%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GRA014+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 : Sat Jul 16 07:24:30 EDT 2022 % Result : Theorem 0.92s 1.07s % Output : Proof 0.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GRA014+1 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n022.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue May 31 03:53:37 EDT 2022 % 0.12/0.34 % CPUTime : % 0.92/1.07 (* PROOF-FOUND *) % 0.92/1.07 % SZS status Theorem % 0.92/1.07 (* BEGIN-PROOF *) % 0.92/1.07 % SZS output start Proof % 0.92/1.07 Theorem goal_to_be_proved : (goal). % 0.92/1.07 Proof. % 0.92/1.07 assert (zenon_L1_ : (~((n4) = (n4))) -> False). % 0.92/1.07 do 0 intro. intros zenon_H6. % 0.92/1.07 apply zenon_H6. apply refl_equal. % 0.92/1.07 (* end of lemma zenon_L1_ *) % 0.92/1.07 assert (zenon_L2_ : (less_than (n2) (n3)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n2) (n4))) -> (less_than (n3) (n4)) -> False). % 0.92/1.07 do 0 intro. intros zenon_H7 zenon_H8 zenon_H9 zenon_Ha. % 0.92/1.07 elim (classic ((~((n2) = (n3)))/\(~(less_than (n2) (n3))))); [ zenon_intro zenon_Hb | zenon_intro zenon_Hc ]. % 0.92/1.07 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.92/1.07 exact (zenon_Hd zenon_H7). % 0.92/1.07 cut ((less_than (n3) (n4)) = (less_than (n2) (n4))). % 0.92/1.07 intro zenon_D_pnotp. % 0.92/1.07 apply zenon_H9. % 0.92/1.07 rewrite <- zenon_D_pnotp. % 0.92/1.07 exact zenon_Ha. % 0.92/1.07 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.92/1.07 cut (((n3) = (n2))); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 0.92/1.07 congruence. % 0.92/1.07 apply (zenon_notand_s _ _ zenon_Hc); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.92/1.07 apply zenon_H11. zenon_intro zenon_H12. % 0.92/1.07 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 0.92/1.07 cut (((n2) = (n2)) = ((n3) = (n2))). % 0.92/1.07 intro zenon_D_pnotp. % 0.92/1.07 apply zenon_Hf. % 0.92/1.07 rewrite <- zenon_D_pnotp. % 0.92/1.07 exact zenon_H13. % 0.92/1.07 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 0.92/1.07 cut (((n2) = (n3))); [idtac | apply NNPP; zenon_intro zenon_He]. % 0.92/1.07 congruence. % 0.92/1.07 exact (zenon_He zenon_H12). % 0.92/1.07 apply zenon_H14. apply refl_equal. % 0.92/1.07 apply zenon_H14. apply refl_equal. % 0.92/1.07 apply zenon_H10. zenon_intro zenon_H7. % 0.92/1.07 generalize (zenon_H8 (n2)). zenon_intro zenon_H15. % 0.92/1.07 generalize (zenon_H15 (n3)). zenon_intro zenon_H16. % 0.92/1.07 generalize (zenon_H16 (n4)). zenon_intro zenon_H17. % 0.92/1.07 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hd | zenon_intro zenon_H18 ]. % 0.92/1.07 exact (zenon_Hd zenon_H7). % 0.92/1.07 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 0.92/1.07 exact (zenon_H1a zenon_Ha). % 0.92/1.07 exact (zenon_H9 zenon_H19). % 0.92/1.07 apply zenon_H6. apply refl_equal. % 0.92/1.07 (* end of lemma zenon_L2_ *) % 0.92/1.07 assert (zenon_L3_ : (~((n5) = (n5))) -> False). % 0.92/1.07 do 0 intro. intros zenon_H1b. % 0.92/1.07 apply zenon_