_Hc1 zenon_Hc0 zenon_H1ae zenon_H35 zenon_Hfd zenon_He7 zenon_H4c. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.46 exact (zenon_H56 zenon_H2c). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.46 apply (zenon_L329_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.46 apply (zenon_L12_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.28/10.46 exact (zenon_H28 zenon_H31). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.28/10.46 apply (zenon_L365_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.28/10.46 apply (zenon_L69_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.28/10.46 exact (zenon_He8 zenon_Heb). % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1b1); [ zenon_intro zenon_H1e | zenon_intro zenon_H1b2 ]. % 10.28/10.46 apply (zenon_L329_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1b2); [ zenon_intro zenon_H1d | zenon_intro zenon_H1b3 ]. % 10.28/10.46 exact (zenon_H192 zenon_H1d). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H77 | zenon_intro zenon_Hf2 ]. % 10.28/10.46 apply (zenon_L22_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.28/10.46 apply (zenon_L331_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.28/10.46 apply (zenon_L886_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.28/10.46 exact (zenon_H1ae zenon_Hb8). % 10.28/10.46 apply (zenon_L887_); trivial. % 10.28/10.46 apply (zenon_L364_); trivial. % 10.28/10.46 apply (zenon_L13_); trivial. % 10.28/10.46 (* end of lemma zenon_L888_ *) % 10.28/10.46 assert (zenon_L889_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (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) (e0)) = (e2))) -> (~((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))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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 (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H151 zenon_H18d zenon_H188 zenon_H86 zenon_H25 zenon_H64 zenon_H27 zenon_H44 zenon_H97 zenon_H95 zenon_H53 zenon_H28 zenon_H35 zenon_H42 zenon_H6f zenon_H4c zenon_Hbc zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H56 zenon_He7 zenon_H192 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hfd zenon_Hde zenon_H1ae zenon_H177 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H3c zenon_H152 zenon_H158 zenon_H114 zenon_H10b zenon_H16b zenon_H1b0 zenon_Hc0 zenon_H1f zenon_H1b1 zenon_H5e zenon_H7d zenon_H7a zenon_H200 zenon_H1dd zenon_Hf8. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.46 exact (zenon_H25 zenon_H2a). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.46 apply (zenon_L363_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_L888_); trivial. % 10.28/10.46 apply (zenon_L24_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 apply (zenon_L267_); trivial. % 10.28/10.46 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.46 (* end of lemma zenon_L889_ *) % 10.28/10.46 assert (zenon_L890_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (e3))) -> False). % 10.28/10.46 do 0 intro. intros zenon_Hc0 zenon_H1e zenon_Hd3 zenon_Hb1 zenon_H191 zenon_He8 zenon_H192 zenon_H53 zenon_Hb0 zenon_Hc1 zenon_H8d zenon_H5e zenon_H7d zenon_H47 zenon_H7f zenon_H80 zenon_H18d zenon_H188 zenon_H86 zenon_H7a zenon_H7e zenon_H8c zenon_H91 zenon_H4c zenon_H74 zenon_H90 zenon_H1b0. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.28/10.46 apply (zenon_L336_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.28/10.46 exact (zenon_Hc1 zenon_Hc4). % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.28/10.46 apply (zenon_L339_); trivial. % 10.28/10.46 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.46 (* end of lemma zenon_L890_ *) % 10.28/10.46 assert (zenon_L891_ : (((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) (e3)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e1)) -> False). % 10.28/10.46 do 0 intro. intros zenon_Hda zenon_H28 zenon_H198 zenon_H1b0 zenon_H90 zenon_H91 zenon_H8c zenon_H7e zenon_H7a zenon_H86 zenon_H188 zenon_H18d zenon_H80 zenon_H7f zenon_H47 zenon_H7d zenon_H5e zenon_H8d zenon_Hc1 zenon_Hb0 zenon_H53 zenon_H192 zenon_He8 zenon_H191 zenon_Hb1 zenon_Hd3 zenon_H1e zenon_Hc0 zenon_H4c zenon_Hf0. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.28/10.46 exact (zenon_H28 zenon_H31). % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.28/10.46 apply (zenon_L239_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L890_); trivial. % 10.28/10.46 apply (zenon_L139_); trivial. % 10.28/10.46 (* end of lemma zenon_L891_ *) % 10.28/10.46 assert (zenon_L892_ : ((~((op (e2) (e2)) = (e1)))\/(~((op (e2) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((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) (e3)) = (op (e2) (e3)))) -> (((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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H22a zenon_H157 zenon_H173 zenon_Hfd zenon_H1fb zenon_H1f8 zenon_H200 zenon_H14d zenon_H44 zenon_H177 zenon_Hc0 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_H1af zenon_H1f zenon_H195 zenon_H1ef zenon_H16b zenon_H114 zenon_H152 zenon_He7 zenon_H204 zenon_H4a zenon_H1ea zenon_H158 zenon_H144 zenon_H6f zenon_Hf8 zenon_Hc5 zenon_H3c zenon_H155 zenon_H53 zenon_H108 zenon_H145 zenon_H86 zenon_H7d zenon_H5e zenon_H12f zenon_H18d zenon_H97 zenon_H187 zenon_H10b zenon_H95 zenon_H35 zenon_H4c zenon_H103 zenon_H132 zenon_H181 zenon_H42 zenon_Hd2 zenon_H56 zenon_Hda zenon_H1dd zenon_H198 zenon_H1b4 zenon_H156 zenon_H192 zenon_H11d zenon_H188 zenon_H191 zenon_Hae zenon_H168 zenon_H150 zenon_He3 zenon_H1b1 zenon_H1cb zenon_H159 zenon_Hec zenon_H12c zenon_Hb0 zenon_Hd3 zenon_H8c zenon_H1b7 zenon_H7a zenon_Hdd zenon_Hce zenon_H128 zenon_H58 zenon_H90 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H64 zenon_H17c zenon_H1e2 zenon_H18a zenon_Hc6 zenon_H112 zenon_Hde zenon_Hab zenon_H67 zenon_H151 zenon_H22b. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H91 | zenon_intro zenon_H1ae ]. % 10.28/10.46 apply (zenon_L881_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.46 apply (zenon_L726_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.46 apply (zenon_L885_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.46 exact (zenon_H192 zenon_H1d). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.46 exact (zenon_H25 zenon_H2a). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.46 exact (zenon_H56 zenon_H2c). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.28/10.46 exact (zenon_H56 zenon_H2c). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.28/10.46 apply (zenon_L326_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.28/10.46 exact (zenon_H28 zenon_H31). % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.28/10.46 apply (zenon_L239_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L21_); trivial. % 10.28/10.46 apply (zenon_L889_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.46 exact (zenon_H27 zenon_H32). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.46 apply (zenon_L331_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.46 apply (zenon_L5_); trivial. % 10.28/10.46 apply (zenon_L891_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.46 apply (zenon_L228_); trivial. % 10.28/10.46 apply (zenon_L610_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_L344_); trivial. % 10.28/10.46 apply (zenon_L24_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 apply (zenon_L360_); trivial. % 10.28/10.46 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.46 apply (zenon_L889_); trivial. % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 exact (zenon_H1ae zenon_Hb8). % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L810_); trivial. % 10.28/10.46 apply (zenon_L817_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L818_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_L888_); trivial. % 10.28/10.46 apply (zenon_L266_); trivial. % 10.28/10.46 apply (zenon_L358_); trivial. % 10.28/10.46 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 exact (zenon_H1ae zenon_Hb8). % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L725_); trivial. % 10.28/10.46 apply (zenon_L343_); trivial. % 10.28/10.46 apply (zenon_L819_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 (* end of lemma zenon_L892_ *) % 10.28/10.46 assert (zenon_L893_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (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)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.28/10.46 do 0 intro. intros zenon_H200 zenon_H25 zenon_H22c zenon_H4c zenon_H10b zenon_Hb0 zenon_H181 zenon_H91 zenon_H12c zenon_Hc8 zenon_H17c zenon_H90 zenon_H1f8 zenon_H6f zenon_H155 zenon_H1e6 zenon_Hda zenon_H28 zenon_H198 zenon_Hf5 zenon_H1f0 zenon_H7e zenon_H56 zenon_H64 zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H128 zenon_H35 zenon_H188 zenon_H95 zenon_H3a zenon_H1fb zenon_H97 zenon_Hd3 zenon_H187 zenon_H108 zenon_H1cb zenon_H100 zenon_H5e zenon_Hb1 zenon_H53 zenon_Hed. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.46 exact (zenon_H25 zenon_H2a). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_L358_); trivial. % 10.28/10.46 apply (zenon_L359_); trivial. % 10.28/10.46 (* end of lemma zenon_L893_ *) % 10.28/10.46 assert (zenon_L894_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.46 do 0 intro. intros zenon_Hf8 zenon_H35 zenon_H95 zenon_H1fb zenon_H128 zenon_H1f8 zenon_H3a zenon_H155 zenon_H181 zenon_Hc8 zenon_H17c zenon_H12c zenon_H191 zenon_Hc1 zenon_H192 zenon_He8 zenon_H10b zenon_H187 zenon_H97 zenon_H108 zenon_H200 zenon_H56 zenon_Hda zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H53 zenon_H90 zenon_H1cb zenon_H7d zenon_H7e zenon_H86 zenon_H8d zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hb1 zenon_Hd3 zenon_Hb0 zenon_H188 zenon_H198 zenon_H28 zenon_H6f zenon_H7a zenon_H64 zenon_H22c zenon_H25 zenon_H18d. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.46 apply (zenon_L762_); trivial. % 10.28/10.46 apply (zenon_L893_); trivial. % 10.28/10.46 (* end of lemma zenon_L894_ *) % 10.28/10.46 assert (zenon_L895_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H168 zenon_Hae zenon_H159 zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H1af zenon_Hd2 zenon_Hf8 zenon_H35 zenon_H95 zenon_H1fb zenon_H128 zenon_H1f8 zenon_H3a zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H10b zenon_H187 zenon_H97 zenon_H108 zenon_H200 zenon_H56 zenon_Hda zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_H53 zenon_H90 zenon_H1cb zenon_H7d zenon_H7e zenon_H86 zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hd3 zenon_Hb0 zenon_H198 zenon_H28 zenon_H6f zenon_H7a zenon_H64 zenon_H22c zenon_H25 zenon_H18d zenon_He7 zenon_Hde zenon_H44 zenon_H22d zenon_H1f zenon_H1b1 zenon_H150 zenon_Hc6 zenon_H156 zenon_H1ea. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L894_); trivial. % 10.28/10.46 apply (zenon_L767_); trivial. % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L314_); trivial. % 10.28/10.46 (* end of lemma zenon_L895_ *) % 10.28/10.46 assert (zenon_L896_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (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 (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((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)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (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) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (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 (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H173 zenon_H67 zenon_Hab zenon_H112 zenon_H18a zenon_H1e2 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H58 zenon_Hce zenon_Hdd zenon_H1b7 zenon_Hec zenon_He3 zenon_H1b4 zenon_H1dd zenon_H42 zenon_H103 zenon_Hc5 zenon_H158 zenon_H174 zenon_H168 zenon_Hae zenon_H159 zenon_H191 zenon_H11d zenon_H192 zenon_H1af zenon_Hd2 zenon_Hf8 zenon_H35 zenon_H95 zenon_H1fb zenon_H128 zenon_H1f8 zenon_H155 zenon_H181 zenon_H17c zenon_H12c zenon_H10b zenon_H187 zenon_H97 zenon_H108 zenon_H200 zenon_Hda zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_H53 zenon_H90 zenon_H1cb zenon_H7d zenon_H7e zenon_H8c zenon_H91 zenon_H5e zenon_H4c zenon_Hd3 zenon_Hb0 zenon_H198 zenon_H6f zenon_H7a zenon_H64 zenon_H22c zenon_H18d zenon_He7 zenon_Hde zenon_H44 zenon_H22d zenon_H1f zenon_H1b1 zenon_H150 zenon_Hc6 zenon_H156 zenon_H1ea zenon_H4a zenon_H132 zenon_H3c zenon_H144 zenon_H145 zenon_H12f zenon_H204 zenon_H188 zenon_H86. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_L322_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.46 exact (zenon_H192 zenon_H1d). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_L895_); trivial. % 10.28/10.46 apply (zenon_L375_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_L315_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 (* end of lemma zenon_L896_ *) % 10.28/10.46 assert (zenon_L897_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H25 zenon_H22c zenon_H64 zenon_H7a zenon_H6f zenon_H28 zenon_H198 zenon_H188 zenon_Hb0 zenon_Hd3 zenon_Hb1 zenon_H4c zenon_H5e zenon_H91 zenon_H8c zenon_H8d zenon_H86 zenon_H7d zenon_H1cb zenon_H90 zenon_H53 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H56 zenon_H168 zenon_Hae zenon_H95 zenon_H155 zenon_H35 zenon_H159 zenon_H191 zenon_H11d zenon_H192 zenon_H156 zenon_H3a zenon_Hc6 zenon_Hf8 zenon_H108 zenon_H18d zenon_H1b0 zenon_H151 zenon_H1ea zenon_H200 zenon_H97 zenon_H187 zenon_H10b zenon_He8 zenon_Hc1 zenon_H12c zenon_H17c zenon_Hc8 zenon_H181 zenon_H1f8 zenon_H128 zenon_H1fb. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.46 exact (zenon_H25 zenon_H2a). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_L344_); trivial. % 10.28/10.46 apply (zenon_L817_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 apply (zenon_L893_); trivial. % 10.28/10.46 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.46 (* end of lemma zenon_L897_ *) % 10.28/10.46 assert (zenon_L898_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (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 (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H151 zenon_H1b0 zenon_H22c zenon_He8 zenon_H1b1 zenon_H191 zenon_Hc1 zenon_H1f zenon_H22d zenon_H44 zenon_H35 zenon_Hde zenon_H5e zenon_H192 zenon_H4c zenon_Hbc zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_He7. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.46 apply (zenon_L767_); trivial. % 10.28/10.46 exact (zenon_H1b0 zenon_Hbd). % 10.28/10.46 (* end of lemma zenon_L898_ *) % 10.28/10.46 assert (zenon_L899_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (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)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H1af zenon_Hd2 zenon_H25 zenon_H22c zenon_H64 zenon_H7a zenon_H6f zenon_H28 zenon_H198 zenon_Hb0 zenon_Hd3 zenon_H4c zenon_H5e zenon_H91 zenon_H8c zenon_H86 zenon_H7d zenon_H1cb zenon_H90 zenon_H53 zenon_Hf5 zenon_H1e6 zenon_H1f0 zenon_Hda zenon_H56 zenon_H168 zenon_Hae zenon_H95 zenon_H155 zenon_H35 zenon_H159 zenon_H156 zenon_H3a zenon_Hc6 zenon_Hf8 zenon_H108 zenon_H18d zenon_H1b0 zenon_H151 zenon_H1ea zenon_H200 zenon_H97 zenon_H187 zenon_H10b zenon_H12c zenon_H17c zenon_H181 zenon_H1f8 zenon_H128 zenon_H1fb zenon_H1b1 zenon_H1f zenon_H22d zenon_H44 zenon_Hde zenon_He7 zenon_H150. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L897_); trivial. % 10.28/10.46 apply (zenon_L898_); trivial. % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L314_); trivial. % 10.28/10.46 (* end of lemma zenon_L899_ *) % 10.28/10.46 assert (zenon_L900_ : ((~((op (e2) (e2)) = (e1)))\/(~((op (e2) (e1)) = (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> ((~((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 (e1) (e0)) = (op (e1) (e3)))) -> (~((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)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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 (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))))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/(~((op (e3) (e1)) = (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H22a zenon_H157 zenon_H173 zenon_H1af zenon_H1fb zenon_H1f8 zenon_H200 zenon_H1f0 zenon_H1e6 zenon_Hf5 zenon_He7 zenon_H44 zenon_H22d zenon_H1f zenon_H204 zenon_H67 zenon_Hab zenon_Hde zenon_H112 zenon_Hc6 zenon_H18a zenon_H1e2 zenon_H17c zenon_H64 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H90 zenon_H58 zenon_H128 zenon_Hce zenon_Hdd zenon_H7a zenon_H1b7 zenon_H8c zenon_Hd3 zenon_Hb0 zenon_H12c zenon_Hec zenon_H159 zenon_H1cb zenon_H1b1 zenon_He3 zenon_H150 zenon_H168 zenon_Hae zenon_H191 zenon_H188 zenon_H11d zenon_H192 zenon_H156 zenon_H1b4 zenon_H198 zenon_H1dd zenon_Hda zenon_Hd2 zenon_H42 zenon_H181 zenon_H132 zenon_H103 zenon_H4c zenon_H35 zenon_H95 zenon_H10b zenon_H187 zenon_H97 zenon_H18d zenon_H12f zenon_H5e zenon_H7d zenon_H86 zenon_H145 zenon_H108 zenon_H53 zenon_H155 zenon_H3c zenon_Hc5 zenon_Hf8 zenon_H6f zenon_H144 zenon_H158 zenon_H1ea zenon_H4a zenon_H22c zenon_H174 zenon_H151 zenon_H16b zenon_H114 zenon_Hc0 zenon_H22b. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H91 | zenon_intro zenon_H1ae ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.46 apply (zenon_L896_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_L816_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.46 exact (zenon_H192 zenon_H1d). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_L899_); trivial. % 10.28/10.46 apply (zenon_L817_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_L819_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H7e | zenon_intro zenon_H1b0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_L714_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.46 exact (zenon_H192 zenon_H1d). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L894_); trivial. % 10.28/10.46 apply (zenon_L773_); trivial. % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 exact (zenon_H1ae zenon_Hb8). % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L314_); trivial. % 10.28/10.46 apply (zenon_L375_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_L315_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_L885_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.46 exact (zenon_H192 zenon_H1d). % 10.28/10.46 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L897_); trivial. % 10.28/10.46 apply (zenon_L774_); trivial. % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 exact (zenon_H1ae zenon_Hb8). % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L810_); trivial. % 10.28/10.46 apply (zenon_L817_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.28/10.46 apply (zenon_L297_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.46 apply (zenon_L818_); trivial. % 10.28/10.46 apply (zenon_L774_); trivial. % 10.28/10.46 apply (zenon_L354_); trivial. % 10.28/10.46 exact (zenon_H1ae zenon_Hb8). % 10.28/10.46 apply (zenon_L321_); trivial. % 10.28/10.46 apply (zenon_L373_); trivial. % 10.28/10.46 apply (zenon_L725_); trivial. % 10.28/10.46 apply (zenon_L343_); trivial. % 10.28/10.46 exact (zenon_H22c zenon_H68). % 10.28/10.46 apply (zenon_L819_); trivial. % 10.28/10.46 apply (zenon_L252_); trivial. % 10.28/10.46 (* end of lemma zenon_L900_ *) % 10.28/10.46 assert (zenon_L901_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H11f zenon_Hcd zenon_H1fb. % 10.28/10.46 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 10.28/10.46 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e2)) = (op (e2) (e3)))). % 10.28/10.46 intro zenon_D_pnotp. % 10.28/10.46 apply zenon_H1fb. % 10.28/10.46 rewrite <- zenon_D_pnotp. % 10.28/10.46 exact zenon_H17d. % 10.28/10.46 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 10.28/10.46 cut (((op (e2) (e3)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 10.28/10.46 congruence. % 10.28/10.46 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e2)))). % 10.28/10.46 intro zenon_D_pnotp. % 10.28/10.46 apply zenon_H231. % 10.28/10.46 rewrite <- zenon_D_pnotp. % 10.28/10.46 exact zenon_H11f. % 10.28/10.46 cut (((e3) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 10.28/10.46 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 10.28/10.46 congruence. % 10.28/10.46 apply zenon_H17e. apply refl_equal. % 10.28/10.46 apply zenon_H20d. apply sym_equal. exact zenon_Hcd. % 10.28/10.46 apply zenon_H17e. apply refl_equal. % 10.28/10.46 apply zenon_H17e. apply refl_equal. % 10.28/10.46 (* end of lemma zenon_L901_ *) % 10.28/10.46 assert (zenon_L902_ : (((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) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_Hc5 zenon_Hb1 zenon_H91 zenon_Hc7 zenon_H11f zenon_H1fb. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 10.28/10.46 exact (zenon_Hb1 zenon_Hb7). % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 10.28/10.46 exact (zenon_H91 zenon_H94). % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 10.28/10.46 exact (zenon_Hc7 zenon_H3a). % 10.28/10.46 apply (zenon_L901_); trivial. % 10.28/10.46 (* end of lemma zenon_L902_ *) % 10.28/10.46 assert (zenon_L903_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.28/10.46 do 0 intro. intros zenon_H157 zenon_H1ba zenon_H2a zenon_H44 zenon_H53 zenon_Hb0 zenon_Hb1 zenon_Hc7 zenon_H1fb zenon_H11f zenon_Hc5. % 10.28/10.46 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.46 apply (zenon_L902_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.28/10.46 apply (zenon_L216_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.28/10.46 apply (zenon_L57_); trivial. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.28/10.46 exact (zenon_Hb1 zenon_Hb7). % 10.28/10.46 apply (zenon_L96_); trivial. % 10.28/10.46 (* end of lemma zenon_L903_ *) % 10.28/10.46 assert (zenon_L904_ : (((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) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 10.28/10.46 do 0 intro. intros zenon_Hc5 zenon_H101 zenon_H155 zenon_H91 zenon_Hc7 zenon_H11f zenon_H1fb. % 10.28/10.46 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 10.28/10.47 apply (zenon_L117_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 10.28/10.47 exact (zenon_H91 zenon_H94). % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 10.28/10.47 exact (zenon_Hc7 zenon_H3a). % 10.28/10.47 apply (zenon_L901_); trivial. % 10.28/10.47 (* end of lemma zenon_L904_ *) % 10.28/10.47 assert (zenon_L905_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (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) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (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))))) -> (~((e2) = (e3))) -> (~((e0) = (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 (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H18d zenon_H205 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_H91 zenon_H155 zenon_H128 zenon_H95 zenon_H44 zenon_H8d zenon_H7f zenon_H7d zenon_H145. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.28/10.47 apply (zenon_L100_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.28/10.47 exact (zenon_He8 zenon_Heb). % 10.28/10.47 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.28/10.47 apply (zenon_L904_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H47 | zenon_intro zenon_H129 ]. % 10.28/10.47 apply (zenon_L338_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H9b | zenon_intro zenon_H12a ]. % 10.28/10.47 apply (zenon_L92_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_Hd0 | zenon_intro zenon_H85 ]. % 10.28/10.47 apply (zenon_L93_); trivial. % 10.28/10.47 exact (zenon_H7f zenon_H85). % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 (* end of lemma zenon_L905_ *) % 10.28/10.47 assert (zenon_L906_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H18d zenon_H11f zenon_H205 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_H7d zenon_H7f zenon_H7e zenon_H86 zenon_H145. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_L119_); trivial. % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 (* end of lemma zenon_L906_ *) % 10.28/10.47 assert (zenon_L907_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_He8 zenon_H155 zenon_H128 zenon_H95 zenon_H7f zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H2a zenon_H1ba zenon_H157. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_L903_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L905_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_L906_); trivial. % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 apply (zenon_L93_); trivial. % 10.28/10.47 apply (zenon_L79_); trivial. % 10.28/10.47 (* end of lemma zenon_L907_ *) % 10.28/10.47 assert (zenon_L908_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.28/10.47 do 0 intro. intros zenon_Hab zenon_H7f zenon_H95 zenon_H7b zenon_H35 zenon_H128 zenon_H15a zenon_H198 zenon_H11f zenon_H4c zenon_H7e. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 10.28/10.47 apply (zenon_L261_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 10.28/10.47 apply (zenon_L194_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 10.28/10.47 apply (zenon_L89_); trivial. % 10.28/10.47 exact (zenon_H7e zenon_H83). % 10.28/10.47 (* end of lemma zenon_L908_ *) % 10.28/10.47 assert (zenon_L909_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((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 (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H18d zenon_H205 zenon_H58 zenon_H2a zenon_H7d zenon_H7f zenon_H7e zenon_H86 zenon_H53 zenon_H11f zenon_Hab zenon_H4c zenon_H15a zenon_H198 zenon_H35 zenon_H95 zenon_H128 zenon_H8c. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.28/10.47 apply (zenon_L213_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.28/10.47 apply (zenon_L26_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.28/10.47 apply (zenon_L96_); trivial. % 10.28/10.47 apply (zenon_L908_); trivial. % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 (* end of lemma zenon_L909_ *) % 10.28/10.47 assert (zenon_L910_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H11f zenon_H74 zenon_Hce. % 10.28/10.47 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H17d | zenon_intro zenon_H17e ]. % 10.28/10.47 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 10.28/10.47 intro zenon_D_pnotp. % 10.28/10.47 apply zenon_Hce. % 10.28/10.47 rewrite <- zenon_D_pnotp. % 10.28/10.47 exact zenon_H17d. % 10.28/10.47 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 10.28/10.47 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H232]. % 10.28/10.47 congruence. % 10.28/10.47 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 10.28/10.47 intro zenon_D_pnotp. % 10.28/10.47 apply zenon_H232. % 10.28/10.47 rewrite <- zenon_D_pnotp. % 10.28/10.47 exact zenon_H11f. % 10.28/10.47 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 10.28/10.47 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 10.28/10.47 congruence. % 10.28/10.47 apply zenon_H17e. apply refl_equal. % 10.28/10.47 apply zenon_H1c2. apply sym_equal. exact zenon_H74. % 10.28/10.47 apply zenon_H17e. apply refl_equal. % 10.28/10.47 apply zenon_H17e. apply refl_equal. % 10.28/10.47 (* end of lemma zenon_L910_ *) % 10.28/10.47 assert (zenon_L911_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.28/10.47 do 0 intro. intros zenon_Hda zenon_H28 zenon_H4c zenon_H15a zenon_Hce zenon_H11f zenon_Hbb zenon_Hbd. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.28/10.47 exact (zenon_H28 zenon_H31). % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.28/10.47 apply (zenon_L236_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L910_); trivial. % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 (* end of lemma zenon_L911_ *) % 10.28/10.47 assert (zenon_L912_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H95 zenon_H7f zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H2a zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.47 apply (zenon_L907_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_L909_); trivial. % 10.28/10.47 apply (zenon_L911_); trivial. % 10.28/10.47 apply (zenon_L213_); trivial. % 10.28/10.47 (* end of lemma zenon_L912_ *) % 10.28/10.47 assert (zenon_L913_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (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)) = (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). % 10.28/10.47 do 0 intro. intros zenon_H18d zenon_H11f zenon_H205 zenon_H56 zenon_H1f zenon_H1d zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H7d zenon_H7f zenon_H7a zenon_H8d zenon_H64. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.47 exact (zenon_H56 zenon_H2c). % 10.28/10.47 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.47 apply (zenon_L1_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.47 apply (zenon_L103_); trivial. % 10.28/10.47 apply (zenon_L87_); trivial. % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 (* end of lemma zenon_L913_ *) % 10.28/10.47 assert (zenon_L914_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.28/10.47 do 0 intro. intros zenon_Hc0 zenon_H53 zenon_H68 zenon_Hc1 zenon_H184 zenon_H11f zenon_Hbb zenon_Hbc. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.28/10.47 apply (zenon_L30_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.28/10.47 exact (zenon_Hc1 zenon_Hc4). % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_L549_); trivial. % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 (* end of lemma zenon_L914_ *) % 10.28/10.47 assert (zenon_L915_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H157 zenon_H112 zenon_H35 zenon_Hcf zenon_H110 zenon_H1d zenon_H4c zenon_H11f zenon_H90. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.28/10.47 apply (zenon_L47_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.28/10.47 apply (zenon_L78_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.28/10.47 exact (zenon_H91 zenon_H94). % 10.28/10.47 apply (zenon_L89_); trivial. % 10.28/10.47 apply (zenon_L79_); trivial. % 10.28/10.47 (* end of lemma zenon_L915_ *) % 10.28/10.47 assert (zenon_L916_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((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)) = (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) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H156 zenon_H90 zenon_H4c zenon_H110 zenon_H35 zenon_H112 zenon_H157 zenon_H150 zenon_H43 zenon_Hbb zenon_H151 zenon_H64 zenon_H7a zenon_H7f zenon_H7d zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_H205 zenon_H11f zenon_H18d zenon_H95 zenon_Hd2. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L913_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_L783_); trivial. % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 apply (zenon_L93_); trivial. % 10.28/10.47 apply (zenon_L915_); trivial. % 10.28/10.47 (* end of lemma zenon_L916_ *) % 10.28/10.47 assert (zenon_L917_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H18d zenon_H205 zenon_H11b zenon_H68 zenon_Hab zenon_H44 zenon_H95 zenon_H128 zenon_H11f zenon_H4c zenon_H1d zenon_H11d zenon_H8d zenon_H7a zenon_H7f zenon_H7d zenon_H53 zenon_H8c. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_L97_); trivial. % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 (* end of lemma zenon_L917_ *) % 10.28/10.47 assert (zenon_L918_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H1af zenon_H18d zenon_H205 zenon_H11b zenon_H68 zenon_Hab zenon_H44 zenon_H95 zenon_H128 zenon_H11f zenon_H4c zenon_H1d zenon_H11d zenon_H7a zenon_H7f zenon_H7d zenon_H53 zenon_H8c zenon_Hc0 zenon_Hbb zenon_H184 zenon_H150. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L917_); trivial. % 10.28/10.47 apply (zenon_L914_); trivial. % 10.28/10.47 apply (zenon_L88_); trivial. % 10.28/10.47 (* end of lemma zenon_L918_ *) % 10.28/10.47 assert (zenon_L919_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H233 zenon_H2a zenon_H12f zenon_H195 zenon_H1d zenon_H1bc zenon_Hcf zenon_Hbc zenon_H16f. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H69 | zenon_intro zenon_H234 ]. % 10.28/10.47 apply (zenon_L100_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H15a | zenon_intro zenon_H235 ]. % 10.28/10.47 apply (zenon_L325_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H6a | zenon_intro zenon_H6c ]. % 10.28/10.47 apply (zenon_L218_); trivial. % 10.28/10.47 apply (zenon_L154_); trivial. % 10.28/10.47 (* end of lemma zenon_L919_ *) % 10.28/10.47 assert (zenon_L920_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((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)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H156 zenon_H150 zenon_H195 zenon_H1d zenon_H1bc zenon_H16f zenon_H233 zenon_H145 zenon_H7d zenon_H7f zenon_H95 zenon_H128 zenon_H155 zenon_He8 zenon_H12f zenon_H205 zenon_H18d zenon_H112 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H2a zenon_H1ba zenon_H157. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_L903_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L905_); trivial. % 10.28/10.47 apply (zenon_L919_); trivial. % 10.28/10.47 apply (zenon_L79_); trivial. % 10.28/10.47 (* end of lemma zenon_L920_ *) % 10.28/10.47 assert (zenon_L921_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H168 zenon_H157 zenon_H1ba zenon_H2a zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_H11f zenon_Hc5 zenon_H112 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H95 zenon_H7f zenon_H7d zenon_H145 zenon_H233 zenon_H16f zenon_H1bc zenon_H1d zenon_H195 zenon_H150 zenon_H156. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.47 apply (zenon_L920_); trivial. % 10.28/10.47 apply (zenon_L325_); trivial. % 10.28/10.47 (* end of lemma zenon_L921_ *) % 10.28/10.47 assert (zenon_L922_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((e0) = (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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (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)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 10.28/10.47 do 0 intro. intros zenon_H173 zenon_H58 zenon_H198 zenon_Hda zenon_Hce zenon_H4a zenon_H174 zenon_H44 zenon_Hab zenon_H11b zenon_Hc0 zenon_Hbb zenon_H184 zenon_H53 zenon_H156 zenon_H90 zenon_H4c zenon_H110 zenon_H35 zenon_H112 zenon_H157 zenon_H150 zenon_H151 zenon_H95 zenon_Hd2 zenon_H86 zenon_H128 zenon_H8c zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H7f zenon_H7d zenon_H3c zenon_Hc5 zenon_H1f zenon_H18d zenon_H11d zenon_H1af zenon_H168 zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H12f zenon_H155 zenon_H145 zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_Hc7 zenon_H205 zenon_H11f. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.47 apply (zenon_L912_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L913_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.47 exact (zenon_H25 zenon_H2a). % 10.28/10.47 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.47 apply (zenon_L914_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.47 exact (zenon_H56 zenon_H2c). % 10.28/10.47 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.47 apply (zenon_L1_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.47 apply (zenon_L12_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.28/10.47 apply (zenon_L916_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.28/10.47 apply (zenon_L26_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.28/10.47 apply (zenon_L96_); trivial. % 10.28/10.47 apply (zenon_L261_); trivial. % 10.28/10.47 apply (zenon_L24_); trivial. % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 apply (zenon_L93_); trivial. % 10.28/10.47 apply (zenon_L915_); trivial. % 10.28/10.47 apply (zenon_L88_); trivial. % 10.28/10.47 apply (zenon_L918_); trivial. % 10.28/10.47 apply (zenon_L921_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.47 exact (zenon_Hc7 zenon_H3a). % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 (* end of lemma zenon_L922_ *) % 10.28/10.47 assert (zenon_L923_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H151 zenon_Hbc zenon_Hbb zenon_H18d zenon_H11f zenon_H205 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_H7d zenon_H86 zenon_H145 zenon_H143 zenon_Hf8. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L906_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 (* end of lemma zenon_L923_ *) % 10.28/10.47 assert (zenon_L924_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_Hf8 zenon_H143 zenon_H8c zenon_H128 zenon_H95 zenon_H35 zenon_H198 zenon_H15a zenon_H4c zenon_Hab zenon_H11f zenon_H53 zenon_H86 zenon_H7e zenon_H7d zenon_H2a zenon_H58 zenon_H205 zenon_H18d. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L909_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 (* end of lemma zenon_L924_ *) % 10.28/10.47 assert (zenon_L925_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H4a zenon_H156 zenon_Hd2 zenon_Hf8 zenon_H143 zenon_H145 zenon_H7d zenon_H95 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H2a zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_H168. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_L903_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L905_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 apply (zenon_L923_); trivial. % 10.28/10.47 apply (zenon_L93_); trivial. % 10.28/10.47 apply (zenon_L79_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_L924_); trivial. % 10.28/10.47 apply (zenon_L911_); trivial. % 10.28/10.47 apply (zenon_L213_); trivial. % 10.28/10.47 (* end of lemma zenon_L925_ *) % 10.28/10.47 assert (zenon_L926_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((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 (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_Hf8 zenon_H143 zenon_H64 zenon_H8d zenon_H7a zenon_H7d zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_H205 zenon_H11f zenon_H18d. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L913_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 (* end of lemma zenon_L926_ *) % 10.28/10.47 assert (zenon_L927_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H151 zenon_Hbc zenon_Hbb zenon_H18d zenon_H11f zenon_H205 zenon_H7a zenon_H43 zenon_H7d zenon_H143 zenon_Hf8. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L783_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 apply (zenon_L41_); trivial. % 10.28/10.47 (* end of lemma zenon_L927_ *) % 10.28/10.47 assert (zenon_L928_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 10.28/10.47 do 0 intro. intros zenon_Hc5 zenon_H5d zenon_H161 zenon_H91 zenon_Hc7 zenon_H11f zenon_H1fb. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hc9 ]. % 10.28/10.47 apply (zenon_L133_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_H94 | zenon_intro zenon_Hcc ]. % 10.28/10.47 exact (zenon_H91 zenon_H94). % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H3a | zenon_intro zenon_Hcd ]. % 10.28/10.47 exact (zenon_Hc7 zenon_H3a). % 10.28/10.47 apply (zenon_L901_); trivial. % 10.28/10.47 (* end of lemma zenon_L928_ *) % 10.28/10.47 assert (zenon_L929_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H165 zenon_H4c zenon_Hc7 zenon_H91 zenon_H5d zenon_Hc5 zenon_H1fb zenon_H11f zenon_H143. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H52 | zenon_intro zenon_H166 ]. % 10.28/10.47 apply (zenon_L130_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H161 | zenon_intro zenon_H167 ]. % 10.28/10.47 apply (zenon_L928_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_Hcd | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L901_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 (* end of lemma zenon_L929_ *) % 10.28/10.47 assert (zenon_L930_ : (((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). % 10.28/10.47 do 0 intro. intros zenon_H90 zenon_Hcf zenon_H35 zenon_H1d zenon_H110 zenon_H91 zenon_H181 zenon_H62. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.28/10.47 apply (zenon_L47_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.28/10.47 apply (zenon_L78_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.28/10.47 exact (zenon_H91 zenon_H94). % 10.28/10.47 apply (zenon_L258_); trivial. % 10.28/10.47 (* end of lemma zenon_L930_ *) % 10.28/10.47 assert (zenon_L931_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H157 zenon_H112 zenon_H56 zenon_H1f zenon_H1d zenon_H165 zenon_H143 zenon_Hc7 zenon_H1fb zenon_H11f zenon_Hc5 zenon_H4c zenon_H90 zenon_H181 zenon_H110 zenon_Hcf zenon_H35 zenon_H64. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.47 exact (zenon_H56 zenon_H2c). % 10.28/10.47 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.47 apply (zenon_L1_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.47 apply (zenon_L929_); trivial. % 10.28/10.47 apply (zenon_L930_); trivial. % 10.28/10.47 apply (zenon_L79_); trivial. % 10.28/10.47 (* end of lemma zenon_L931_ *) % 10.28/10.47 assert (zenon_L932_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (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 (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 (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H156 zenon_H35 zenon_H110 zenon_H181 zenon_H90 zenon_H4c zenon_H1fb zenon_H165 zenon_H112 zenon_H157 zenon_H150 zenon_H43 zenon_Hbb zenon_H151 zenon_H18d zenon_H11f zenon_H205 zenon_H56 zenon_H1f zenon_H1d zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H7d zenon_H7a zenon_H64 zenon_H143 zenon_Hf8 zenon_H95 zenon_Hd2. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_L926_); trivial. % 10.28/10.47 apply (zenon_L927_); trivial. % 10.28/10.47 apply (zenon_L93_); trivial. % 10.28/10.47 apply (zenon_L931_); trivial. % 10.28/10.47 (* end of lemma zenon_L932_ *) % 10.28/10.47 assert (zenon_L933_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H1af zenon_Hf8 zenon_H143 zenon_H8c zenon_H53 zenon_H7d zenon_H7a zenon_H11d zenon_H1d zenon_H4c zenon_H11f zenon_H128 zenon_H95 zenon_H44 zenon_Hab zenon_H68 zenon_H11b zenon_H205 zenon_H18d zenon_Hc0 zenon_Hbb zenon_H184 zenon_H150. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_L917_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 apply (zenon_L914_); trivial. % 10.28/10.47 apply (zenon_L88_); trivial. % 10.28/10.47 (* end of lemma zenon_L933_ *) % 10.28/10.47 assert (zenon_L934_ : (((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) (e2)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f zenon_H1d zenon_H143 zenon_H11f zenon_H1fb zenon_Hc5 zenon_H91 zenon_Hc7 zenon_H4c zenon_H165 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.47 exact (zenon_H56 zenon_H2c). % 10.28/10.47 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.47 apply (zenon_L1_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.47 apply (zenon_L929_); trivial. % 10.28/10.47 apply (zenon_L87_); trivial. % 10.28/10.47 (* end of lemma zenon_L934_ *) % 10.28/10.47 assert (zenon_L935_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H150 zenon_H12f zenon_H2a zenon_H195 zenon_H1bc zenon_Hcf zenon_H16f zenon_H233 zenon_H18d zenon_H205 zenon_H56 zenon_H1f zenon_H1d zenon_H165 zenon_H143 zenon_H91 zenon_Hc7 zenon_H1fb zenon_H11f zenon_Hc5 zenon_H4c zenon_H7d zenon_H7a zenon_H64 zenon_Hf8. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.47 apply (zenon_L934_); trivial. % 10.28/10.47 apply (zenon_L385_); trivial. % 10.28/10.47 exact (zenon_H143 zenon_Hed). % 10.28/10.47 apply (zenon_L919_); trivial. % 10.28/10.47 (* end of lemma zenon_L935_ *) % 10.28/10.47 assert (zenon_L936_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H156 zenon_H150 zenon_H12f zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H18d zenon_H205 zenon_H56 zenon_H1f zenon_H1d zenon_H165 zenon_H143 zenon_H4c zenon_H7d zenon_H7a zenon_H64 zenon_Hf8 zenon_H112 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H2a zenon_H1ba zenon_H157. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.47 apply (zenon_L903_); trivial. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.47 apply (zenon_L935_); trivial. % 10.28/10.47 apply (zenon_L79_); trivial. % 10.28/10.47 (* end of lemma zenon_L936_ *) % 10.28/10.47 assert (zenon_L937_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> False). % 10.28/10.47 do 0 intro. intros zenon_H26 zenon_H2a zenon_H68. % 10.28/10.47 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 10.28/10.47 intro zenon_D_pnotp. % 10.28/10.47 apply zenon_H26. % 10.28/10.47 rewrite <- zenon_D_pnotp. % 10.28/10.47 exact zenon_H2a. % 10.28/10.47 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H236]. % 10.28/10.47 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 10.28/10.47 congruence. % 10.28/10.47 apply zenon_H131. apply refl_equal. % 10.28/10.47 apply zenon_H236. apply sym_equal. exact zenon_H68. % 10.28/10.47 (* end of lemma zenon_L937_ *) % 10.28/10.47 assert (zenon_L938_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((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)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (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 (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 10.28/10.47 do 0 intro. intros zenon_H174 zenon_H26 zenon_H157 zenon_H1ba zenon_H2a zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_H11f zenon_Hc5 zenon_H112 zenon_Hf8 zenon_H64 zenon_H7a zenon_H7d zenon_H4c zenon_H143 zenon_H165 zenon_H1d zenon_H1f zenon_H205 zenon_H18d zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H12f zenon_H150 zenon_H156. % 10.28/10.47 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.47 apply (zenon_L936_); trivial. % 10.28/10.47 apply (zenon_L937_); trivial. % 10.28/10.47 (* end of lemma zenon_L938_ *) % 10.28/10.47 assert (zenon_L939_ : ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H95 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H11f zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.28/10.48 apply (zenon_L922_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.48 apply (zenon_L925_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.48 apply (zenon_L926_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.28/10.48 exact (zenon_H25 zenon_H2a). % 10.28/10.48 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.28/10.48 apply (zenon_L918_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.48 exact (zenon_H56 zenon_H2c). % 10.28/10.48 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.48 apply (zenon_L1_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.48 apply (zenon_L12_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.28/10.48 apply (zenon_L932_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.28/10.48 apply (zenon_L26_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.28/10.48 apply (zenon_L96_); trivial. % 10.28/10.48 apply (zenon_L261_); trivial. % 10.28/10.48 apply (zenon_L24_); trivial. % 10.28/10.48 apply (zenon_L385_); trivial. % 10.28/10.48 exact (zenon_H143 zenon_Hed). % 10.28/10.48 apply (zenon_L41_); trivial. % 10.28/10.48 apply (zenon_L93_); trivial. % 10.28/10.48 apply (zenon_L915_); trivial. % 10.28/10.48 apply (zenon_L933_); trivial. % 10.28/10.48 apply (zenon_L938_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.48 exact (zenon_Hc7 zenon_H3a). % 10.28/10.48 apply (zenon_L385_); trivial. % 10.28/10.48 (* end of lemma zenon_L939_ *) % 10.28/10.48 assert (zenon_L940_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H12c zenon_H73 zenon_Hb8 zenon_Hc8 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H95 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 10.28/10.48 apply (zenon_L20_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 10.28/10.48 apply (zenon_L40_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 10.28/10.48 exact (zenon_Hc8 zenon_Hcd). % 10.28/10.48 apply (zenon_L939_); trivial. % 10.28/10.48 (* end of lemma zenon_L940_ *) % 10.28/10.48 assert (zenon_L941_ : (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H53 zenon_H73 zenon_H95 zenon_Hb8 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.48 apply (zenon_L940_); trivial. % 10.28/10.48 apply (zenon_L164_); trivial. % 10.28/10.48 (* end of lemma zenon_L941_ *) % 10.28/10.48 assert (zenon_L942_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.28/10.48 do 0 intro. intros zenon_Hde zenon_H68 zenon_Haf zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H73 zenon_H53 zenon_H95 zenon_Hbd. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.28/10.48 apply (zenon_L16_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.28/10.48 exact (zenon_Haf zenon_Hb4). % 10.28/10.48 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.28/10.48 apply (zenon_L941_); trivial. % 10.28/10.48 apply (zenon_L50_); trivial. % 10.28/10.48 (* end of lemma zenon_L942_ *) % 10.28/10.48 assert (zenon_L943_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H18d zenon_Hd2 zenon_H17a zenon_H157 zenon_H27 zenon_H44 zenon_H68 zenon_H97 zenon_Haf zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7f zenon_H7d zenon_H90 zenon_Hc1 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_Hda zenon_Hce zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.48 apply (zenon_L43_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.28/10.48 apply (zenon_L175_); trivial. % 10.28/10.48 apply (zenon_L942_); trivial. % 10.28/10.48 (* end of lemma zenon_L943_ *) % 10.28/10.48 assert (zenon_L944_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((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)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H1ef zenon_H110 zenon_H191 zenon_Haf zenon_He8 zenon_H157 zenon_H145 zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_H2a zenon_H12f zenon_H64 zenon_H187 zenon_H27 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H35 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H77 zenon_Hd3 zenon_H56 zenon_Hd2 zenon_H1af. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.28/10.48 apply (zenon_L205_); trivial. % 10.28/10.48 apply (zenon_L78_); trivial. % 10.28/10.48 (* end of lemma zenon_L944_ *) % 10.28/10.48 assert (zenon_L945_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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). % 10.28/10.48 do 0 intro. intros zenon_H64 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_Hc5 zenon_H7d zenon_H8d zenon_H7a zenon_H7f zenon_H80. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.48 exact (zenon_H56 zenon_H2c). % 10.28/10.48 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.48 apply (zenon_L196_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.48 apply (zenon_L103_); trivial. % 10.28/10.48 apply (zenon_L87_); trivial. % 10.28/10.48 (* end of lemma zenon_L945_ *) % 10.28/10.48 assert (zenon_L946_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.28/10.48 do 0 intro. intros zenon_Hb0 zenon_H2a zenon_H1ba zenon_H5e zenon_Hb1 zenon_H1e2 zenon_He3 zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H35 zenon_H77 zenon_Hc7 zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_H84 zenon_H86. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.28/10.48 apply (zenon_L216_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.28/10.48 apply (zenon_L22_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.28/10.48 exact (zenon_Hb1 zenon_Hb7). % 10.28/10.48 apply (zenon_L430_); trivial. % 10.28/10.48 (* end of lemma zenon_L946_ *) % 10.28/10.48 assert (zenon_L947_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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). % 10.28/10.48 do 0 intro. intros zenon_H18d zenon_H1ba zenon_H2a zenon_H5e zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H35 zenon_H28 zenon_H4c zenon_H15a zenon_H95 zenon_He3 zenon_Hda zenon_Hb0 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H7d zenon_H7f zenon_H7a zenon_H8d zenon_H64. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.48 apply (zenon_L945_); trivial. % 10.28/10.48 apply (zenon_L946_); trivial. % 10.28/10.48 (* end of lemma zenon_L947_ *) % 10.28/10.48 assert (zenon_L948_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H12c zenon_Hcf zenon_H77 zenon_Hc8 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H95 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H74 | zenon_intro zenon_H12d ]. % 10.28/10.48 apply (zenon_L155_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H12e ]. % 10.28/10.48 apply (zenon_L48_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_Hcd | zenon_intro zenon_H11f ]. % 10.28/10.48 exact (zenon_Hc8 zenon_Hcd). % 10.28/10.48 apply (zenon_L939_); trivial. % 10.28/10.48 (* end of lemma zenon_L948_ *) % 10.28/10.48 assert (zenon_L949_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.28/10.48 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H1c0 zenon_H15a zenon_H2a zenon_H1c3 zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc8 zenon_H77 zenon_H12c zenon_H95 zenon_Hbc. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.28/10.48 exact (zenon_H27 zenon_H32). % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.28/10.48 apply (zenon_L220_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.28/10.48 apply (zenon_L948_); trivial. % 10.28/10.48 apply (zenon_L51_); trivial. % 10.28/10.48 (* end of lemma zenon_L949_ *) % 10.28/10.48 assert (zenon_L950_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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)) = (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)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((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). % 10.28/10.48 do 0 intro. intros zenon_H18d zenon_H86 zenon_H56 zenon_Hd3 zenon_H77 zenon_H42 zenon_H181 zenon_H28 zenon_H95 zenon_H4c zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_Hce zenon_Hd0 zenon_Hdd zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H187 zenon_H35 zenon_Hc7 zenon_H1e2 zenon_H198 zenon_H17c zenon_Hb0 zenon_H15a zenon_H97 zenon_H27 zenon_H7d zenon_H7f zenon_H7a zenon_H8d zenon_H64. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.28/10.48 apply (zenon_L273_); trivial. % 10.28/10.48 apply (zenon_L280_); trivial. % 10.28/10.48 (* end of lemma zenon_L950_ *) % 10.28/10.48 assert (zenon_L951_ : ((~((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) (e3)) = (op (e3) (e3)))) -> (~((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H150 zenon_H64 zenon_H7a zenon_H7f zenon_H7d zenon_H27 zenon_H97 zenon_H15a zenon_Hb0 zenon_H17c zenon_H198 zenon_H1e2 zenon_Hc7 zenon_H35 zenon_H187 zenon_H18a zenon_Hb1 zenon_H5e zenon_H53 zenon_Hdd zenon_Hd0 zenon_Hce zenon_H1ba zenon_H2a zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hda zenon_H4c zenon_H95 zenon_H28 zenon_H181 zenon_H42 zenon_H77 zenon_Hd3 zenon_H56 zenon_H86 zenon_H18d. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.48 apply (zenon_L950_); trivial. % 10.28/10.48 apply (zenon_L221_); trivial. % 10.28/10.48 (* end of lemma zenon_L951_ *) % 10.28/10.48 assert (zenon_L952_ : (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H95 zenon_Hcf zenon_H4c zenon_H77 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.48 apply (zenon_L948_); trivial. % 10.28/10.48 apply (zenon_L44_); trivial. % 10.28/10.48 (* end of lemma zenon_L952_ *) % 10.28/10.48 assert (zenon_L953_ : (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((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)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H27 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H157 zenon_H44 zenon_H53 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hdd zenon_H64 zenon_H7a zenon_H7f zenon_H7d zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H56 zenon_Hb0 zenon_Hda zenon_He3 zenon_H95 zenon_H15a zenon_H4c zenon_H28 zenon_H35 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H5e zenon_H2a zenon_H1ba zenon_H18d zenon_H97 zenon_H187 zenon_H42. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.28/10.48 apply (zenon_L947_); trivial. % 10.28/10.48 apply (zenon_L949_); trivial. % 10.28/10.48 apply (zenon_L951_); trivial. % 10.28/10.48 apply (zenon_L952_); trivial. % 10.28/10.48 (* end of lemma zenon_L953_ *) % 10.28/10.48 assert (zenon_L954_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((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)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H1ef zenon_H110 zenon_H191 zenon_Haf zenon_H157 zenon_H145 zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_H2a zenon_H12f zenon_H64 zenon_H187 zenon_H27 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H35 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H77 zenon_Hd3 zenon_H56 zenon_Hd2 zenon_H1af zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H200 zenon_H1f zenon_H11d zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H128 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hdd zenon_H7a zenon_H7f zenon_H7d zenon_H3c zenon_Hb0 zenon_Hda zenon_He3 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H1ba zenon_H18d zenon_H97. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.48 apply (zenon_L944_); trivial. % 10.28/10.48 apply (zenon_L953_); trivial. % 10.28/10.48 apply (zenon_L213_); trivial. % 10.28/10.48 (* end of lemma zenon_L954_ *) % 10.28/10.48 assert (zenon_L955_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.28/10.48 do 0 intro. intros zenon_H64 zenon_H56 zenon_Hd3 zenon_H181 zenon_Hd0 zenon_H35 zenon_He7 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_H95 zenon_H4c zenon_H77 zenon_H84 zenon_H17a zenon_H27 zenon_H42 zenon_H9a zenon_H187. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.48 exact (zenon_H56 zenon_H2c). % 10.28/10.48 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.48 apply (zenon_L196_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.48 exact (zenon_H27 zenon_H32). % 10.28/10.48 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.48 apply (zenon_L400_); trivial. % 10.28/10.48 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.48 apply (zenon_L70_); trivial. % 10.28/10.48 apply (zenon_L163_); trivial. % 10.28/10.48 apply (zenon_L202_); trivial. % 10.28/10.48 (* end of lemma zenon_L955_ *) % 10.28/10.48 assert (zenon_L956_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H9a zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.49 exact (zenon_H56 zenon_H2c). % 10.28/10.49 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.49 apply (zenon_L196_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.49 apply (zenon_L103_); trivial. % 10.28/10.49 apply (zenon_L202_); trivial. % 10.28/10.49 apply (zenon_L955_); trivial. % 10.28/10.49 apply (zenon_L952_); trivial. % 10.28/10.49 (* end of lemma zenon_L956_ *) % 10.28/10.49 assert (zenon_L957_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.28/10.49 do 0 intro. intros zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.49 apply (zenon_L190_); trivial. % 10.28/10.49 apply (zenon_L956_); trivial. % 10.28/10.49 (* end of lemma zenon_L957_ *) % 10.28/10.49 assert (zenon_L958_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H1ef zenon_H191 zenon_Haf zenon_He8 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.28/10.49 apply (zenon_L957_); trivial. % 10.28/10.49 apply (zenon_L78_); trivial. % 10.28/10.49 (* end of lemma zenon_L958_ *) % 10.28/10.49 assert (zenon_L959_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H1e2 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H4c zenon_H95 zenon_H35 zenon_H77 zenon_Hc7 zenon_H18a zenon_H43 zenon_H187 zenon_H15a zenon_H198 zenon_H17c zenon_H84 zenon_H86. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 10.28/10.49 apply (zenon_L952_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 10.28/10.49 apply (zenon_L203_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 10.28/10.49 exact (zenon_Hc7 zenon_H3a). % 10.28/10.49 apply (zenon_L426_); trivial. % 10.28/10.49 (* end of lemma zenon_L959_ *) % 10.28/10.49 assert (zenon_L960_ : (((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)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H18a zenon_H17c zenon_H43 zenon_H1e2 zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_Haf zenon_H191 zenon_H1ef. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.49 apply (zenon_L958_); trivial. % 10.28/10.49 apply (zenon_L959_); trivial. % 10.28/10.49 (* end of lemma zenon_L960_ *) % 10.28/10.49 assert (zenon_L961_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (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)) = (op (e2) (e3)))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H1e2 zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_Hb0 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc8 zenon_H12c zenon_H35 zenon_H77 zenon_Hc7 zenon_H42 zenon_H27 zenon_H44 zenon_H7a zenon_H84 zenon_H95 zenon_H68 zenon_H53 zenon_H28 zenon_H97 zenon_H181. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_Hcf | zenon_intro zenon_H1e3 ]. % 10.28/10.49 apply (zenon_L948_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H1e4 ]. % 10.28/10.49 apply (zenon_L203_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd0 ]. % 10.28/10.49 exact (zenon_Hc7 zenon_H3a). % 10.28/10.49 apply (zenon_L171_); trivial. % 10.28/10.49 (* end of lemma zenon_L961_ *) % 10.28/10.49 assert (zenon_L962_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H77 zenon_H4c zenon_H95 zenon_H42 zenon_H28 zenon_H84 zenon_H97 zenon_H68 zenon_H27 zenon_H1e2. % 10.28/10.49 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.49 apply (zenon_L961_); trivial. % 10.28/10.49 apply (zenon_L171_); trivial. % 10.28/10.49 (* end of lemma zenon_L962_ *) % 10.28/10.49 assert (zenon_L963_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H1e2 zenon_H27 zenon_H68 zenon_H97 zenon_H84 zenon_H42 zenon_H95 zenon_H4c zenon_H77 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.49 apply (zenon_L962_); trivial. % 10.28/10.49 apply (zenon_L85_); trivial. % 10.28/10.49 (* end of lemma zenon_L963_ *) % 10.28/10.49 assert (zenon_L964_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H97 zenon_Hdd zenon_H1e2 zenon_H17c zenon_H18a zenon_He3 zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_Haf zenon_H191 zenon_H1ef. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.28/10.49 apply (zenon_L958_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.28/10.49 exact (zenon_H27 zenon_H32). % 10.28/10.49 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.28/10.49 apply (zenon_L238_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.28/10.49 apply (zenon_L296_); trivial. % 10.28/10.49 apply (zenon_L831_); trivial. % 10.28/10.49 apply (zenon_L296_); trivial. % 10.28/10.49 apply (zenon_L960_); trivial. % 10.28/10.49 apply (zenon_L963_); trivial. % 10.28/10.49 (* end of lemma zenon_L964_ *) % 10.28/10.49 assert (zenon_L965_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((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 (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H1c3 zenon_H1c0 zenon_H7f zenon_H97 zenon_Hdd zenon_H1e2 zenon_H17c zenon_H18a zenon_He3 zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_H5e zenon_Hc0 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_Haf zenon_H191 zenon_H1ef. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.28/10.49 apply (zenon_L954_); trivial. % 10.28/10.49 apply (zenon_L937_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.28/10.49 apply (zenon_L78_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.28/10.49 exact (zenon_Hc7 zenon_H3a). % 10.28/10.49 apply (zenon_L964_); trivial. % 10.28/10.49 (* end of lemma zenon_L965_ *) % 10.28/10.49 assert (zenon_L966_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((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 (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H42 zenon_H27 zenon_H53 zenon_Hb8 zenon_H95 zenon_Hc1 zenon_Hc0 zenon_H44 zenon_He8 zenon_He7 zenon_H35 zenon_H5d zenon_Hd0 zenon_H181. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.28/10.49 exact (zenon_H27 zenon_H32). % 10.28/10.49 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.28/10.49 apply (zenon_L185_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.28/10.49 apply (zenon_L70_); trivial. % 10.28/10.49 apply (zenon_L163_); trivial. % 10.28/10.49 (* end of lemma zenon_L966_ *) % 10.28/10.49 assert (zenon_L967_ : (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.28/10.49 do 0 intro. intros zenon_H56 zenon_H1d zenon_H42 zenon_He8 zenon_Hc1 zenon_He7 zenon_H27 zenon_H18a zenon_H84 zenon_H17c zenon_H43 zenon_H187 zenon_H53 zenon_H73 zenon_H95 zenon_Hb8 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.28/10.49 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.28/10.49 apply (zenon_L940_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.28/10.49 exact (zenon_H56 zenon_H2c). % 10.28/10.49 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.28/10.49 apply (zenon_L1_); trivial. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.28/10.49 apply (zenon_L966_); trivial. % 10.28/10.49 apply (zenon_L411_); trivial. % 10.28/10.49 (* end of lemma zenon_L967_ *) % 10.28/10.49 assert (zenon_L968_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.28/10.49 do 0 intro. intros zenon_Hd2 zenon_H187 zenon_H43 zenon_H11d zenon_H1d zenon_H17c zenon_H86 zenon_H84 zenon_H18a zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H56 zenon_H42 zenon_He8 zenon_He7 zenon_H27 zenon_H53 zenon_H95 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.28/10.49 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.28/10.49 apply (zenon_L638_); trivial. % 10.28/10.49 apply (zenon_L967_); trivial. % 10.28/10.49 apply (zenon_L88_); trivial. % 10.28/10.49 (* end of lemma zenon_L968_ *) % 10.28/10.49 assert (zenon_L969_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H95 zenon_H53 zenon_H27 zenon_He7 zenon_He8 zenon_H42 zenon_H56 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H18a zenon_H86 zenon_H17c zenon_H1d zenon_H11d zenon_H187 zenon_Hd2 zenon_H7a zenon_H43 zenon_H7e zenon_H7f zenon_H7d. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.50 apply (zenon_L24_); trivial. % 10.36/10.50 apply (zenon_L968_); trivial. % 10.36/10.50 (* end of lemma zenon_L969_ *) % 10.36/10.50 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) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H195 zenon_H1d zenon_H73 zenon_H14d zenon_H5e zenon_H53 zenon_H7f zenon_H44 zenon_H95 zenon_Hbd zenon_H35 zenon_H177 zenon_H8d. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.50 exact (zenon_H56 zenon_H2c). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.50 apply (zenon_L325_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.50 apply (zenon_L165_); trivial. % 10.36/10.50 apply (zenon_L340_); trivial. % 10.36/10.50 (* end of lemma zenon_L970_ *) % 10.36/10.50 assert (zenon_L971_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (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 (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H95 zenon_H53 zenon_H27 zenon_He7 zenon_He8 zenon_H42 zenon_H56 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H18a zenon_H86 zenon_H17c zenon_H1d zenon_H11d zenon_H187 zenon_Hd2 zenon_H7a zenon_H43 zenon_H7f zenon_H7d zenon_H1b4 zenon_H177 zenon_H14d. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.50 apply (zenon_L969_); trivial. % 10.36/10.50 apply (zenon_L970_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.50 apply (zenon_L969_); trivial. % 10.36/10.50 apply (zenon_L41_); trivial. % 10.36/10.50 (* end of lemma zenon_L971_ *) % 10.36/10.50 assert (zenon_L972_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H25 zenon_H28 zenon_Hde zenon_Hc1 zenon_H91 zenon_H1c3 zenon_H1c0 zenon_H97 zenon_Hdd zenon_H1e2 zenon_He3 zenon_H17a zenon_Hd3 zenon_Haf zenon_H191 zenon_H1ef zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H95 zenon_H53 zenon_H27 zenon_He7 zenon_He8 zenon_H42 zenon_H56 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H18a zenon_H86 zenon_H17c zenon_H1d zenon_H11d zenon_H187 zenon_Hd2 zenon_H7a zenon_H7f zenon_H7d zenon_H1b4 zenon_H177 zenon_H14d. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.50 exact (zenon_H25 zenon_H2a). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.50 apply (zenon_L943_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.50 exact (zenon_H56 zenon_H2c). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.50 apply (zenon_L1_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.50 apply (zenon_L12_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.36/10.50 apply (zenon_L165_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.36/10.50 apply (zenon_L965_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.36/10.50 exact (zenon_H91 zenon_H94). % 10.36/10.50 apply (zenon_L258_); trivial. % 10.36/10.50 apply (zenon_L971_); trivial. % 10.36/10.50 (* end of lemma zenon_L972_ *) % 10.36/10.50 assert (zenon_L973_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (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 (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (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 (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (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 (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H14d zenon_H177 zenon_H1b4 zenon_He8 zenon_H56 zenon_H1d zenon_H1e2 zenon_He3 zenon_Hdd zenon_H1c0 zenon_H1c3 zenon_Hd3 zenon_He7 zenon_H191 zenon_H1ef zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H1ba zenon_Hce zenon_Hda zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H110 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_Hde zenon_H90 zenon_H7d zenon_H7f zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H4c zenon_H5e zenon_Hc0 zenon_H184 zenon_Haf zenon_H97 zenon_H44 zenon_H27 zenon_H157 zenon_H17a zenon_Hd2 zenon_H18d zenon_H25. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.50 apply (zenon_L972_); trivial. % 10.36/10.50 apply (zenon_L941_); trivial. % 10.36/10.50 apply (zenon_L88_); trivial. % 10.36/10.50 (* end of lemma zenon_L973_ *) % 10.36/10.50 assert (zenon_L974_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (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)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (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 (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H14d zenon_H177 zenon_H1b4 zenon_H7d zenon_H7f zenon_H43 zenon_H7a zenon_Hd2 zenon_H187 zenon_H11d zenon_H1d zenon_H17c zenon_H86 zenon_H18a zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H56 zenon_H42 zenon_He7 zenon_H27 zenon_H53 zenon_H95 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.50 apply (zenon_L971_); trivial. % 10.36/10.50 apply (zenon_L325_); trivial. % 10.36/10.50 (* end of lemma zenon_L974_ *) % 10.36/10.50 assert (zenon_L975_ : ((op (e1) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1d zenon_H18d zenon_Hd2 zenon_H17a zenon_H157 zenon_H27 zenon_H44 zenon_H68 zenon_H97 zenon_Haf zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7f zenon_H7d zenon_H90 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_Hda zenon_Hce zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.50 apply (zenon_L943_); trivial. % 10.36/10.50 apply (zenon_L941_); trivial. % 10.36/10.50 apply (zenon_L88_); trivial. % 10.36/10.50 (* end of lemma zenon_L975_ *) % 10.36/10.50 assert (zenon_L976_ : ((op (e2) (e0)) = (e0)) -> (((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) (e1)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H73 zenon_H191 zenon_Haf zenon_H192 zenon_He8 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H91 zenon_H17c zenon_H9a. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.36/10.50 apply (zenon_L165_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.36/10.50 apply (zenon_L957_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.36/10.50 exact (zenon_H91 zenon_H94). % 10.36/10.50 apply (zenon_L166_); trivial. % 10.36/10.50 (* end of lemma zenon_L976_ *) % 10.36/10.50 assert (zenon_L977_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H17c zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H73 zenon_H5e zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.50 apply (zenon_L190_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.50 apply (zenon_L976_); trivial. % 10.36/10.50 apply (zenon_L941_); trivial. % 10.36/10.50 (* end of lemma zenon_L977_ *) % 10.36/10.50 assert (zenon_L978_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 10.36/10.50 do 0 intro. intros zenon_Hd2 zenon_H27 zenon_H35 zenon_H15a zenon_Hce zenon_Hda zenon_H95 zenon_H53 zenon_H4c zenon_H28 zenon_Hdd zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.50 apply (zenon_L43_); trivial. % 10.36/10.50 apply (zenon_L275_); trivial. % 10.36/10.50 (* end of lemma zenon_L978_ *) % 10.36/10.50 assert (zenon_L979_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_Hdd zenon_H28 zenon_H4c zenon_H53 zenon_H95 zenon_Hda zenon_Hce zenon_H15a zenon_H35 zenon_H27 zenon_Hd2. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.50 apply (zenon_L978_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.50 apply (zenon_L940_); trivial. % 10.36/10.50 apply (zenon_L275_); trivial. % 10.36/10.50 (* end of lemma zenon_L979_ *) % 10.36/10.50 assert (zenon_L980_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e2) = (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) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H95 zenon_H53 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H18a zenon_H84 zenon_H86 zenon_H17c zenon_H15a zenon_H198 zenon_H43 zenon_H187 zenon_Hd2. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.50 apply (zenon_L847_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.50 apply (zenon_L940_); trivial. % 10.36/10.50 apply (zenon_L426_); trivial. % 10.36/10.50 (* end of lemma zenon_L980_ *) % 10.36/10.50 assert (zenon_L981_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H17c zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H73 zenon_H5e zenon_Haf zenon_H191 zenon_H43 zenon_H18a zenon_Hc6 zenon_H1ef. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.50 apply (zenon_L977_); trivial. % 10.36/10.50 apply (zenon_L968_); trivial. % 10.36/10.50 apply (zenon_L980_); trivial. % 10.36/10.50 (* end of lemma zenon_L981_ *) % 10.36/10.50 assert (zenon_L982_ : (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H27 zenon_H68 zenon_H97 zenon_H84 zenon_H28 zenon_H42 zenon_H53 zenon_H73 zenon_H95 zenon_Hb8 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.51 apply (zenon_L940_); trivial. % 10.36/10.51 apply (zenon_L171_); trivial. % 10.36/10.51 (* end of lemma zenon_L982_ *) % 10.36/10.51 assert (zenon_L983_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (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)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_Hd2 zenon_H27 zenon_H44 zenon_H68 zenon_H97 zenon_H84 zenon_H7a zenon_H95 zenon_H53 zenon_H181 zenon_H42 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.51 apply (zenon_L172_); trivial. % 10.36/10.51 apply (zenon_L982_); trivial. % 10.36/10.51 apply (zenon_L85_); trivial. % 10.36/10.51 (* end of lemma zenon_L983_ *) % 10.36/10.51 assert (zenon_L984_ : (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H143 zenon_H25 zenon_H18d zenon_Hd2 zenon_H17a zenon_H157 zenon_H27 zenon_H44 zenon_H97 zenon_Haf zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_Hda zenon_Hce zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H1ef zenon_H191 zenon_He7 zenon_Hd3 zenon_H1c3 zenon_H1c0 zenon_Hdd zenon_He3 zenon_H1e2 zenon_H1d zenon_H56 zenon_He8 zenon_H1b4 zenon_H177 zenon_H14d. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.51 apply (zenon_L972_); trivial. % 10.36/10.51 exact (zenon_H143 zenon_Hed). % 10.36/10.51 apply (zenon_L941_); trivial. % 10.36/10.51 apply (zenon_L88_); trivial. % 10.36/10.51 (* end of lemma zenon_L984_ *) % 10.36/10.51 assert (zenon_L985_ : (~((op (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)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H143 zenon_H7d zenon_H7e zenon_H43 zenon_H7a zenon_Hd2 zenon_H187 zenon_H11d zenon_H1d zenon_H17c zenon_H86 zenon_H18a zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H56 zenon_H42 zenon_He8 zenon_He7 zenon_H27 zenon_H53 zenon_H95 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.51 apply (zenon_L969_); trivial. % 10.36/10.51 exact (zenon_H143 zenon_Hed). % 10.36/10.51 (* end of lemma zenon_L985_ *) % 10.36/10.51 assert (zenon_L986_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_Hf8 zenon_H143 zenon_H56 zenon_H195 zenon_H1d zenon_H5e zenon_H73 zenon_H14d zenon_H8d zenon_H35 zenon_H95 zenon_H44 zenon_H177 zenon_Hbd zenon_H53 zenon_H1b4. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.51 apply (zenon_L970_); trivial. % 10.36/10.51 exact (zenon_H143 zenon_Hed). % 10.36/10.51 (* end of lemma zenon_L986_ *) % 10.36/10.51 assert (zenon_L987_ : (((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 (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) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H1b4 zenon_H177 zenon_H14d zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H95 zenon_H53 zenon_H27 zenon_He7 zenon_H42 zenon_H56 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H18a zenon_H86 zenon_H17c zenon_H1d zenon_H11d zenon_H187 zenon_Hd2 zenon_H7a zenon_H43 zenon_H7d zenon_H143. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.51 apply (zenon_L985_); trivial. % 10.36/10.51 apply (zenon_L986_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.51 apply (zenon_L985_); trivial. % 10.36/10.51 apply (zenon_L41_); trivial. % 10.36/10.51 apply (zenon_L325_); trivial. % 10.36/10.51 (* end of lemma zenon_L987_ *) % 10.36/10.51 assert (zenon_L988_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (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 (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (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 (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (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 (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H1ba zenon_H73 zenon_H14d zenon_H177 zenon_H1b4 zenon_H1e2 zenon_He3 zenon_Hdd zenon_H1c0 zenon_H1c3 zenon_Hd3 zenon_He7 zenon_H191 zenon_H1ef zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_Hce zenon_Hda zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H110 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H42 zenon_H181 zenon_H53 zenon_H95 zenon_Hde zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H4c zenon_H5e zenon_Hc0 zenon_H184 zenon_Haf zenon_H97 zenon_H44 zenon_H27 zenon_H157 zenon_H17a zenon_Hd2 zenon_H18d. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.51 apply (zenon_L216_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.51 apply (zenon_L973_); trivial. % 10.36/10.51 apply (zenon_L325_); trivial. % 10.36/10.51 apply (zenon_L974_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_L975_); trivial. % 10.36/10.51 apply (zenon_L85_); trivial. % 10.36/10.51 apply (zenon_L216_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.51 exact (zenon_Hc7 zenon_H3a). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.51 apply (zenon_L977_); trivial. % 10.36/10.51 apply (zenon_L973_); trivial. % 10.36/10.51 apply (zenon_L979_); trivial. % 10.36/10.51 apply (zenon_L981_); trivial. % 10.36/10.51 apply (zenon_L983_); trivial. % 10.36/10.51 apply (zenon_L216_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.51 apply (zenon_L216_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.51 apply (zenon_L984_); trivial. % 10.36/10.51 apply (zenon_L979_); trivial. % 10.36/10.51 apply (zenon_L987_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.51 apply (zenon_L43_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.51 apply (zenon_L175_); trivial. % 10.36/10.51 exact (zenon_H143 zenon_Hed). % 10.36/10.51 apply (zenon_L942_); trivial. % 10.36/10.51 apply (zenon_L941_); trivial. % 10.36/10.51 apply (zenon_L88_); trivial. % 10.36/10.51 apply (zenon_L85_); trivial. % 10.36/10.51 apply (zenon_L216_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.51 exact (zenon_Hc7 zenon_H3a). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.51 apply (zenon_L977_); trivial. % 10.36/10.51 apply (zenon_L984_); trivial. % 10.36/10.51 apply (zenon_L979_); trivial. % 10.36/10.51 apply (zenon_L981_); trivial. % 10.36/10.51 apply (zenon_L983_); trivial. % 10.36/10.51 apply (zenon_L216_); trivial. % 10.36/10.51 (* end of lemma zenon_L988_ *) % 10.36/10.51 assert (zenon_L989_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (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)) = (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H157 zenon_H77 zenon_H35 zenon_H145 zenon_H9a zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.51 apply (zenon_L215_); trivial. % 10.36/10.51 apply (zenon_L203_); trivial. % 10.36/10.51 (* end of lemma zenon_L989_ *) % 10.36/10.51 assert (zenon_L990_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((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)) = (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 (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H238 zenon_H86 zenon_H17c zenon_H198 zenon_H18a zenon_Hda zenon_H28 zenon_H4c zenon_H95 zenon_He3 zenon_H1e2 zenon_Hb1 zenon_H1ba zenon_Hb0 zenon_H192 zenon_H239 zenon_H157 zenon_H77 zenon_H35 zenon_H145 zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H1b7 zenon_H84 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.51 apply (zenon_L946_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.51 exact (zenon_H192 zenon_H1d). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.51 exact (zenon_H239 zenon_H100). % 10.36/10.51 apply (zenon_L989_); trivial. % 10.36/10.51 (* end of lemma zenon_L990_ *) % 10.36/10.51 assert (zenon_L991_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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). % 10.36/10.51 do 0 intro. intros zenon_H18d zenon_Hb0 zenon_Hda zenon_He3 zenon_H95 zenon_H4c zenon_H28 zenon_H35 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H5e zenon_H2a zenon_H1ba zenon_H192 zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_He8 zenon_H12f zenon_H1b7 zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H238 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H7d zenon_H7f zenon_H7a zenon_H8d zenon_H64. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.51 apply (zenon_L945_); trivial. % 10.36/10.51 apply (zenon_L990_); trivial. % 10.36/10.51 (* end of lemma zenon_L991_ *) % 10.36/10.51 assert (zenon_L992_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H18d zenon_Hbc zenon_He3 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_H7d zenon_H7f zenon_H7e zenon_H86 zenon_H145. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.51 apply (zenon_L119_); trivial. % 10.36/10.51 apply (zenon_L266_); trivial. % 10.36/10.51 (* end of lemma zenon_L992_ *) % 10.36/10.51 assert (zenon_L993_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (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)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((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))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((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). % 10.36/10.51 do 0 intro. intros zenon_H18d zenon_Hb0 zenon_Hda zenon_He3 zenon_H28 zenon_Hc7 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_Hb1 zenon_H2a zenon_H1ba zenon_H192 zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_Hc5 zenon_H12f zenon_H1b7 zenon_H187 zenon_H58 zenon_Hd2 zenon_H238 zenon_H56 zenon_Hd3 zenon_H77 zenon_H44 zenon_He8 zenon_H5e zenon_Hc0 zenon_He7 zenon_H53 zenon_H35 zenon_H181 zenon_Hd0 zenon_H42 zenon_H4c zenon_H95 zenon_H27 zenon_H7d zenon_H7f zenon_H7a zenon_H8d zenon_H64. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.51 exact (zenon_H56 zenon_H2c). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.51 apply (zenon_L196_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.51 apply (zenon_L201_); trivial. % 10.36/10.51 apply (zenon_L87_); trivial. % 10.36/10.51 apply (zenon_L990_); trivial. % 10.36/10.51 (* end of lemma zenon_L993_ *) % 10.36/10.51 assert (zenon_L994_ : (((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 (e1) (e2)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H238 zenon_H35 zenon_H6a zenon_H192 zenon_H239 zenon_H62 zenon_H187. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.51 apply (zenon_L238_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.51 exact (zenon_H192 zenon_H1d). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.51 exact (zenon_H239 zenon_H100). % 10.36/10.51 apply (zenon_L202_); trivial. % 10.36/10.51 (* end of lemma zenon_L994_ *) % 10.36/10.51 assert (zenon_L995_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.36/10.51 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H187 zenon_H62 zenon_H239 zenon_H192 zenon_H238 zenon_H76 zenon_H35 zenon_H95 zenon_Hbc. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.51 exact (zenon_H27 zenon_H32). % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.51 apply (zenon_L994_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.51 apply (zenon_L47_); trivial. % 10.36/10.51 apply (zenon_L51_); trivial. % 10.36/10.51 (* end of lemma zenon_L995_ *) % 10.36/10.51 assert (zenon_L996_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((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)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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))) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((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 (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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (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) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H1ef zenon_H150 zenon_Hbb zenon_H151 zenon_H64 zenon_H7a zenon_H7f zenon_H7d zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H56 zenon_H238 zenon_Hd2 zenon_H58 zenon_H187 zenon_H181 zenon_H1b7 zenon_H12f zenon_H155 zenon_H145 zenon_H157 zenon_H239 zenon_H1ba zenon_H2a zenon_H5e zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H35 zenon_H4c zenon_H95 zenon_He3 zenon_Hda zenon_Hb0 zenon_H18d zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_Hce zenon_Hdd zenon_H97 zenon_H27 zenon_H42 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H128 zenon_H112 zenon_H1fb zenon_H8c zenon_Hab zenon_H168 zenon_H204 zenon_H195 zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.51 apply (zenon_L991_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.51 apply (zenon_L992_); trivial. % 10.36/10.51 apply (zenon_L41_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.51 apply (zenon_L993_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.51 exact (zenon_H56 zenon_H2c). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.51 apply (zenon_L196_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.51 apply (zenon_L201_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.51 exact (zenon_H56 zenon_H2c). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.51 apply (zenon_L951_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.51 apply (zenon_L995_); trivial. % 10.36/10.51 apply (zenon_L139_); trivial. % 10.36/10.51 apply (zenon_L203_); trivial. % 10.36/10.51 apply (zenon_L952_); trivial. % 10.36/10.51 apply (zenon_L78_); trivial. % 10.36/10.51 apply (zenon_L953_); trivial. % 10.36/10.51 apply (zenon_L213_); trivial. % 10.36/10.51 (* end of lemma zenon_L996_ *) % 10.36/10.51 assert (zenon_L997_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H56 zenon_Hd3 zenon_H51 zenon_Hdd zenon_H27 zenon_H187 zenon_H239 zenon_H192 zenon_H238 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hb0 zenon_H53 zenon_H5e zenon_Hb1 zenon_H1e2 zenon_He3 zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H35 zenon_H77 zenon_Hc7 zenon_H18a zenon_H15a zenon_H198 zenon_H17c zenon_H84 zenon_H86. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.51 exact (zenon_H56 zenon_H2c). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.51 apply (zenon_L196_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.51 apply (zenon_L12_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.51 exact (zenon_H27 zenon_H32). % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.51 apply (zenon_L994_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.51 apply (zenon_L952_); trivial. % 10.36/10.51 apply (zenon_L831_); trivial. % 10.36/10.51 (* end of lemma zenon_L997_ *) % 10.36/10.51 assert (zenon_L998_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((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) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H1ef zenon_H1e2 zenon_H187 zenon_H43 zenon_H17c zenon_H84 zenon_H18a zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H77 zenon_H4c zenon_H95 zenon_H239 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H17a zenon_He8 zenon_H42 zenon_H238. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.51 apply (zenon_L959_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.51 exact (zenon_H192 zenon_H1d). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.51 exact (zenon_H239 zenon_H100). % 10.36/10.51 apply (zenon_L956_); trivial. % 10.36/10.52 apply (zenon_L78_); trivial. % 10.36/10.52 (* end of lemma zenon_L998_ *) % 10.36/10.52 assert (zenon_L999_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H238 zenon_H42 zenon_H17a zenon_He7 zenon_H27 zenon_H56 zenon_Hd3 zenon_H239 zenon_H95 zenon_H4c zenon_H77 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H18a zenon_H84 zenon_H17c zenon_H43 zenon_H187 zenon_H1e2 zenon_H1ef. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.52 apply (zenon_L998_); trivial. % 10.36/10.52 apply (zenon_L959_); trivial. % 10.36/10.52 (* end of lemma zenon_L999_ *) % 10.36/10.52 assert (zenon_L1000_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.36/10.52 do 0 intro. intros zenon_H238 zenon_H4c zenon_H6c zenon_H192 zenon_H239 zenon_H5e zenon_H87. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.52 apply (zenon_L236_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.52 exact (zenon_H192 zenon_H1d). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.52 exact (zenon_H239 zenon_H100). % 10.36/10.52 apply (zenon_L192_); trivial. % 10.36/10.52 (* end of lemma zenon_L1000_ *) % 10.36/10.52 assert (zenon_L1001_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H156 zenon_H1ba zenon_H2a zenon_H5e zenon_H77 zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_Hc7 zenon_H35 zenon_H28 zenon_H4c zenon_H15a zenon_H95 zenon_He3 zenon_H84 zenon_Hda zenon_Hb0. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.52 apply (zenon_L946_); trivial. % 10.36/10.52 apply (zenon_L296_); trivial. % 10.36/10.52 (* end of lemma zenon_L1001_ *) % 10.36/10.52 assert (zenon_L1002_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H174 zenon_H26 zenon_H168 zenon_H156 zenon_Hce zenon_H1b4 zenon_H112 zenon_Hb0 zenon_Hda zenon_H84 zenon_He3 zenon_H95 zenon_H4c zenon_H35 zenon_Hc7 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H77 zenon_H5e zenon_H2a zenon_H1ba zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_Hc5 zenon_H12f zenon_H1b7 zenon_H7a zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H238 zenon_H110 zenon_H1ef zenon_H4a. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.52 apply (zenon_L990_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.52 exact (zenon_H56 zenon_H2c). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.52 apply (zenon_L296_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.52 apply (zenon_L47_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.36/10.52 exact (zenon_H28 zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.36/10.52 apply (zenon_L100_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.36/10.52 exact (zenon_He8 zenon_Heb). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.36/10.52 apply (zenon_L118_); trivial. % 10.36/10.52 apply (zenon_L1000_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.36/10.52 apply (zenon_L155_); trivial. % 10.36/10.52 apply (zenon_L139_); trivial. % 10.36/10.52 apply (zenon_L44_); trivial. % 10.36/10.52 apply (zenon_L79_); trivial. % 10.36/10.52 apply (zenon_L78_); trivial. % 10.36/10.52 apply (zenon_L1001_); trivial. % 10.36/10.52 apply (zenon_L213_); trivial. % 10.36/10.52 apply (zenon_L937_); trivial. % 10.36/10.52 (* end of lemma zenon_L1002_ *) % 10.36/10.52 assert (zenon_L1003_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e1) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H1b7 zenon_H1b4 zenon_H1ef zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_H5e zenon_Hc0 zenon_H84 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H191 zenon_H239 zenon_H1ea zenon_Hdd zenon_H17c zenon_H18a zenon_He3 zenon_H238 zenon_H97 zenon_H1e2. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.52 apply (zenon_L957_); trivial. % 10.36/10.52 exact (zenon_H239 zenon_H100). % 10.36/10.52 apply (zenon_L78_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.52 exact (zenon_H25 zenon_H2a). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.52 apply (zenon_L963_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.52 apply (zenon_L997_); trivial. % 10.36/10.52 apply (zenon_L999_); trivial. % 10.36/10.52 apply (zenon_L952_); trivial. % 10.36/10.52 apply (zenon_L325_); trivial. % 10.36/10.52 apply (zenon_L999_); trivial. % 10.36/10.52 apply (zenon_L963_); trivial. % 10.36/10.52 apply (zenon_L1002_); trivial. % 10.36/10.52 (* end of lemma zenon_L1003_ *) % 10.36/10.52 assert (zenon_L1004_ : (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e1) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H7f zenon_H1c3 zenon_H1c0 zenon_H1b7 zenon_H1b4 zenon_H1ef zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_H5e zenon_Hc0 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H191 zenon_H239 zenon_H1ea zenon_Hdd zenon_H17c zenon_H18a zenon_He3 zenon_H238 zenon_H97 zenon_H1e2. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.52 apply (zenon_L996_); trivial. % 10.36/10.52 apply (zenon_L937_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.52 apply (zenon_L78_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.52 exact (zenon_Hc7 zenon_H3a). % 10.36/10.52 apply (zenon_L1003_); trivial. % 10.36/10.52 (* end of lemma zenon_L1004_ *) % 10.36/10.52 assert (zenon_L1005_ : (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((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 (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H56 zenon_H1d zenon_H51 zenon_H73 zenon_H1e2 zenon_H97 zenon_H238 zenon_He3 zenon_H18a zenon_H17c zenon_Hdd zenon_H1ea zenon_H239 zenon_H191 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_Hc0 zenon_H5e zenon_H44 zenon_H35 zenon_H42 zenon_Hd2 zenon_H1ef zenon_H1b4 zenon_H1b7 zenon_H1c0 zenon_H1c3 zenon_H7f zenon_H91 zenon_H181. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.52 exact (zenon_H56 zenon_H2c). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.52 apply (zenon_L1_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.52 apply (zenon_L12_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.36/10.52 apply (zenon_L165_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.36/10.52 apply (zenon_L1004_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.36/10.52 exact (zenon_H91 zenon_H94). % 10.36/10.52 apply (zenon_L258_); trivial. % 10.36/10.52 (* end of lemma zenon_L1005_ *) % 10.36/10.52 assert (zenon_L1006_ : (~((op (e0) (e0)) = (e0))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (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) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (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 (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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (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 (e0) (e0)) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H25 zenon_Hd0 zenon_H28 zenon_H84 zenon_H91 zenon_H1c3 zenon_H1c0 zenon_H1b7 zenon_H1ef zenon_H17a zenon_Hd3 zenon_H191 zenon_H239 zenon_H1ea zenon_Hdd zenon_He3 zenon_H238 zenon_H97 zenon_H1e2 zenon_H14d zenon_H177 zenon_H1b4 zenon_H7d zenon_H7f zenon_H7a zenon_Hd2 zenon_H187 zenon_H11d zenon_H1d zenon_H17c zenon_H86 zenon_H18a zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H56 zenon_H42 zenon_He7 zenon_H27 zenon_H53 zenon_H95 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.52 exact (zenon_H25 zenon_H2a). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.52 apply (zenon_L171_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.52 apply (zenon_L1005_); trivial. % 10.36/10.52 apply (zenon_L974_); trivial. % 10.36/10.52 (* end of lemma zenon_L1006_ *) % 10.36/10.52 assert (zenon_L1007_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (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)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((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)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((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)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((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 (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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (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) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (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 (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H14d zenon_H177 zenon_Hc6 zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_Hde zenon_Hc1 zenon_H90 zenon_H7d zenon_H7f zenon_H7e zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H91 zenon_H4c zenon_H73 zenon_H5e zenon_Hc0 zenon_Hd0 zenon_H184 zenon_Haf zenon_H97 zenon_H44 zenon_H27 zenon_H1ea zenon_H191 zenon_H17a zenon_H1ef zenon_H150 zenon_Hbb zenon_H151 zenon_H64 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H238 zenon_Hd2 zenon_H58 zenon_H1b7 zenon_H12f zenon_H155 zenon_H145 zenon_H157 zenon_H239 zenon_H1ba zenon_H1e2 zenon_H198 zenon_H35 zenon_He3 zenon_Hda zenon_Hb0 zenon_H18d zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_Hce zenon_Hdd zenon_He7 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H128 zenon_H112 zenon_H1fb zenon_Hab zenon_H168 zenon_H204 zenon_H195 zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H200 zenon_H110 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H1d zenon_H1f zenon_H56. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.52 exact (zenon_H25 zenon_H2a). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.52 apply (zenon_L169_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.52 apply (zenon_L1005_); trivial. % 10.36/10.52 apply (zenon_L24_); trivial. % 10.36/10.52 apply (zenon_L1006_); trivial. % 10.36/10.52 (* end of lemma zenon_L1007_ *) % 10.36/10.52 assert (zenon_L1008_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (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))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((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)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (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)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (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) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H1ea zenon_H239 zenon_H191 zenon_H192 zenon_He8 zenon_H5e zenon_H73 zenon_Hd2 zenon_H42 zenon_H181 zenon_H35 zenon_H44 zenon_Hc0 zenon_H84 zenon_H17a zenon_H4c zenon_H95 zenon_He7 zenon_H27 zenon_H56 zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H187 zenon_H64 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H53 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H7a zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H17c. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.52 apply (zenon_L977_); trivial. % 10.36/10.52 exact (zenon_H239 zenon_H100). % 10.36/10.52 (* end of lemma zenon_L1008_ *) % 10.36/10.52 assert (zenon_L1009_ : ((op (e2) (e0)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (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) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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 (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.36/10.52 do 0 intro. intros zenon_H73 zenon_H238 zenon_H42 zenon_He8 zenon_H17a zenon_He7 zenon_H27 zenon_H56 zenon_Hd3 zenon_H239 zenon_H95 zenon_H4c zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H18a zenon_H84 zenon_H43 zenon_H187 zenon_H1e2 zenon_H1ef zenon_H91 zenon_H17c zenon_H9a. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.36/10.52 apply (zenon_L165_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.36/10.52 apply (zenon_L998_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.36/10.52 exact (zenon_H91 zenon_H94). % 10.36/10.52 apply (zenon_L166_); trivial. % 10.36/10.52 (* end of lemma zenon_L1009_ *) % 10.36/10.52 assert (zenon_L1010_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((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) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H1ea zenon_H191 zenon_H5e zenon_H73 zenon_H1ef zenon_H1e2 zenon_H187 zenon_H43 zenon_H17c zenon_H84 zenon_H18a zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H4c zenon_H95 zenon_H239 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H17a zenon_H42 zenon_H238 zenon_Hc6. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_L190_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_L1009_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 exact (zenon_H239 zenon_H100). % 10.36/10.53 apply (zenon_L968_); trivial. % 10.36/10.53 apply (zenon_L980_); trivial. % 10.36/10.53 (* end of lemma zenon_L1010_ *) % 10.36/10.53 assert (zenon_L1011_ : (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (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))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H143 zenon_H56 zenon_H1f zenon_H1d zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H200 zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_Hab zenon_H1fb zenon_H112 zenon_H128 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_He7 zenon_Hdd zenon_Hce zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H18d zenon_Hb0 zenon_Hda zenon_He3 zenon_H35 zenon_H198 zenon_H1e2 zenon_H1ba zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_H12f zenon_H1b7 zenon_H58 zenon_Hd2 zenon_H238 zenon_Hd3 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H64 zenon_H151 zenon_Hbb zenon_H150 zenon_H1ef zenon_H17a zenon_H191 zenon_H1ea zenon_H27 zenon_H44 zenon_H97 zenon_Haf zenon_H184 zenon_Hd0 zenon_Hc0 zenon_H5e zenon_H73 zenon_H4c zenon_H91 zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7e zenon_H7d zenon_H90 zenon_Hc1 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H25 zenon_Hc6 zenon_H177 zenon_H14d. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.53 apply (zenon_L1007_); trivial. % 10.36/10.53 exact (zenon_H143 zenon_Hed). % 10.36/10.53 (* end of lemma zenon_L1011_ *) % 10.36/10.53 assert (zenon_L1012_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (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) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H1b4 zenon_H27 zenon_He7 zenon_He8 zenon_H177 zenon_H10b zenon_H114 zenon_H42 zenon_H9a zenon_H56 zenon_H143 zenon_H53 zenon_H73 zenon_H95 zenon_Hb8 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_H4c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L940_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.53 exact (zenon_H56 zenon_H2c). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.53 apply (zenon_L194_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.53 apply (zenon_L165_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.36/10.53 exact (zenon_H27 zenon_H32). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.36/10.53 apply (zenon_L648_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.36/10.53 apply (zenon_L629_); trivial. % 10.36/10.53 apply (zenon_L163_); trivial. % 10.36/10.53 exact (zenon_H143 zenon_Hed). % 10.36/10.53 (* end of lemma zenon_L1012_ *) % 10.36/10.53 assert (zenon_L1013_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((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) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H1ea zenon_H191 zenon_H143 zenon_H114 zenon_H10b zenon_H177 zenon_H1b4 zenon_H5e zenon_H73 zenon_H1ef zenon_H1e2 zenon_H187 zenon_H43 zenon_H17c zenon_H84 zenon_H18a zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H4c zenon_H95 zenon_H239 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H17a zenon_H42 zenon_H238 zenon_Hc6. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_L190_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_L1009_); trivial. % 10.36/10.53 apply (zenon_L1012_); trivial. % 10.36/10.53 exact (zenon_H239 zenon_H100). % 10.36/10.53 apply (zenon_L968_); trivial. % 10.36/10.53 apply (zenon_L980_); trivial. % 10.36/10.53 (* end of lemma zenon_L1013_ *) % 10.36/10.53 assert (zenon_L1014_ : (~((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 (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 (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H10b zenon_H114 zenon_H177 zenon_H14d zenon_Hdd zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_He3 zenon_H18a zenon_H1e2 zenon_H1b7 zenon_H238 zenon_H1ef zenon_H97 zenon_H143 zenon_Hc6 zenon_H17c zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H73 zenon_H5e zenon_H191 zenon_H239 zenon_H1ea. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.53 apply (zenon_L1008_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.53 apply (zenon_L1006_); trivial. % 10.36/10.53 exact (zenon_H143 zenon_Hed). % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L979_); trivial. % 10.36/10.53 apply (zenon_L1013_); trivial. % 10.36/10.53 apply (zenon_L983_); trivial. % 10.36/10.53 apply (zenon_L216_); trivial. % 10.36/10.53 (* end of lemma zenon_L1014_ *) % 10.36/10.53 assert (zenon_L1015_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H10b zenon_H114 zenon_H1ba zenon_H73 zenon_H1f zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H200 zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_Hab zenon_H1fb zenon_H112 zenon_H128 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_He7 zenon_Hdd zenon_Hce zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H18d zenon_Hb0 zenon_Hda zenon_He3 zenon_H35 zenon_H198 zenon_H1e2 zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_H12f zenon_H1b7 zenon_H58 zenon_Hd2 zenon_H238 zenon_Hd3 zenon_H3c zenon_H64 zenon_H151 zenon_Hbb zenon_H150 zenon_H1ef zenon_H17a zenon_H191 zenon_H1ea zenon_H27 zenon_H44 zenon_H97 zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hde zenon_H95 zenon_H53 zenon_H181 zenon_H42 zenon_H177 zenon_H14d zenon_Hc6 zenon_Hc7 zenon_Hc5. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.53 apply (zenon_L216_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1007_); trivial. % 10.36/10.53 apply (zenon_L970_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1007_); trivial. % 10.36/10.53 apply (zenon_L41_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L88_); trivial. % 10.36/10.53 exact (zenon_H239 zenon_H100). % 10.36/10.53 apply (zenon_L974_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.53 apply (zenon_L975_); trivial. % 10.36/10.53 exact (zenon_H239 zenon_H100). % 10.36/10.53 apply (zenon_L85_); trivial. % 10.36/10.53 apply (zenon_L216_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.53 exact (zenon_Hc7 zenon_H3a). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.53 apply (zenon_L1008_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_L1006_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L979_); trivial. % 10.36/10.53 apply (zenon_L1010_); trivial. % 10.36/10.53 apply (zenon_L983_); trivial. % 10.36/10.53 apply (zenon_L216_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.53 apply (zenon_L216_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1011_); trivial. % 10.36/10.53 apply (zenon_L986_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1011_); trivial. % 10.36/10.53 apply (zenon_L41_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L88_); trivial. % 10.36/10.53 exact (zenon_H239 zenon_H100). % 10.36/10.53 apply (zenon_L987_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.53 apply (zenon_L169_); trivial. % 10.36/10.53 apply (zenon_L1014_); trivial. % 10.36/10.53 exact (zenon_H143 zenon_Hed). % 10.36/10.53 apply (zenon_L942_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L88_); trivial. % 10.36/10.53 exact (zenon_H239 zenon_H100). % 10.36/10.53 apply (zenon_L85_); trivial. % 10.36/10.53 apply (zenon_L216_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.53 exact (zenon_Hc7 zenon_H3a). % 10.36/10.53 apply (zenon_L1014_); trivial. % 10.36/10.53 (* end of lemma zenon_L1015_ *) % 10.36/10.53 assert (zenon_L1016_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H200 zenon_H25 zenon_H181 zenon_H97 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H44 zenon_H27 zenon_H42 zenon_H23c zenon_H18a zenon_H187 zenon_H1d zenon_H11d zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.53 exact (zenon_H25 zenon_H2a). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.53 apply (zenon_L171_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.53 exact (zenon_H23c zenon_H51). % 10.36/10.53 apply (zenon_L637_); trivial. % 10.36/10.53 (* end of lemma zenon_L1016_ *) % 10.36/10.53 assert (zenon_L1017_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (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 (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (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 (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H18d zenon_H1d zenon_H11d zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_Hde zenon_Hc1 zenon_H90 zenon_H7d zenon_H7f zenon_H7e zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H91 zenon_H4c zenon_H73 zenon_H5e zenon_Hc0 zenon_Hd0 zenon_H184 zenon_Haf zenon_H97 zenon_H44 zenon_H27 zenon_H23c zenon_H200. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.53 exact (zenon_H25 zenon_H2a). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.53 apply (zenon_L169_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.53 exact (zenon_H23c zenon_H51). % 10.36/10.53 apply (zenon_L24_); trivial. % 10.36/10.53 apply (zenon_L1016_); trivial. % 10.36/10.53 (* end of lemma zenon_L1017_ *) % 10.36/10.53 assert (zenon_L1018_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((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))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.53 do 0 intro. intros zenon_Hd2 zenon_H151 zenon_H56 zenon_H195 zenon_H14d zenon_H35 zenon_H177 zenon_H1b4 zenon_H200 zenon_H23c zenon_H27 zenon_H44 zenon_H97 zenon_Haf zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7f zenon_H7d zenon_H90 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H25 zenon_H11d zenon_H1d zenon_H18d zenon_Hbb zenon_H150 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H64 zenon_H110 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1017_); trivial. % 10.36/10.53 apply (zenon_L970_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1017_); trivial. % 10.36/10.53 apply (zenon_L41_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L88_); trivial. % 10.36/10.53 (* end of lemma zenon_L1018_ *) % 10.36/10.53 assert (zenon_L1019_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (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 (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (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 (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H18d zenon_H1d zenon_H11d zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_Hde zenon_H90 zenon_H7d zenon_H7f zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H4c zenon_H5e zenon_Hc0 zenon_H184 zenon_Haf zenon_H97 zenon_H44 zenon_H27 zenon_H23c zenon_H200 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_Hd2 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H68 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.53 apply (zenon_L43_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.53 apply (zenon_L1017_); trivial. % 10.36/10.53 apply (zenon_L942_); trivial. % 10.36/10.53 apply (zenon_L941_); trivial. % 10.36/10.53 apply (zenon_L88_); trivial. % 10.36/10.53 (* end of lemma zenon_L1019_ *) % 10.36/10.53 assert (zenon_L1020_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e2) (e2)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (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 (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H67 zenon_H23c zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc5 zenon_Hc7 zenon_H73 zenon_Hc6 zenon_H42 zenon_H181 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H68 zenon_H44 zenon_Hd2. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.53 apply (zenon_L983_); trivial. % 10.36/10.53 exact (zenon_H23c zenon_H51). % 10.36/10.53 (* end of lemma zenon_L1020_ *) % 10.36/10.53 assert (zenon_L1021_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (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))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hf8 zenon_H143 zenon_H200 zenon_H23c zenon_H27 zenon_H44 zenon_H97 zenon_Haf zenon_H184 zenon_Hd0 zenon_Hc0 zenon_H5e zenon_H73 zenon_H4c zenon_H91 zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7e zenon_H7d zenon_H90 zenon_Hc1 zenon_Hde zenon_H95 zenon_H53 zenon_H28 zenon_H181 zenon_H42 zenon_H25 zenon_H11d zenon_H1d zenon_H18d. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_L1017_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 (* end of lemma zenon_L1021_ *) % 10.36/10.54 assert (zenon_L1022_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((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))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (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 (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (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 (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((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 (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hd2 zenon_H151 zenon_H1b4 zenon_H177 zenon_H35 zenon_H14d zenon_H195 zenon_H56 zenon_H18d zenon_H1d zenon_H11d zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_Hde zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H4c zenon_H5e zenon_Hc0 zenon_H184 zenon_Haf zenon_H97 zenon_H44 zenon_H27 zenon_H23c zenon_H200 zenon_H143 zenon_Hf8 zenon_Hbb zenon_H150 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_H237 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H64 zenon_H110 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_L43_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.54 apply (zenon_L1021_); trivial. % 10.36/10.54 apply (zenon_L986_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.54 apply (zenon_L1021_); trivial. % 10.36/10.54 apply (zenon_L41_); trivial. % 10.36/10.54 apply (zenon_L941_); trivial. % 10.36/10.54 apply (zenon_L88_); trivial. % 10.36/10.54 (* end of lemma zenon_L1022_ *) % 10.36/10.54 assert (zenon_L1023_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hd2 zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H44 zenon_H27 zenon_H23c zenon_H18a zenon_H86 zenon_H17c zenon_H1d zenon_H11d zenon_H187 zenon_H200 zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_L43_); trivial. % 10.36/10.54 apply (zenon_L1016_); trivial. % 10.36/10.54 (* end of lemma zenon_L1023_ *) % 10.36/10.54 assert (zenon_L1024_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hf8 zenon_H143 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_Hde zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H4c zenon_H5e zenon_Hc0 zenon_H184 zenon_Haf zenon_H97 zenon_H68 zenon_H44 zenon_H27 zenon_Hd2 zenon_H25 zenon_H23c zenon_H1d zenon_H11d zenon_H200 zenon_H18d zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_H237 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_L43_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H80 | zenon_intro zenon_H84 ]. % 10.36/10.54 apply (zenon_L169_); trivial. % 10.36/10.54 apply (zenon_L1023_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_L942_); trivial. % 10.36/10.54 apply (zenon_L941_); trivial. % 10.36/10.54 apply (zenon_L88_); trivial. % 10.36/10.54 (* end of lemma zenon_L1024_ *) % 10.36/10.54 assert (zenon_L1025_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H17c zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H73 zenon_H5e zenon_H1b4 zenon_H177 zenon_H10b zenon_H114 zenon_H143 zenon_He8 zenon_H192 zenon_Haf zenon_H191. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_L190_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_L976_); trivial. % 10.36/10.54 apply (zenon_L1012_); trivial. % 10.36/10.54 (* end of lemma zenon_L1025_ *) % 10.36/10.54 assert (zenon_L1026_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hd2 zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H44 zenon_H27 zenon_H23c zenon_H18a zenon_H86 zenon_H17c zenon_H1d zenon_H11d zenon_H187 zenon_H200 zenon_Hc6 zenon_H73 zenon_Hc7 zenon_Hc5 zenon_He7 zenon_He8 zenon_H56 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H4c zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_L1023_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.54 exact (zenon_H25 zenon_H2a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.54 apply (zenon_L982_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L967_); trivial. % 10.36/10.54 apply (zenon_L88_); trivial. % 10.36/10.54 (* end of lemma zenon_L1026_ *) % 10.36/10.54 assert (zenon_L1027_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H10b zenon_H114 zenon_H1ba zenon_H73 zenon_H67 zenon_Hd2 zenon_H151 zenon_H195 zenon_H14d zenon_H35 zenon_H177 zenon_H1b4 zenon_H200 zenon_H23c zenon_H44 zenon_H97 zenon_Haf zenon_H184 zenon_Hc0 zenon_H5e zenon_H4c zenon_H8c zenon_H17c zenon_H187 zenon_H18a zenon_H86 zenon_H7a zenon_H7d zenon_H90 zenon_Hde zenon_H95 zenon_H53 zenon_H181 zenon_H42 zenon_H11d zenon_H18d zenon_Hbb zenon_H150 zenon_Hc6 zenon_Hc7 zenon_Hc5 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H145 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H157 zenon_Hce zenon_Hda zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H1f zenon_H3c zenon_H64 zenon_H110 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_He7 zenon_Hdd zenon_Hd3 zenon_H17a zenon_H191 zenon_H1ef. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_L1018_); trivial. % 10.36/10.54 apply (zenon_L974_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_L1019_); trivial. % 10.36/10.54 apply (zenon_L85_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.54 exact (zenon_Hc7 zenon_H3a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_L977_); trivial. % 10.36/10.54 apply (zenon_L1018_); trivial. % 10.36/10.54 apply (zenon_L979_); trivial. % 10.36/10.54 apply (zenon_L981_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L1020_); trivial. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_L1022_); trivial. % 10.36/10.54 apply (zenon_L987_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_L1024_); trivial. % 10.36/10.54 apply (zenon_L85_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.54 exact (zenon_Hc7 zenon_H3a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_L1025_); trivial. % 10.36/10.54 apply (zenon_L1026_); trivial. % 10.36/10.54 apply (zenon_L979_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_L1025_); trivial. % 10.36/10.54 apply (zenon_L968_); trivial. % 10.36/10.54 apply (zenon_L980_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L1020_); trivial. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 (* end of lemma zenon_L1027_ *) % 10.36/10.54 assert (zenon_L1028_ : (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (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))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H25 zenon_H42 zenon_H181 zenon_H28 zenon_H53 zenon_H95 zenon_H7a zenon_H84 zenon_H97 zenon_H44 zenon_H27 zenon_H23c zenon_H9a zenon_H238 zenon_He8 zenon_H17a zenon_He7 zenon_H56 zenon_Hd3 zenon_H239 zenon_H4c zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_H1fb zenon_Hb0 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H64 zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H18a zenon_H17c zenon_H187 zenon_H1e2 zenon_H1ef zenon_H5e zenon_Hc6 zenon_H73 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_L43_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.54 exact (zenon_H25 zenon_H2a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.54 apply (zenon_L171_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L1009_); trivial. % 10.36/10.54 (* end of lemma zenon_L1028_ *) % 10.36/10.54 assert (zenon_L1029_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e0)) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (e0))) -> (((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))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H114 zenon_H10b zenon_H1ba zenon_H73 zenon_H67 zenon_H1ea zenon_H239 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H110 zenon_H64 zenon_H3c zenon_H1f zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_Hda zenon_Hce zenon_H157 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hc5 zenon_Hc7 zenon_Hc6 zenon_H150 zenon_Hbb zenon_H18d zenon_H11d zenon_H42 zenon_H181 zenon_H53 zenon_H95 zenon_Hde zenon_H90 zenon_H7d zenon_H7a zenon_H86 zenon_H18a zenon_H187 zenon_H17c zenon_H8c zenon_H4c zenon_H5e zenon_Hc0 zenon_H184 zenon_H97 zenon_H44 zenon_H23c zenon_H200 zenon_H1b4 zenon_H177 zenon_H35 zenon_H14d zenon_H195 zenon_H151 zenon_Hd2 zenon_He7 zenon_Hdd zenon_H191 zenon_H1ef zenon_H1e2 zenon_Hd3 zenon_H17a zenon_H238. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.54 apply (zenon_L1018_); trivial. % 10.36/10.54 exact (zenon_H239 zenon_H100). % 10.36/10.54 apply (zenon_L974_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.54 apply (zenon_L1019_); trivial. % 10.36/10.54 exact (zenon_H239 zenon_H100). % 10.36/10.54 apply (zenon_L85_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.54 exact (zenon_Hc7 zenon_H3a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_L190_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_L1028_); trivial. % 10.36/10.54 apply (zenon_L941_); trivial. % 10.36/10.54 exact (zenon_H239 zenon_H100). % 10.36/10.54 apply (zenon_L1026_); trivial. % 10.36/10.54 apply (zenon_L979_); trivial. % 10.36/10.54 apply (zenon_L1010_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L1020_); trivial. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.54 apply (zenon_L1022_); trivial. % 10.36/10.54 exact (zenon_H239 zenon_H100). % 10.36/10.54 apply (zenon_L987_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.54 apply (zenon_L1024_); trivial. % 10.36/10.54 exact (zenon_H239 zenon_H100). % 10.36/10.54 apply (zenon_L85_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.54 exact (zenon_Hc7 zenon_H3a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_L190_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_L1028_); trivial. % 10.36/10.54 apply (zenon_L1012_); trivial. % 10.36/10.54 exact (zenon_H239 zenon_H100). % 10.36/10.54 apply (zenon_L1026_); trivial. % 10.36/10.54 apply (zenon_L979_); trivial. % 10.36/10.54 apply (zenon_L1013_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L1020_); trivial. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 (* end of lemma zenon_L1029_ *) % 10.36/10.54 assert (zenon_L1030_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (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)) = (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)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H150 zenon_H18d zenon_H86 zenon_H56 zenon_Hd3 zenon_H77 zenon_H42 zenon_H181 zenon_H28 zenon_H95 zenon_H4c zenon_Hda zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H2a zenon_H1ba zenon_Hce zenon_Hd0 zenon_Hdd zenon_H53 zenon_H5e zenon_Hb1 zenon_H18a zenon_H187 zenon_H35 zenon_Hc7 zenon_H1e2 zenon_H198 zenon_H17c zenon_Hb0 zenon_H15a zenon_H97 zenon_H27 zenon_H7d zenon_H7a zenon_H64 zenon_H143 zenon_Hf8. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_L950_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_L221_); trivial. % 10.36/10.54 (* end of lemma zenon_L1030_ *) % 10.36/10.54 assert (zenon_L1031_ : (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (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 (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (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 (e3) (e2)) = (e3))) -> ((~((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) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H27 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H157 zenon_H44 zenon_H53 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H145 zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_H237 zenon_Hdd zenon_H18d zenon_H1ba zenon_H2a zenon_H5e zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H35 zenon_H28 zenon_H4c zenon_H15a zenon_H95 zenon_He3 zenon_Hda zenon_Hb0 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H7d zenon_H7a zenon_H64 zenon_H143 zenon_Hf8 zenon_H42 zenon_H187 zenon_H97. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_L947_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_L949_); trivial. % 10.36/10.54 apply (zenon_L1030_); trivial. % 10.36/10.54 apply (zenon_L952_); trivial. % 10.36/10.54 (* end of lemma zenon_L1031_ *) % 10.36/10.54 assert (zenon_L1032_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((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)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (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 (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1ef zenon_H110 zenon_H191 zenon_Haf zenon_H157 zenon_H145 zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_H2a zenon_H12f zenon_H64 zenon_H187 zenon_H27 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H35 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H77 zenon_Hd3 zenon_H56 zenon_Hd2 zenon_H1af zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H200 zenon_H1f zenon_H11d zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H128 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_H237 zenon_Hdd zenon_H18d zenon_H1ba zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_He3 zenon_Hda zenon_Hb0 zenon_H3c zenon_H7d zenon_H7a zenon_H143 zenon_Hf8 zenon_H97. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_L944_); trivial. % 10.36/10.54 apply (zenon_L1031_); trivial. % 10.36/10.54 apply (zenon_L213_); trivial. % 10.36/10.54 (* end of lemma zenon_L1032_ *) % 10.36/10.54 assert (zenon_L1033_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (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 (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((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 (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H97 zenon_H18d zenon_H1ba zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_He3 zenon_Hda zenon_Hb0 zenon_H3c zenon_H7d zenon_H7a zenon_Hdd zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H128 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_H1fb zenon_Hce zenon_H8c zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H16f zenon_H233 zenon_H11d zenon_H1f zenon_H200 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1af zenon_Hd2 zenon_Hd3 zenon_H77 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H35 zenon_H181 zenon_H42 zenon_H4c zenon_H95 zenon_H27 zenon_H187 zenon_H64 zenon_H12f zenon_Hc5 zenon_Hc7 zenon_H155 zenon_H5e zenon_H145 zenon_H157 zenon_Haf zenon_H191 zenon_H110 zenon_H1ef zenon_H17a. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.54 apply (zenon_L965_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_L1032_); trivial. % 10.36/10.54 apply (zenon_L937_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.54 apply (zenon_L78_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.54 exact (zenon_Hc7 zenon_H3a). % 10.36/10.54 apply (zenon_L964_); trivial. % 10.36/10.54 (* end of lemma zenon_L1033_ *) % 10.36/10.54 assert (zenon_L1034_ : ((~((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)))) -> (~((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H151 zenon_Hbb zenon_H18d zenon_Hbc zenon_He3 zenon_H12f zenon_H2a zenon_He8 zenon_Hc5 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H155 zenon_H7d zenon_H86 zenon_H145 zenon_H143 zenon_Hf8. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_L992_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_L41_); trivial. % 10.36/10.54 (* end of lemma zenon_L1034_ *) % 10.36/10.54 assert (zenon_L1035_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((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 (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (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 (e3) (e2)) = (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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (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) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1ef zenon_H150 zenon_Hbb zenon_H151 zenon_H18d zenon_Hb0 zenon_Hda zenon_He3 zenon_H95 zenon_H4c zenon_H35 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H5e zenon_H2a zenon_H1ba zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_H12f zenon_H1b7 zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H238 zenon_H56 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H7d zenon_H7a zenon_H64 zenon_H143 zenon_Hf8 zenon_H1b4 zenon_H97 zenon_Hdd zenon_Hce zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H42 zenon_H27 zenon_H237 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H128 zenon_H112 zenon_H1fb zenon_H8c zenon_Hab zenon_H168 zenon_H204 zenon_H195 zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_L991_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_L1034_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_L993_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.54 exact (zenon_H56 zenon_H2c). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.54 apply (zenon_L196_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.54 apply (zenon_L201_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.54 exact (zenon_H56 zenon_H2c). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.54 apply (zenon_L1030_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.54 apply (zenon_L995_); trivial. % 10.36/10.54 apply (zenon_L139_); trivial. % 10.36/10.54 apply (zenon_L203_); trivial. % 10.36/10.54 apply (zenon_L952_); trivial. % 10.36/10.54 apply (zenon_L78_); trivial. % 10.36/10.54 apply (zenon_L1031_); trivial. % 10.36/10.54 apply (zenon_L213_); trivial. % 10.36/10.54 (* end of lemma zenon_L1035_ *) % 10.36/10.54 assert (zenon_L1036_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (~((e0) = (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))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (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 (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (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 (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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_Hab zenon_H8c zenon_H1fb zenon_H112 zenon_H128 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H44 zenon_Hc0 zenon_He7 zenon_H53 zenon_H42 zenon_H27 zenon_H97 zenon_Hdd zenon_Hce zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H1b4 zenon_H18d zenon_Hb0 zenon_Hda zenon_He3 zenon_H95 zenon_H4c zenon_H35 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H5e zenon_H1ba zenon_H239 zenon_H157 zenon_H145 zenon_H155 zenon_H12f zenon_H1b7 zenon_H181 zenon_H187 zenon_H58 zenon_Hd2 zenon_H238 zenon_Hd3 zenon_H77 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_H7d zenon_H7a zenon_H64 zenon_H151 zenon_Hbb zenon_H150 zenon_H1ef zenon_H17a zenon_H191 zenon_H1ea. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.54 apply (zenon_L1004_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_L1035_); trivial. % 10.36/10.54 apply (zenon_L937_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.54 apply (zenon_L78_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.54 exact (zenon_Hc7 zenon_H3a). % 10.36/10.54 apply (zenon_L1003_); trivial. % 10.36/10.54 (* end of lemma zenon_L1036_ *) % 10.36/10.54 assert (zenon_L1037_ : (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H25 zenon_H1e2 zenon_H27 zenon_H97 zenon_H28 zenon_H42 zenon_H95 zenon_H4c zenon_H77 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H23c zenon_H18a zenon_H187 zenon_H15a zenon_H198 zenon_H17c zenon_Hd0 zenon_H84 zenon_H86. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.54 exact (zenon_H25 zenon_H2a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.54 apply (zenon_L962_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L426_); trivial. % 10.36/10.54 (* end of lemma zenon_L1037_ *) % 10.36/10.54 assert (zenon_L1038_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H67 zenon_H23c zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_Hc0 zenon_H184 zenon_H90 zenon_H110 zenon_H5e zenon_H200 zenon_H64 zenon_H7a zenon_H3c zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H35 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H44 zenon_H53 zenon_Hb0 zenon_Hc7 zenon_H1fb zenon_Hc5 zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_Hd2 zenon_H156 zenon_H4a zenon_H181 zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H77 zenon_H4c zenon_H95 zenon_H42 zenon_H84 zenon_H97 zenon_H68 zenon_H1e2. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_L963_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 (* end of lemma zenon_L1038_ *) % 10.36/10.54 assert (zenon_L1039_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1ef zenon_H191 zenon_Haf zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H25 zenon_H1e2 zenon_H97 zenon_H23c zenon_H17c zenon_H18a zenon_H67. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_L958_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.54 exact (zenon_H25 zenon_H2a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.54 apply (zenon_L961_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L959_); trivial. % 10.36/10.54 apply (zenon_L1037_); trivial. % 10.36/10.54 apply (zenon_L960_); trivial. % 10.36/10.54 exact (zenon_H23c zenon_H51). % 10.36/10.54 apply (zenon_L1038_); trivial. % 10.36/10.54 (* end of lemma zenon_L1039_ *) % 10.36/10.54 assert (zenon_L1040_ : (((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 (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H238 zenon_H35 zenon_H6a zenon_H192 zenon_H101 zenon_H5e zenon_H62 zenon_H187. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.54 apply (zenon_L238_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.54 exact (zenon_H192 zenon_H1d). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_L71_); trivial. % 10.36/10.54 apply (zenon_L202_); trivial. % 10.36/10.54 (* end of lemma zenon_L1040_ *) % 10.36/10.54 assert (zenon_L1041_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hb0 zenon_H2a zenon_H1ba zenon_H77 zenon_H5e zenon_Hb1 zenon_H17c zenon_H87. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.36/10.54 apply (zenon_L216_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.36/10.54 apply (zenon_L22_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.36/10.54 exact (zenon_Hb1 zenon_Hb7). % 10.36/10.54 apply (zenon_L270_); trivial. % 10.36/10.54 (* end of lemma zenon_L1041_ *) % 10.36/10.54 assert (zenon_L1042_ : (((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) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H145 zenon_H12f zenon_He8 zenon_H187 zenon_H62 zenon_H192 zenon_H6a zenon_H35 zenon_H238 zenon_Hb0 zenon_H2a zenon_H1ba zenon_H77 zenon_H5e zenon_Hb1 zenon_H17c. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.36/10.54 apply (zenon_L100_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.36/10.54 exact (zenon_He8 zenon_Heb). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.36/10.54 apply (zenon_L1040_); trivial. % 10.36/10.54 apply (zenon_L1041_); trivial. % 10.36/10.54 (* end of lemma zenon_L1042_ *) % 10.36/10.54 assert (zenon_L1043_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H238 zenon_H6c zenon_H192 zenon_H101 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H1ba zenon_H53 zenon_Hb0 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H95 zenon_H4c zenon_H17a zenon_H84 zenon_Hc0 zenon_H5e zenon_He8 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.54 apply (zenon_L236_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.54 exact (zenon_H192 zenon_H1d). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.54 apply (zenon_L71_); trivial. % 10.36/10.54 apply (zenon_L956_); trivial. % 10.36/10.54 (* end of lemma zenon_L1043_ *) % 10.36/10.54 assert (zenon_L1044_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e1)) = (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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (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) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((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 (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((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) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hdd zenon_H62 zenon_H28 zenon_H17c zenon_Hb1 zenon_H5e zenon_H77 zenon_H1ba zenon_H2a zenon_Hb0 zenon_H238 zenon_H192 zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H7a zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H198 zenon_H8c zenon_Hda zenon_Hce zenon_H157 zenon_H53 zenon_H1fb zenon_H112 zenon_H150 zenon_H86 zenon_Hbb zenon_H151 zenon_H145 zenon_H7d zenon_H128 zenon_H155 zenon_H12f zenon_H205 zenon_H18d zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_H64 zenon_H187 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_Hd3 zenon_H56 zenon_H27 zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_He8 zenon_H44 zenon_H35 zenon_H181 zenon_H42 zenon_Hd2 zenon_H4c zenon_H76 zenon_H95. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.54 exact (zenon_H27 zenon_H32). % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.54 apply (zenon_L1042_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.54 apply (zenon_L47_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.36/10.54 exact (zenon_H28 zenon_H31). % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.36/10.54 apply (zenon_L100_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.36/10.54 exact (zenon_He8 zenon_Heb). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.36/10.54 apply (zenon_L1043_); trivial. % 10.36/10.54 apply (zenon_L1041_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_L21_); trivial. % 10.36/10.54 apply (zenon_L51_); trivial. % 10.36/10.54 (* end of lemma zenon_L1044_ *) % 10.36/10.54 assert (zenon_L1045_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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))) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (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)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((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 (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e2)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1ef zenon_H18d zenon_H1ba zenon_H2a zenon_H5e zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H35 zenon_H4c zenon_H95 zenon_He3 zenon_Hda zenon_Hb0 zenon_H7d zenon_H7a zenon_H64 zenon_Hdd zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H110 zenon_H200 zenon_H1f zenon_H11d zenon_H1af zenon_H233 zenon_H16f zenon_H1bc zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H157 zenon_H53 zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H128 zenon_H155 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_He7 zenon_H17a zenon_H84 zenon_Hc0 zenon_H44 zenon_H181 zenon_H42 zenon_Hd2 zenon_H12f zenon_H238 zenon_H187 zenon_H145 zenon_H27 zenon_H1b4 zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H56 zenon_H143. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.54 exact (zenon_H56 zenon_H2c). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.54 apply (zenon_L196_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.54 apply (zenon_L103_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.54 exact (zenon_H56 zenon_H2c). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.54 apply (zenon_L947_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.54 apply (zenon_L1044_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.54 exact (zenon_H27 zenon_H32). % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.54 apply (zenon_L1042_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.54 apply (zenon_L948_); trivial. % 10.36/10.54 apply (zenon_L211_); trivial. % 10.36/10.54 exact (zenon_H143 zenon_Hed). % 10.36/10.54 apply (zenon_L1034_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.54 exact (zenon_H56 zenon_H2c). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.54 apply (zenon_L196_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.54 apply (zenon_L201_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.54 exact (zenon_H56 zenon_H2c). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.54 apply (zenon_L1001_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.54 apply (zenon_L1044_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.54 exact (zenon_H27 zenon_H32). % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.54 apply (zenon_L1042_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.54 apply (zenon_L44_); trivial. % 10.36/10.54 apply (zenon_L211_); trivial. % 10.36/10.54 apply (zenon_L203_); trivial. % 10.36/10.54 apply (zenon_L952_); trivial. % 10.36/10.54 apply (zenon_L78_); trivial. % 10.36/10.54 apply (zenon_L1001_); trivial. % 10.36/10.54 apply (zenon_L213_); trivial. % 10.36/10.55 (* end of lemma zenon_L1045_ *) % 10.36/10.55 assert (zenon_L1046_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((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)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((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 (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((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)) = (op (e0) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1b4 zenon_H238 zenon_H1ef zenon_H110 zenon_H191 zenon_Haf zenon_H157 zenon_H145 zenon_H5e zenon_H155 zenon_Hc7 zenon_Hc5 zenon_H12f zenon_H64 zenon_H187 zenon_H95 zenon_H4c zenon_H42 zenon_H181 zenon_H35 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H77 zenon_Hd3 zenon_Hd2 zenon_H1af zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H12c zenon_H173 zenon_H174 zenon_H11b zenon_H184 zenon_H90 zenon_H200 zenon_H1f zenon_H11d zenon_H233 zenon_H16f zenon_H195 zenon_H204 zenon_H168 zenon_H58 zenon_Hab zenon_H8c zenon_Hce zenon_H1fb zenon_H112 zenon_H150 zenon_Hbb zenon_H151 zenon_H128 zenon_H205 zenon_H156 zenon_H4a zenon_H165 zenon_H26 zenon_Hf8 zenon_H237 zenon_Hdd zenon_H7a zenon_H7d zenon_H3c zenon_Hb0 zenon_Hda zenon_He3 zenon_H18a zenon_H86 zenon_H198 zenon_H17c zenon_H1e2 zenon_H1ba zenon_H18d zenon_H97 zenon_H23c zenon_H67 zenon_H17a. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_L954_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L937_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.55 apply (zenon_L78_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.55 exact (zenon_Hc7 zenon_H3a). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.55 apply (zenon_L1039_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.55 apply (zenon_L958_); trivial. % 10.36/10.55 apply (zenon_L1001_); trivial. % 10.36/10.55 apply (zenon_L960_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L1038_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_L1032_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L937_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.55 apply (zenon_L78_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.55 exact (zenon_Hc7 zenon_H3a). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.55 apply (zenon_L1039_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_L1045_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L1038_); trivial. % 10.36/10.55 (* end of lemma zenon_L1046_ *) % 10.36/10.55 assert (zenon_L1047_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1b7 zenon_He3 zenon_H1b4 zenon_H67 zenon_H1e2 zenon_H97 zenon_H84 zenon_H42 zenon_H95 zenon_H4c zenon_H77 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H181 zenon_H4a zenon_H156 zenon_Hd2 zenon_H18d zenon_H205 zenon_H12f zenon_H155 zenon_H128 zenon_H7d zenon_H145 zenon_H151 zenon_Hbb zenon_H86 zenon_H150 zenon_H112 zenon_Hc5 zenon_H1fb zenon_Hc7 zenon_Hb0 zenon_H53 zenon_H44 zenon_H1ba zenon_H157 zenon_Hce zenon_Hda zenon_H8c zenon_H35 zenon_H198 zenon_Hab zenon_H58 zenon_H168 zenon_H204 zenon_H195 zenon_H1bc zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H3c zenon_H7a zenon_H64 zenon_H200 zenon_H5e zenon_H110 zenon_H90 zenon_H184 zenon_Hc0 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H23c zenon_H238 zenon_H17a zenon_He7 zenon_Hd3 zenon_H239 zenon_H18a zenon_H17c zenon_H187 zenon_H1ef. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.36/10.55 exact (zenon_H25 zenon_H2a). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.36/10.55 apply (zenon_L963_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L999_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L1038_); trivial. % 10.36/10.55 apply (zenon_L1002_); trivial. % 10.36/10.55 (* end of lemma zenon_L1047_ *) % 10.36/10.55 assert (zenon_L1048_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (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))) -> (~((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) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((~((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 (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 (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (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))))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/(~((op (e3) (e2)) = (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (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) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1ef zenon_H150 zenon_Hbb zenon_H151 zenon_H64 zenon_H7a zenon_H7d zenon_H3c zenon_Hc7 zenon_Hc5 zenon_H77 zenon_Hd3 zenon_H238 zenon_Hd2 zenon_H58 zenon_H187 zenon_H181 zenon_H1b7 zenon_H12f zenon_H155 zenon_H145 zenon_H157 zenon_H239 zenon_H1ba zenon_H5e zenon_H1e2 zenon_H17c zenon_H198 zenon_H86 zenon_H18a zenon_H35 zenon_H4c zenon_H95 zenon_He3 zenon_Hda zenon_Hb0 zenon_H18d zenon_H1b4 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_Hce zenon_Hdd zenon_H97 zenon_H42 zenon_H53 zenon_He7 zenon_Hc0 zenon_H44 zenon_H237 zenon_Hf8 zenon_H26 zenon_H165 zenon_H4a zenon_H156 zenon_H205 zenon_H128 zenon_H112 zenon_H1fb zenon_H8c zenon_Hab zenon_H168 zenon_H204 zenon_H195 zenon_H16f zenon_H233 zenon_H1af zenon_H11d zenon_H1f zenon_H200 zenon_H110 zenon_H90 zenon_H184 zenon_H11b zenon_H174 zenon_H173 zenon_H12c zenon_H23c zenon_H67 zenon_H17a. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H7f | zenon_intro zenon_H143 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_L996_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L937_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.55 apply (zenon_L78_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.55 exact (zenon_Hc7 zenon_H3a). % 10.36/10.55 apply (zenon_L1047_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.55 apply (zenon_L1035_); trivial. % 10.36/10.55 exact (zenon_H23c zenon_H51). % 10.36/10.55 apply (zenon_L937_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.55 apply (zenon_L78_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.55 exact (zenon_Hc7 zenon_H3a). % 10.36/10.55 apply (zenon_L1047_); trivial. % 10.36/10.55 (* end of lemma zenon_L1048_ *) % 10.36/10.55 assert (zenon_L1049_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((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 (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.55 do 0 intro. intros zenon_H108 zenon_Hc8 zenon_Hc7 zenon_H3c zenon_Hc5 zenon_H4c zenon_H91 zenon_H5e zenon_H62 zenon_H1cb zenon_H103 zenon_Hb1 zenon_H53 zenon_Hed. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 10.36/10.55 apply (zenon_L129_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 10.36/10.55 apply (zenon_L230_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 10.36/10.55 exact (zenon_Hb1 zenon_Hb7). % 10.36/10.55 apply (zenon_L73_); trivial. % 10.36/10.55 (* end of lemma zenon_L1049_ *) % 10.36/10.55 assert (zenon_L1050_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H177 zenon_H168 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H91 zenon_H103 zenon_H4c zenon_H5e zenon_H1cb zenon_H53 zenon_H108 zenon_Hb1 zenon_H3c zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_Hf8. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.55 apply (zenon_L56_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.55 exact (zenon_H56 zenon_H2c). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.55 apply (zenon_L1_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.55 apply (zenon_L103_); trivial. % 10.36/10.55 apply (zenon_L1049_); trivial. % 10.36/10.55 apply (zenon_L160_); trivial. % 10.36/10.55 (* end of lemma zenon_L1050_ *) % 10.36/10.55 assert (zenon_L1051_ : (((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 (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.36/10.55 do 0 intro. intros zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_Haf zenon_H78 zenon_H44 zenon_Hf2 zenon_H35. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.36/10.55 apply (zenon_L331_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.36/10.55 exact (zenon_Haf zenon_Hb4). % 10.36/10.55 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.36/10.55 apply (zenon_L57_); trivial. % 10.36/10.55 apply (zenon_L63_); trivial. % 10.36/10.55 (* end of lemma zenon_L1051_ *) % 10.36/10.55 assert (zenon_L1052_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (~((e0) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.36/10.55 do 0 intro. intros zenon_He7 zenon_H35 zenon_H44 zenon_Haf zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hc1 zenon_Hde zenon_H5e zenon_Hf2. % 10.36/10.55 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.36/10.55 apply (zenon_L323_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.36/10.55 exact (zenon_He8 zenon_Heb). % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.36/10.55 apply (zenon_L1051_); trivial. % 10.36/10.55 apply (zenon_L206_); trivial. % 10.36/10.55 (* end of lemma zenon_L1052_ *) % 10.36/10.55 assert (zenon_L1053_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (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). % 10.36/10.55 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f0 zenon_Hf2 zenon_H6f zenon_H100 zenon_H42 zenon_H27 zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H3c zenon_H3a zenon_H35. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.36/10.55 exact (zenon_H56 zenon_H2c). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.36/10.55 apply (zenon_L327_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.36/10.55 apply (zenon_L228_); trivial. % 10.36/10.55 apply (zenon_L610_); trivial. % 10.36/10.55 (* end of lemma zenon_L1053_ *) % 10.36/10.55 assert (zenon_L1054_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1ef zenon_H169 zenon_He7 zenon_H5e zenon_H44 zenon_H35 zenon_Hf2 zenon_Hde zenon_He8 zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H27 zenon_H3c zenon_H3a zenon_H42 zenon_H6f zenon_H1f0 zenon_H56 zenon_H1ea. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.55 apply (zenon_L1052_); trivial. % 10.36/10.55 apply (zenon_L1053_); trivial. % 10.36/10.55 apply (zenon_L140_); trivial. % 10.36/10.55 (* end of lemma zenon_L1054_ *) % 10.36/10.55 assert (zenon_L1055_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.36/10.55 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H35 zenon_H15a zenon_Hc6 zenon_H3a zenon_H14d zenon_H44 zenon_H5e zenon_H80 zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_H16b zenon_H8d. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.55 exact (zenon_H27 zenon_H32). % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.55 apply (zenon_L238_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.55 apply (zenon_L321_); trivial. % 10.36/10.55 apply (zenon_L209_); trivial. % 10.36/10.55 (* end of lemma zenon_L1055_ *) % 10.36/10.55 assert (zenon_L1056_ : ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H23d zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H135 zenon_H144 zenon_H12f zenon_H95 zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.36/10.55 apply (zenon_L158_); trivial. % 10.36/10.55 apply (zenon_L158_); trivial. % 10.36/10.55 (* end of lemma zenon_L1056_ *) % 10.36/10.55 assert (zenon_L1057_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H177 zenon_Hbc zenon_Hf2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H23d zenon_H7f. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.36/10.55 apply (zenon_L51_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.36/10.55 apply (zenon_L63_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.36/10.55 apply (zenon_L1056_); trivial. % 10.36/10.55 exact (zenon_H7f zenon_H85). % 10.36/10.55 (* end of lemma zenon_L1057_ *) % 10.36/10.55 assert (zenon_L1058_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1dd zenon_H95 zenon_Hbc zenon_H35 zenon_Hf2 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.55 apply (zenon_L1057_); trivial. % 10.36/10.55 apply (zenon_L267_); trivial. % 10.36/10.55 (* end of lemma zenon_L1058_ *) % 10.36/10.55 assert (zenon_L1059_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_H27 zenon_H35 zenon_H15a zenon_Hc6 zenon_H3a zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_Hf2 zenon_H5e zenon_H44 zenon_Hdd. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.36/10.55 apply (zenon_L1055_); trivial. % 10.36/10.55 apply (zenon_L1058_); trivial. % 10.36/10.55 (* end of lemma zenon_L1059_ *) % 10.36/10.55 assert (zenon_L1060_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (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) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.36/10.55 do 0 intro. intros zenon_Hdd zenon_H16b zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H56 zenon_H1f0 zenon_H6f zenon_H42 zenon_H3a zenon_H3c zenon_H27 zenon_H64 zenon_H191 zenon_Hc1 zenon_H1f zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_H169 zenon_H1ef. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.55 apply (zenon_L1054_); trivial. % 10.36/10.55 apply (zenon_L1059_); trivial. % 10.36/10.55 (* end of lemma zenon_L1060_ *) % 10.36/10.55 assert (zenon_L1061_ : (~((op (e3) (e1)) = (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) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> False). % 10.36/10.55 do 0 intro. intros zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H27 zenon_H3c zenon_H3a zenon_H42 zenon_H6f zenon_H1f0 zenon_H56 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.55 apply (zenon_L56_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf0 | zenon_intro zenon_Hf6 ]. % 10.36/10.55 apply (zenon_L62_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf2 | zenon_intro zenon_Hf7 ]. % 10.36/10.55 apply (zenon_L1060_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H83 ]. % 10.36/10.55 apply (zenon_L64_); trivial. % 10.36/10.55 exact (zenon_H7e zenon_H83). % 10.36/10.55 apply (zenon_L160_); trivial. % 10.36/10.55 (* end of lemma zenon_L1061_ *) % 10.36/10.55 assert (zenon_L1062_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_Hf8 zenon_H6f zenon_H51 zenon_H159 zenon_H15a zenon_H155 zenon_H3a zenon_H1e6 zenon_H1f8 zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.55 apply (zenon_L56_); trivial. % 10.36/10.55 apply (zenon_L490_); trivial. % 10.36/10.55 (* end of lemma zenon_L1062_ *) % 10.36/10.55 assert (zenon_L1063_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1f8 zenon_H1e6 zenon_H3a zenon_H155 zenon_H15a zenon_H159 zenon_H51 zenon_H6f zenon_Hf8. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.55 apply (zenon_L1062_); trivial. % 10.36/10.55 apply (zenon_L160_); trivial. % 10.36/10.55 (* end of lemma zenon_L1063_ *) % 10.36/10.55 assert (zenon_L1064_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H156 zenon_H3a zenon_Hc6 zenon_Hfd zenon_H68 zenon_H5e zenon_H100 zenon_H1dd zenon_He4 zenon_H108. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.55 apply (zenon_L509_); trivial. % 10.36/10.55 apply (zenon_L321_); trivial. % 10.36/10.55 (* end of lemma zenon_L1064_ *) % 10.36/10.55 assert (zenon_L1065_ : (((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 (e2) (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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_H97 zenon_H28 zenon_H53 zenon_H68 zenon_H10b zenon_Hed zenon_H95. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.36/10.55 exact (zenon_H27 zenon_H32). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.36/10.55 apply (zenon_L16_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.36/10.55 apply (zenon_L5_); trivial. % 10.36/10.55 apply (zenon_L76_); trivial. % 10.36/10.55 (* end of lemma zenon_L1065_ *) % 10.36/10.55 assert (zenon_L1066_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_Hf8 zenon_H27 zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H28 zenon_H42 zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.56 apply (zenon_L56_); trivial. % 10.36/10.56 apply (zenon_L1065_); trivial. % 10.36/10.56 (* end of lemma zenon_L1066_ *) % 10.36/10.56 assert (zenon_L1067_ : (((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). % 10.36/10.56 do 0 intro. intros zenon_H118 zenon_H68 zenon_Hd3 zenon_H1d zenon_H110 zenon_H216 zenon_H3a zenon_Hbd zenon_H114. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H78 | zenon_intro zenon_H119 ]. % 10.36/10.56 apply (zenon_L46_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H77 | zenon_intro zenon_H11a ]. % 10.36/10.56 apply (zenon_L78_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hb9 ]. % 10.36/10.56 apply (zenon_L500_); trivial. % 10.36/10.56 apply (zenon_L80_); trivial. % 10.36/10.56 (* end of lemma zenon_L1067_ *) % 10.36/10.56 assert (zenon_L1068_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H151 zenon_Hd3 zenon_H110 zenon_H1d zenon_H216 zenon_H114 zenon_H118 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H42 zenon_H28 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3a zenon_H3c zenon_H68 zenon_H44 zenon_H27 zenon_Hf8. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.56 apply (zenon_L1066_); trivial. % 10.36/10.56 apply (zenon_L1067_); trivial. % 10.36/10.56 (* end of lemma zenon_L1068_ *) % 10.36/10.56 assert (zenon_L1069_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1ef zenon_Hf8 zenon_H27 zenon_H44 zenon_H3c zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H28 zenon_H42 zenon_He3 zenon_H80 zenon_H7d zenon_H118 zenon_H114 zenon_H216 zenon_H110 zenon_Hd3 zenon_H151 zenon_H191 zenon_Hc1 zenon_H68 zenon_H1f zenon_H156 zenon_H3a zenon_Hc6 zenon_Hfd zenon_H5e zenon_H1dd zenon_He4 zenon_H108 zenon_H1ea. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.56 apply (zenon_L323_); trivial. % 10.36/10.56 apply (zenon_L1064_); trivial. % 10.36/10.56 apply (zenon_L1068_); trivial. % 10.36/10.56 (* end of lemma zenon_L1069_ *) % 10.36/10.56 assert (zenon_L1070_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H67 zenon_H1ea zenon_H108 zenon_He4 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H3a zenon_H156 zenon_H1f zenon_H68 zenon_Hc1 zenon_H191 zenon_H151 zenon_Hd3 zenon_H110 zenon_H216 zenon_H114 zenon_H118 zenon_H7d zenon_H80 zenon_He3 zenon_H42 zenon_H28 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3c zenon_H44 zenon_Hf8 zenon_H1ef. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.56 apply (zenon_L1069_); trivial. % 10.36/10.56 apply (zenon_L69_); trivial. % 10.36/10.56 (* end of lemma zenon_L1070_ *) % 10.36/10.56 assert (zenon_L1071_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H216 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H3c zenon_H3a zenon_H42 zenon_H6f zenon_H1f0 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e zenon_H97 zenon_H1e6 zenon_Hc0 zenon_H1f8 zenon_H67. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.56 apply (zenon_L1061_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.56 apply (zenon_L676_); trivial. % 10.36/10.56 apply (zenon_L1063_); trivial. % 10.36/10.56 apply (zenon_L1070_); trivial. % 10.36/10.56 (* end of lemma zenon_L1071_ *) % 10.36/10.56 assert (zenon_L1072_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((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 (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H35 zenon_Hed zenon_H1dd zenon_H95 zenon_H15a zenon_H4c zenon_H28 zenon_Hda zenon_He4 zenon_H44. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.36/10.56 exact (zenon_H27 zenon_H32). % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.36/10.56 apply (zenon_L238_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.36/10.56 apply (zenon_L306_); trivial. % 10.36/10.56 apply (zenon_L99_); trivial. % 10.36/10.56 (* end of lemma zenon_L1072_ *) % 10.36/10.56 assert (zenon_L1073_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (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))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1b4 zenon_H5e zenon_Hcf zenon_H27 zenon_H35 zenon_Hda zenon_H1dd zenon_H95 zenon_H4c zenon_H28 zenon_H44 zenon_Hdd zenon_H56 zenon_Hf8. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.56 apply (zenon_L56_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.56 exact (zenon_H56 zenon_H2c). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.56 apply (zenon_L1072_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.56 apply (zenon_L47_); trivial. % 10.36/10.56 apply (zenon_L62_); trivial. % 10.36/10.56 apply (zenon_L160_); trivial. % 10.36/10.56 (* end of lemma zenon_L1073_ *) % 10.36/10.56 assert (zenon_L1074_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_He7 zenon_He8 zenon_Hc1 zenon_Hc0 zenon_H177 zenon_H168 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H103 zenon_H4c zenon_H5e zenon_H1cb zenon_H53 zenon_H108 zenon_Hb1 zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_Hf8 zenon_H1dd zenon_H51 zenon_H1f8 zenon_H1e6 zenon_H6f. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.36/10.56 apply (zenon_L1050_); trivial. % 10.36/10.56 apply (zenon_L675_); trivial. % 10.36/10.56 apply (zenon_L187_); trivial. % 10.36/10.56 (* end of lemma zenon_L1074_ *) % 10.36/10.56 assert (zenon_L1075_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (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) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H195 zenon_He7 zenon_Hc1 zenon_Hc0 zenon_H177 zenon_H168 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H103 zenon_H4c zenon_H5e zenon_H1cb zenon_H53 zenon_H108 zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_Hf8 zenon_H1dd zenon_H51 zenon_H1f8 zenon_H1e6 zenon_H6f zenon_Hc6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.56 apply (zenon_L1074_); trivial. % 10.36/10.56 apply (zenon_L670_); trivial. % 10.36/10.56 apply (zenon_L325_); trivial. % 10.36/10.56 (* end of lemma zenon_L1075_ *) % 10.36/10.56 assert (zenon_L1076_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H191 zenon_H195 zenon_H1ef zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H64 zenon_H16e zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_He7 zenon_Hbb zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_H68 zenon_H44 zenon_Hf8 zenon_H1d zenon_H1ea. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.56 apply (zenon_L644_); trivial. % 10.36/10.56 apply (zenon_L439_); trivial. % 10.36/10.56 (* end of lemma zenon_L1076_ *) % 10.36/10.56 assert (zenon_L1077_ : (((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)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (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) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((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 (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1b4 zenon_H1cb zenon_H195 zenon_H67 zenon_H1f8 zenon_Hc0 zenon_H1e6 zenon_H97 zenon_H5e zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H1f0 zenon_H6f zenon_H42 zenon_H3c zenon_H64 zenon_H191 zenon_Hc1 zenon_H1f zenon_Hde zenon_H35 zenon_H44 zenon_He7 zenon_H169 zenon_H1ef zenon_He3 zenon_He4 zenon_H7d zenon_Hec zenon_H216 zenon_H80. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.56 apply (zenon_L111_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.36/10.56 apply (zenon_L1050_); trivial. % 10.36/10.56 apply (zenon_L1071_); trivial. % 10.36/10.56 apply (zenon_L187_); trivial. % 10.36/10.56 apply (zenon_L1073_); trivial. % 10.36/10.56 apply (zenon_L325_); trivial. % 10.36/10.56 apply (zenon_L1075_); trivial. % 10.36/10.56 apply (zenon_L1076_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.56 apply (zenon_L1071_); trivial. % 10.36/10.56 exact (zenon_H80 zenon_H84). % 10.36/10.56 (* end of lemma zenon_L1077_ *) % 10.36/10.56 assert (zenon_L1078_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (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))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((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) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hf8 zenon_H56 zenon_H1f zenon_H1d zenon_Hc5 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H108 zenon_H53 zenon_H1cb zenon_H5e zenon_H4c zenon_H103 zenon_H91 zenon_H64 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H44 zenon_H95 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H35 zenon_H168 zenon_H177. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.56 apply (zenon_L1050_); trivial. % 10.36/10.56 exact (zenon_H127 zenon_Hd0). % 10.36/10.56 (* end of lemma zenon_L1078_ *) % 10.36/10.56 assert (zenon_L1079_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((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 (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H5e zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H56 zenon_H1f0 zenon_H6f zenon_H42 zenon_H3a zenon_H3c zenon_H27 zenon_H64 zenon_H191 zenon_Hc1 zenon_H1f zenon_Hde zenon_H35 zenon_H44 zenon_He7 zenon_H169 zenon_H1ef zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.56 apply (zenon_L1061_); trivial. % 10.36/10.56 exact (zenon_H127 zenon_Hd0). % 10.36/10.56 (* end of lemma zenon_L1079_ *) % 10.36/10.56 assert (zenon_L1080_ : ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H3a zenon_Hc6 zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H28 zenon_He7 zenon_Hbb zenon_H192 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hfd zenon_H1dd zenon_H108 zenon_H10b zenon_H4c zenon_H97 zenon_H51 zenon_H5e zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H56 zenon_Hf8 zenon_H127 zenon_Hd2. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.56 apply (zenon_L662_); trivial. % 10.36/10.56 exact (zenon_H127 zenon_Hd0). % 10.36/10.56 apply (zenon_L321_); trivial. % 10.36/10.56 (* end of lemma zenon_L1080_ *) % 10.36/10.56 assert (zenon_L1081_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (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) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (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))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((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 (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (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 (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1ef zenon_H6f zenon_H1f8 zenon_Hd2 zenon_H127 zenon_Hf8 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_He7 zenon_Hbb zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_H44 zenon_H1f zenon_H191 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_H173 zenon_H16e zenon_H64 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_H3a zenon_Hc6 zenon_H1dd zenon_H97 zenon_H51 zenon_H1f0 zenon_H1e6 zenon_H56 zenon_H1ea. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.56 apply (zenon_L668_); trivial. % 10.36/10.56 exact (zenon_H127 zenon_Hd0). % 10.36/10.56 apply (zenon_L1080_); trivial. % 10.36/10.56 apply (zenon_L675_); trivial. % 10.36/10.56 (* end of lemma zenon_L1081_ *) % 10.36/10.56 assert (zenon_L1082_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (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) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H158 zenon_H152 zenon_H108 zenon_H44 zenon_H165 zenon_H135 zenon_H95 zenon_H4c zenon_H159 zenon_H15a zenon_H35 zenon_H103 zenon_H155 zenon_H3c zenon_H91 zenon_Hc5 zenon_H127 zenon_Hd2. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.57 apply (zenon_L136_); trivial. % 10.36/10.57 exact (zenon_H127 zenon_Hd0). % 10.36/10.57 apply (zenon_L116_); trivial. % 10.36/10.57 (* end of lemma zenon_L1082_ *) % 10.36/10.57 assert (zenon_L1083_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (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) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hf8 zenon_Hec zenon_H44 zenon_He4 zenon_H95 zenon_Hbd zenon_H158 zenon_H152 zenon_H108 zenon_H165 zenon_H4c zenon_H159 zenon_H15a zenon_H35 zenon_H103 zenon_H155 zenon_H3c zenon_H91 zenon_Hc5 zenon_H127 zenon_Hd2 zenon_H177. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.36/10.57 apply (zenon_L99_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.36/10.57 apply (zenon_L50_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.36/10.57 apply (zenon_L1082_); trivial. % 10.36/10.57 exact (zenon_H7f zenon_H85). % 10.36/10.57 apply (zenon_L60_); trivial. % 10.36/10.57 (* end of lemma zenon_L1083_ *) % 10.36/10.57 assert (zenon_L1084_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H157 zenon_H216 zenon_Hf8 zenon_H6f zenon_H51 zenon_H159 zenon_H15a zenon_H155 zenon_H3a zenon_H1e6 zenon_H1f8 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H44 zenon_H95 zenon_H158 zenon_H152 zenon_H108 zenon_H165 zenon_H4c zenon_H35 zenon_H103 zenon_H3c zenon_Hc5 zenon_H127 zenon_Hd2 zenon_H177 zenon_H151. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.57 apply (zenon_L1062_); trivial. % 10.36/10.57 apply (zenon_L1083_); trivial. % 10.36/10.57 apply (zenon_L500_); trivial. % 10.36/10.57 (* end of lemma zenon_L1084_ *) % 10.36/10.57 assert (zenon_L1085_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (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 (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H5e zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H1f0 zenon_H6f zenon_H42 zenon_H3a zenon_H3c zenon_H64 zenon_H191 zenon_Hc1 zenon_H1f zenon_Hde zenon_H35 zenon_H44 zenon_He7 zenon_H169 zenon_H1ef zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H216 zenon_H1e6 zenon_H97 zenon_Hc0 zenon_H1f8 zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.57 apply (zenon_L1079_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.57 apply (zenon_L1081_); trivial. % 10.36/10.57 apply (zenon_L1084_); trivial. % 10.36/10.57 apply (zenon_L1070_); trivial. % 10.36/10.57 (* end of lemma zenon_L1085_ *) % 10.36/10.57 assert (zenon_L1086_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((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 (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hf8 zenon_He7 zenon_Hbb zenon_Hb8 zenon_H44 zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.57 apply (zenon_L187_); trivial. % 10.36/10.57 exact (zenon_H127 zenon_Hd0). % 10.36/10.57 (* end of lemma zenon_L1086_ *) % 10.36/10.57 assert (zenon_L1087_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (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))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hf8 zenon_H56 zenon_Hdd zenon_H44 zenon_H28 zenon_H4c zenon_H95 zenon_H1dd zenon_Hda zenon_H35 zenon_H27 zenon_Hcf zenon_H5e zenon_H1b4 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.57 apply (zenon_L1073_); trivial. % 10.36/10.57 exact (zenon_H127 zenon_Hd0). % 10.36/10.57 (* end of lemma zenon_L1087_ *) % 10.36/10.57 assert (zenon_L1088_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (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))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H3c zenon_H51 zenon_H91 zenon_Hc7 zenon_Hc5. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.57 apply (zenon_L129_); trivial. % 10.36/10.57 exact (zenon_H127 zenon_Hd0). % 10.36/10.57 (* end of lemma zenon_L1088_ *) % 10.36/10.57 assert (zenon_L1089_ : (((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)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (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 (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H1b4 zenon_H1cb zenon_H195 zenon_H67 zenon_H1f8 zenon_Hc0 zenon_H97 zenon_H1e6 zenon_H216 zenon_Hec zenon_H7d zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H3c zenon_H42 zenon_H6f zenon_H1f0 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e zenon_H127 zenon_Hd2 zenon_H80. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.36/10.57 apply (zenon_L111_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.36/10.57 apply (zenon_L1078_); trivial. % 10.36/10.57 apply (zenon_L1085_); trivial. % 10.36/10.57 apply (zenon_L1086_); trivial. % 10.36/10.57 apply (zenon_L1087_); trivial. % 10.36/10.57 apply (zenon_L325_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.36/10.57 apply (zenon_L1088_); trivial. % 10.36/10.57 apply (zenon_L1081_); trivial. % 10.36/10.57 apply (zenon_L1086_); trivial. % 10.36/10.57 apply (zenon_L325_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.36/10.57 apply (zenon_L593_); trivial. % 10.36/10.57 exact (zenon_H127 zenon_Hd0). % 10.36/10.57 apply (zenon_L149_); trivial. % 10.36/10.57 apply (zenon_L439_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.36/10.57 apply (zenon_L1085_); trivial. % 10.36/10.57 exact (zenon_H80 zenon_H84). % 10.36/10.57 (* end of lemma zenon_L1089_ *) % 10.36/10.57 assert (zenon_L1090_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((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)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hda zenon_H203 zenon_H64 zenon_H56 zenon_H7e zenon_H1e6 zenon_H1f0 zenon_Hf5 zenon_H51 zenon_H97 zenon_H28 zenon_H191 zenon_He8 zenon_H192 zenon_Hc1 zenon_H108 zenon_Hfd zenon_H5e zenon_Hb1 zenon_He7 zenon_H10b zenon_Hed zenon_H238 zenon_H4c zenon_H76 zenon_H151 zenon_Hbb zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1dd zenon_Hf8. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.36/10.57 exact (zenon_H28 zenon_H31). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.36/10.57 apply (zenon_L236_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.36/10.57 exact (zenon_H192 zenon_H1d). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.36/10.57 apply (zenon_L511_); trivial. % 10.36/10.57 exact (zenon_H203 zenon_H9a). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.36/10.57 apply (zenon_L21_); trivial. % 10.36/10.57 apply (zenon_L674_); trivial. % 10.36/10.57 (* end of lemma zenon_L1090_ *) % 10.36/10.57 assert (zenon_L1091_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e1))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1b4 zenon_H28 zenon_H238 zenon_H203 zenon_Hf5 zenon_H1f0 zenon_H5e zenon_H97 zenon_H10b zenon_H108 zenon_H1dd zenon_Hb1 zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_Hbb zenon_He7 zenon_H64 zenon_H192 zenon_H4c zenon_H151 zenon_Hf8 zenon_Hda zenon_H6f zenon_H51 zenon_H159 zenon_H155 zenon_H3a zenon_H1e6 zenon_H1f8 zenon_H56. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.36/10.57 apply (zenon_L56_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.36/10.57 exact (zenon_H56 zenon_H2c). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.36/10.57 apply (zenon_L490_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.36/10.57 apply (zenon_L1090_); trivial. % 10.36/10.57 apply (zenon_L62_); trivial. % 10.36/10.57 apply (zenon_L160_); trivial. % 10.36/10.57 (* end of lemma zenon_L1091_ *) % 10.36/10.57 assert (zenon_L1092_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (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) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H67 zenon_H1f8 zenon_H1e6 zenon_H97 zenon_H238 zenon_H1b4 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_H191 zenon_H64 zenon_H3c zenon_H3a zenon_H42 zenon_H6f zenon_H1f0 zenon_H56 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e zenon_H203 zenon_H1af. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.57 apply (zenon_L1061_); trivial. % 10.36/10.57 exact (zenon_H203 zenon_H9a). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.57 apply (zenon_L1091_); trivial. % 10.36/10.57 apply (zenon_L321_); trivial. % 10.36/10.57 exact (zenon_H203 zenon_H9a). % 10.36/10.57 apply (zenon_L675_); trivial. % 10.36/10.57 apply (zenon_L1063_); trivial. % 10.36/10.57 (* end of lemma zenon_L1092_ *) % 10.36/10.57 assert (zenon_L1093_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((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). % 10.36/10.57 do 0 intro. intros zenon_H1af zenon_H203 zenon_H1f zenon_H68 zenon_H192 zenon_Haf zenon_H191. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.36/10.57 apply (zenon_L323_); trivial. % 10.36/10.57 exact (zenon_H203 zenon_H9a). % 10.36/10.57 (* end of lemma zenon_L1093_ *) % 10.36/10.57 assert (zenon_L1094_ : ((op (e3) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 10.36/10.57 do 0 intro. intros zenon_He4 zenon_H73 zenon_H1c0. % 10.36/10.57 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H170 | zenon_intro zenon_Hbf ]. % 10.36/10.57 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 10.36/10.57 intro zenon_D_pnotp. % 10.36/10.57 apply zenon_H1c0. % 10.36/10.57 rewrite <- zenon_D_pnotp. % 10.36/10.57 exact zenon_H170. % 10.36/10.57 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 10.36/10.57 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 10.36/10.57 congruence. % 10.36/10.57 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 10.36/10.57 intro zenon_D_pnotp. % 10.36/10.57 apply zenon_H1c1. % 10.36/10.57 rewrite <- zenon_D_pnotp. % 10.36/10.57 exact zenon_He4. % 10.36/10.57 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 10.36/10.57 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 10.36/10.57 congruence. % 10.36/10.57 apply zenon_Hbf. apply refl_equal. % 10.36/10.57 apply zenon_H1bb. apply sym_equal. exact zenon_H73. % 10.36/10.57 apply zenon_Hbf. apply refl_equal. % 10.36/10.57 apply zenon_Hbf. apply refl_equal. % 10.36/10.57 (* end of lemma zenon_L1094_ *) % 10.36/10.57 assert (zenon_L1095_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hab zenon_H35 zenon_H47 zenon_H203 zenon_H5e zenon_H89 zenon_H7e. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 10.36/10.57 apply (zenon_L260_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 10.36/10.57 exact (zenon_H203 zenon_H9a). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 10.36/10.57 apply (zenon_L27_); trivial. % 10.36/10.57 exact (zenon_H7e zenon_H83). % 10.36/10.57 (* end of lemma zenon_L1095_ *) % 10.36/10.57 assert (zenon_L1096_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hb0 zenon_H1c0 zenon_He4 zenon_H68 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H35 zenon_H47 zenon_H203 zenon_H5e zenon_H7e. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.36/10.57 apply (zenon_L1094_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.36/10.57 apply (zenon_L46_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.36/10.57 exact (zenon_Hb1 zenon_Hb7). % 10.36/10.57 apply (zenon_L1095_); trivial. % 10.36/10.57 (* end of lemma zenon_L1096_ *) % 10.36/10.57 assert (zenon_L1097_ : (((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 (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (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 (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_Hb0 zenon_H1c0 zenon_He4 zenon_H68 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H35 zenon_H203 zenon_H5e zenon_H7e. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.36/10.57 exact (zenon_H27 zenon_H32). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.36/10.57 apply (zenon_L16_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.36/10.57 apply (zenon_L5_); trivial. % 10.36/10.57 apply (zenon_L1096_); trivial. % 10.36/10.57 (* end of lemma zenon_L1097_ *) % 10.36/10.57 assert (zenon_L1098_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H156 zenon_Hc6 zenon_H42 zenon_H1c0 zenon_He4 zenon_Hd3 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_Hb0 zenon_H3a zenon_H3c zenon_H68 zenon_H44 zenon_H27 zenon_H118 zenon_H114 zenon_H216 zenon_H1d zenon_H110 zenon_H151. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.36/10.57 apply (zenon_L1097_); trivial. % 10.36/10.57 apply (zenon_L1067_); trivial. % 10.36/10.57 apply (zenon_L321_); trivial. % 10.36/10.57 (* end of lemma zenon_L1098_ *) % 10.36/10.57 assert (zenon_L1099_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (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 (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.45/10.57 do 0 intro. intros zenon_H67 zenon_H1ea zenon_H108 zenon_He4 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H3a zenon_H156 zenon_H191 zenon_H68 zenon_H1f zenon_H203 zenon_H1af zenon_H42 zenon_H1c0 zenon_Hd3 zenon_Hab zenon_H35 zenon_Hb0 zenon_H3c zenon_H44 zenon_H118 zenon_H114 zenon_H216 zenon_H110 zenon_H151 zenon_H1ef. % 10.45/10.57 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.57 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.57 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.57 apply (zenon_L1093_); trivial. % 10.45/10.57 apply (zenon_L1064_); trivial. % 10.45/10.57 apply (zenon_L1098_); trivial. % 10.45/10.57 apply (zenon_L69_); trivial. % 10.45/10.57 (* end of lemma zenon_L1099_ *) % 10.45/10.57 assert (zenon_L1100_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (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) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.45/10.57 do 0 intro. intros zenon_H216 zenon_Hb0 zenon_Hab zenon_H1c0 zenon_H1af zenon_H203 zenon_H5e zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H1f0 zenon_H6f zenon_H42 zenon_H3a zenon_H3c zenon_H64 zenon_H191 zenon_H1f zenon_Hde zenon_H35 zenon_H44 zenon_He7 zenon_H169 zenon_H1ef zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H1b4 zenon_H238 zenon_H97 zenon_H1e6 zenon_H1f8 zenon_H67. % 10.45/10.57 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.57 apply (zenon_L1092_); trivial. % 10.45/10.57 apply (zenon_L1099_); trivial. % 10.45/10.57 (* end of lemma zenon_L1100_ *) % 10.45/10.57 assert (zenon_L1101_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.57 do 0 intro. intros zenon_Hab zenon_H4c zenon_H57 zenon_H203 zenon_H5e zenon_H89 zenon_H7e. % 10.45/10.57 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 10.45/10.57 apply (zenon_L13_); trivial. % 10.45/10.57 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 10.45/10.57 exact (zenon_H203 zenon_H9a). % 10.45/10.57 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 10.45/10.57 apply (zenon_L27_); trivial. % 10.45/10.57 exact (zenon_H7e zenon_H83). % 10.45/10.57 (* end of lemma zenon_L1101_ *) % 10.45/10.57 assert (zenon_L1102_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.57 do 0 intro. intros zenon_Hb0 zenon_H1c0 zenon_He4 zenon_H68 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H4c zenon_H57 zenon_H203 zenon_H5e zenon_H7e. % 10.45/10.57 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb5 ]. % 10.45/10.57 apply (zenon_L1094_); trivial. % 10.45/10.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H78 | zenon_intro zenon_Hb6 ]. % 10.45/10.57 apply (zenon_L46_); trivial. % 10.45/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H89 ]. % 10.45/10.57 exact (zenon_Hb1 zenon_Hb7). % 10.45/10.57 apply (zenon_L1101_); trivial. % 10.45/10.57 (* end of lemma zenon_L1102_ *) % 10.45/10.57 assert (zenon_L1103_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e0) (e1)) = (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) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.57 do 0 intro. intros zenon_H97 zenon_H28 zenon_H53 zenon_H10b zenon_Hed zenon_Hb0 zenon_H1c0 zenon_He4 zenon_H68 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H4c zenon_H203 zenon_H5e zenon_H7e. % 10.45/10.57 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.57 exact (zenon_H28 zenon_H31). % 10.45/10.57 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.57 apply (zenon_L30_); trivial. % 10.45/10.57 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.57 apply (zenon_L75_); trivial. % 10.45/10.57 apply (zenon_L1102_); trivial. % 10.45/10.57 (* end of lemma zenon_L1103_ *) % 10.45/10.57 assert (zenon_L1104_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.45/10.57 do 0 intro. intros zenon_Hf8 zenon_H28 zenon_H53 zenon_H68 zenon_H10b zenon_Hb0 zenon_H4c zenon_H203 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hd3 zenon_H1c0 zenon_H97 zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 10.45/10.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.57 apply (zenon_L56_); trivial. % 10.45/10.57 apply (zenon_L1103_); trivial. % 10.45/10.57 (* end of lemma zenon_L1104_ *) % 10.45/10.57 assert (zenon_L1105_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (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))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H97 zenon_H1c0 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H5e zenon_H203 zenon_H4c zenon_Hb0 zenon_H10b zenon_H68 zenon_H53 zenon_H28 zenon_Hf8. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.58 apply (zenon_L1104_); trivial. % 10.45/10.58 apply (zenon_L160_); trivial. % 10.45/10.58 (* end of lemma zenon_L1105_ *) % 10.45/10.58 assert (zenon_L1106_ : (((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) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.58 do 0 intro. intros zenon_Hde zenon_H44 zenon_H68 zenon_Haf zenon_Hcf zenon_H112 zenon_Hf5 zenon_H5e zenon_He4 zenon_H35 zenon_Hed zenon_H4c zenon_H7e. % 10.45/10.58 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.45/10.58 apply (zenon_L16_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.45/10.58 exact (zenon_Haf zenon_Hb4). % 10.45/10.58 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.45/10.58 apply (zenon_L79_); trivial. % 10.45/10.58 apply (zenon_L65_); trivial. % 10.45/10.58 (* end of lemma zenon_L1106_ *) % 10.45/10.58 assert (zenon_L1107_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> False). % 10.45/10.58 do 0 intro. intros zenon_Hf8 zenon_H44 zenon_H68 zenon_Haf zenon_H112 zenon_Hcf zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_He3 zenon_He4 zenon_H7e zenon_H80 zenon_H7d. % 10.45/10.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.58 apply (zenon_L56_); trivial. % 10.45/10.58 apply (zenon_L1106_); trivial. % 10.45/10.58 (* end of lemma zenon_L1107_ *) % 10.45/10.58 assert (zenon_L1108_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H151 zenon_Hd3 zenon_H110 zenon_H1d zenon_H114 zenon_H118 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_Hcf zenon_H112 zenon_Haf zenon_H68 zenon_H44 zenon_Hf8. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.58 apply (zenon_L1107_); trivial. % 10.45/10.58 apply (zenon_L81_); trivial. % 10.45/10.58 (* end of lemma zenon_L1108_ *) % 10.45/10.58 assert (zenon_L1109_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.58 do 0 intro. intros zenon_Hc0 zenon_H1cb zenon_H195 zenon_H67 zenon_H1f8 zenon_H1e6 zenon_H97 zenon_H238 zenon_H1b4 zenon_Hec zenon_H7d zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_H191 zenon_H64 zenon_H3c zenon_H42 zenon_H6f zenon_H1f0 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e zenon_H203 zenon_H1af zenon_H1c0 zenon_Hab zenon_Hb0 zenon_H216 zenon_H80. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.58 apply (zenon_L111_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.58 apply (zenon_L1050_); trivial. % 10.45/10.58 apply (zenon_L1092_); trivial. % 10.45/10.58 apply (zenon_L187_); trivial. % 10.45/10.58 apply (zenon_L1073_); trivial. % 10.45/10.58 exact (zenon_H203 zenon_H9a). % 10.45/10.58 apply (zenon_L325_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.58 apply (zenon_L129_); trivial. % 10.45/10.58 apply (zenon_L1100_); trivial. % 10.45/10.58 apply (zenon_L187_); trivial. % 10.45/10.58 exact (zenon_H203 zenon_H9a). % 10.45/10.58 apply (zenon_L325_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.58 apply (zenon_L1105_); trivial. % 10.45/10.58 apply (zenon_L1108_); trivial. % 10.45/10.58 apply (zenon_L149_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.58 apply (zenon_L1100_); trivial. % 10.45/10.58 exact (zenon_H80 zenon_H84). % 10.45/10.58 (* end of lemma zenon_L1109_ *) % 10.45/10.58 assert (zenon_L1110_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (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) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H1af zenon_H203 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_H191 zenon_H64 zenon_H27 zenon_H3c zenon_H3a zenon_H42 zenon_H6f zenon_H1f0 zenon_H56 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e zenon_H127 zenon_Hd2. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.58 apply (zenon_L1079_); trivial. % 10.45/10.58 exact (zenon_H203 zenon_H9a). % 10.45/10.58 (* end of lemma zenon_L1110_ *) % 10.45/10.58 assert (zenon_L1111_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e0) (e0)) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H1ef zenon_Hc6 zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_H16e zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1b4 zenon_H28 zenon_H238 zenon_H203 zenon_Hf5 zenon_H1f0 zenon_H5e zenon_H97 zenon_H10b zenon_H108 zenon_H1dd zenon_Hfd zenon_He8 zenon_H191 zenon_Hbb zenon_He7 zenon_H64 zenon_H4c zenon_H151 zenon_Hf8 zenon_Hda zenon_H6f zenon_H51 zenon_H159 zenon_H155 zenon_H3a zenon_H1e6 zenon_H1f8 zenon_H56 zenon_H127 zenon_Hd2 zenon_H1af. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.58 apply (zenon_L1091_); trivial. % 10.45/10.58 exact (zenon_H127 zenon_Hd0). % 10.45/10.58 apply (zenon_L321_); trivial. % 10.45/10.58 exact (zenon_H203 zenon_H9a). % 10.45/10.58 apply (zenon_L675_); trivial. % 10.45/10.58 (* end of lemma zenon_L1111_ *) % 10.45/10.58 assert (zenon_L1112_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e3) (e1)) = (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) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.45/10.58 do 0 intro. intros zenon_Hb0 zenon_Hab zenon_H1c0 zenon_H1af zenon_H203 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1ef zenon_H169 zenon_He7 zenon_H44 zenon_H35 zenon_Hde zenon_H1f zenon_H191 zenon_H64 zenon_H3c zenon_H3a zenon_H42 zenon_H6f zenon_H1f0 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H5e zenon_H127 zenon_Hd2 zenon_H216 zenon_H1f8 zenon_H1e6 zenon_H97 zenon_H238 zenon_H1b4 zenon_H67. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.58 apply (zenon_L1110_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.58 apply (zenon_L1111_); trivial. % 10.45/10.58 apply (zenon_L1084_); trivial. % 10.45/10.58 apply (zenon_L1099_); trivial. % 10.45/10.58 (* end of lemma zenon_L1112_ *) % 10.45/10.58 assert (zenon_L1113_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.58 do 0 intro. intros zenon_Hc0 zenon_H1cb zenon_H195 zenon_H67 zenon_H1b4 zenon_H238 zenon_H97 zenon_H1e6 zenon_H1f8 zenon_H216 zenon_Hd2 zenon_H127 zenon_H5e zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H1f0 zenon_H6f zenon_H42 zenon_H3c zenon_H64 zenon_H191 zenon_H1f zenon_Hde zenon_H35 zenon_H44 zenon_He7 zenon_H169 zenon_H1ef zenon_He3 zenon_He4 zenon_H7d zenon_Hec zenon_H203 zenon_H1af zenon_H1c0 zenon_Hab zenon_Hb0 zenon_H80. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.58 apply (zenon_L111_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.58 apply (zenon_L1078_); trivial. % 10.45/10.58 apply (zenon_L1110_); trivial. % 10.45/10.58 apply (zenon_L1086_); trivial. % 10.45/10.58 apply (zenon_L1087_); trivial. % 10.45/10.58 exact (zenon_H203 zenon_H9a). % 10.45/10.58 apply (zenon_L325_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.58 apply (zenon_L1088_); trivial. % 10.45/10.58 apply (zenon_L1112_); trivial. % 10.45/10.58 apply (zenon_L1086_); trivial. % 10.45/10.58 exact (zenon_H203 zenon_H9a). % 10.45/10.58 apply (zenon_L325_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.58 apply (zenon_L1105_); trivial. % 10.45/10.58 exact (zenon_H127 zenon_Hd0). % 10.45/10.58 apply (zenon_L1108_); trivial. % 10.45/10.58 apply (zenon_L149_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.58 apply (zenon_L1112_); trivial. % 10.45/10.58 exact (zenon_H80 zenon_H84). % 10.45/10.58 (* end of lemma zenon_L1113_ *) % 10.45/10.58 assert (zenon_L1114_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H4a zenon_H23e zenon_H158 zenon_H152 zenon_Hfd zenon_H68 zenon_H103 zenon_H35 zenon_H10b zenon_H135 zenon_H144 zenon_H1d zenon_H16e zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H44 zenon_H108 zenon_H151 zenon_H16b zenon_H80 zenon_H95 zenon_Hd3 zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_H4c zenon_Hda zenon_H156. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.58 apply (zenon_L157_); trivial. % 10.45/10.58 exact (zenon_H23e zenon_H43). % 10.45/10.58 (* end of lemma zenon_L1114_ *) % 10.45/10.58 assert (zenon_L1115_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H156 zenon_H51 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H4c zenon_H64 zenon_Hf5 zenon_H7a zenon_H135 zenon_H35 zenon_H169 zenon_H5e zenon_H53 zenon_H44 zenon_H14d zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_H95 zenon_H80 zenon_H16b zenon_H151 zenon_H152 zenon_H158. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.58 apply (zenon_L148_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.58 apply (zenon_L367_); trivial. % 10.45/10.58 apply (zenon_L79_); trivial. % 10.45/10.58 (* end of lemma zenon_L1115_ *) % 10.45/10.58 assert (zenon_L1116_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (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))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H150 zenon_H151 zenon_Hbb zenon_H4c zenon_H169 zenon_H1d zenon_H35 zenon_H135 zenon_Hf5 zenon_H14d zenon_H44 zenon_H53 zenon_H2a zenon_H14a zenon_H95 zenon_H80 zenon_H16b. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_Hbc | zenon_intro zenon_H16c ]. % 10.45/10.58 apply (zenon_L146_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_Hbd | zenon_intro zenon_H16d ]. % 10.45/10.58 apply (zenon_L114_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hed | zenon_intro zenon_H84 ]. % 10.45/10.58 apply (zenon_L109_); trivial. % 10.45/10.58 exact (zenon_H80 zenon_H84). % 10.45/10.58 apply (zenon_L146_); trivial. % 10.45/10.58 (* end of lemma zenon_L1116_ *) % 10.45/10.58 assert (zenon_L1117_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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) (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) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H173 zenon_H155 zenon_Hf8 zenon_H12f zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H165 zenon_H159 zenon_H168 zenon_H174 zenon_H4a zenon_H23e zenon_H158 zenon_Hfd zenon_H103 zenon_H35 zenon_H10b zenon_H144 zenon_H16e zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H44 zenon_H108 zenon_H151 zenon_H16b zenon_H95 zenon_Hd3 zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_H4c zenon_Hda zenon_H156 zenon_H157 zenon_H150 zenon_Hbb zenon_H64 zenon_H7a zenon_H5e zenon_H53 zenon_H14d zenon_H1f zenon_H200 zenon_H14a zenon_H204 zenon_H152 zenon_H135 zenon_H80. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.58 apply (zenon_L138_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.58 exact (zenon_H25 zenon_H2a). % 10.45/10.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.58 apply (zenon_L1114_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.58 apply (zenon_L1115_); trivial. % 10.45/10.58 exact (zenon_H23e zenon_H43). % 10.45/10.58 apply (zenon_L1114_); trivial. % 10.45/10.58 apply (zenon_L1116_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.58 apply (zenon_L116_); trivial. % 10.45/10.58 exact (zenon_H80 zenon_H84). % 10.45/10.58 (* end of lemma zenon_L1117_ *) % 10.45/10.58 assert (zenon_L1118_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (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))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H177 zenon_He4 zenon_Hbd zenon_H80 zenon_H152 zenon_H204 zenon_H14a zenon_H200 zenon_H1f zenon_H14d zenon_H53 zenon_H5e zenon_H7a zenon_H64 zenon_Hbb zenon_H150 zenon_H157 zenon_H156 zenon_Hda zenon_H4c zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_Hd3 zenon_H95 zenon_H16b zenon_H151 zenon_H108 zenon_H44 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H16e zenon_H144 zenon_H10b zenon_H35 zenon_H103 zenon_Hfd zenon_H158 zenon_H23e zenon_H4a zenon_H174 zenon_H168 zenon_H159 zenon_H165 zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_H12f zenon_Hf8 zenon_H155 zenon_H173 zenon_H7f. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.45/10.58 apply (zenon_L99_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.45/10.58 apply (zenon_L50_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.45/10.58 apply (zenon_L1117_); trivial. % 10.45/10.58 exact (zenon_H7f zenon_H85). % 10.45/10.58 (* end of lemma zenon_L1118_ *) % 10.45/10.58 assert (zenon_L1119_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.58 do 0 intro. intros zenon_Hec zenon_H44 zenon_He4 zenon_H95 zenon_Hbd zenon_H173 zenon_H174 zenon_H4a zenon_H23e zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H5e zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.58 apply (zenon_L1118_); trivial. % 10.45/10.58 apply (zenon_L60_); trivial. % 10.45/10.58 (* end of lemma zenon_L1119_ *) % 10.45/10.58 assert (zenon_L1120_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((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))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H1f zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H3c zenon_H91 zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H44 zenon_Haf zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_Hbb zenon_He7 zenon_Hf5 zenon_H4c zenon_H35 zenon_H5e zenon_Hde zenon_H25 zenon_Hf8. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.58 apply (zenon_L56_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.58 exact (zenon_H25 zenon_H2a). % 10.45/10.58 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.58 apply (zenon_L66_); trivial. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.58 apply (zenon_L129_); trivial. % 10.45/10.58 exact (zenon_H23e zenon_H43). % 10.45/10.58 apply (zenon_L1119_); trivial. % 10.45/10.58 (* end of lemma zenon_L1120_ *) % 10.45/10.58 assert (zenon_L1121_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (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) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.45/10.58 do 0 intro. intros zenon_H67 zenon_H1ef zenon_Hf8 zenon_H44 zenon_H3c zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H42 zenon_He3 zenon_H80 zenon_H7d zenon_H118 zenon_H114 zenon_H216 zenon_H110 zenon_Hd3 zenon_H151 zenon_H191 zenon_Hc1 zenon_H68 zenon_H1f zenon_H156 zenon_H3a zenon_Hc6 zenon_Hfd zenon_H5e zenon_H1dd zenon_He4 zenon_H108 zenon_H1ea zenon_H23e zenon_H4a. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.58 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.59 apply (zenon_L1069_); trivial. % 10.45/10.59 exact (zenon_H23e zenon_H43). % 10.45/10.59 apply (zenon_L69_); trivial. % 10.45/10.59 (* end of lemma zenon_L1121_ *) % 10.45/10.59 assert (zenon_L1122_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H204 zenon_H200 zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H16b zenon_H16e zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_He7 zenon_Hbb zenon_H192 zenon_Haf zenon_Hf5 zenon_H4c zenon_H35 zenon_Hde zenon_He8 zenon_H4a zenon_H23e zenon_H1ea zenon_H108 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H3a zenon_H156 zenon_H1f zenon_Hc1 zenon_H191 zenon_H151 zenon_Hd3 zenon_H110 zenon_H216 zenon_H114 zenon_H118 zenon_H42 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3c zenon_H44 zenon_Hf8 zenon_H1ef zenon_H67. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L56_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.59 apply (zenon_L1121_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.59 exact (zenon_He8 zenon_Heb). % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.59 apply (zenon_L667_); trivial. % 10.45/10.59 apply (zenon_L58_); trivial. % 10.45/10.59 apply (zenon_L1119_); trivial. % 10.45/10.59 (* end of lemma zenon_L1122_ *) % 10.45/10.59 assert (zenon_L1123_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H1f zenon_H7a zenon_Hda zenon_H169 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_H4a zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H56 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_H5e zenon_H4c zenon_H108 zenon_H1dd zenon_Hb1 zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_H192 zenon_Hbb zenon_He7 zenon_H64 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H28 zenon_H42 zenon_H25 zenon_Hf8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L56_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.59 exact (zenon_H25 zenon_H2a). % 10.45/10.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.59 apply (zenon_L1065_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.59 apply (zenon_L511_); trivial. % 10.45/10.59 exact (zenon_H23e zenon_H43). % 10.45/10.59 apply (zenon_L1119_); trivial. % 10.45/10.59 (* end of lemma zenon_L1123_ *) % 10.45/10.59 assert (zenon_L1124_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H1f zenon_H5e zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H6f zenon_H16e zenon_H1d zenon_H155 zenon_H1e6 zenon_H1f8 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H28 zenon_H42 zenon_H25 zenon_Hf8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L56_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.59 exact (zenon_H25 zenon_H2a). % 10.45/10.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.59 apply (zenon_L1065_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.59 apply (zenon_L672_); trivial. % 10.45/10.59 exact (zenon_H23e zenon_H43). % 10.45/10.59 apply (zenon_L1119_); trivial. % 10.45/10.59 (* end of lemma zenon_L1124_ *) % 10.45/10.59 assert (zenon_L1125_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (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) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((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)) = (e0))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H1f zenon_H5e zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H1f8 zenon_H1e6 zenon_H155 zenon_H15a zenon_H159 zenon_H6f zenon_Hf8 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H28 zenon_H42 zenon_H25. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L56_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.59 exact (zenon_H25 zenon_H2a). % 10.45/10.59 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.59 apply (zenon_L1065_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.59 apply (zenon_L1062_); trivial. % 10.45/10.59 exact (zenon_H23e zenon_H43). % 10.45/10.59 apply (zenon_L1119_); trivial. % 10.45/10.59 (* end of lemma zenon_L1125_ *) % 10.45/10.59 assert (zenon_L1126_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H7a zenon_Hda zenon_H169 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H28 zenon_He7 zenon_Hbb zenon_H192 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hfd zenon_Hb1 zenon_H1dd zenon_H108 zenon_H10b zenon_H4c zenon_H97 zenon_H51 zenon_H5e zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H56 zenon_Hf8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_L512_); trivial. % 10.45/10.59 apply (zenon_L1119_); trivial. % 10.45/10.59 (* end of lemma zenon_L1126_ *) % 10.45/10.59 assert (zenon_L1127_ : ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H3a zenon_Hc6 zenon_Hf8 zenon_H56 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_H5e zenon_H51 zenon_H97 zenon_H4c zenon_H10b zenon_H108 zenon_H1dd zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_H192 zenon_Hbb zenon_He7 zenon_H28 zenon_H64 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H44 zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_H23e zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H169 zenon_Hda zenon_H7a zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.59 apply (zenon_L1126_); trivial. % 10.45/10.59 apply (zenon_L321_); trivial. % 10.45/10.59 (* end of lemma zenon_L1127_ *) % 10.45/10.59 assert (zenon_L1128_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H5e zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_Hfd zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1f8 zenon_H1e6 zenon_H3a zenon_H155 zenon_H1d zenon_H16e zenon_H51 zenon_H6f zenon_Hf8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L56_); trivial. % 10.45/10.59 apply (zenon_L672_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L1118_); trivial. % 10.45/10.59 apply (zenon_L672_); trivial. % 10.45/10.59 (* end of lemma zenon_L1128_ *) % 10.45/10.59 assert (zenon_L1129_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H6f zenon_H51 zenon_H15a zenon_H3a zenon_H1e6 zenon_H1f8 zenon_H44 zenon_He4 zenon_H95 zenon_Hbd zenon_H173 zenon_H174 zenon_H4a zenon_H23e zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H5e zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.59 apply (zenon_L1118_); trivial. % 10.45/10.59 apply (zenon_L490_); trivial. % 10.45/10.59 (* end of lemma zenon_L1129_ *) % 10.45/10.59 assert (zenon_L1130_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H5e zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1f8 zenon_H1e6 zenon_H3a zenon_H155 zenon_H15a zenon_H159 zenon_H51 zenon_H6f zenon_Hf8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_L1062_); trivial. % 10.45/10.59 apply (zenon_L1129_); trivial. % 10.45/10.59 (* end of lemma zenon_L1130_ *) % 10.45/10.59 assert (zenon_L1131_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H56 zenon_H1e6 zenon_H1f0 zenon_H25 zenon_H67 zenon_H1ef zenon_Hf8 zenon_H44 zenon_H3c zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H42 zenon_H118 zenon_H114 zenon_H216 zenon_H110 zenon_Hd3 zenon_H151 zenon_H191 zenon_Hc1 zenon_H1f zenon_H156 zenon_H3a zenon_Hc6 zenon_Hfd zenon_H5e zenon_H1dd zenon_H108 zenon_H1ea zenon_H23e zenon_H4a zenon_Hde zenon_H35 zenon_H4c zenon_Hf5 zenon_Hbb zenon_He7 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H173 zenon_H174 zenon_H16e zenon_H16b zenon_H16f zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H200 zenon_H204 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_H6f zenon_H1f8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.59 apply (zenon_L1122_); trivial. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.59 apply (zenon_L1123_); trivial. % 10.45/10.59 apply (zenon_L321_); trivial. % 10.45/10.59 apply (zenon_L1124_); trivial. % 10.45/10.59 apply (zenon_L1125_); trivial. % 10.45/10.59 exact (zenon_H23e zenon_H43). % 10.45/10.59 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.59 apply (zenon_L1122_); trivial. % 10.45/10.59 apply (zenon_L1127_); trivial. % 10.45/10.59 apply (zenon_L1128_); trivial. % 10.45/10.59 apply (zenon_L1130_); trivial. % 10.45/10.59 exact (zenon_H23e zenon_H43). % 10.45/10.59 (* end of lemma zenon_L1131_ *) % 10.45/10.59 assert (zenon_L1132_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((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 (e2) (e1)) = (op (e2) (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (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)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((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 (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H1f8 zenon_H6f zenon_H1ea zenon_H1dd zenon_Hc6 zenon_H191 zenon_H216 zenon_H42 zenon_H97 zenon_H1ef zenon_H67 zenon_H1f0 zenon_H1e6 zenon_H56 zenon_Hf8 zenon_H25 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_He7 zenon_Hbb zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_Haf zenon_H44 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H3c zenon_H23e zenon_H200 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H1f zenon_H204 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.59 apply (zenon_L1120_); trivial. % 10.45/10.59 apply (zenon_L1131_); trivial. % 10.45/10.59 (* end of lemma zenon_L1132_ *) % 10.45/10.59 assert (zenon_L1133_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.59 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H5e zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hc0 zenon_Hec zenon_H95 zenon_Hc1 zenon_H53 zenon_He8 zenon_H44 zenon_Hb8 zenon_Hbb zenon_He7 zenon_Hf8. % 10.45/10.59 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.59 apply (zenon_L186_); trivial. % 10.45/10.59 apply (zenon_L1119_); trivial. % 10.45/10.59 (* end of lemma zenon_L1133_ *) % 10.45/10.59 assert (zenon_L1134_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.60 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_He7 zenon_Hbb zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_Haf zenon_H68 zenon_H44 zenon_Hf8. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.60 apply (zenon_L67_); trivial. % 10.45/10.60 apply (zenon_L1119_); trivial. % 10.45/10.60 (* end of lemma zenon_L1134_ *) % 10.45/10.60 assert (zenon_L1135_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hc0 zenon_H195 zenon_H1f8 zenon_H6f zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H204 zenon_H200 zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H16b zenon_H16e zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_He4 zenon_He3 zenon_He7 zenon_Hbb zenon_Hf5 zenon_H4c zenon_H35 zenon_Hde zenon_H4a zenon_H23e zenon_H1ea zenon_H108 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H156 zenon_H1f zenon_Hc1 zenon_H191 zenon_H151 zenon_Hd3 zenon_H110 zenon_H216 zenon_H114 zenon_H118 zenon_H42 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3c zenon_H44 zenon_Hf8 zenon_H1ef zenon_H67 zenon_H1f0 zenon_H1e6 zenon_H80. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.60 apply (zenon_L111_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.60 apply (zenon_L1132_); trivial. % 10.45/10.60 apply (zenon_L1133_); trivial. % 10.45/10.60 apply (zenon_L149_); trivial. % 10.45/10.60 apply (zenon_L325_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.60 apply (zenon_L1134_); trivial. % 10.45/10.60 apply (zenon_L149_); trivial. % 10.45/10.60 apply (zenon_L439_); trivial. % 10.45/10.60 apply (zenon_L111_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.60 apply (zenon_L1131_); trivial. % 10.45/10.60 apply (zenon_L1121_); trivial. % 10.45/10.60 apply (zenon_L111_); trivial. % 10.45/10.60 exact (zenon_H80 zenon_H84). % 10.45/10.60 (* end of lemma zenon_L1135_ *) % 10.45/10.60 assert (zenon_L1136_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H67 zenon_H1ef zenon_Hf8 zenon_H44 zenon_H3c zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H42 zenon_H118 zenon_H114 zenon_H216 zenon_H110 zenon_Hd3 zenon_H151 zenon_H191 zenon_Hc1 zenon_H1f zenon_H156 zenon_H3a zenon_Hc6 zenon_Hfd zenon_H5e zenon_H1dd zenon_H108 zenon_H1ea zenon_H23e zenon_H4a zenon_He8 zenon_Hde zenon_H35 zenon_H4c zenon_Hf5 zenon_Haf zenon_H192 zenon_Hbb zenon_He7 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H173 zenon_H174 zenon_H16e zenon_H16b zenon_H16f zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H200 zenon_H204 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1122_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 (* end of lemma zenon_L1136_ *) % 10.45/10.60 assert (zenon_L1137_ : ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.45/10.60 do 0 intro. intros zenon_H3a zenon_Hc6 zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H3c zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H7a zenon_Hda zenon_H169 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H64 zenon_H28 zenon_He7 zenon_Hbb zenon_H192 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hfd zenon_H1dd zenon_H108 zenon_H10b zenon_H4c zenon_H97 zenon_H51 zenon_H5e zenon_H1f0 zenon_H1e6 zenon_H100 zenon_Hf5 zenon_H56 zenon_Hf8 zenon_H127 zenon_Hd2. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1126_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 apply (zenon_L321_); trivial. % 10.45/10.60 (* end of lemma zenon_L1137_ *) % 10.45/10.60 assert (zenon_L1138_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (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 (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hf8 zenon_H6f zenon_H51 zenon_H16e zenon_H1d zenon_H155 zenon_H3a zenon_H1e6 zenon_H1f8 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_H44 zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_H23e zenon_Hfd zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H5e zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1128_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 (* end of lemma zenon_L1138_ *) % 10.45/10.60 assert (zenon_L1139_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> False). % 10.45/10.60 do 0 intro. intros zenon_H56 zenon_H1e6 zenon_H1f0 zenon_H51 zenon_H28 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H204 zenon_H200 zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H16b zenon_H16e zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_He7 zenon_Hbb zenon_Hf5 zenon_H4c zenon_H35 zenon_Hde zenon_H4a zenon_H23e zenon_H1ea zenon_H108 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H3a zenon_H156 zenon_H1f zenon_Hc1 zenon_H191 zenon_H151 zenon_Hd3 zenon_H110 zenon_H216 zenon_H114 zenon_H118 zenon_H42 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3c zenon_H44 zenon_Hf8 zenon_H1ef zenon_H67 zenon_H127 zenon_Hd2 zenon_H6f zenon_H1f8. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.60 apply (zenon_L1136_); trivial. % 10.45/10.60 apply (zenon_L1137_); trivial. % 10.45/10.60 apply (zenon_L1138_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1130_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 (* end of lemma zenon_L1139_ *) % 10.45/10.60 assert (zenon_L1140_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 10.45/10.60 do 0 intro. intros zenon_H25 zenon_H1f0 zenon_H1e6 zenon_H56 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H204 zenon_H200 zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H16b zenon_H16e zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_He7 zenon_Hbb zenon_Hf5 zenon_H4c zenon_H35 zenon_Hde zenon_H4a zenon_H23e zenon_H1ea zenon_H108 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H3a zenon_H156 zenon_H1f zenon_Hc1 zenon_H191 zenon_H151 zenon_Hd3 zenon_H110 zenon_H216 zenon_H114 zenon_H118 zenon_H42 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3c zenon_H44 zenon_Hf8 zenon_H1ef zenon_H67 zenon_H127 zenon_Hd2 zenon_H1f8 zenon_H6f. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.60 apply (zenon_L1136_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1123_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 apply (zenon_L321_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1124_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1125_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 exact (zenon_H23e zenon_H43). % 10.45/10.60 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.60 apply (zenon_L1139_); trivial. % 10.45/10.60 exact (zenon_H23e zenon_H43). % 10.45/10.60 (* end of lemma zenon_L1140_ *) % 10.45/10.60 assert (zenon_L1141_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((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 (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (~((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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hf8 zenon_He7 zenon_Hbb zenon_Hb8 zenon_H44 zenon_He8 zenon_H53 zenon_Hc1 zenon_H95 zenon_Hec zenon_Hc0 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_H173 zenon_H174 zenon_H4a zenon_H23e zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H5e zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1133_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 (* end of lemma zenon_L1141_ *) % 10.45/10.60 assert (zenon_L1142_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((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 (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 10.45/10.60 do 0 intro. intros zenon_H1f0 zenon_H1e6 zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H204 zenon_H200 zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_H16f zenon_H16b zenon_H16e zenon_H174 zenon_H173 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_He7 zenon_Hbb zenon_Hf5 zenon_H4c zenon_H35 zenon_Hde zenon_H4a zenon_H23e zenon_H1ea zenon_H108 zenon_H1dd zenon_H5e zenon_Hfd zenon_Hc6 zenon_H3a zenon_H156 zenon_H1f zenon_Hc1 zenon_H191 zenon_H151 zenon_Hd3 zenon_H110 zenon_H216 zenon_H114 zenon_H118 zenon_H42 zenon_H53 zenon_H10b zenon_H95 zenon_H97 zenon_H3c zenon_H44 zenon_Hf8 zenon_H1ef zenon_H67 zenon_H127 zenon_Hd2 zenon_H1f8 zenon_H6f. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.60 apply (zenon_L1140_); trivial. % 10.45/10.60 apply (zenon_L1121_); trivial. % 10.45/10.60 apply (zenon_L111_); trivial. % 10.45/10.60 (* end of lemma zenon_L1142_ *) % 10.45/10.60 assert (zenon_L1143_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (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) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hc0 zenon_H195 zenon_H6f zenon_H1f8 zenon_Hd2 zenon_H127 zenon_H67 zenon_H1ef zenon_Hf8 zenon_H44 zenon_H3c zenon_H97 zenon_H95 zenon_H10b zenon_H53 zenon_H42 zenon_H118 zenon_H114 zenon_H216 zenon_H110 zenon_Hd3 zenon_H151 zenon_H191 zenon_Hc1 zenon_H1f zenon_H156 zenon_Hc6 zenon_Hfd zenon_H5e zenon_H1dd zenon_H108 zenon_H1ea zenon_H23e zenon_H4a zenon_Hde zenon_H35 zenon_H4c zenon_Hf5 zenon_Hbb zenon_He7 zenon_He3 zenon_He4 zenon_H7d zenon_Hec zenon_H173 zenon_H174 zenon_H16e zenon_H16b zenon_H16f zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H200 zenon_H204 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H159 zenon_H103 zenon_H168 zenon_H177 zenon_H1e6 zenon_H1f0 zenon_H80. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.60 apply (zenon_L111_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1120_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 apply (zenon_L1140_); trivial. % 10.45/10.60 apply (zenon_L1141_); trivial. % 10.45/10.60 apply (zenon_L149_); trivial. % 10.45/10.60 apply (zenon_L325_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.60 apply (zenon_L1134_); trivial. % 10.45/10.60 exact (zenon_H127 zenon_Hd0). % 10.45/10.60 apply (zenon_L149_); trivial. % 10.45/10.60 apply (zenon_L325_); trivial. % 10.45/10.60 apply (zenon_L111_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.60 apply (zenon_L1142_); trivial. % 10.45/10.60 exact (zenon_H80 zenon_H84). % 10.45/10.60 (* end of lemma zenon_L1143_ *) % 10.45/10.60 assert (zenon_L1144_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((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))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.60 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H1f zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H3c zenon_H91 zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H28 zenon_H53 zenon_H10b zenon_Hb0 zenon_H4c zenon_H203 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hd3 zenon_H1c0 zenon_H97 zenon_H25 zenon_Hf8. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.60 apply (zenon_L56_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.60 exact (zenon_H25 zenon_H2a). % 10.45/10.60 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.60 apply (zenon_L1103_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.60 apply (zenon_L129_); trivial. % 10.45/10.60 exact (zenon_H23e zenon_H43). % 10.45/10.60 apply (zenon_L1119_); trivial. % 10.45/10.60 (* end of lemma zenon_L1144_ *) % 10.45/10.60 assert (zenon_L1145_ : (((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) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hab zenon_H80 zenon_H7f zenon_H7a zenon_H8d zenon_H7d zenon_H203 zenon_H5e zenon_H89 zenon_H7e. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 10.45/10.60 apply (zenon_L87_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 10.45/10.60 exact (zenon_H203 zenon_H9a). % 10.45/10.60 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 10.45/10.60 apply (zenon_L27_); trivial. % 10.45/10.60 exact (zenon_H7e zenon_H83). % 10.45/10.60 (* end of lemma zenon_L1145_ *) % 10.45/10.60 assert (zenon_L1146_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> False). % 10.45/10.60 do 0 intro. intros zenon_Hf8 zenon_H6f zenon_H51 zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H35 zenon_H15a zenon_Haf zenon_H155 zenon_H3a zenon_H8c zenon_H7d zenon_H80 zenon_H7a zenon_H8d zenon_H203 zenon_H5e zenon_H7e zenon_Hab zenon_H44 zenon_H23e zenon_Hae. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.45/10.60 apply (zenon_L238_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.45/10.60 exact (zenon_Haf zenon_Hb4). % 10.45/10.60 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.45/10.60 apply (zenon_L223_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.45/10.60 exact (zenon_H23e zenon_H43). % 10.45/10.60 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.45/10.60 apply (zenon_L92_); trivial. % 10.45/10.60 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.45/10.60 apply (zenon_L1145_); trivial. % 10.45/10.60 exact (zenon_H8d zenon_H7b). % 10.45/10.60 apply (zenon_L490_); trivial. % 10.45/10.60 (* end of lemma zenon_L1146_ *) % 10.45/10.60 assert (zenon_L1147_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_He4 zenon_Hae zenon_H23e zenon_H44 zenon_Hab zenon_H5e zenon_H203 zenon_H8d zenon_H7a zenon_H80 zenon_H7d zenon_H8c zenon_H3a zenon_H155 zenon_Haf zenon_H15a zenon_H35 zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H51 zenon_H6f zenon_Hf8. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.61 apply (zenon_L1146_); trivial. % 10.45/10.61 apply (zenon_L1129_); trivial. % 10.45/10.61 (* end of lemma zenon_L1147_ *) % 10.45/10.61 assert (zenon_L1148_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H1b4 zenon_H6f zenon_H159 zenon_H1f8 zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H8c zenon_H7a zenon_H8d zenon_Hab zenon_H44 zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_H169 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H103 zenon_H168 zenon_H177 zenon_Hf8 zenon_H1dd zenon_He3 zenon_H80 zenon_H7d zenon_Hbb zenon_H151 zenon_H4c zenon_H238 zenon_Hed zenon_H10b zenon_He7 zenon_Hb1 zenon_Hfd zenon_H108 zenon_Hc1 zenon_H192 zenon_He8 zenon_H191 zenon_H28 zenon_H97 zenon_H51 zenon_Hf5 zenon_H1f0 zenon_H1e6 zenon_H7e zenon_H56 zenon_H64 zenon_H203 zenon_Hda zenon_He4 zenon_H5e. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.45/10.61 exact (zenon_H56 zenon_H2c). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.45/10.61 apply (zenon_L1147_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.45/10.61 apply (zenon_L1090_); trivial. % 10.45/10.61 apply (zenon_L62_); trivial. % 10.45/10.61 (* end of lemma zenon_L1148_ *) % 10.45/10.61 assert (zenon_L1149_ : (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H25 zenon_H42 zenon_H1c0 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_Hb0 zenon_H3a zenon_H3c zenon_H44 zenon_H27 zenon_H1b4 zenon_H28 zenon_H238 zenon_H1f0 zenon_H97 zenon_H1dd zenon_He8 zenon_H191 zenon_Hc1 zenon_He7 zenon_H192 zenon_Hf8 zenon_H6f zenon_H159 zenon_H1e6 zenon_H1f8 zenon_Haf zenon_H155 zenon_H8c zenon_H7a zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177 zenon_H56 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.61 apply (zenon_L56_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.61 exact (zenon_H25 zenon_H2a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.61 apply (zenon_L1097_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.61 apply (zenon_L1148_); trivial. % 10.45/10.61 exact (zenon_H23e zenon_H43). % 10.45/10.61 apply (zenon_L1119_); trivial. % 10.45/10.61 apply (zenon_L674_); trivial. % 10.45/10.61 (* end of lemma zenon_L1149_ *) % 10.45/10.61 assert (zenon_L1150_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H1f zenon_H7a zenon_Hda zenon_H169 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H16b zenon_H16e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H56 zenon_Hf5 zenon_H100 zenon_H1e6 zenon_H1f0 zenon_H97 zenon_H4c zenon_H10b zenon_H108 zenon_H1dd zenon_Hfd zenon_He8 zenon_H191 zenon_Hc1 zenon_H192 zenon_Hbb zenon_He7 zenon_H28 zenon_H64 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_Hb0 zenon_H35 zenon_H203 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hd3 zenon_H1c0 zenon_H42 zenon_H25 zenon_Hf8. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.61 apply (zenon_L56_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.61 exact (zenon_H25 zenon_H2a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.61 apply (zenon_L1097_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.61 apply (zenon_L511_); trivial. % 10.45/10.61 exact (zenon_H23e zenon_H43). % 10.45/10.61 apply (zenon_L1119_); trivial. % 10.45/10.61 (* end of lemma zenon_L1150_ *) % 10.45/10.61 assert (zenon_L1151_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (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) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((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 (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H1f zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H16b zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H200 zenon_H23e zenon_H6f zenon_H16e zenon_H1d zenon_H155 zenon_H1e6 zenon_H1f8 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_Hb0 zenon_H35 zenon_H203 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hd3 zenon_H1c0 zenon_H42 zenon_H25 zenon_Hf8. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.61 apply (zenon_L56_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.61 exact (zenon_H25 zenon_H2a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.61 apply (zenon_L1097_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.61 apply (zenon_L672_); trivial. % 10.45/10.61 exact (zenon_H23e zenon_H43). % 10.45/10.61 apply (zenon_L1119_); trivial. % 10.45/10.61 (* end of lemma zenon_L1151_ *) % 10.45/10.61 assert (zenon_L1152_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H1ef zenon_H1af zenon_H25 zenon_H42 zenon_H1c0 zenon_Hd3 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_Hb0 zenon_H3a zenon_H3c zenon_H44 zenon_H27 zenon_H1b4 zenon_H28 zenon_H238 zenon_H1f0 zenon_H97 zenon_H1dd zenon_He8 zenon_H191 zenon_He7 zenon_Hf8 zenon_H6f zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H155 zenon_H8c zenon_H7a zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177 zenon_H56 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_Hc6 zenon_H1ea. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.61 apply (zenon_L1149_); trivial. % 10.45/10.61 apply (zenon_L321_); trivial. % 10.45/10.61 exact (zenon_H203 zenon_H9a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.61 apply (zenon_L1150_); trivial. % 10.45/10.61 apply (zenon_L321_); trivial. % 10.45/10.61 exact (zenon_H203 zenon_H9a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.61 apply (zenon_L1151_); trivial. % 10.45/10.61 apply (zenon_L321_); trivial. % 10.45/10.61 (* end of lemma zenon_L1152_ *) % 10.45/10.61 assert (zenon_L1153_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H97 zenon_H28 zenon_He4 zenon_Hbb zenon_H44 zenon_Hb8 zenon_He8 zenon_H53 zenon_He7 zenon_H10b zenon_Hed zenon_H62 zenon_H4c. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.61 exact (zenon_H28 zenon_H31). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.61 apply (zenon_L59_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.61 apply (zenon_L75_); trivial. % 10.45/10.61 apply (zenon_L13_); trivial. % 10.45/10.61 (* end of lemma zenon_L1153_ *) % 10.45/10.61 assert (zenon_L1154_ : (((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 (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f zenon_H1d zenon_H5e zenon_H51 zenon_H97 zenon_H28 zenon_He4 zenon_Hbb zenon_H44 zenon_Hb8 zenon_He8 zenon_H53 zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.61 exact (zenon_H56 zenon_H2c). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.61 apply (zenon_L1_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.61 apply (zenon_L12_); trivial. % 10.45/10.61 apply (zenon_L1153_); trivial. % 10.45/10.61 (* end of lemma zenon_L1154_ *) % 10.45/10.61 assert (zenon_L1155_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H200 zenon_H25 zenon_H7d zenon_H80 zenon_H7e zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_Hcf zenon_H112 zenon_Haf zenon_H44 zenon_Hf8 zenon_Hc8 zenon_Hc7 zenon_H91 zenon_H3c zenon_Hc5 zenon_H23e. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.61 exact (zenon_H25 zenon_H2a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.61 apply (zenon_L1107_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.61 apply (zenon_L129_); trivial. % 10.45/10.61 exact (zenon_H23e zenon_H43). % 10.45/10.61 (* end of lemma zenon_L1155_ *) % 10.45/10.61 assert (zenon_L1156_ : (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H56 zenon_H177 zenon_H168 zenon_H103 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_Hae zenon_H23e zenon_H44 zenon_Hab zenon_H5e zenon_H203 zenon_H7a zenon_H8c zenon_H3a zenon_H155 zenon_Haf zenon_H35 zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H51 zenon_H6f zenon_Hf8 zenon_H192 zenon_He7 zenon_Hc1 zenon_H191 zenon_He8 zenon_Hb1 zenon_H1dd zenon_H97 zenon_H1f0 zenon_H238 zenon_H28 zenon_H1b4 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.61 apply (zenon_L56_); trivial. % 10.45/10.61 apply (zenon_L1148_); trivial. % 10.45/10.61 apply (zenon_L1119_); trivial. % 10.45/10.61 apply (zenon_L674_); trivial. % 10.45/10.61 (* end of lemma zenon_L1156_ *) % 10.45/10.61 assert (zenon_L1157_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e0)) = (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). % 10.45/10.61 do 0 intro. intros zenon_H1c3 zenon_He4 zenon_H15a zenon_H1bc zenon_Hc6 zenon_H3a zenon_Hbc zenon_H1c0. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H73 | zenon_intro zenon_H1c4 ]. % 10.45/10.61 apply (zenon_L1094_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H76 | zenon_intro zenon_H1c5 ]. % 10.45/10.61 apply (zenon_L217_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H74 ]. % 10.45/10.61 apply (zenon_L321_); trivial. % 10.45/10.61 apply (zenon_L219_); trivial. % 10.45/10.61 (* end of lemma zenon_L1157_ *) % 10.45/10.61 assert (zenon_L1158_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H1c0 zenon_H1bc zenon_Hc6 zenon_H1c3 zenon_Hf8 zenon_H6f zenon_H51 zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H35 zenon_H15a zenon_Haf zenon_H155 zenon_H3a zenon_H8c zenon_H7d zenon_H80 zenon_H7a zenon_H203 zenon_H5e zenon_Hab zenon_H44 zenon_H23e zenon_Hae zenon_He4 zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.61 apply (zenon_L1147_); trivial. % 10.45/10.61 apply (zenon_L1157_); trivial. % 10.45/10.61 (* end of lemma zenon_L1158_ *) % 10.45/10.61 assert (zenon_L1159_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H1c0 zenon_H1bc zenon_H1c3 zenon_H1ea zenon_Hc6 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1b4 zenon_H28 zenon_H238 zenon_H1f0 zenon_H97 zenon_H1dd zenon_H191 zenon_He7 zenon_Hf8 zenon_H6f zenon_H51 zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H35 zenon_H155 zenon_H3a zenon_H8c zenon_H7a zenon_H203 zenon_H5e zenon_Hab zenon_H44 zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177 zenon_H56 zenon_H1af zenon_H1ef. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.61 apply (zenon_L1156_); trivial. % 10.45/10.61 apply (zenon_L321_); trivial. % 10.45/10.61 exact (zenon_H203 zenon_H9a). % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.61 apply (zenon_L1127_); trivial. % 10.45/10.61 exact (zenon_H203 zenon_H9a). % 10.45/10.61 apply (zenon_L1128_); trivial. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.61 apply (zenon_L1158_); trivial. % 10.45/10.61 apply (zenon_L123_); trivial. % 10.45/10.61 (* end of lemma zenon_L1159_ *) % 10.45/10.61 assert (zenon_L1160_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 10.45/10.61 do 0 intro. intros zenon_H1ef zenon_H1af zenon_H56 zenon_H177 zenon_H168 zenon_H103 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_Hae zenon_H23e zenon_H44 zenon_Hab zenon_H5e zenon_H203 zenon_H7a zenon_H8c zenon_H155 zenon_H35 zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H6f zenon_Hf8 zenon_He7 zenon_H191 zenon_H1dd zenon_H97 zenon_H1f0 zenon_H238 zenon_H28 zenon_H1b4 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_Hc6 zenon_H1ea zenon_H1c3 zenon_H1bc zenon_H1c0 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5. % 10.45/10.61 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.61 apply (zenon_L129_); trivial. % 10.45/10.61 apply (zenon_L1159_); trivial. % 10.45/10.61 (* end of lemma zenon_L1160_ *) % 10.45/10.61 assert (zenon_L1161_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (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))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H16b zenon_H16e zenon_Hfd zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H97 zenon_H1c0 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H5e zenon_H203 zenon_H4c zenon_Hb0 zenon_H10b zenon_H68 zenon_H53 zenon_H28 zenon_Hf8. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_L1104_); trivial. % 10.45/10.62 apply (zenon_L1119_); trivial. % 10.45/10.62 (* end of lemma zenon_L1161_ *) % 10.45/10.62 assert (zenon_L1162_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (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) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H1bc zenon_Hc6 zenon_H1c3 zenon_H200 zenon_Hae zenon_H23e zenon_H7a zenon_H80 zenon_H7d zenon_H8c zenon_H155 zenon_Haf zenon_H15a zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H6f zenon_Hf8 zenon_H27 zenon_H44 zenon_H3c zenon_H3a zenon_Hb0 zenon_H35 zenon_H203 zenon_H5e zenon_Hab zenon_Hb1 zenon_Hd3 zenon_He4 zenon_H1c0 zenon_H42 zenon_H25 zenon_Hec zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.62 exact (zenon_H25 zenon_H2a). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.62 apply (zenon_L1097_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_L1146_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_L1119_); trivial. % 10.45/10.62 apply (zenon_L1157_); trivial. % 10.45/10.62 (* end of lemma zenon_L1162_ *) % 10.45/10.62 assert (zenon_L1163_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (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 (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.62 do 0 intro. intros zenon_Hde zenon_H195 zenon_H216 zenon_H1ef zenon_H1af zenon_H42 zenon_H1c0 zenon_Hd3 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_Hb0 zenon_H3c zenon_H44 zenon_H1b4 zenon_H238 zenon_H1f0 zenon_H97 zenon_H1dd zenon_H191 zenon_He7 zenon_Hf8 zenon_H6f zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H155 zenon_H8c zenon_H7a zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177 zenon_He3 zenon_He4 zenon_H7d zenon_Hec zenon_Hc6 zenon_H1ea zenon_H1bc zenon_H1c3 zenon_H67 zenon_H80. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.62 apply (zenon_L111_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.62 apply (zenon_L1144_); trivial. % 10.45/10.62 apply (zenon_L1152_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.62 apply (zenon_L56_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.62 exact (zenon_H25 zenon_H2a). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.62 apply (zenon_L1103_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_L1154_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_L1119_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_L1155_); trivial. % 10.45/10.62 apply (zenon_L1119_); trivial. % 10.45/10.62 apply (zenon_L1152_); trivial. % 10.45/10.62 apply (zenon_L79_); trivial. % 10.45/10.62 apply (zenon_L149_); trivial. % 10.45/10.62 apply (zenon_L325_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.62 apply (zenon_L1160_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.62 apply (zenon_L56_); trivial. % 10.45/10.62 apply (zenon_L1154_); trivial. % 10.45/10.62 apply (zenon_L1119_); trivial. % 10.45/10.62 apply (zenon_L325_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_L1161_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_L1155_); trivial. % 10.45/10.62 apply (zenon_L81_); trivial. % 10.45/10.62 apply (zenon_L1098_); trivial. % 10.45/10.62 apply (zenon_L79_); trivial. % 10.45/10.62 apply (zenon_L149_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_L69_); trivial. % 10.45/10.62 apply (zenon_L111_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.62 apply (zenon_L1152_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_L1162_); trivial. % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 apply (zenon_L123_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_L1159_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 apply (zenon_L1099_); trivial. % 10.45/10.62 apply (zenon_L111_); trivial. % 10.45/10.62 exact (zenon_H80 zenon_H84). % 10.45/10.62 (* end of lemma zenon_L1163_ *) % 10.45/10.62 assert (zenon_L1164_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((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)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.62 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hf8 zenon_H25 zenon_H42 zenon_H1c0 zenon_Hd3 zenon_Hb1 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_Hb0 zenon_H3a zenon_H3c zenon_H44 zenon_H27 zenon_H1f8 zenon_H1e6 zenon_H155 zenon_H1d zenon_H16e zenon_H6f zenon_H23e zenon_H200 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H1f zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H177. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_L1151_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 (* end of lemma zenon_L1164_ *) % 10.45/10.62 assert (zenon_L1165_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H200 zenon_H25 zenon_H114 zenon_Hbd zenon_H112 zenon_Hcf zenon_H110 zenon_H1d zenon_Hd3 zenon_H118 zenon_Hc5 zenon_Hc7 zenon_H91 zenon_H3c zenon_H127 zenon_Hd2 zenon_H23e. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.62 exact (zenon_H25 zenon_H2a). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.62 apply (zenon_L81_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_L1088_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 (* end of lemma zenon_L1165_ *) % 10.45/10.62 assert (zenon_L1166_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (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) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H157 zenon_H151 zenon_H25 zenon_H118 zenon_H114 zenon_H1d zenon_H110 zenon_Hd3 zenon_Hd2 zenon_H127 zenon_H3c zenon_Hc5 zenon_H23e zenon_H200 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_Hcf zenon_H112 zenon_Haf zenon_H68 zenon_H44 zenon_Hf8 zenon_Hc6 zenon_H158. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_L1107_); trivial. % 10.45/10.62 apply (zenon_L1165_); trivial. % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 apply (zenon_L79_); trivial. % 10.45/10.62 (* end of lemma zenon_L1166_ *) % 10.45/10.62 assert (zenon_L1167_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.62 do 0 intro. intros zenon_Hc6 zenon_Hde zenon_H1d zenon_H25 zenon_H177 zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H3c zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H7a zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H16b zenon_H16e zenon_Hfd zenon_H23e zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_H44 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H97 zenon_H1c0 zenon_Hd3 zenon_Hab zenon_H5e zenon_H203 zenon_H4c zenon_Hb0 zenon_H10b zenon_H68 zenon_H53 zenon_Hf8 zenon_H127 zenon_Hd2 zenon_H1ea. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_L1161_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 apply (zenon_L1166_); trivial. % 10.45/10.62 apply (zenon_L149_); trivial. % 10.45/10.62 exact (zenon_H23e zenon_H43). % 10.45/10.62 (* end of lemma zenon_L1167_ *) % 10.45/10.62 assert (zenon_L1168_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 10.45/10.62 do 0 intro. intros zenon_He7 zenon_H1ea zenon_Hd2 zenon_H127 zenon_Hf8 zenon_H53 zenon_H10b zenon_Hb0 zenon_H4c zenon_H203 zenon_H5e zenon_Hab zenon_Hd3 zenon_H1c0 zenon_H97 zenon_He3 zenon_H80 zenon_H7d zenon_Hec zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_H23e zenon_Hfd zenon_H16e zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H7a zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_H12f zenon_H144 zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H177 zenon_H25 zenon_H1d zenon_Hde zenon_Hc6 zenon_He8 zenon_Hb8 zenon_H44 zenon_Hbb zenon_He4. % 10.45/10.62 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.62 apply (zenon_L1167_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.62 exact (zenon_He8 zenon_Heb). % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.62 apply (zenon_L57_); trivial. % 10.45/10.62 apply (zenon_L58_); trivial. % 10.45/10.62 (* end of lemma zenon_L1168_ *) % 10.45/10.62 assert (zenon_L1169_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H200 zenon_H23e zenon_H3c zenon_H91 zenon_Hc7 zenon_Hc5 zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_Hde zenon_H5e zenon_H35 zenon_H4c zenon_Hf5 zenon_Hcf zenon_H112 zenon_Haf zenon_H44 zenon_Hf8 zenon_H25 zenon_H127 zenon_Hd2 zenon_Hd3 zenon_H110 zenon_H1d zenon_H114 zenon_H118 zenon_H151. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.62 apply (zenon_L1155_); trivial. % 10.45/10.62 apply (zenon_L1165_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 (* end of lemma zenon_L1169_ *) % 10.45/10.62 assert (zenon_L1170_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((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 (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H1bc zenon_H1c3 zenon_H1ea zenon_Hc6 zenon_H25 zenon_H42 zenon_H1c0 zenon_Hd3 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_Hb0 zenon_H3a zenon_H3c zenon_H44 zenon_H27 zenon_H1b4 zenon_H28 zenon_H238 zenon_H1f0 zenon_H97 zenon_H1dd zenon_H191 zenon_He7 zenon_Hf8 zenon_H6f zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H155 zenon_H8c zenon_H7a zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177 zenon_H56 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H127 zenon_Hd2 zenon_H1af zenon_H1ef. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_L1149_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 exact (zenon_H203 zenon_H9a). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_L1150_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 exact (zenon_H203 zenon_H9a). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_L1164_); trivial. % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_L1162_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 apply (zenon_L123_); trivial. % 10.45/10.62 (* end of lemma zenon_L1170_ *) % 10.45/10.62 assert (zenon_L1171_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((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 (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (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)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.62 do 0 intro. intros zenon_H1ef zenon_H1af zenon_Hd2 zenon_H127 zenon_Hec zenon_H7d zenon_H80 zenon_He4 zenon_He3 zenon_H1b4 zenon_H28 zenon_H238 zenon_H1f0 zenon_H97 zenon_H1dd zenon_He8 zenon_H191 zenon_He7 zenon_Hf8 zenon_H6f zenon_H51 zenon_H159 zenon_H1e6 zenon_H1f8 zenon_H35 zenon_H155 zenon_H3a zenon_H8c zenon_H7a zenon_H203 zenon_H5e zenon_Hab zenon_H44 zenon_H23e zenon_Hae zenon_H95 zenon_H173 zenon_H174 zenon_H4a zenon_Hfd zenon_H16e zenon_H16b zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_Hda zenon_H64 zenon_H1f zenon_H200 zenon_H204 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H86 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H103 zenon_H168 zenon_H177 zenon_H56 zenon_Hc6 zenon_H1ea. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.62 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.62 apply (zenon_L1156_); trivial. % 10.45/10.62 exact (zenon_H127 zenon_Hd0). % 10.45/10.62 apply (zenon_L321_); trivial. % 10.45/10.62 exact (zenon_H203 zenon_H9a). % 10.45/10.62 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.62 apply (zenon_L1137_); trivial. % 10.45/10.62 exact (zenon_H203 zenon_H9a). % 10.45/10.62 apply (zenon_L1138_); trivial. % 10.45/10.62 (* end of lemma zenon_L1171_ *) % 10.45/10.62 assert (zenon_L1172_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (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)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (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)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H1ea zenon_Hc6 zenon_H56 zenon_H177 zenon_H168 zenon_H103 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_Hae zenon_H23e zenon_H44 zenon_Hab zenon_H5e zenon_H203 zenon_H7a zenon_H8c zenon_H155 zenon_H35 zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H6f zenon_Hf8 zenon_He7 zenon_H191 zenon_He8 zenon_H1dd zenon_H97 zenon_H1f0 zenon_H238 zenon_H28 zenon_H1b4 zenon_He3 zenon_He4 zenon_H80 zenon_H7d zenon_Hec zenon_H1af zenon_H1ef zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_H127 zenon_Hd2. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_L1088_); trivial. % 10.45/10.63 apply (zenon_L1171_); trivial. % 10.45/10.63 (* end of lemma zenon_L1172_ *) % 10.45/10.63 assert (zenon_L1173_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((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)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.63 do 0 intro. intros zenon_Hde zenon_H195 zenon_H216 zenon_H1ef zenon_H1af zenon_Hd2 zenon_H127 zenon_Hec zenon_H7d zenon_He4 zenon_He3 zenon_H177 zenon_H168 zenon_H103 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H86 zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H204 zenon_H200 zenon_H1f zenon_H64 zenon_Hda zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_H16b zenon_H16e zenon_Hfd zenon_H4a zenon_H174 zenon_H173 zenon_H95 zenon_Hae zenon_H23e zenon_H7a zenon_H8c zenon_H155 zenon_H1f8 zenon_H1e6 zenon_H159 zenon_H6f zenon_Hf8 zenon_He7 zenon_H191 zenon_H1dd zenon_H97 zenon_H1f0 zenon_H238 zenon_H1b4 zenon_H44 zenon_H3c zenon_Hb0 zenon_H35 zenon_H203 zenon_H5e zenon_Hab zenon_Hd3 zenon_H1c0 zenon_H42 zenon_Hc6 zenon_H1ea zenon_H1c3 zenon_H1bc zenon_H67 zenon_H80. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.63 apply (zenon_L111_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L1144_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L1164_); trivial. % 10.45/10.63 apply (zenon_L1168_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_L1169_); trivial. % 10.45/10.63 apply (zenon_L1170_); trivial. % 10.45/10.63 apply (zenon_L79_); trivial. % 10.45/10.63 apply (zenon_L149_); trivial. % 10.45/10.63 apply (zenon_L325_); trivial. % 10.45/10.63 exact (zenon_H23e zenon_H43). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_L1172_); trivial. % 10.45/10.63 apply (zenon_L1168_); trivial. % 10.45/10.63 apply (zenon_L325_); trivial. % 10.45/10.63 exact (zenon_H23e zenon_H43). % 10.45/10.63 apply (zenon_L1167_); trivial. % 10.45/10.63 apply (zenon_L111_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.63 apply (zenon_L1170_); trivial. % 10.45/10.63 exact (zenon_H23e zenon_H43). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.63 apply (zenon_L1171_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L1158_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L123_); trivial. % 10.45/10.63 exact (zenon_H23e zenon_H43). % 10.45/10.63 apply (zenon_L1099_); trivial. % 10.45/10.63 apply (zenon_L111_); trivial. % 10.45/10.63 exact (zenon_H80 zenon_H84). % 10.45/10.63 (* end of lemma zenon_L1173_ *) % 10.45/10.63 assert (zenon_L1174_ : (((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)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.63 do 0 intro. intros zenon_He7 zenon_H2a zenon_H26 zenon_H35 zenon_H44 zenon_H4b zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hc1 zenon_Hde zenon_H5e zenon_Hf2. % 10.45/10.63 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.63 apply (zenon_L937_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.63 exact (zenon_He8 zenon_Heb). % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.63 apply (zenon_L765_); trivial. % 10.45/10.63 apply (zenon_L206_); trivial. % 10.45/10.63 (* end of lemma zenon_L1174_ *) % 10.45/10.63 assert (zenon_L1175_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H44 zenon_H35 zenon_H26 zenon_H2a zenon_He7 zenon_H10b zenon_Hed zenon_H62 zenon_H4c. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.63 exact (zenon_H28 zenon_H31). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.63 apply (zenon_L1174_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.63 apply (zenon_L75_); trivial. % 10.45/10.63 apply (zenon_L13_); trivial. % 10.45/10.63 (* end of lemma zenon_L1175_ *) % 10.45/10.63 assert (zenon_L1176_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f0 zenon_H6f zenon_H100 zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H44 zenon_H35 zenon_H26 zenon_H2a zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.63 exact (zenon_H56 zenon_H2c). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.63 apply (zenon_L327_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.63 apply (zenon_L228_); trivial. % 10.45/10.63 apply (zenon_L1175_); trivial. % 10.45/10.63 (* end of lemma zenon_L1176_ *) % 10.45/10.63 assert (zenon_L1177_ : ((~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((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))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H151 zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H64 zenon_H28 zenon_He7 zenon_H191 zenon_Hc1 zenon_H1f zenon_H192 zenon_H44 zenon_H35 zenon_Hde zenon_H26 zenon_H10b zenon_H4c zenon_H97 zenon_H6f zenon_Hf2 zenon_H1f0 zenon_H56 zenon_Hf8. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.63 apply (zenon_L225_); trivial. % 10.45/10.63 apply (zenon_L1176_); trivial. % 10.45/10.63 apply (zenon_L207_); trivial. % 10.45/10.63 (* end of lemma zenon_L1177_ *) % 10.45/10.63 assert (zenon_L1178_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H1ef zenon_H169 zenon_He7 zenon_H5e zenon_H44 zenon_H35 zenon_Hf2 zenon_Hde zenon_He8 zenon_H1f zenon_Hc1 zenon_H191 zenon_H151 zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_H2a zenon_H12f zenon_H64 zenon_H28 zenon_H26 zenon_H10b zenon_H4c zenon_H97 zenon_H6f zenon_H1f0 zenon_H56 zenon_Hf8 zenon_H1ea. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.63 apply (zenon_L1052_); trivial. % 10.45/10.63 apply (zenon_L1177_); trivial. % 10.45/10.63 apply (zenon_L140_); trivial. % 10.45/10.63 (* end of lemma zenon_L1178_ *) % 10.45/10.63 assert (zenon_L1179_ : (((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). % 10.45/10.63 do 0 intro. intros zenon_H1c3 zenon_H2a zenon_H1ba zenon_H15a zenon_H1bc zenon_Hc6 zenon_H3a zenon_Hbc zenon_H1c0. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H73 | zenon_intro zenon_H1c4 ]. % 10.45/10.63 apply (zenon_L216_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H76 | zenon_intro zenon_H1c5 ]. % 10.45/10.63 apply (zenon_L217_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_Hcf | zenon_intro zenon_H74 ]. % 10.45/10.63 apply (zenon_L321_); trivial. % 10.45/10.63 apply (zenon_L219_); trivial. % 10.45/10.63 (* end of lemma zenon_L1179_ *) % 10.45/10.63 assert (zenon_L1180_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (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 (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H150 zenon_H1ba zenon_H2a zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H27 zenon_H35 zenon_H15a zenon_Hc6 zenon_H3a zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_Hf2 zenon_H5e zenon_H44 zenon_Hdd. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.63 apply (zenon_L1055_); trivial. % 10.45/10.63 apply (zenon_L1179_); trivial. % 10.45/10.63 (* end of lemma zenon_L1180_ *) % 10.45/10.63 assert (zenon_L1181_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (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 (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 (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H168 zenon_Hdd zenon_H16b zenon_H80 zenon_H53 zenon_H14d zenon_Hc6 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H150 zenon_H64 zenon_H27 zenon_H191 zenon_Hc1 zenon_H1f zenon_H3c zenon_H3a zenon_H97 zenon_H95 zenon_H4c zenon_H26 zenon_H2a zenon_Hde zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_H28 zenon_H42 zenon_Hf2 zenon_H1f0 zenon_H56 zenon_H169 zenon_H1ef. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.63 exact (zenon_H56 zenon_H2c). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.63 apply (zenon_L327_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.45/10.63 exact (zenon_H27 zenon_H32). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.45/10.63 apply (zenon_L331_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.45/10.63 apply (zenon_L5_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.63 exact (zenon_H28 zenon_H31). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.63 apply (zenon_L1174_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.63 apply (zenon_L130_); trivial. % 10.45/10.63 apply (zenon_L54_); trivial. % 10.45/10.63 apply (zenon_L610_); trivial. % 10.45/10.63 apply (zenon_L140_); trivial. % 10.45/10.63 apply (zenon_L1180_); trivial. % 10.45/10.63 (* end of lemma zenon_L1181_ *) % 10.45/10.63 assert (zenon_L1182_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (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 (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((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))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_H27 zenon_H35 zenon_H15a zenon_H112 zenon_Hb8 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_Hf2 zenon_H5e zenon_H44 zenon_Hdd. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.45/10.63 exact (zenon_H27 zenon_H32). % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.45/10.63 apply (zenon_L238_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.45/10.63 apply (zenon_L79_); trivial. % 10.45/10.63 apply (zenon_L209_); trivial. % 10.45/10.63 apply (zenon_L1058_); trivial. % 10.45/10.63 (* end of lemma zenon_L1182_ *) % 10.45/10.63 assert (zenon_L1183_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.63 do 0 intro. intros zenon_Hdd zenon_H27 zenon_H35 zenon_H1dd zenon_H95 zenon_H15a zenon_H4c zenon_H28 zenon_Hda zenon_H14d zenon_H44 zenon_Hf2 zenon_H5e zenon_Hed zenon_H53 zenon_H8d. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.45/10.63 exact (zenon_H27 zenon_H32). % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.45/10.63 apply (zenon_L238_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.45/10.63 apply (zenon_L306_); trivial. % 10.45/10.63 apply (zenon_L792_); trivial. % 10.45/10.63 (* end of lemma zenon_L1183_ *) % 10.45/10.63 assert (zenon_L1184_ : (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H35 zenon_Hf2 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_Hcf zenon_H95 zenon_H15a zenon_H4c zenon_H28 zenon_Hdd zenon_H1dd zenon_H27. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.45/10.63 exact (zenon_H28 zenon_H31). % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.45/10.63 apply (zenon_L236_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.45/10.63 apply (zenon_L155_); trivial. % 10.45/10.63 apply (zenon_L1057_); trivial. % 10.45/10.63 apply (zenon_L1183_); trivial. % 10.45/10.63 apply (zenon_L1058_); trivial. % 10.45/10.63 (* end of lemma zenon_L1184_ *) % 10.45/10.63 assert (zenon_L1185_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((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) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (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)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H158 zenon_H1ef zenon_H169 zenon_H42 zenon_H28 zenon_He7 zenon_H5e zenon_H44 zenon_H35 zenon_Hde zenon_H2a zenon_H26 zenon_H4c zenon_H95 zenon_H97 zenon_H1f zenon_Hc1 zenon_H191 zenon_H27 zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hc6 zenon_H14d zenon_H53 zenon_H80 zenon_H16b zenon_Hdd zenon_H168 zenon_H56 zenon_H1f0 zenon_Hf2 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H103 zenon_Hec zenon_H15a zenon_H159 zenon_H1cb zenon_H64 zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H157 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H165 zenon_H108 zenon_H23d zenon_H1dd zenon_H112. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_L832_); trivial. % 10.45/10.63 apply (zenon_L1181_); trivial. % 10.45/10.63 apply (zenon_L1182_); trivial. % 10.45/10.63 apply (zenon_L1184_); trivial. % 10.45/10.63 (* end of lemma zenon_L1185_ *) % 10.45/10.63 assert (zenon_L1186_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (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)))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (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)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H157 zenon_Hcf zenon_H112 zenon_Hd2 zenon_H127 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_H155 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H95 zenon_H135 zenon_Hf8 zenon_Hbb zenon_H150 zenon_H152 zenon_H158. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L121_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 apply (zenon_L79_); trivial. % 10.45/10.63 (* end of lemma zenon_L1186_ *) % 10.45/10.63 assert (zenon_L1187_ : ((~((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 (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H168 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H4c zenon_H165 zenon_H158 zenon_H152 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H2a zenon_H144 zenon_H135 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H127 zenon_Hd2 zenon_H157 zenon_H112 zenon_H155 zenon_H156. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L115_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 apply (zenon_L1186_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L127_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_L1082_); trivial. % 10.45/10.63 apply (zenon_L79_); trivial. % 10.45/10.63 (* end of lemma zenon_L1187_ *) % 10.45/10.63 assert (zenon_L1188_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((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))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H158 zenon_H152 zenon_H150 zenon_Hbb zenon_H4c zenon_H64 zenon_Hf5 zenon_H7a zenon_H135 zenon_H35 zenon_H169 zenon_H5e zenon_H53 zenon_H44 zenon_H14d zenon_Hb1 zenon_H3c zenon_Hc5 zenon_H1d zenon_H1f zenon_H56 zenon_H95 zenon_H80 zenon_H16b zenon_H151 zenon_H127 zenon_Hd2. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L147_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 (* end of lemma zenon_L1188_ *) % 10.45/10.63 assert (zenon_L1189_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H158 zenon_H135 zenon_H152 zenon_Hc5 zenon_H91 zenon_H51 zenon_H3c zenon_H127 zenon_Hd2. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_L1088_); trivial. % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 (* end of lemma zenon_L1189_ *) % 10.45/10.63 assert (zenon_L1190_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H157 zenon_Hcf zenon_H112 zenon_Hd2 zenon_H127 zenon_H3c zenon_H51 zenon_Hc5 zenon_H152 zenon_H135 zenon_H158. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_L1189_); trivial. % 10.45/10.63 apply (zenon_L79_); trivial. % 10.45/10.63 (* end of lemma zenon_L1190_ *) % 10.45/10.63 assert (zenon_L1191_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((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 (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H156 zenon_H51 zenon_H112 zenon_H157 zenon_Hd2 zenon_H127 zenon_H151 zenon_H16b zenon_H80 zenon_H95 zenon_H56 zenon_H1f zenon_H1d zenon_Hc5 zenon_H3c zenon_H14d zenon_H44 zenon_H53 zenon_H5e zenon_H169 zenon_H35 zenon_H135 zenon_H7a zenon_Hf5 zenon_H64 zenon_H4c zenon_Hbb zenon_H150 zenon_H152 zenon_H158. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_L1188_); trivial. % 10.45/10.63 apply (zenon_L1190_); trivial. % 10.45/10.63 (* end of lemma zenon_L1191_ *) % 10.45/10.63 assert (zenon_L1192_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H156 zenon_Hda zenon_H4c zenon_H169 zenon_Hf5 zenon_H16f zenon_H118 zenon_H114 zenon_H112 zenon_H110 zenon_Hd3 zenon_H95 zenon_H80 zenon_H16b zenon_H28 zenon_H151 zenon_Hd2 zenon_H127 zenon_Hfd zenon_H68 zenon_H103 zenon_H35 zenon_H10b zenon_H135 zenon_H144 zenon_H1d zenon_H16e zenon_H3c zenon_Hc5 zenon_H44 zenon_H108 zenon_H152 zenon_H158. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_L153_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 apply (zenon_L156_); trivial. % 10.45/10.63 (* end of lemma zenon_L1192_ *) % 10.45/10.63 assert (zenon_L1193_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (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) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((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 (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (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)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H173 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_H12f zenon_Hf8 zenon_H159 zenon_H168 zenon_H108 zenon_H165 zenon_H16e zenon_H103 zenon_H155 zenon_H157 zenon_H112 zenon_H156 zenon_Hd2 zenon_H127 zenon_H151 zenon_H16b zenon_H95 zenon_H1f zenon_Hc5 zenon_H3c zenon_H14d zenon_H44 zenon_H53 zenon_H5e zenon_H169 zenon_H35 zenon_H7a zenon_Hf5 zenon_H64 zenon_H4c zenon_Hbb zenon_H150 zenon_H158 zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H10b zenon_H144 zenon_H174 zenon_H152 zenon_H135 zenon_H80. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.63 apply (zenon_L1187_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.63 apply (zenon_L1188_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 10.45/10.63 apply (zenon_L1191_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 10.45/10.63 apply (zenon_L118_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 10.45/10.63 apply (zenon_L150_); trivial. % 10.45/10.63 apply (zenon_L113_); trivial. % 10.45/10.63 exact (zenon_H127 zenon_Hd0). % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 apply (zenon_L79_); trivial. % 10.45/10.63 apply (zenon_L1192_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 exact (zenon_H80 zenon_H84). % 10.45/10.63 (* end of lemma zenon_L1193_ *) % 10.45/10.63 assert (zenon_L1194_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H4a zenon_H23e zenon_H158 zenon_H152 zenon_H108 zenon_H44 zenon_Hc5 zenon_H3c zenon_H16e zenon_H1d zenon_H144 zenon_H135 zenon_H10b zenon_H35 zenon_H103 zenon_H68 zenon_Hfd zenon_H127 zenon_Hd2 zenon_H151 zenon_H16b zenon_H80 zenon_H95 zenon_Hd3 zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_H4c zenon_Hda zenon_H156. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.63 apply (zenon_L1192_); trivial. % 10.45/10.63 exact (zenon_H23e zenon_H43). % 10.45/10.63 (* end of lemma zenon_L1194_ *) % 10.45/10.63 assert (zenon_L1195_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (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) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H173 zenon_H155 zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_H12f zenon_Hf8 zenon_H165 zenon_H159 zenon_H168 zenon_H174 zenon_H4a zenon_H23e zenon_H158 zenon_H108 zenon_H44 zenon_Hc5 zenon_H3c zenon_H16e zenon_H144 zenon_H10b zenon_H35 zenon_H103 zenon_Hfd zenon_H127 zenon_Hd2 zenon_H151 zenon_H16b zenon_H95 zenon_Hd3 zenon_H110 zenon_H112 zenon_H114 zenon_H118 zenon_H16f zenon_Hf5 zenon_H169 zenon_H4c zenon_Hda zenon_H156 zenon_H157 zenon_H1f zenon_H14d zenon_H53 zenon_H5e zenon_H7a zenon_H64 zenon_Hbb zenon_H150 zenon_H200 zenon_H14a zenon_H204 zenon_H152 zenon_H135 zenon_H80. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.63 apply (zenon_L1187_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.63 exact (zenon_H25 zenon_H2a). % 10.45/10.63 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.63 apply (zenon_L1194_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.63 apply (zenon_L1191_); trivial. % 10.45/10.63 exact (zenon_H23e zenon_H43). % 10.45/10.63 apply (zenon_L1194_); trivial. % 10.45/10.63 apply (zenon_L1116_); trivial. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.63 apply (zenon_L116_); trivial. % 10.45/10.63 exact (zenon_H80 zenon_H84). % 10.45/10.63 (* end of lemma zenon_L1195_ *) % 10.45/10.63 assert (zenon_L1196_ : ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> False). % 10.45/10.63 do 0 intro. intros zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H35 zenon_H159 zenon_H108 zenon_H165 zenon_H4c zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H135 zenon_H144 zenon_H12f zenon_H95 zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H5e zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H28 | zenon_intro zenon_H23e ]. % 10.45/10.63 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.45/10.63 apply (zenon_L1056_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.45/10.64 apply (zenon_L1193_); trivial. % 10.45/10.64 apply (zenon_L1193_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.45/10.64 apply (zenon_L1117_); trivial. % 10.45/10.64 apply (zenon_L1117_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.45/10.64 apply (zenon_L1195_); trivial. % 10.45/10.64 apply (zenon_L1195_); trivial. % 10.45/10.64 (* end of lemma zenon_L1196_ *) % 10.45/10.64 assert (zenon_L1197_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e2)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H177 zenon_H80 zenon_H106 zenon_Hf2 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H7f. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.45/10.64 apply (zenon_L208_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.45/10.64 apply (zenon_L63_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.45/10.64 apply (zenon_L1196_); trivial. % 10.45/10.64 exact (zenon_H7f zenon_H85). % 10.45/10.64 (* end of lemma zenon_L1197_ *) % 10.45/10.64 assert (zenon_L1198_ : ((op (e0) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H68 zenon_H100 zenon_Hb1 zenon_H177 zenon_H80 zenon_Hf2 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H7f. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H108); [ zenon_intro zenon_H51 | zenon_intro zenon_H109 ]. % 10.45/10.64 apply (zenon_L69_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H109); [ zenon_intro zenon_H101 | zenon_intro zenon_H10a ]. % 10.45/10.64 apply (zenon_L71_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hb7 | zenon_intro zenon_H106 ]. % 10.45/10.64 exact (zenon_Hb1 zenon_Hb7). % 10.45/10.64 apply (zenon_L1197_); trivial. % 10.45/10.64 (* end of lemma zenon_L1198_ *) % 10.45/10.64 assert (zenon_L1199_ : (((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 (e2) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.45/10.64 do 0 intro. intros zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H78 zenon_H4b zenon_H216 zenon_H3a zenon_Hf2 zenon_H35. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.45/10.64 apply (zenon_L331_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.45/10.64 apply (zenon_L334_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.45/10.64 apply (zenon_L500_); trivial. % 10.45/10.64 apply (zenon_L63_); trivial. % 10.45/10.64 (* end of lemma zenon_L1199_ *) % 10.45/10.64 assert (zenon_L1200_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H177 zenon_H44 zenon_He4 zenon_H35 zenon_Hf2 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H7f. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.45/10.64 apply (zenon_L99_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.45/10.64 apply (zenon_L63_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.45/10.64 apply (zenon_L367_); trivial. % 10.45/10.64 exact (zenon_H7f zenon_H85). % 10.45/10.64 (* end of lemma zenon_L1200_ *) % 10.45/10.64 assert (zenon_L1201_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H177 zenon_H80 zenon_H52 zenon_H10b zenon_Hb9 zenon_H114 zenon_H95 zenon_H16b zenon_H35 zenon_Hf2 zenon_H106 zenon_H44 zenon_H7f. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H178 ]. % 10.45/10.64 apply (zenon_L366_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H178); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H179 ]. % 10.45/10.64 apply (zenon_L63_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H135 | zenon_intro zenon_H85 ]. % 10.45/10.64 apply (zenon_L113_); trivial. % 10.45/10.64 exact (zenon_H7f zenon_H85). % 10.45/10.64 (* end of lemma zenon_L1201_ *) % 10.45/10.64 assert (zenon_L1202_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H14d zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H5e zenon_H7f zenon_H44 zenon_Hf2 zenon_H35 zenon_H16b zenon_H95 zenon_H114 zenon_Hb9 zenon_H10b zenon_H52 zenon_H80 zenon_H177 zenon_H8d. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 10.45/10.64 apply (zenon_L1200_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 10.45/10.64 apply (zenon_L206_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 10.45/10.64 apply (zenon_L1201_); trivial. % 10.45/10.64 exact (zenon_H8d zenon_H7b). % 10.45/10.64 (* end of lemma zenon_L1202_ *) % 10.45/10.64 assert (zenon_L1203_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.64 do 0 intro. intros zenon_He7 zenon_Hfd zenon_H35 zenon_H3a zenon_H216 zenon_Hc0 zenon_Hc1 zenon_H8d zenon_H177 zenon_H80 zenon_H52 zenon_H10b zenon_H114 zenon_H95 zenon_H16b zenon_H44 zenon_H7f zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_H14d zenon_H4c zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hde zenon_H5e zenon_Hf2. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.64 apply (zenon_L69_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.64 exact (zenon_He8 zenon_Heb). % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H34 | zenon_intro zenon_He1 ]. % 10.45/10.64 apply (zenon_L331_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H4b | zenon_intro zenon_Hc2 ]. % 10.45/10.64 apply (zenon_L334_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 10.45/10.64 exact (zenon_Hc1 zenon_Hc4). % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hbd ]. % 10.45/10.64 apply (zenon_L1202_); trivial. % 10.45/10.64 apply (zenon_L207_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hd6 ]. % 10.45/10.64 apply (zenon_L500_); trivial. % 10.45/10.64 apply (zenon_L63_); trivial. % 10.45/10.64 apply (zenon_L206_); trivial. % 10.45/10.64 (* end of lemma zenon_L1203_ *) % 10.45/10.64 assert (zenon_L1204_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H56 zenon_H1f0 zenon_H6f zenon_H97 zenon_H28 zenon_H100 zenon_Hb1 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_Hda zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H53 zenon_H14a zenon_H151 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_Hf2 zenon_H5e zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H14d zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H7f zenon_H44 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H80 zenon_H177 zenon_H8d zenon_Hc1 zenon_Hc0 zenon_H216 zenon_H3a zenon_H35 zenon_Hfd zenon_He7 zenon_H4c. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.64 exact (zenon_H56 zenon_H2c). % 10.45/10.64 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.64 apply (zenon_L327_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.64 apply (zenon_L228_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.64 exact (zenon_H28 zenon_H31). % 10.45/10.64 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.64 apply (zenon_L1198_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.64 exact (zenon_He8 zenon_Heb). % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.64 apply (zenon_L1199_); trivial. % 10.45/10.64 apply (zenon_L206_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.64 apply (zenon_L1203_); trivial. % 10.45/10.64 apply (zenon_L13_); trivial. % 10.45/10.64 (* end of lemma zenon_L1204_ *) % 10.45/10.64 assert (zenon_L1205_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H64 zenon_H56 zenon_H1f0 zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H44 zenon_H35 zenon_H144 zenon_Hfd zenon_H6f zenon_H100 zenon_H3c zenon_H3a zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.64 exact (zenon_H56 zenon_H2c). % 10.45/10.64 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.64 apply (zenon_L327_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.64 apply (zenon_L228_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.64 exact (zenon_H28 zenon_H31). % 10.45/10.64 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.64 apply (zenon_L345_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.64 exact (zenon_He8 zenon_Heb). % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.64 apply (zenon_L765_); trivial. % 10.45/10.64 apply (zenon_L206_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.64 apply (zenon_L75_); trivial. % 10.45/10.64 apply (zenon_L13_); trivial. % 10.45/10.64 (* end of lemma zenon_L1205_ *) % 10.45/10.64 assert (zenon_L1206_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H1dd zenon_H28 zenon_He7 zenon_H191 zenon_Hc1 zenon_H192 zenon_H216 zenon_H3a zenon_Hde zenon_He8 zenon_Hfd zenon_H5e zenon_Hb1 zenon_H177 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H35 zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_Hc0 zenon_Hc8 zenon_H91 zenon_H51 zenon_H97 zenon_H100 zenon_H6f zenon_Hf2 zenon_H1f0 zenon_H56. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.64 apply (zenon_L1204_); trivial. % 10.45/10.64 apply (zenon_L1205_); trivial. % 10.45/10.64 apply (zenon_L1058_); trivial. % 10.45/10.64 (* end of lemma zenon_L1206_ *) % 10.45/10.64 assert (zenon_L1207_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.45/10.64 do 0 intro. intros zenon_Hc6 zenon_H1dd zenon_H28 zenon_He7 zenon_H191 zenon_Hc1 zenon_H192 zenon_H216 zenon_H3a zenon_Hde zenon_He8 zenon_Hfd zenon_H5e zenon_H177 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H35 zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_Hc0 zenon_Hc8 zenon_H51 zenon_H97 zenon_H100 zenon_H6f zenon_Hf2 zenon_H1f0 zenon_H56. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.64 apply (zenon_L1206_); trivial. % 10.45/10.64 apply (zenon_L500_); trivial. % 10.45/10.64 apply (zenon_L321_); trivial. % 10.45/10.64 (* end of lemma zenon_L1207_ *) % 10.45/10.64 assert (zenon_L1208_ : (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (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)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H28 zenon_H1dd zenon_H16b zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H5e zenon_H44 zenon_H35 zenon_Hf2 zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H177 zenon_H1cb zenon_H15a zenon_Hec zenon_H6f zenon_H3a zenon_H1e6 zenon_H1f8 zenon_H1f0 zenon_H56. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H14d); [ zenon_intro zenon_He4 | zenon_intro zenon_H14e ]. % 10.45/10.64 apply (zenon_L1200_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ]. % 10.45/10.64 apply (zenon_L206_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H106 | zenon_intro zenon_H7b ]. % 10.45/10.64 apply (zenon_L1197_); trivial. % 10.45/10.64 exact (zenon_H8d zenon_H7b). % 10.45/10.64 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.64 exact (zenon_H56 zenon_H2c). % 10.45/10.64 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.64 apply (zenon_L327_); trivial. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.64 apply (zenon_L349_); trivial. % 10.45/10.64 apply (zenon_L264_); trivial. % 10.45/10.64 apply (zenon_L1058_); trivial. % 10.45/10.64 (* end of lemma zenon_L1208_ *) % 10.45/10.64 assert (zenon_L1209_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H216 zenon_H56 zenon_H1f0 zenon_H1f8 zenon_H1e6 zenon_H3a zenon_H6f zenon_Hec zenon_H15a zenon_H1cb zenon_H177 zenon_Hc5 zenon_Hc8 zenon_H51 zenon_H3c zenon_H152 zenon_H158 zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_H1dd zenon_H28. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.64 apply (zenon_L1208_); trivial. % 10.45/10.64 apply (zenon_L500_); trivial. % 10.45/10.64 (* end of lemma zenon_L1209_ *) % 10.45/10.64 assert (zenon_L1210_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((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 (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 10.45/10.64 do 0 intro. intros zenon_Hc6 zenon_H16b zenon_H80 zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_H35 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H177 zenon_H100 zenon_H5e zenon_H68 zenon_Hfd zenon_H3a zenon_H6f. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.64 apply (zenon_L1198_); trivial. % 10.45/10.64 apply (zenon_L345_); trivial. % 10.45/10.64 apply (zenon_L321_); trivial. % 10.45/10.64 (* end of lemma zenon_L1210_ *) % 10.45/10.64 assert (zenon_L1211_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.64 do 0 intro. intros zenon_H1ef zenon_H191 zenon_Hc1 zenon_H68 zenon_H1f zenon_Hc6 zenon_H16b zenon_H80 zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_H35 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H177 zenon_H5e zenon_Hfd zenon_H3a zenon_H6f zenon_H1ea. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.64 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.64 apply (zenon_L323_); trivial. % 10.45/10.64 apply (zenon_L1210_); trivial. % 10.45/10.64 apply (zenon_L140_); trivial. % 10.45/10.64 (* end of lemma zenon_L1211_ *) % 10.45/10.64 assert (zenon_L1212_ : (~((op (e0) (e0)) = (op (e0) (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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (((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 (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H26 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_H67 zenon_H216 zenon_H240 zenon_Hd2 zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_Hc0 zenon_H97 zenon_H1f8 zenon_H1e6 zenon_Hec zenon_H1cb zenon_H1ef zenon_H169 zenon_He7 zenon_H5e zenon_H44 zenon_H35 zenon_Hf2 zenon_Hde zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H3c zenon_H42 zenon_H6f zenon_H1f0 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H80. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1178_); trivial. % 10.45/10.65 apply (zenon_L1185_); trivial. % 10.45/10.65 apply (zenon_L101_); trivial. % 10.45/10.65 apply (zenon_L937_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_L1060_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1052_); trivial. % 10.45/10.65 apply (zenon_L1207_); trivial. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_L1209_); trivial. % 10.45/10.65 apply (zenon_L1211_); trivial. % 10.45/10.65 exact (zenon_H80 zenon_H84). % 10.45/10.65 (* end of lemma zenon_L1212_ *) % 10.45/10.65 assert (zenon_L1213_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (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))) -> (((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 (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 10.45/10.65 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H56 zenon_H1f0 zenon_Hf2 zenon_Hc5 zenon_Hc7 zenon_H3c zenon_Hb1 zenon_H103 zenon_Hec zenon_H91 zenon_H15a zenon_H159 zenon_H1cb zenon_H64. % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.65 apply (zenon_L832_); trivial. % 10.45/10.65 exact (zenon_H127 zenon_Hd0). % 10.45/10.65 (* end of lemma zenon_L1213_ *) % 10.45/10.65 assert (zenon_L1214_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.65 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hdd zenon_H44 zenon_H5e zenon_Hf2 zenon_H16b zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_H3a zenon_Hc6 zenon_H15a zenon_H35 zenon_H27 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177. % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.65 apply (zenon_L1059_); trivial. % 10.45/10.65 exact (zenon_H127 zenon_Hd0). % 10.45/10.65 (* end of lemma zenon_L1214_ *) % 10.45/10.65 assert (zenon_L1215_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((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 (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.65 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_Hdd zenon_H44 zenon_H5e zenon_Hf2 zenon_H16b zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hb8 zenon_H112 zenon_H15a zenon_H35 zenon_H27 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177. % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.65 apply (zenon_L1182_); trivial. % 10.45/10.65 exact (zenon_H127 zenon_Hd0). % 10.45/10.65 (* end of lemma zenon_L1215_ *) % 10.45/10.65 assert (zenon_L1216_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.45/10.65 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H27 zenon_H1dd zenon_Hdd zenon_H28 zenon_H4c zenon_H15a zenon_H95 zenon_Hcf zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_Hf2 zenon_H35. % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.65 apply (zenon_L1184_); trivial. % 10.45/10.65 exact (zenon_H127 zenon_Hd0). % 10.45/10.65 (* end of lemma zenon_L1216_ *) % 10.45/10.65 assert (zenon_L1217_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.65 do 0 intro. intros zenon_He7 zenon_H1ea zenon_H6f zenon_H3a zenon_Hfd zenon_H177 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H95 zenon_H4c zenon_H53 zenon_H80 zenon_H16b zenon_Hc6 zenon_H1ef zenon_H35 zenon_H44 zenon_Haf zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hc1 zenon_Hde zenon_H5e zenon_Hf2. % 10.45/10.65 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.65 apply (zenon_L1211_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.65 exact (zenon_He8 zenon_Heb). % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.65 apply (zenon_L1051_); trivial. % 10.45/10.65 apply (zenon_L206_); trivial. % 10.45/10.65 (* end of lemma zenon_L1217_ *) % 10.45/10.65 assert (zenon_L1218_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.45/10.65 do 0 intro. intros zenon_Hc6 zenon_H127 zenon_H56 zenon_H1f0 zenon_Hf2 zenon_H6f zenon_H100 zenon_H97 zenon_H51 zenon_Hc0 zenon_H16b zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H35 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H177 zenon_H5e zenon_Hfd zenon_He8 zenon_Hde zenon_H3a zenon_H216 zenon_H192 zenon_Hc1 zenon_H191 zenon_He7 zenon_H28 zenon_H1dd. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.65 apply (zenon_L1206_); trivial. % 10.45/10.65 exact (zenon_H127 zenon_Hd0). % 10.45/10.65 apply (zenon_L500_); trivial. % 10.45/10.65 apply (zenon_L321_); trivial. % 10.45/10.65 (* end of lemma zenon_L1218_ *) % 10.45/10.65 assert (zenon_L1219_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (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 (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.45/10.65 do 0 intro. intros zenon_He7 zenon_Hde zenon_He8 zenon_H1ea zenon_H6f zenon_H3a zenon_Hfd zenon_H5e zenon_H177 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H35 zenon_H95 zenon_H4c zenon_Hf2 zenon_H53 zenon_H80 zenon_H16b zenon_Hc6 zenon_H1f zenon_Hc1 zenon_H191 zenon_H1ef zenon_H127 zenon_H56 zenon_H1f0 zenon_H97 zenon_H51 zenon_Hc0 zenon_H216 zenon_H28 zenon_H1dd. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1217_); trivial. % 10.45/10.65 apply (zenon_L1218_); trivial. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 (* end of lemma zenon_L1219_ *) % 10.45/10.65 assert (zenon_L1220_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (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)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((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 (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e3)) = (e2))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H216 zenon_H28 zenon_H1dd zenon_H16b zenon_H80 zenon_H53 zenon_H4c zenon_H95 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H151 zenon_H14a zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H5e zenon_H44 zenon_H35 zenon_Hf2 zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_Hc5 zenon_H177 zenon_H1cb zenon_H15a zenon_Hec zenon_H6f zenon_H3a zenon_H1e6 zenon_H1f8 zenon_H1f0 zenon_H56 zenon_H127. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.65 apply (zenon_L1208_); trivial. % 10.45/10.65 exact (zenon_H127 zenon_Hd0). % 10.45/10.65 apply (zenon_L500_); trivial. % 10.45/10.65 (* end of lemma zenon_L1220_ *) % 10.45/10.65 assert (zenon_L1221_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (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 (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H26 zenon_H67 zenon_H240 zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H97 zenon_Hc0 zenon_H216 zenon_H1cb zenon_Hec zenon_H1e6 zenon_H1f8 zenon_H1ef zenon_H169 zenon_He7 zenon_H5e zenon_H44 zenon_H35 zenon_Hf2 zenon_Hde zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H3c zenon_H42 zenon_H6f zenon_H1f0 zenon_H1ea zenon_Hd2 zenon_H127 zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H80. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1178_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.65 apply (zenon_L1213_); trivial. % 10.45/10.65 apply (zenon_L1214_); trivial. % 10.45/10.65 apply (zenon_L1215_); trivial. % 10.45/10.65 apply (zenon_L1216_); trivial. % 10.45/10.65 apply (zenon_L101_); trivial. % 10.45/10.65 apply (zenon_L937_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1054_); trivial. % 10.45/10.65 apply (zenon_L1214_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1219_); trivial. % 10.45/10.65 apply (zenon_L1220_); trivial. % 10.45/10.65 apply (zenon_L1211_); trivial. % 10.45/10.65 exact (zenon_H80 zenon_H84). % 10.45/10.65 (* end of lemma zenon_L1221_ *) % 10.45/10.65 assert (zenon_L1222_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (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 (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H1af zenon_H203 zenon_H191 zenon_Haf zenon_H192 zenon_H1f zenon_He8 zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.65 apply (zenon_L1052_); trivial. % 10.45/10.65 exact (zenon_H203 zenon_H9a). % 10.45/10.65 (* end of lemma zenon_L1222_ *) % 10.45/10.65 assert (zenon_L1223_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((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))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H1af zenon_H203 zenon_Hf8 zenon_H56 zenon_H1f0 zenon_Hf2 zenon_H6f zenon_H97 zenon_H4c zenon_H10b zenon_H26 zenon_Hde zenon_H35 zenon_H44 zenon_H192 zenon_H1f zenon_H191 zenon_He7 zenon_H28 zenon_H64 zenon_H12f zenon_H2a zenon_He8 zenon_H5e zenon_H100 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H151. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.65 apply (zenon_L1177_); trivial. % 10.45/10.65 exact (zenon_H203 zenon_H9a). % 10.45/10.65 (* end of lemma zenon_L1223_ *) % 10.45/10.65 assert (zenon_L1224_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H1ef zenon_H169 zenon_H1af zenon_H203 zenon_H191 zenon_H1f zenon_He8 zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_Hf8 zenon_H56 zenon_H1f0 zenon_H6f zenon_H97 zenon_H4c zenon_H10b zenon_H26 zenon_H28 zenon_H64 zenon_H12f zenon_H2a zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H151 zenon_H1ea. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1222_); trivial. % 10.45/10.65 apply (zenon_L1223_); trivial. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 (* end of lemma zenon_L1224_ *) % 10.45/10.65 assert (zenon_L1225_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H1ef zenon_H169 zenon_H1af zenon_H203 zenon_H191 zenon_H1f zenon_He8 zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_H56 zenon_H1f0 zenon_H6f zenon_H42 zenon_H3a zenon_H3c zenon_H27 zenon_H64 zenon_H1ea. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1222_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.65 apply (zenon_L1053_); trivial. % 10.45/10.65 exact (zenon_H203 zenon_H9a). % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 (* end of lemma zenon_L1225_ *) % 10.45/10.65 assert (zenon_L1226_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H1ef zenon_H1af zenon_H203 zenon_H1f zenon_H68 zenon_H191 zenon_Hc6 zenon_H16b zenon_H80 zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_H35 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H177 zenon_H5e zenon_Hfd zenon_H3a zenon_H6f zenon_H1ea. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1093_); trivial. % 10.45/10.65 apply (zenon_L1210_); trivial. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 (* end of lemma zenon_L1226_ *) % 10.45/10.65 assert (zenon_L1227_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e0) (e0)) = (e2)))\/((op (e0) (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 (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H26 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H67 zenon_H97 zenon_Hc0 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_Hd2 zenon_H240 zenon_H216 zenon_H1f8 zenon_H1e6 zenon_Hec zenon_H1cb zenon_H1ef zenon_H169 zenon_H1af zenon_H203 zenon_H191 zenon_H1f zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_H1f0 zenon_H6f zenon_H42 zenon_H3c zenon_H64 zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hc6 zenon_H14d zenon_H95 zenon_H4c zenon_H53 zenon_H16b zenon_Hdd zenon_H80. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1224_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.65 apply (zenon_L1185_); trivial. % 10.45/10.65 exact (zenon_H203 zenon_H9a). % 10.45/10.65 apply (zenon_L101_); trivial. % 10.45/10.65 apply (zenon_L937_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1225_); trivial. % 10.45/10.65 apply (zenon_L1059_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1222_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.65 apply (zenon_L1207_); trivial. % 10.45/10.65 exact (zenon_H203 zenon_H9a). % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_L1209_); trivial. % 10.45/10.65 apply (zenon_L1226_); trivial. % 10.45/10.65 exact (zenon_H80 zenon_H84). % 10.45/10.65 (* end of lemma zenon_L1227_ *) % 10.45/10.65 assert (zenon_L1228_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (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 (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))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H67 zenon_H132 zenon_H1ef zenon_H169 zenon_H1af zenon_H203 zenon_H191 zenon_H1f zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_Hf8 zenon_H56 zenon_H1f0 zenon_H6f zenon_H97 zenon_H4c zenon_H10b zenon_H26 zenon_H28 zenon_H64 zenon_H12f zenon_H2a zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H151 zenon_H1ea zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hc6 zenon_H3a zenon_H14d zenon_H95 zenon_H53 zenon_H16b zenon_Hdd zenon_H168. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1224_); trivial. % 10.45/10.65 apply (zenon_L1180_); trivial. % 10.45/10.65 apply (zenon_L101_); trivial. % 10.45/10.65 (* end of lemma zenon_L1228_ *) % 10.45/10.65 assert (zenon_L1229_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((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 (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (((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 (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.65 do 0 intro. intros zenon_H26 zenon_H1c3 zenon_H1c0 zenon_H1bc zenon_H1ba zenon_H67 zenon_H216 zenon_H240 zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_Hc0 zenon_H97 zenon_H1cb zenon_Hec zenon_H1e6 zenon_H1f8 zenon_H1ef zenon_H169 zenon_H1af zenon_H203 zenon_H191 zenon_H1f zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H5e zenon_He7 zenon_H1f0 zenon_H6f zenon_H42 zenon_H3c zenon_H64 zenon_H1ea zenon_Hd2 zenon_H127 zenon_Hdd zenon_H16b zenon_H53 zenon_H4c zenon_H95 zenon_H14d zenon_Hc6 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177 zenon_H80. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1224_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.65 apply (zenon_L1213_); trivial. % 10.45/10.65 apply (zenon_L1228_); trivial. % 10.45/10.65 apply (zenon_L1215_); trivial. % 10.45/10.65 apply (zenon_L1216_); trivial. % 10.45/10.65 apply (zenon_L101_); trivial. % 10.45/10.65 apply (zenon_L937_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_L1225_); trivial. % 10.45/10.65 apply (zenon_L1214_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.65 apply (zenon_L1222_); trivial. % 10.45/10.65 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.65 apply (zenon_L1218_); trivial. % 10.45/10.65 exact (zenon_H203 zenon_H9a). % 10.45/10.65 apply (zenon_L140_); trivial. % 10.45/10.65 apply (zenon_L1220_); trivial. % 10.45/10.65 apply (zenon_L1226_); trivial. % 10.45/10.65 exact (zenon_H80 zenon_H84). % 10.45/10.65 (* end of lemma zenon_L1229_ *) % 10.45/10.65 assert (zenon_L1230_ : ((op (e3) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.45/10.65 do 0 intro. intros zenon_Hf2 zenon_H77 zenon_H114. % 10.45/10.65 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H115 | zenon_intro zenon_Hef ]. % 10.45/10.65 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 10.45/10.65 intro zenon_D_pnotp. % 10.45/10.65 apply zenon_H114. % 10.45/10.65 rewrite <- zenon_D_pnotp. % 10.45/10.65 exact zenon_H115. % 10.45/10.65 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 10.45/10.65 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 10.45/10.65 congruence. % 10.45/10.65 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 10.45/10.65 intro zenon_D_pnotp. % 10.45/10.65 apply zenon_H116. % 10.45/10.65 rewrite <- zenon_D_pnotp. % 10.45/10.65 exact zenon_Hf2. % 10.45/10.65 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.45/10.65 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 10.45/10.65 congruence. % 10.45/10.65 apply zenon_Hef. apply refl_equal. % 10.45/10.65 apply zenon_H111. apply sym_equal. exact zenon_H77. % 10.45/10.65 apply zenon_Hef. apply refl_equal. % 10.45/10.65 apply zenon_Hef. apply refl_equal. % 10.45/10.65 (* end of lemma zenon_L1230_ *) % 10.45/10.65 assert (zenon_L1231_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H8a zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.45/10.66 apply (zenon_L26_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.45/10.66 apply (zenon_L27_); trivial. % 10.45/10.66 exact (zenon_H8d zenon_H7b). % 10.45/10.66 (* end of lemma zenon_L1231_ *) % 10.45/10.66 assert (zenon_L1232_ : (((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)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H90 zenon_H4c zenon_H74 zenon_H114 zenon_Hf2 zenon_H91 zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H7e zenon_H86 zenon_H7d zenon_H5e zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.45/10.66 apply (zenon_L21_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.45/10.66 apply (zenon_L1230_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.45/10.66 exact (zenon_H91 zenon_H94). % 10.45/10.66 apply (zenon_L1231_); trivial. % 10.45/10.66 (* end of lemma zenon_L1232_ *) % 10.45/10.66 assert (zenon_L1233_ : ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H15a zenon_H8d zenon_H7e zenon_H80 zenon_H23e zenon_H8c zenon_H91 zenon_H90 zenon_H177 zenon_Hf2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H5e zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H95 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H4c zenon_H165 zenon_H108 zenon_H159 zenon_H35 zenon_H103 zenon_H168 zenon_H23d zenon_H7f. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.45/10.66 exact (zenon_H28 zenon_H31). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.45/10.66 apply (zenon_L236_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_L1232_); trivial. % 10.45/10.66 apply (zenon_L1057_); trivial. % 10.45/10.66 (* end of lemma zenon_L1233_ *) % 10.45/10.66 assert (zenon_L1234_ : (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H27 zenon_H1dd zenon_Hdd zenon_H28 zenon_H4c zenon_H15a zenon_H90 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_H5e zenon_H8c zenon_H91 zenon_Hf2 zenon_H114 zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H35 zenon_H95. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_L1233_); trivial. % 10.45/10.66 apply (zenon_L1183_); trivial. % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 apply (zenon_L1058_); trivial. % 10.45/10.66 (* end of lemma zenon_L1234_ *) % 10.45/10.66 assert (zenon_L1235_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> (((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 (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H1dd zenon_H23e zenon_H56 zenon_H1f0 zenon_H6f zenon_H97 zenon_H91 zenon_Hc8 zenon_Hc0 zenon_He8 zenon_Hde zenon_H3a zenon_H216 zenon_H192 zenon_Hc1 zenon_H191 zenon_He7 zenon_H28 zenon_Hfd zenon_H5e zenon_H100 zenon_Hb1 zenon_H177 zenon_H240 zenon_Hd2 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H7d zenon_H86 zenon_H145 zenon_H14d zenon_H44 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H4a zenon_H200 zenon_H204 zenon_H23f zenon_H35 zenon_H95 zenon_H4c zenon_Hf2 zenon_H53 zenon_H80 zenon_H16b zenon_H25. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.66 exact (zenon_H25 zenon_H2a). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.66 apply (zenon_L1198_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_L1204_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L1205_); trivial. % 10.45/10.66 apply (zenon_L1058_); trivial. % 10.45/10.66 (* end of lemma zenon_L1235_ *) % 10.45/10.66 assert (zenon_L1236_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.45/10.66 do 0 intro. intros zenon_H1b7 zenon_H23e zenon_H8a zenon_H181 zenon_H9b zenon_H187 zenon_H188. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1b7); [ zenon_intro zenon_H43 | zenon_intro zenon_H1b8 ]. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H62 | zenon_intro zenon_H1b9 ]. % 10.45/10.66 apply (zenon_L258_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 10.45/10.66 apply (zenon_L243_); trivial. % 10.45/10.66 apply (zenon_L167_); trivial. % 10.45/10.66 (* end of lemma zenon_L1236_ *) % 10.45/10.66 assert (zenon_L1237_ : (((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)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.45/10.66 do 0 intro. intros zenon_H90 zenon_H4c zenon_H74 zenon_H114 zenon_Hf2 zenon_H91 zenon_H1b7 zenon_H23e zenon_H181 zenon_H9b zenon_H187 zenon_H188. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H76 | zenon_intro zenon_H92 ]. % 10.45/10.66 apply (zenon_L21_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H77 | zenon_intro zenon_H93 ]. % 10.45/10.66 apply (zenon_L1230_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H8a ]. % 10.45/10.66 exact (zenon_H91 zenon_H94). % 10.45/10.66 apply (zenon_L1236_); trivial. % 10.45/10.66 (* end of lemma zenon_L1237_ *) % 10.45/10.66 assert (zenon_L1238_ : (((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 (e2) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (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 (e2) (e2)) = (e2)) -> (~((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 (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hda zenon_H28 zenon_H187 zenon_H181 zenon_H23e zenon_H1b7 zenon_H91 zenon_Hf2 zenon_H114 zenon_H4c zenon_H90 zenon_H1e6 zenon_Hc1 zenon_H15a zenon_H1de zenon_H3a zenon_H155 zenon_Haf zenon_H35 zenon_Hae zenon_H1dd zenon_Hed. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H31 | zenon_intro zenon_Hdb ]. % 10.45/10.66 exact (zenon_H28 zenon_H31). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H6c | zenon_intro zenon_Hdc ]. % 10.45/10.66 apply (zenon_L236_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.45/10.66 apply (zenon_L238_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.45/10.66 exact (zenon_Haf zenon_Hb4). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.45/10.66 apply (zenon_L223_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.45/10.66 apply (zenon_L236_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.45/10.66 exact (zenon_Hc1 zenon_Hc4). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.45/10.66 apply (zenon_L282_); trivial. % 10.45/10.66 apply (zenon_L1237_); trivial. % 10.45/10.66 apply (zenon_L267_); trivial. % 10.45/10.66 (* end of lemma zenon_L1238_ *) % 10.45/10.66 assert (zenon_L1239_ : (((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)))) -> (~((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)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hae zenon_Hc1 zenon_H1e6 zenon_H181 zenon_H187 zenon_H1b7 zenon_H1de zenon_H3a zenon_Haf zenon_H1dd zenon_H28 zenon_H4c zenon_H15a zenon_H90 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_H5e zenon_H8c zenon_H91 zenon_Hf2 zenon_H114 zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_Hf8 zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H151 zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H35 zenon_H95. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_L1233_); trivial. % 10.45/10.66 apply (zenon_L1238_); trivial. % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 apply (zenon_L1058_); trivial. % 10.45/10.66 (* end of lemma zenon_L1239_ *) % 10.45/10.66 assert (zenon_L1240_ : ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((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) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (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)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H174 zenon_H4a zenon_H23e zenon_H1ef zenon_H169 zenon_H1f0 zenon_Hf2 zenon_H42 zenon_He7 zenon_H5e zenon_H44 zenon_H35 zenon_Hde zenon_H2a zenon_H26 zenon_H4c zenon_H95 zenon_H97 zenon_H3a zenon_H3c zenon_H1f zenon_Hc1 zenon_H191 zenon_H64 zenon_H150 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hc6 zenon_H14d zenon_H53 zenon_H80 zenon_H16b zenon_Hdd zenon_H168 zenon_H132 zenon_H67. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_L1181_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L101_); trivial. % 10.45/10.66 apply (zenon_L937_); trivial. % 10.45/10.66 (* end of lemma zenon_L1240_ *) % 10.45/10.66 assert (zenon_L1241_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (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 (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H8c zenon_H90 zenon_H1de zenon_H1b7 zenon_H187 zenon_H181 zenon_H1e6 zenon_Hae zenon_H216 zenon_Hc0 zenon_Hc8 zenon_H97 zenon_H1f0 zenon_H23e zenon_H1dd zenon_H1ef zenon_H191 zenon_Hc1 zenon_H1f zenon_Hc6 zenon_H16b zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_H35 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H177 zenon_H5e zenon_Hfd zenon_H6f zenon_H1ea zenon_Hde zenon_He7 zenon_H42 zenon_H26 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hdd zenon_H67 zenon_H80. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.66 apply (zenon_L1178_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_L1234_); trivial. % 10.45/10.66 apply (zenon_L1182_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L101_); trivial. % 10.45/10.66 apply (zenon_L937_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.66 apply (zenon_L140_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.66 apply (zenon_L1217_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_L1235_); trivial. % 10.45/10.66 apply (zenon_L500_); trivial. % 10.45/10.66 apply (zenon_L321_); trivial. % 10.45/10.66 apply (zenon_L140_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_L1239_); trivial. % 10.45/10.66 apply (zenon_L500_); trivial. % 10.45/10.66 apply (zenon_L123_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L1211_); trivial. % 10.45/10.66 apply (zenon_L1240_); trivial. % 10.45/10.66 exact (zenon_H80 zenon_H84). % 10.45/10.66 (* end of lemma zenon_L1241_ *) % 10.45/10.66 assert (zenon_L1242_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e3) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (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 (e0) (e0)) = (e2))) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H95 zenon_H35 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H114 zenon_Hf2 zenon_H91 zenon_H8c zenon_H5e zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_H90 zenon_H15a zenon_H4c zenon_H28 zenon_Hdd zenon_H1dd zenon_H27. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.66 apply (zenon_L1234_); trivial. % 10.45/10.66 exact (zenon_H127 zenon_Hd0). % 10.45/10.66 (* end of lemma zenon_L1242_ *) % 10.45/10.66 assert (zenon_L1243_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (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 (e3) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (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) (e1)) = (op (e2) (e2)))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H1ea zenon_Hd2 zenon_H127 zenon_H95 zenon_H35 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H114 zenon_Hf2 zenon_H8c zenon_H5e zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_H90 zenon_H15a zenon_H4c zenon_H28 zenon_H1dd zenon_H3a zenon_H1de zenon_H1b7 zenon_H187 zenon_H181 zenon_H1e6 zenon_Hc1 zenon_Hae zenon_H216. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.66 apply (zenon_L1239_); trivial. % 10.45/10.66 exact (zenon_H127 zenon_Hd0). % 10.45/10.66 apply (zenon_L500_); trivial. % 10.45/10.66 apply (zenon_L123_); trivial. % 10.45/10.66 (* end of lemma zenon_L1243_ *) % 10.45/10.66 assert (zenon_L1244_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (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 (e2) (e0)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e3)))\/(~((op (e0) (e3)) = (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((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 (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/(~((op (e2) (e3)) = (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (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 (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hae zenon_H1e6 zenon_H181 zenon_H187 zenon_H1b7 zenon_H1de zenon_H90 zenon_H8c zenon_H1dd zenon_H23e zenon_H1f0 zenon_H97 zenon_Hc0 zenon_H216 zenon_H127 zenon_H1ef zenon_H191 zenon_Hc1 zenon_H1f zenon_Hc6 zenon_H16b zenon_H53 zenon_Hf2 zenon_H4c zenon_H95 zenon_H35 zenon_H23f zenon_H204 zenon_H200 zenon_H4a zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H151 zenon_H14a zenon_H44 zenon_H14d zenon_H145 zenon_H86 zenon_H7d zenon_H132 zenon_Hc5 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hf8 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_Hd2 zenon_H240 zenon_H177 zenon_H5e zenon_Hfd zenon_H6f zenon_H1ea zenon_Hde zenon_He7 zenon_H42 zenon_H26 zenon_H1ba zenon_H1bc zenon_H1c0 zenon_H1c3 zenon_Hdd zenon_H67 zenon_H80. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.66 apply (zenon_L1178_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_L1242_); trivial. % 10.45/10.66 apply (zenon_L1215_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L101_); trivial. % 10.45/10.66 apply (zenon_L937_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.66 apply (zenon_L140_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.66 apply (zenon_L1217_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.66 apply (zenon_L1235_); trivial. % 10.45/10.66 exact (zenon_H127 zenon_Hd0). % 10.45/10.66 apply (zenon_L500_); trivial. % 10.45/10.66 apply (zenon_L321_); trivial. % 10.45/10.66 apply (zenon_L140_); trivial. % 10.45/10.66 apply (zenon_L1243_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L1211_); trivial. % 10.45/10.66 apply (zenon_L1240_); trivial. % 10.45/10.66 exact (zenon_H80 zenon_H84). % 10.45/10.66 (* end of lemma zenon_L1244_ *) % 10.45/10.66 assert (zenon_L1245_ : (((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 (e0) (e2)) = (e3)) -> (~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H145 zenon_H2a zenon_H12f zenon_He8 zenon_Hc8 zenon_Hc7 zenon_H52 zenon_Hb1 zenon_Hc5 zenon_H7d zenon_H86 zenon_H7e zenon_H7f zenon_H80. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.45/10.66 apply (zenon_L100_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.45/10.66 exact (zenon_He8 zenon_Heb). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.45/10.66 apply (zenon_L108_); trivial. % 10.45/10.66 apply (zenon_L26_); trivial. % 10.45/10.66 (* end of lemma zenon_L1245_ *) % 10.45/10.66 assert (zenon_L1246_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H7e zenon_H5e zenon_H203 zenon_H57 zenon_H4c zenon_Hab zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.45/10.66 apply (zenon_L26_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.45/10.66 apply (zenon_L1101_); trivial. % 10.45/10.66 exact (zenon_H8d zenon_H7b). % 10.45/10.66 (* end of lemma zenon_L1246_ *) % 10.45/10.66 assert (zenon_L1247_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (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))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (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)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_Hf5 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H144 zenon_H132 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_H56 zenon_H1f0 zenon_H3c zenon_H10b zenon_H64 zenon_H28 zenon_He7 zenon_H5e zenon_H191 zenon_Hc1 zenon_H1f zenon_H192 zenon_H44 zenon_H35 zenon_Hf2 zenon_Hde zenon_He8 zenon_H2a zenon_H26 zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_Hb1 zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_H12f zenon_H8c zenon_H4c zenon_H203 zenon_Hab zenon_H23e zenon_H97 zenon_H151. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.66 exact (zenon_H28 zenon_H31). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.66 apply (zenon_L1174_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.66 apply (zenon_L1245_); trivial. % 10.45/10.66 apply (zenon_L1246_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.66 exact (zenon_H56 zenon_H2c). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.66 apply (zenon_L327_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.66 apply (zenon_L103_); trivial. % 10.45/10.66 apply (zenon_L1175_); trivial. % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 apply (zenon_L1058_); trivial. % 10.45/10.66 (* end of lemma zenon_L1247_ *) % 10.45/10.66 assert (zenon_L1248_ : (((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) (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 (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hab zenon_Hf2 zenon_Hec zenon_H91 zenon_H159 zenon_H15a zenon_H1cb zenon_H103 zenon_H203 zenon_H5e zenon_H89 zenon_H7e. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 10.45/10.66 apply (zenon_L264_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 10.45/10.66 exact (zenon_H203 zenon_H9a). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 10.45/10.66 apply (zenon_L27_); trivial. % 10.45/10.66 exact (zenon_H7e zenon_H83). % 10.45/10.66 (* end of lemma zenon_L1248_ *) % 10.45/10.66 assert (zenon_L1249_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (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 (e0) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H7e zenon_H5e zenon_H203 zenon_H103 zenon_H1cb zenon_H15a zenon_H159 zenon_H91 zenon_Hec zenon_Hf2 zenon_Hab zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.45/10.66 apply (zenon_L26_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.45/10.66 apply (zenon_L1248_); trivial. % 10.45/10.66 exact (zenon_H8d zenon_H7b). % 10.45/10.66 (* end of lemma zenon_L1249_ *) % 10.45/10.66 assert (zenon_L1250_ : (((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) (e3)) = (e1))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hab zenon_H1cb zenon_H5d zenon_H203 zenon_H188 zenon_H187 zenon_H9b zenon_H181 zenon_H23e zenon_H1b7 zenon_H7e. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H62 | zenon_intro zenon_Hac ]. % 10.45/10.66 apply (zenon_L229_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_H9a | zenon_intro zenon_Had ]. % 10.45/10.66 exact (zenon_H203 zenon_H9a). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H8a | zenon_intro zenon_H83 ]. % 10.45/10.66 apply (zenon_L1236_); trivial. % 10.45/10.66 exact (zenon_H7e zenon_H83). % 10.45/10.66 (* end of lemma zenon_L1250_ *) % 10.45/10.66 assert (zenon_L1251_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (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) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.66 do 0 intro. intros zenon_H103 zenon_H7e zenon_H1b7 zenon_H23e zenon_H181 zenon_H9b zenon_H187 zenon_H188 zenon_H203 zenon_H1cb zenon_Hab zenon_H15a zenon_H159 zenon_H91 zenon_Hec zenon_Hf2. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_H5d | zenon_intro zenon_H104 ]. % 10.45/10.66 apply (zenon_L1250_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_H100 | zenon_intro zenon_H105 ]. % 10.45/10.66 apply (zenon_L123_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H94 | zenon_intro zenon_Hf3 ]. % 10.45/10.66 exact (zenon_H91 zenon_H94). % 10.45/10.66 apply (zenon_L263_); trivial. % 10.45/10.66 (* end of lemma zenon_L1251_ *) % 10.45/10.66 assert (zenon_L1252_ : (((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) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (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) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.66 do 0 intro. intros zenon_Hae zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H1de zenon_H4c zenon_Hc1 zenon_H1e6 zenon_Hed zenon_H103 zenon_H7e zenon_H1b7 zenon_H23e zenon_H181 zenon_H187 zenon_H203 zenon_H1cb zenon_Hab zenon_H15a zenon_H159 zenon_H91 zenon_Hec zenon_Hf2. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.45/10.66 apply (zenon_L238_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.45/10.66 exact (zenon_Haf zenon_Hb4). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.45/10.66 apply (zenon_L223_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.45/10.66 apply (zenon_L236_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.45/10.66 exact (zenon_Hc1 zenon_Hc4). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.45/10.66 apply (zenon_L282_); trivial. % 10.45/10.66 apply (zenon_L1251_); trivial. % 10.45/10.66 (* end of lemma zenon_L1252_ *) % 10.45/10.66 assert (zenon_L1253_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H151 zenon_H8c zenon_H8d zenon_H103 zenon_Hf2 zenon_Hec zenon_H91 zenon_H15a zenon_H159 zenon_H1cb zenon_H203 zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_Hae zenon_H4c zenon_Hc1 zenon_H1e6 zenon_H1b7 zenon_H187 zenon_H181 zenon_H1de zenon_H3a zenon_H155 zenon_Haf zenon_H35 zenon_Hf8. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_L1249_); trivial. % 10.45/10.66 apply (zenon_L1252_); trivial. % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 (* end of lemma zenon_L1253_ *) % 10.45/10.66 assert (zenon_L1254_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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))) -> (~((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))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H150 zenon_H1ba zenon_H2a zenon_H1bc zenon_Hc6 zenon_H1c0 zenon_H1c3 zenon_Hf8 zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H1de zenon_H181 zenon_H187 zenon_H1b7 zenon_H1e6 zenon_Hc1 zenon_H4c zenon_Hae zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H1cb zenon_H159 zenon_H15a zenon_H91 zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_L1253_); trivial. % 10.45/10.66 apply (zenon_L1179_); trivial. % 10.45/10.66 (* end of lemma zenon_L1254_ *) % 10.45/10.66 assert (zenon_L1255_ : (((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)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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))) -> (~((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))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (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) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H145 zenon_H12f zenon_He8 zenon_H203 zenon_H5e zenon_H192 zenon_H150 zenon_H1ba zenon_H2a zenon_H1bc zenon_Hc6 zenon_H1c0 zenon_H1c3 zenon_Hf8 zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H1de zenon_H181 zenon_H187 zenon_H1b7 zenon_H1e6 zenon_Hc1 zenon_H4c zenon_Hae zenon_H23e zenon_Hab zenon_H1cb zenon_H159 zenon_H91 zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151 zenon_H238 zenon_H7d zenon_H86 zenon_H7e zenon_H7f zenon_H80. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H69 | zenon_intro zenon_H146 ]. % 10.45/10.66 apply (zenon_L100_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_Heb | zenon_intro zenon_H147 ]. % 10.45/10.66 exact (zenon_He8 zenon_Heb). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H101 | zenon_intro zenon_H87 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.45/10.66 apply (zenon_L1254_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.45/10.66 exact (zenon_H192 zenon_H1d). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.45/10.66 apply (zenon_L71_); trivial. % 10.45/10.66 exact (zenon_H203 zenon_H9a). % 10.45/10.66 apply (zenon_L26_); trivial. % 10.45/10.66 (* end of lemma zenon_L1255_ *) % 10.45/10.66 assert (zenon_L1256_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((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))) -> (~((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))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (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))))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H145 zenon_H150 zenon_H1ba zenon_H1bc zenon_Hc6 zenon_H1c0 zenon_H1c3 zenon_Hf8 zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H1de zenon_H181 zenon_H187 zenon_H1b7 zenon_H1e6 zenon_Hc1 zenon_H4c zenon_Hae zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H1cb zenon_H159 zenon_H91 zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151 zenon_H192 zenon_H238 zenon_He8 zenon_H2a zenon_H12f zenon_H132 zenon_H6f zenon_H3c zenon_H10b zenon_H144. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_L1255_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.45/10.66 apply (zenon_L1252_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.45/10.66 exact (zenon_H192 zenon_H1d). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.45/10.66 apply (zenon_L303_); trivial. % 10.45/10.66 exact (zenon_H203 zenon_H9a). % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 (* end of lemma zenon_L1256_ *) % 10.45/10.66 assert (zenon_L1257_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H157 zenon_H216 zenon_H144 zenon_H10b zenon_H3c zenon_H6f zenon_H132 zenon_H12f zenon_H2a zenon_He8 zenon_H238 zenon_H192 zenon_H151 zenon_H8c zenon_H103 zenon_Hf2 zenon_Hec zenon_H159 zenon_H1cb zenon_H203 zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_Hae zenon_H4c zenon_Hc1 zenon_H1e6 zenon_H1b7 zenon_H187 zenon_H181 zenon_H1de zenon_H3a zenon_H155 zenon_Haf zenon_H35 zenon_Hf8 zenon_H1c3 zenon_H1c0 zenon_Hc6 zenon_H1bc zenon_H1ba zenon_H150 zenon_H145. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.66 apply (zenon_L1256_); trivial. % 10.45/10.66 apply (zenon_L500_); trivial. % 10.45/10.66 (* end of lemma zenon_L1257_ *) % 10.45/10.66 assert (zenon_L1258_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e3)) = (e1))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H238 zenon_H76 zenon_H1bc zenon_H192 zenon_H6f zenon_H5d zenon_H203. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H15a | zenon_intro zenon_H23a ]. % 10.45/10.66 apply (zenon_L217_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1d | zenon_intro zenon_H23b ]. % 10.45/10.66 exact (zenon_H192 zenon_H1d). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H100 | zenon_intro zenon_H9a ]. % 10.45/10.66 apply (zenon_L228_); trivial. % 10.45/10.66 exact (zenon_H203 zenon_H9a). % 10.45/10.66 (* end of lemma zenon_L1258_ *) % 10.45/10.66 assert (zenon_L1259_ : (((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)))) -> ((op (e2) (e0)) = (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 (e1) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_Hed zenon_H1dd zenon_Hcf zenon_H95 zenon_H4c zenon_H28 zenon_Hda zenon_H203 zenon_H5d zenon_H6f zenon_H192 zenon_H1bc zenon_H238 zenon_Hf2 zenon_Hbb. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.45/10.66 exact (zenon_H56 zenon_H2c). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.45/10.66 apply (zenon_L306_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.45/10.66 apply (zenon_L1258_); trivial. % 10.45/10.66 apply (zenon_L387_); trivial. % 10.45/10.66 (* end of lemma zenon_L1259_ *) % 10.45/10.66 assert (zenon_L1260_ : ((~((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 (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (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)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H151 zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_H155 zenon_H91 zenon_Hc7 zenon_Hc8 zenon_Hc5 zenon_He8 zenon_H2a zenon_H12f zenon_H64 zenon_He7 zenon_H5e zenon_H191 zenon_Hc1 zenon_H1f zenon_H44 zenon_H35 zenon_Hde zenon_H26 zenon_H10b zenon_H97 zenon_Hda zenon_H1dd zenon_Hcf zenon_H95 zenon_H4c zenon_H28 zenon_H238 zenon_H203 zenon_H6f zenon_H192 zenon_H1bc zenon_Hbb zenon_H1b4 zenon_Hf2 zenon_H1f0 zenon_H56 zenon_Hf8. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_L119_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.66 exact (zenon_H56 zenon_H2c). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.66 apply (zenon_L327_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.66 apply (zenon_L1259_); trivial. % 10.45/10.66 apply (zenon_L1175_); trivial. % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 (* end of lemma zenon_L1260_ *) % 10.45/10.66 assert (zenon_L1261_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H7e zenon_H5e zenon_H203 zenon_H47 zenon_H35 zenon_Hab zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H43 | zenon_intro zenon_H8e ]. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H87 | zenon_intro zenon_H8f ]. % 10.45/10.66 apply (zenon_L26_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H89 | zenon_intro zenon_H7b ]. % 10.45/10.66 apply (zenon_L1095_); trivial. % 10.45/10.66 exact (zenon_H8d zenon_H7b). % 10.45/10.66 (* end of lemma zenon_L1261_ *) % 10.45/10.66 assert (zenon_L1262_ : (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H42 zenon_H27 zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H7e zenon_H5e zenon_H203 zenon_H35 zenon_Hab zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 10.45/10.66 exact (zenon_H27 zenon_H32). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H34 | zenon_intro zenon_H46 ]. % 10.45/10.66 apply (zenon_L16_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3b | zenon_intro zenon_H47 ]. % 10.45/10.66 apply (zenon_L5_); trivial. % 10.45/10.66 apply (zenon_L1261_); trivial. % 10.45/10.66 (* end of lemma zenon_L1262_ *) % 10.45/10.66 assert (zenon_L1263_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_Hfd zenon_H6f zenon_H100 zenon_H10b zenon_H144 zenon_H27 zenon_H44 zenon_H68 zenon_H3c zenon_H3a zenon_H8c zenon_H35 zenon_H203 zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_H42 zenon_H4c zenon_Hf2 zenon_H151. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.66 apply (zenon_L1262_); trivial. % 10.45/10.66 apply (zenon_L345_); trivial. % 10.45/10.66 apply (zenon_L207_); trivial. % 10.45/10.66 apply (zenon_L1058_); trivial. % 10.45/10.66 (* end of lemma zenon_L1263_ *) % 10.45/10.66 assert (zenon_L1264_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_H1f zenon_H68 zenon_H191 zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_Hfd zenon_H6f zenon_H10b zenon_H144 zenon_H44 zenon_H3c zenon_H3a zenon_H8c zenon_H35 zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_H42 zenon_H4c zenon_Hf2 zenon_H151 zenon_H1ea zenon_H4a. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.66 apply (zenon_L1093_); trivial. % 10.45/10.66 apply (zenon_L1263_); trivial. % 10.45/10.66 apply (zenon_L140_); trivial. % 10.45/10.66 exact (zenon_H23e zenon_H43). % 10.45/10.66 apply (zenon_L69_); trivial. % 10.45/10.66 (* end of lemma zenon_L1264_ *) % 10.45/10.66 assert (zenon_L1265_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (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 (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.66 do 0 intro. intros zenon_He7 zenon_H4a zenon_H1ea zenon_H151 zenon_H4c zenon_H42 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H8c zenon_H3a zenon_H3c zenon_H144 zenon_H10b zenon_H6f zenon_Hfd zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H203 zenon_H1af zenon_H1ef zenon_H67 zenon_H35 zenon_H44 zenon_H4b zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hc1 zenon_Hde zenon_H5e zenon_Hf2. % 10.45/10.66 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.66 apply (zenon_L1264_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.66 exact (zenon_He8 zenon_Heb). % 10.45/10.66 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.66 apply (zenon_L765_); trivial. % 10.45/10.66 apply (zenon_L206_); trivial. % 10.45/10.66 (* end of lemma zenon_L1265_ *) % 10.45/10.66 assert (zenon_L1266_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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 (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (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 (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.45/10.66 do 0 intro. intros zenon_H97 zenon_H28 zenon_H67 zenon_H1ef zenon_H1af zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_Hda zenon_H16f zenon_H118 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H132 zenon_H145 zenon_H53 zenon_H14a zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H1dd zenon_Hf8 zenon_H6f zenon_H144 zenon_H42 zenon_H151 zenon_H1ea zenon_H4a zenon_Hf2 zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H14d zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H44 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H177 zenon_Hc1 zenon_Hc0 zenon_H216 zenon_H3a zenon_H35 zenon_Hfd zenon_He7 zenon_H8c zenon_H23e zenon_H80 zenon_H7f zenon_H86 zenon_H7d zenon_H7e zenon_H5e zenon_H203 zenon_H4c zenon_Hab zenon_H8d. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.66 exact (zenon_H28 zenon_H31). % 10.45/10.66 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.66 apply (zenon_L1265_); trivial. % 10.45/10.66 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.66 apply (zenon_L1203_); trivial. % 10.45/10.66 apply (zenon_L1246_); trivial. % 10.45/10.67 (* end of lemma zenon_L1266_ *) % 10.45/10.67 assert (zenon_L1267_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (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) (e3)) = (e2))) -> (~((op (e3) (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))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (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)))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((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)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (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) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (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))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H200 zenon_H25 zenon_H27 zenon_H8d zenon_Hab zenon_H4c zenon_H203 zenon_H5e zenon_H7e zenon_H7d zenon_H86 zenon_H7f zenon_H80 zenon_H8c zenon_He7 zenon_Hfd zenon_H35 zenon_H3a zenon_H216 zenon_Hc0 zenon_Hc1 zenon_H177 zenon_H10b zenon_H114 zenon_H95 zenon_H16b zenon_H44 zenon_Hc5 zenon_Hc8 zenon_H91 zenon_H3c zenon_H152 zenon_H158 zenon_H14d zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hde zenon_Hf2 zenon_H4a zenon_H1ea zenon_H151 zenon_H42 zenon_H144 zenon_H6f zenon_Hf8 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H14a zenon_H53 zenon_H145 zenon_H132 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H1af zenon_H1ef zenon_H67 zenon_H28 zenon_H97 zenon_H23e. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.67 exact (zenon_H25 zenon_H2a). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.67 apply (zenon_L1262_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.67 apply (zenon_L1266_); trivial. % 10.45/10.67 exact (zenon_H23e zenon_H43). % 10.45/10.67 (* end of lemma zenon_L1267_ *) % 10.45/10.67 assert (zenon_L1268_ : (((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)) -> (((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) (e3)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.45/10.67 do 0 intro. intros zenon_Hae zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H1de zenon_H4c zenon_H15a zenon_Hc1 zenon_H1e6 zenon_Hed zenon_Hab zenon_H1cb zenon_H5d zenon_H203 zenon_H187 zenon_H181 zenon_H23e zenon_H1b7 zenon_H7e. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb2 ]. % 10.45/10.67 apply (zenon_L238_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 10.45/10.67 exact (zenon_Haf zenon_Hb4). % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6e | zenon_intro zenon_H9b ]. % 10.45/10.67 apply (zenon_L223_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_H6c | zenon_intro zenon_H1df ]. % 10.45/10.67 apply (zenon_L236_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H1e0 ]. % 10.45/10.67 exact (zenon_Hc1 zenon_Hc4). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H161 | zenon_intro zenon_H188 ]. % 10.45/10.67 apply (zenon_L282_); trivial. % 10.45/10.67 apply (zenon_L1250_); trivial. % 10.45/10.67 (* end of lemma zenon_L1268_ *) % 10.45/10.67 assert (zenon_L1269_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (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 (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (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))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H7e zenon_H1b7 zenon_H23e zenon_H181 zenon_H187 zenon_H1cb zenon_Hab zenon_Hed zenon_H1e6 zenon_Hc1 zenon_H4c zenon_H1de zenon_H3a zenon_H155 zenon_Haf zenon_H35 zenon_Hae zenon_H203 zenon_H5d zenon_H6f zenon_H192 zenon_H1bc zenon_H238 zenon_Hf2 zenon_Hbb. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.45/10.67 exact (zenon_H56 zenon_H2c). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.45/10.67 apply (zenon_L1268_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.45/10.67 apply (zenon_L1258_); trivial. % 10.45/10.67 apply (zenon_L387_); trivial. % 10.45/10.67 (* end of lemma zenon_L1269_ *) % 10.45/10.67 assert (zenon_L1270_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (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 (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H1f0 zenon_H238 zenon_H1bc zenon_Hae zenon_Haf zenon_H1de zenon_H1e6 zenon_H1cb zenon_H187 zenon_H181 zenon_H1b7 zenon_H7e zenon_H56 zenon_H1b4 zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H44 zenon_H35 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_Hfd zenon_H6f zenon_H144 zenon_H3c zenon_H3a zenon_H8c zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_H42 zenon_H151 zenon_H1ea zenon_H4a zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.67 exact (zenon_H56 zenon_H2c). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.67 apply (zenon_L327_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.67 apply (zenon_L1269_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.67 exact (zenon_H28 zenon_H31). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.67 apply (zenon_L1265_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.67 apply (zenon_L75_); trivial. % 10.45/10.67 apply (zenon_L13_); trivial. % 10.45/10.67 (* end of lemma zenon_L1270_ *) % 10.45/10.67 assert (zenon_L1271_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((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))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_H35 zenon_Haf zenon_H155 zenon_H3a zenon_H1de zenon_H181 zenon_H187 zenon_H1b7 zenon_H1e6 zenon_Hc1 zenon_H4c zenon_Hae zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H1cb zenon_H159 zenon_H15a zenon_H91 zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.67 apply (zenon_L1253_); trivial. % 10.45/10.67 apply (zenon_L1058_); trivial. % 10.45/10.67 (* end of lemma zenon_L1271_ *) % 10.45/10.67 assert (zenon_L1272_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H1ea zenon_H216 zenon_H151 zenon_H8c zenon_H103 zenon_Hf2 zenon_Hec zenon_H15a zenon_H159 zenon_H1cb zenon_H203 zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_Hae zenon_H4c zenon_H1e6 zenon_H1b7 zenon_H187 zenon_H181 zenon_H1de zenon_H3a zenon_H155 zenon_H35 zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H1af. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_L1271_); trivial. % 10.45/10.67 apply (zenon_L500_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_L123_); trivial. % 10.45/10.67 (* end of lemma zenon_L1272_ *) % 10.45/10.67 assert (zenon_L1273_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((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) (e2)) = (e1))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H56 zenon_H1f0 zenon_H100 zenon_H28 zenon_He7 zenon_Hc1 zenon_H192 zenon_Hde zenon_He8 zenon_H4a zenon_H1ea zenon_H151 zenon_Hf2 zenon_H4c zenon_H42 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H35 zenon_H8c zenon_H3a zenon_H3c zenon_H44 zenon_H144 zenon_H10b zenon_H6f zenon_Hfd zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H191 zenon_H1f zenon_H203 zenon_H1af zenon_H1ef zenon_H67 zenon_Hc0 zenon_H91 zenon_H8d zenon_H216 zenon_H51 zenon_H7e zenon_H97. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.67 apply (zenon_L1266_); trivial. % 10.45/10.67 apply (zenon_L1205_); trivial. % 10.45/10.67 (* end of lemma zenon_L1273_ *) % 10.45/10.67 assert (zenon_L1274_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H151 zenon_Hf2 zenon_H4c zenon_H145 zenon_H86 zenon_H80 zenon_H7d zenon_H100 zenon_H5e zenon_He8 zenon_H2a zenon_H12f zenon_H144 zenon_H10b zenon_H3a zenon_H3c zenon_H6f zenon_H132 zenon_Hf8. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.67 apply (zenon_L225_); trivial. % 10.45/10.67 apply (zenon_L303_); trivial. % 10.45/10.67 apply (zenon_L207_); trivial. % 10.45/10.67 (* end of lemma zenon_L1274_ *) % 10.45/10.67 assert (zenon_L1275_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> ((~((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 (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((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) (e1)) = (op (e3) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H168 zenon_H1ea zenon_H157 zenon_H216 zenon_H144 zenon_H10b zenon_H3c zenon_H6f zenon_H132 zenon_H12f zenon_H2a zenon_H238 zenon_H151 zenon_H8c zenon_H103 zenon_Hf2 zenon_Hec zenon_H159 zenon_H1cb zenon_H203 zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_Hae zenon_H4c zenon_H1e6 zenon_H1b7 zenon_H187 zenon_H181 zenon_H1de zenon_H3a zenon_H155 zenon_H35 zenon_Hf8 zenon_H1c3 zenon_H1c0 zenon_Hc6 zenon_H1bc zenon_H1ba zenon_H150 zenon_H145 zenon_H1af zenon_H169 zenon_H1ef. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_L1257_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_L1274_); trivial. % 10.45/10.67 apply (zenon_L140_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_L1254_); trivial. % 10.45/10.67 apply (zenon_L500_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_L123_); trivial. % 10.45/10.67 (* end of lemma zenon_L1275_ *) % 10.45/10.67 assert (zenon_L1276_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (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 (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.67 do 0 intro. intros zenon_Hdd zenon_H26 zenon_H1f0 zenon_H1b4 zenon_H1bc zenon_H238 zenon_H1de zenon_H1cb zenon_H1b7 zenon_H187 zenon_H181 zenon_H1e6 zenon_Hae zenon_H42 zenon_H23e zenon_H7d zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H35 zenon_H8c zenon_H3c zenon_H44 zenon_H97 zenon_H216 zenon_Hc0 zenon_H67 zenon_H1ef zenon_H1af zenon_H1f zenon_H191 zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_Hfd zenon_H6f zenon_H10b zenon_H144 zenon_H4c zenon_Hf2 zenon_H151 zenon_H1ea zenon_H4a zenon_Hde zenon_He7 zenon_H200 zenon_Hec zenon_H1c3 zenon_H1c0 zenon_Hc6 zenon_H1ba zenon_H204 zenon_H80. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.67 apply (zenon_L1247_); trivial. % 10.45/10.67 apply (zenon_L1257_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.67 apply (zenon_L1260_); trivial. % 10.45/10.67 apply (zenon_L321_); trivial. % 10.45/10.67 apply (zenon_L79_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_L1223_); trivial. % 10.45/10.67 apply (zenon_L140_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.67 apply (zenon_L1249_); trivial. % 10.45/10.67 apply (zenon_L1183_); trivial. % 10.45/10.67 apply (zenon_L207_); trivial. % 10.45/10.67 apply (zenon_L1058_); trivial. % 10.45/10.67 apply (zenon_L1182_); trivial. % 10.45/10.67 exact (zenon_H23e zenon_H43). % 10.45/10.67 apply (zenon_L101_); trivial. % 10.45/10.67 apply (zenon_L937_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.67 apply (zenon_L140_); trivial. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.67 apply (zenon_L1267_); trivial. % 10.45/10.67 apply (zenon_L1270_); trivial. % 10.45/10.67 apply (zenon_L207_); trivial. % 10.45/10.67 apply (zenon_L1058_); trivial. % 10.45/10.67 apply (zenon_L500_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.67 apply (zenon_L1267_); trivial. % 10.45/10.67 apply (zenon_L1205_); trivial. % 10.45/10.67 apply (zenon_L207_); trivial. % 10.45/10.67 apply (zenon_L1058_); trivial. % 10.45/10.67 apply (zenon_L500_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_L140_); trivial. % 10.45/10.67 apply (zenon_L1272_); trivial. % 10.45/10.67 exact (zenon_H23e zenon_H43). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.67 apply (zenon_L1266_); trivial. % 10.45/10.67 apply (zenon_L1270_); trivial. % 10.45/10.67 apply (zenon_L207_); trivial. % 10.45/10.67 apply (zenon_L1058_); trivial. % 10.45/10.67 apply (zenon_L500_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.67 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.67 apply (zenon_L1273_); trivial. % 10.45/10.67 apply (zenon_L207_); trivial. % 10.45/10.67 apply (zenon_L1058_); trivial. % 10.45/10.67 apply (zenon_L500_); trivial. % 10.45/10.67 exact (zenon_H203 zenon_H9a). % 10.45/10.67 apply (zenon_L140_); trivial. % 10.45/10.67 apply (zenon_L1272_); trivial. % 10.45/10.67 exact (zenon_H23e zenon_H43). % 10.45/10.67 apply (zenon_L1264_); trivial. % 10.45/10.67 apply (zenon_L1275_); trivial. % 10.45/10.67 exact (zenon_H80 zenon_H84). % 10.45/10.67 (* end of lemma zenon_L1276_ *) % 10.45/10.67 assert (zenon_L1277_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (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)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((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) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((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))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.45/10.67 do 0 intro. intros zenon_Hd2 zenon_H127 zenon_H151 zenon_H97 zenon_H23e zenon_Hab zenon_H203 zenon_H4c zenon_H8c zenon_H12f zenon_Hc5 zenon_Hc7 zenon_Hb1 zenon_H7d zenon_H80 zenon_H86 zenon_H145 zenon_H26 zenon_H2a zenon_He8 zenon_Hde zenon_Hf2 zenon_H35 zenon_H44 zenon_H192 zenon_H1f zenon_Hc1 zenon_H191 zenon_H5e zenon_He7 zenon_H28 zenon_H64 zenon_H10b zenon_H3c zenon_H1f0 zenon_H56 zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H132 zenon_H144 zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H16e zenon_H173 zenon_H177. % 10.45/10.67 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.67 apply (zenon_L1247_); trivial. % 10.45/10.67 exact (zenon_H127 zenon_Hd0). % 10.45/10.67 (* end of lemma zenon_L1277_ *) % 10.45/10.67 assert (zenon_L1278_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (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) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 10.45/10.67 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc8 zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H168 zenon_H23d zenon_H35 zenon_Hf8 zenon_H28 zenon_H4c zenon_H95 zenon_Hcf zenon_H1dd zenon_Hda zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H1cb zenon_H159 zenon_H15a zenon_H91 zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.68 apply (zenon_L1249_); trivial. % 10.45/10.68 apply (zenon_L306_); trivial. % 10.45/10.68 apply (zenon_L207_); trivial. % 10.45/10.68 apply (zenon_L1058_); trivial. % 10.45/10.68 (* end of lemma zenon_L1278_ *) % 10.45/10.68 assert (zenon_L1279_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (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) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_Hfd zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H168 zenon_H23d zenon_H35 zenon_Hf8 zenon_H28 zenon_H4c zenon_H95 zenon_Hcf zenon_H1dd zenon_Hda zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H1cb zenon_H159 zenon_H15a zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151 zenon_H127 zenon_Hd2. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.68 apply (zenon_L1278_); trivial. % 10.45/10.68 exact (zenon_H127 zenon_Hd0). % 10.45/10.68 apply (zenon_L79_); trivial. % 10.45/10.68 (* end of lemma zenon_L1279_ *) % 10.45/10.68 assert (zenon_L1280_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((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 (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H1b4 zenon_H56 zenon_H151 zenon_H8c zenon_H103 zenon_Hec zenon_H91 zenon_H159 zenon_H1cb zenon_H5e zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_Hae zenon_H4c zenon_Hc1 zenon_H1e6 zenon_H1b7 zenon_H187 zenon_H181 zenon_H1de zenon_H3a zenon_H155 zenon_Haf zenon_H35 zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H44 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_Hc8 zenon_H3c zenon_H10b zenon_H144 zenon_H12f zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H174 zenon_Hfd zenon_H28 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H203 zenon_H5d zenon_H6f zenon_H192 zenon_H1bc zenon_H238 zenon_Hf2 zenon_Hbb. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1b4); [ zenon_intro zenon_H2c | zenon_intro zenon_H1b5 ]. % 10.45/10.68 exact (zenon_H56 zenon_H2c). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1b5); [ zenon_intro zenon_H15a | zenon_intro zenon_H1b6 ]. % 10.45/10.68 apply (zenon_L1271_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H76 | zenon_intro zenon_Hf0 ]. % 10.45/10.68 apply (zenon_L1258_); trivial. % 10.45/10.68 apply (zenon_L387_); trivial. % 10.45/10.68 (* end of lemma zenon_L1280_ *) % 10.45/10.68 assert (zenon_L1281_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_H1f zenon_H68 zenon_H191 zenon_Hd2 zenon_H127 zenon_H151 zenon_Hf2 zenon_H4c zenon_H42 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H35 zenon_H8c zenon_H3a zenon_H3c zenon_H44 zenon_H144 zenon_H10b zenon_H6f zenon_Hfd zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H4a. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.68 apply (zenon_L1093_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.68 apply (zenon_L1263_); trivial. % 10.45/10.68 exact (zenon_H127 zenon_Hd0). % 10.45/10.68 apply (zenon_L140_); trivial. % 10.45/10.68 exact (zenon_H23e zenon_H43). % 10.45/10.68 apply (zenon_L69_); trivial. % 10.45/10.68 (* end of lemma zenon_L1281_ *) % 10.45/10.68 assert (zenon_L1282_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.45/10.68 do 0 intro. intros zenon_He7 zenon_H4a zenon_H1ea zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H174 zenon_H156 zenon_H155 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H159 zenon_H103 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_Hfd zenon_H6f zenon_H10b zenon_H144 zenon_H44 zenon_H3c zenon_H8c zenon_Hab zenon_H86 zenon_H80 zenon_H7d zenon_H23e zenon_H42 zenon_H4c zenon_H151 zenon_H127 zenon_Hd2 zenon_H203 zenon_H1af zenon_H1ef zenon_H67 zenon_H35 zenon_H3a zenon_H216 zenon_H4b zenon_H191 zenon_He8 zenon_H192 zenon_H1f zenon_Hc1 zenon_Hde zenon_H5e zenon_Hf2. % 10.45/10.68 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_H68 | zenon_intro zenon_He9 ]. % 10.45/10.68 apply (zenon_L1281_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 10.45/10.68 exact (zenon_He8 zenon_Heb). % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H78 | zenon_intro zenon_He5 ]. % 10.45/10.68 apply (zenon_L1199_); trivial. % 10.45/10.68 apply (zenon_L206_); trivial. % 10.45/10.68 (* end of lemma zenon_L1282_ *) % 10.45/10.68 assert (zenon_L1283_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (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) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H97 zenon_H28 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_Hd2 zenon_H127 zenon_H151 zenon_H42 zenon_H23e zenon_H7d zenon_H86 zenon_Hab zenon_H8c zenon_H144 zenon_H6f zenon_Hf8 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H14a zenon_H53 zenon_H145 zenon_H132 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H1ea zenon_H4a zenon_Hf2 zenon_H5e zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H14d zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H7f zenon_H44 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H80 zenon_H177 zenon_H8d zenon_Hc1 zenon_Hc0 zenon_H216 zenon_H3a zenon_H35 zenon_Hfd zenon_He7 zenon_H62 zenon_H4c. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.68 exact (zenon_H28 zenon_H31). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.68 apply (zenon_L1282_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.68 apply (zenon_L1203_); trivial. % 10.45/10.68 apply (zenon_L13_); trivial. % 10.45/10.68 (* end of lemma zenon_L1283_ *) % 10.45/10.68 assert (zenon_L1284_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((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 (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (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) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H1f0 zenon_H238 zenon_H1bc zenon_Haf zenon_H1de zenon_H181 zenon_H187 zenon_H1b7 zenon_H1e6 zenon_Hae zenon_H1cb zenon_Hec zenon_H56 zenon_H1b4 zenon_H97 zenon_H28 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_Hd2 zenon_H127 zenon_H151 zenon_H42 zenon_H23e zenon_H7d zenon_H86 zenon_Hab zenon_H8c zenon_H144 zenon_H6f zenon_Hf8 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H14a zenon_H53 zenon_H145 zenon_H132 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H1ea zenon_H4a zenon_Hf2 zenon_H5e zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H14d zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H7f zenon_H44 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H80 zenon_H177 zenon_H8d zenon_Hc1 zenon_Hc0 zenon_H216 zenon_H3a zenon_H35 zenon_Hfd zenon_He7 zenon_H4c. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.68 exact (zenon_H56 zenon_H2c). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.68 apply (zenon_L327_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.68 apply (zenon_L1280_); trivial. % 10.45/10.68 apply (zenon_L1283_); trivial. % 10.45/10.68 (* end of lemma zenon_L1284_ *) % 10.45/10.68 assert (zenon_L1285_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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 (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H216 zenon_H3a zenon_H35 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_Hd2 zenon_H127 zenon_H151 zenon_H42 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H8c zenon_H3c zenon_H44 zenon_H144 zenon_H6f zenon_Hfd zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H4a zenon_He7 zenon_H10b zenon_Hed zenon_H62 zenon_H4c. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H97); [ zenon_intro zenon_H31 | zenon_intro zenon_H98 ]. % 10.45/10.68 exact (zenon_H28 zenon_H31). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H4b | zenon_intro zenon_H99 ]. % 10.45/10.68 apply (zenon_L1282_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H52 | zenon_intro zenon_H57 ]. % 10.45/10.68 apply (zenon_L75_); trivial. % 10.45/10.68 apply (zenon_L13_); trivial. % 10.45/10.68 (* end of lemma zenon_L1285_ *) % 10.45/10.68 assert (zenon_L1286_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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 (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H1f0 zenon_H238 zenon_H1bc zenon_Hae zenon_Haf zenon_H1de zenon_H1e6 zenon_H1cb zenon_H187 zenon_H181 zenon_H1b7 zenon_H7e zenon_H56 zenon_H1b4 zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H216 zenon_H3a zenon_H35 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_Hd2 zenon_H127 zenon_H151 zenon_H42 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H8c zenon_H3c zenon_H44 zenon_H144 zenon_H6f zenon_Hfd zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H4a zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.68 exact (zenon_H56 zenon_H2c). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.68 apply (zenon_L327_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.68 apply (zenon_L1269_); trivial. % 10.45/10.68 apply (zenon_L1285_); trivial. % 10.45/10.68 (* end of lemma zenon_L1286_ *) % 10.45/10.68 assert (zenon_L1287_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (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) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (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 (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H56 zenon_H1f0 zenon_H100 zenon_H97 zenon_H28 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_Hd2 zenon_H127 zenon_H151 zenon_H42 zenon_H23e zenon_H7d zenon_H86 zenon_Hab zenon_H8c zenon_H144 zenon_H6f zenon_Hf8 zenon_H1dd zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H14a zenon_H53 zenon_H145 zenon_H132 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H118 zenon_H16f zenon_Hda zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H1ea zenon_H4a zenon_Hf2 zenon_H5e zenon_Hde zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H14d zenon_H158 zenon_H152 zenon_H3c zenon_H51 zenon_H91 zenon_Hc8 zenon_Hc5 zenon_H7f zenon_H44 zenon_H16b zenon_H95 zenon_H114 zenon_H10b zenon_H80 zenon_H177 zenon_H8d zenon_Hc1 zenon_Hc0 zenon_H216 zenon_H3a zenon_H35 zenon_Hfd zenon_He7 zenon_H4c. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.68 exact (zenon_H56 zenon_H2c). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.68 apply (zenon_L327_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.68 apply (zenon_L228_); trivial. % 10.45/10.68 apply (zenon_L1283_); trivial. % 10.45/10.68 (* end of lemma zenon_L1287_ *) % 10.45/10.68 assert (zenon_L1288_ : (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((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 (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((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 (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H56 zenon_H1f0 zenon_H100 zenon_H97 zenon_H28 zenon_Hf2 zenon_H5e zenon_Hde zenon_Hc1 zenon_H1f zenon_H192 zenon_He8 zenon_H191 zenon_H216 zenon_H3a zenon_H35 zenon_H67 zenon_H1ef zenon_H1af zenon_H203 zenon_Hd2 zenon_H127 zenon_H151 zenon_H42 zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H8c zenon_H3c zenon_H44 zenon_H144 zenon_H6f zenon_Hfd zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H103 zenon_H159 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H155 zenon_H156 zenon_H174 zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H1ea zenon_H4a zenon_He7 zenon_H10b zenon_Hed zenon_H4c. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H2c | zenon_intro zenon_H65 ]. % 10.45/10.68 exact (zenon_H56 zenon_H2c). % 10.45/10.68 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H1e | zenon_intro zenon_H66 ]. % 10.45/10.68 apply (zenon_L327_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H5d | zenon_intro zenon_H62 ]. % 10.45/10.68 apply (zenon_L228_); trivial. % 10.45/10.68 apply (zenon_L1285_); trivial. % 10.45/10.68 (* end of lemma zenon_L1288_ *) % 10.45/10.68 assert (zenon_L1289_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (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)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (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)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (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))))) -> (~((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) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 10.45/10.68 do 0 intro. intros zenon_H1ea zenon_H216 zenon_H177 zenon_H173 zenon_H16e zenon_H64 zenon_Hf5 zenon_H7a zenon_H169 zenon_H1f zenon_H16b zenon_Hda zenon_H16f zenon_H118 zenon_H114 zenon_H110 zenon_Hd3 zenon_H28 zenon_Hfd zenon_H174 zenon_H156 zenon_H112 zenon_H157 zenon_H150 zenon_Hbb zenon_H12f zenon_H144 zenon_H10b zenon_H3c zenon_Hc5 zenon_H132 zenon_H145 zenon_H14d zenon_H44 zenon_H53 zenon_H14a zenon_H152 zenon_H158 zenon_H165 zenon_H108 zenon_H168 zenon_H23d zenon_H95 zenon_H1dd zenon_Hf8 zenon_H35 zenon_H155 zenon_H3a zenon_H1de zenon_H181 zenon_H187 zenon_H1b7 zenon_H1e6 zenon_H4c zenon_Hae zenon_H23e zenon_H7d zenon_H80 zenon_H86 zenon_Hab zenon_H5e zenon_H203 zenon_H1cb zenon_H159 zenon_H15a zenon_Hec zenon_Hf2 zenon_H103 zenon_H8c zenon_H151 zenon_H127 zenon_Hd2 zenon_H1af. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.68 apply (zenon_L1271_); trivial. % 10.45/10.68 exact (zenon_H127 zenon_Hd0). % 10.45/10.68 apply (zenon_L500_); trivial. % 10.45/10.68 exact (zenon_H203 zenon_H9a). % 10.45/10.68 apply (zenon_L123_); trivial. % 10.45/10.68 (* end of lemma zenon_L1289_ *) % 10.45/10.68 assert (zenon_L1290_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/(~((op (e3) (e3)) = (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 (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (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) (e3)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((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))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e3) (e3)) = (e3))) -> False). % 10.45/10.68 do 0 intro. intros zenon_Hdd zenon_H26 zenon_H200 zenon_H1f0 zenon_Hf2 zenon_H1b4 zenon_H1bc zenon_H6f zenon_H238 zenon_H151 zenon_H103 zenon_Hec zenon_H159 zenon_H1cb zenon_Hae zenon_H4c zenon_H1e6 zenon_H1b7 zenon_H187 zenon_H181 zenon_H1de zenon_H155 zenon_Hf8 zenon_H1dd zenon_H95 zenon_H23d zenon_H168 zenon_H108 zenon_H165 zenon_H158 zenon_H152 zenon_H14a zenon_H53 zenon_H14d zenon_H145 zenon_H132 zenon_Hc5 zenon_H10b zenon_H144 zenon_H12f zenon_Hbb zenon_H150 zenon_H157 zenon_H112 zenon_H156 zenon_H174 zenon_Hfd zenon_Hd3 zenon_H110 zenon_H114 zenon_H118 zenon_H16f zenon_Hda zenon_H16b zenon_H1f zenon_H169 zenon_H7a zenon_Hf5 zenon_H64 zenon_H16e zenon_H173 zenon_H177 zenon_H97 zenon_Hc0 zenon_H67 zenon_H1ef zenon_H1af zenon_H191 zenon_Hd2 zenon_H127 zenon_H1ea zenon_H4a zenon_Hde zenon_H216 zenon_He7 zenon_H44 zenon_H3c zenon_H8c zenon_H35 zenon_H203 zenon_H5e zenon_Hab zenon_H86 zenon_H7d zenon_H23e zenon_H42 zenon_H1c3 zenon_H1c0 zenon_Hc6 zenon_H1ba zenon_H204 zenon_H80. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H2a | zenon_intro zenon_H175 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hcf ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.68 apply (zenon_L1277_); trivial. % 10.45/10.68 apply (zenon_L1256_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.68 apply (zenon_L1277_); trivial. % 10.45/10.68 apply (zenon_L500_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H3a ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.68 apply (zenon_L1260_); trivial. % 10.45/10.68 exact (zenon_H127 zenon_Hd0). % 10.45/10.68 apply (zenon_L321_); trivial. % 10.45/10.68 apply (zenon_L79_); trivial. % 10.45/10.68 exact (zenon_H203 zenon_H9a). % 10.45/10.68 apply (zenon_L1223_); trivial. % 10.45/10.68 apply (zenon_L140_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H32 | zenon_intro zenon_Hdf ]. % 10.45/10.68 exact (zenon_H27 zenon_H32). % 10.45/10.68 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H6a | zenon_intro zenon_He0 ]. % 10.45/10.68 apply (zenon_L238_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd8 ]. % 10.45/10.68 apply (zenon_L1279_); trivial. % 10.45/10.68 apply (zenon_L209_); trivial. % 10.45/10.68 apply (zenon_L1058_); trivial. % 10.45/10.68 exact (zenon_H127 zenon_Hd0). % 10.45/10.68 exact (zenon_H23e zenon_H43). % 10.45/10.68 apply (zenon_L101_); trivial. % 10.45/10.68 apply (zenon_L937_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H1d | zenon_intro zenon_H176 ]. % 10.45/10.68 apply (zenon_L140_); trivial. % 10.45/10.68 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H3a | zenon_intro zenon_H84 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H56 | zenon_intro zenon_H68 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H27 | zenon_intro zenon_H51 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.69 exact (zenon_H25 zenon_H2a). % 10.45/10.69 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.69 apply (zenon_L1262_); trivial. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.69 apply (zenon_L1284_); trivial. % 10.45/10.69 exact (zenon_H23e zenon_H43). % 10.45/10.69 apply (zenon_L1286_); trivial. % 10.45/10.69 apply (zenon_L207_); trivial. % 10.45/10.69 apply (zenon_L1058_); trivial. % 10.45/10.69 exact (zenon_H127 zenon_Hd0). % 10.45/10.69 apply (zenon_L500_); trivial. % 10.45/10.69 exact (zenon_H203 zenon_H9a). % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H200); [ zenon_intro zenon_H2a | zenon_intro zenon_H201 ]. % 10.45/10.69 exact (zenon_H25 zenon_H2a). % 10.45/10.69 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H68 | zenon_intro zenon_H202 ]. % 10.45/10.69 apply (zenon_L1262_); trivial. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H51 | zenon_intro zenon_H43 ]. % 10.45/10.69 apply (zenon_L1287_); trivial. % 10.45/10.69 exact (zenon_H23e zenon_H43). % 10.45/10.69 apply (zenon_L1288_); trivial. % 10.45/10.69 apply (zenon_L207_); trivial. % 10.45/10.69 apply (zenon_L1058_); trivial. % 10.45/10.69 exact (zenon_H127 zenon_Hd0). % 10.45/10.69 apply (zenon_L500_); trivial. % 10.45/10.69 exact (zenon_H203 zenon_H9a). % 10.45/10.69 apply (zenon_L140_); trivial. % 10.45/10.69 apply (zenon_L1289_); trivial. % 10.45/10.69 exact (zenon_H23e zenon_H43). % 10.45/10.69 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H28 | zenon_intro zenon_H43 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H168); [ zenon_intro zenon_He8 | zenon_intro zenon_H15a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H192 | zenon_intro zenon_H1d ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_Haf | zenon_intro zenon_H100 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H7e | zenon_intro zenon_Hbd ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.69 apply (zenon_L1284_); trivial. % 10.45/10.69 apply (zenon_L1286_); trivial. % 10.45/10.69 apply (zenon_L207_); trivial. % 10.45/10.69 apply (zenon_L1058_); trivial. % 10.45/10.69 exact (zenon_H127 zenon_Hd0). % 10.45/10.69 apply (zenon_L500_); trivial. % 10.45/10.69 exact (zenon_H203 zenon_H9a). % 10.45/10.69 apply (zenon_or_s _ _ zenon_H1af); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H9a ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H91 | zenon_intro zenon_Hb8 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hd2); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hd0 ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H8d | zenon_intro zenon_Hbc ]. % 10.45/10.69 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H7f | zenon_intro zenon_Hed ]. % 10.45/10.69 apply (zenon_L1287_); trivial. % 10.45/10.69 apply (zenon_L1288_); trivial. % 10.45/10.69 apply (zenon_L1058_); trivial. % 10.45/10.69 exact (zenon_H127 zenon_Hd0). % 10.45/10.69 apply (zenon_L500_); trivial. % 10.45/10.69 exact (zenon_H203 zenon_H9a). % 10.45/10.69 apply (zenon_L140_); trivial. % 10.45/10.69 apply (zenon_L1289_); trivial. % 10.45/10.69 exact (zenon_H23e zenon_H43). % 10.45/10.69 apply (zenon_L1281_); trivial. % 10.45/10.69 apply (zenon_L1275_); trivial. % 10.45/10.69 exact (zenon_H80 zenon_H84). % 10.45/10.69 (* end of lemma zenon_L1290_ *) % 10.45/10.69 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H24. zenon_intro zenon_H241. % 10.45/10.69 apply (zenon_and_s _ _ zenon_H241). zenon_intro zenon_H22d. zenon_intro zenon_H242. % 10.45/10.69 apply (zenon_and_s _ _ zenon_H242). zenon_intro zenon_H144. zenon_intro zenon_H243. % 10.45/10.69 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_H1b7. zenon_intro zenon_H244. % 10.45/10.69 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H233. zenon_intro zenon_H245. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H245). zenon_intro zenon_H191. zenon_intro zenon_H246. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H246). zenon_intro zenon_H1f8. zenon_intro zenon_H247. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H247). zenon_intro zenon_H18a. zenon_intro zenon_H248. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H248). zenon_intro zenon_H1c3. zenon_intro zenon_H249. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H249). zenon_intro zenon_H118. zenon_intro zenon_H24a. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H24a). zenon_intro zenon_Hc5. zenon_intro zenon_H24b. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H24b). zenon_intro zenon_H21d. zenon_intro zenon_H24c. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H24c). zenon_intro zenon_H24e. zenon_intro zenon_H24d. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H24d). zenon_intro zenon_H250. zenon_intro zenon_H24f. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H24f). zenon_intro zenon_H212. zenon_intro zenon_H7d. % 10.57/10.69 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H200. zenon_intro zenon_H251. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H251). zenon_intro zenon_H18e. zenon_intro zenon_H252. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H252). zenon_intro zenon_H64. zenon_intro zenon_H253. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H253). zenon_intro zenon_H1b4. zenon_intro zenon_H254. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H254). zenon_intro zenon_H42. zenon_intro zenon_H255. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H255). zenon_intro zenon_Hdd. zenon_intro zenon_H256. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H256). zenon_intro zenon_H97. zenon_intro zenon_H257. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H257). zenon_intro zenon_Hda. zenon_intro zenon_H258. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H258). zenon_intro zenon_H145. zenon_intro zenon_H259. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_He7. zenon_intro zenon_H25a. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H25a). zenon_intro zenon_H238. zenon_intro zenon_H25b. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H25b). zenon_intro zenon_H1b1. zenon_intro zenon_H25c. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H25c). zenon_intro zenon_Hae. zenon_intro zenon_H25d. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_Hde. zenon_intro zenon_H25e. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H25e). zenon_intro zenon_H1de. zenon_intro zenon_H25f. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H25f). zenon_intro zenon_Hc0. zenon_intro zenon_H260. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H260). zenon_intro zenon_Hb0. zenon_intro zenon_H261. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H108. zenon_intro zenon_H262. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H262). zenon_intro zenon_H90. zenon_intro zenon_H263. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H263). zenon_intro zenon_H103. zenon_intro zenon_H264. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H1e2. zenon_intro zenon_H265. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H265). zenon_intro zenon_H267. zenon_intro zenon_H266. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H266). zenon_intro zenon_H12c. zenon_intro zenon_H268. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H268). zenon_intro zenon_H165. zenon_intro zenon_H269. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H269). zenon_intro zenon_H14d. zenon_intro zenon_H26a. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H26a). zenon_intro zenon_H8c. zenon_intro zenon_H26b. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_Hf5. zenon_intro zenon_H26c. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H26c). zenon_intro zenon_Hab. zenon_intro zenon_H26d. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H26d). zenon_intro zenon_H177. zenon_intro zenon_H26e. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H26e). zenon_intro zenon_H128. zenon_intro zenon_H26f. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H26f). zenon_intro zenon_H16b. zenon_intro zenon_H270. % 10.57/10.69 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H12f. zenon_intro zenon_H271. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_H1ba. zenon_intro zenon_H272. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H272). zenon_intro zenon_H14a. zenon_intro zenon_H273. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H1bc. zenon_intro zenon_H274. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_H16f. zenon_intro zenon_H275. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H1c0. zenon_intro zenon_H276. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H276). zenon_intro zenon_H1f. zenon_intro zenon_H277. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H277). zenon_intro zenon_Hd3. zenon_intro zenon_H278. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H278). zenon_intro zenon_H1f0. zenon_intro zenon_H279. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H279). zenon_intro zenon_H110. zenon_intro zenon_H27a. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H27a). zenon_intro zenon_H169. zenon_intro zenon_H27b. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H27b). zenon_intro zenon_H114. zenon_intro zenon_H27c. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_H6f. zenon_intro zenon_H27d. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H27d). zenon_intro zenon_H3c. zenon_intro zenon_H27e. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H27e). zenon_intro zenon_H10b. zenon_intro zenon_H27f. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H155. zenon_intro zenon_H280. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H1e6. zenon_intro zenon_H281. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_H152. zenon_intro zenon_H282. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H282). zenon_intro zenon_H187. zenon_intro zenon_H283. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H283). zenon_intro zenon_H181. zenon_intro zenon_H284. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H284). zenon_intro zenon_H7a. zenon_intro zenon_H285. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H285). zenon_intro zenon_H17c. zenon_intro zenon_H286. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H286). zenon_intro zenon_H86. zenon_intro zenon_H287. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H287). zenon_intro zenon_H205. zenon_intro zenon_H288. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H26. zenon_intro zenon_H289. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H289). zenon_intro zenon_H132. zenon_intro zenon_H28a. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H28a). zenon_intro zenon_H58. zenon_intro zenon_H28b. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H28b). zenon_intro zenon_Hfd. zenon_intro zenon_H28c. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H28c). zenon_intro zenon_H11b. zenon_intro zenon_H28d. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H1cb. zenon_intro zenon_H28e. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H28e). zenon_intro zenon_H195. zenon_intro zenon_H28f. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H28f). zenon_intro zenon_H159. zenon_intro zenon_H290. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H290). zenon_intro zenon_H198. zenon_intro zenon_H291. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_H16e. zenon_intro zenon_H292. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H11d. zenon_intro zenon_H293. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_H230. zenon_intro zenon_H294. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H112. zenon_intro zenon_H295. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_Hc6. zenon_intro zenon_H296. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_Hce. zenon_intro zenon_H297. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H297). zenon_intro zenon_H216. zenon_intro zenon_H298. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H184. zenon_intro zenon_H299. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H1fb. zenon_intro zenon_H29a. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_Hbb. zenon_intro zenon_H29b. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H29b). zenon_intro zenon_H1dd. zenon_intro zenon_H29c. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_He3. zenon_intro zenon_H29d. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H29d). zenon_intro zenon_Hec. zenon_intro zenon_H29e. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H17a. zenon_intro zenon_H29f. % 10.57/10.69 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H5e. zenon_intro zenon_H2a0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H44. zenon_intro zenon_H2a1. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a1). zenon_intro zenon_H53. zenon_intro zenon_H2a2. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H35. zenon_intro zenon_H2a3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H4c. zenon_intro zenon_H95. % 10.57/10.69 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H2a5. zenon_intro zenon_H2a4. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H173. zenon_intro zenon_H2a6. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H204. zenon_intro zenon_H2a7. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H174. zenon_intro zenon_H2a8. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H67. zenon_intro zenon_H2a9. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H4a. zenon_intro zenon_H2aa. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2aa). zenon_intro zenon_H168. zenon_intro zenon_H2ab. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H1ef. zenon_intro zenon_H2ac. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H1ea. zenon_intro zenon_H2ad. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_H1af. zenon_intro zenon_H2ae. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H156. zenon_intro zenon_H2af. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H157. zenon_intro zenon_H2b0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H158. zenon_intro zenon_H2b1. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_Hd2. zenon_intro zenon_H2b2. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H150. zenon_intro zenon_H2b3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H151. zenon_intro zenon_H2b4. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_Hf8. zenon_intro zenon_H18d. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H2b6 | zenon_intro zenon_H2b5 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H2a. zenon_intro zenon_H2b7. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2b9. zenon_intro zenon_H2b8. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H25 | zenon_intro zenon_H25 ]. % 10.57/10.69 exact (zenon_H25 zenon_H2a). % 10.57/10.69 exact (zenon_H25 zenon_H2a). % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2b5); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2ba ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H1e. zenon_intro zenon_H2b7. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2b9. zenon_intro zenon_H2b8. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H224. zenon_intro zenon_H2bc. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H226. zenon_intro zenon_H225. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H25 | zenon_intro zenon_H25 ]. % 10.57/10.69 apply (zenon_L588_); trivial. % 10.57/10.69 apply (zenon_L588_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H2be | zenon_intro zenon_H2bd ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H3b. zenon_intro zenon_H2b7. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2b9. zenon_intro zenon_H2b8. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H224. zenon_intro zenon_H2bc. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H226. zenon_intro zenon_H225. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H25 | zenon_intro zenon_H25 ]. % 10.57/10.69 apply (zenon_L647_); trivial. % 10.57/10.69 apply (zenon_L647_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H2c0 | zenon_intro zenon_H2bf ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H57. zenon_intro zenon_H2b7. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2b9. zenon_intro zenon_H2b8. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H224. zenon_intro zenon_H2bc. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2bc). zenon_intro zenon_H226. zenon_intro zenon_H225. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H25 | zenon_intro zenon_H25 ]. % 10.57/10.69 apply (zenon_L692_); trivial. % 10.57/10.69 apply (zenon_L692_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2bf); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2c1 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H69. zenon_intro zenon_H2c3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H2c5. zenon_intro zenon_H2c4. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H22a. zenon_intro zenon_H22b. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H56 | zenon_intro zenon_H22c ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 apply (zenon_L751_); trivial. % 10.57/10.69 apply (zenon_L751_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 apply (zenon_L798_); trivial. % 10.57/10.69 apply (zenon_L798_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c1); [ zenon_intro zenon_H2c9 | zenon_intro zenon_H2c8 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H1d. zenon_intro zenon_H2c3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H2c5. zenon_intro zenon_H2c4. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 exact (zenon_H192 zenon_H1d). % 10.57/10.69 exact (zenon_H192 zenon_H1d). % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c8); [ zenon_intro zenon_H2cb | zenon_intro zenon_H2ca ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2cb). zenon_intro zenon_H6e. zenon_intro zenon_H2c3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H2c5. zenon_intro zenon_H2c4. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H22a. zenon_intro zenon_H22b. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H56 | zenon_intro zenon_H22c ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 apply (zenon_L866_); trivial. % 10.57/10.69 apply (zenon_L866_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 apply (zenon_L880_); trivial. % 10.57/10.69 apply (zenon_L880_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H2cd | zenon_intro zenon_H2cc ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2cd). zenon_intro zenon_H188. zenon_intro zenon_H2c3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H2c5. zenon_intro zenon_H2c4. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H22a. zenon_intro zenon_H22b. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_H56 | zenon_intro zenon_H22c ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 apply (zenon_L892_); trivial. % 10.57/10.69 apply (zenon_L892_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_H192 | zenon_intro zenon_H192 ]. % 10.57/10.69 apply (zenon_L900_); trivial. % 10.57/10.69 apply (zenon_L900_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2cc); [ zenon_intro zenon_H2cf | zenon_intro zenon_H2ce ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H73. zenon_intro zenon_H2d0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d4. zenon_intro zenon_H2d3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H2d5. zenon_intro zenon_H237. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H27 | zenon_intro zenon_H23c ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Haf | zenon_intro zenon_H239 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L988_); trivial. % 10.57/10.69 apply (zenon_L988_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1015_); trivial. % 10.57/10.69 apply (zenon_L1015_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Haf | zenon_intro zenon_H239 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1027_); trivial. % 10.57/10.69 apply (zenon_L1027_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1029_); trivial. % 10.57/10.69 apply (zenon_L1029_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2ce); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H2d6 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H77. zenon_intro zenon_H2d0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d4. zenon_intro zenon_H2d3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H2d5. zenon_intro zenon_H237. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H27 | zenon_intro zenon_H23c ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Haf | zenon_intro zenon_H239 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1033_); trivial. % 10.57/10.69 apply (zenon_L1033_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1036_); trivial. % 10.57/10.69 apply (zenon_L1036_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_Haf | zenon_intro zenon_H239 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1046_); trivial. % 10.57/10.69 apply (zenon_L1046_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L1048_); trivial. % 10.57/10.69 apply (zenon_L1048_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2d8 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d9). zenon_intro zenon_H3a. zenon_intro zenon_H2d0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d4. zenon_intro zenon_H2d3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H2d5. zenon_intro zenon_H237. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 exact (zenon_Hc7 zenon_H3a). % 10.57/10.69 exact (zenon_Hc7 zenon_H3a). % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_H2db | zenon_intro zenon_H2da ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H11f. zenon_intro zenon_H2d0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d4. zenon_intro zenon_H2d3. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H2d5. zenon_intro zenon_H237. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc7 ]. % 10.57/10.69 apply (zenon_L939_); trivial. % 10.57/10.69 apply (zenon_L939_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2da); [ zenon_intro zenon_H2dd | zenon_intro zenon_H2dc ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_He4. zenon_intro zenon_H2de. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H23f. zenon_intro zenon_H2df. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H240. zenon_intro zenon_H23d. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H28 | zenon_intro zenon_H23e ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H203 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1077_); trivial. % 10.57/10.69 apply (zenon_L1077_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1089_); trivial. % 10.57/10.69 apply (zenon_L1089_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1109_); trivial. % 10.57/10.69 apply (zenon_L1109_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1113_); trivial. % 10.57/10.69 apply (zenon_L1113_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H203 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1135_); trivial. % 10.57/10.69 apply (zenon_L1135_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1143_); trivial. % 10.57/10.69 apply (zenon_L1143_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1163_); trivial. % 10.57/10.69 apply (zenon_L1163_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1173_); trivial. % 10.57/10.69 apply (zenon_L1173_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H2e3 | zenon_intro zenon_H2e2 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_Hf2. zenon_intro zenon_H2de. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H23f. zenon_intro zenon_H2df. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H240. zenon_intro zenon_H23d. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H28 | zenon_intro zenon_H23e ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H203 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1212_); trivial. % 10.57/10.69 apply (zenon_L1212_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1221_); trivial. % 10.57/10.69 apply (zenon_L1221_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1227_); trivial. % 10.57/10.69 apply (zenon_L1227_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1229_); trivial. % 10.57/10.69 apply (zenon_L1229_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H203 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1241_); trivial. % 10.57/10.69 apply (zenon_L1241_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1244_); trivial. % 10.57/10.69 apply (zenon_L1244_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_Hc8 | zenon_intro zenon_H127 ]. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1276_); trivial. % 10.57/10.69 apply (zenon_L1276_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 apply (zenon_L1290_); trivial. % 10.57/10.69 apply (zenon_L1290_); trivial. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e4 ]. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H135. zenon_intro zenon_H2de. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H23f. zenon_intro zenon_H2df. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H240. zenon_intro zenon_H23d. % 10.57/10.69 apply (zenon_L1196_); trivial. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e4). zenon_intro zenon_H84. zenon_intro zenon_H2de. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H23f. zenon_intro zenon_H2df. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0. % 10.57/10.69 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H240. zenon_intro zenon_H23d. % 10.57/10.69 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H80 | zenon_intro zenon_H80 ]. % 10.57/10.69 exact (zenon_H80 zenon_H84). % 10.57/10.69 exact (zenon_H80 zenon_H84). % 10.57/10.69 Qed. % 10.57/10.69 % SZS output end Proof % 10.57/10.69 (* END-PROOF *) % 10.57/10.69 nodes searched: 200868 % 10.57/10.69 max branch formulas: 301 % 10.57/10.69 proof nodes created: 11988 % 10.57/10.69 formulas created: 57459 % 10.57/10.69 %------------------------------------------------------------------------------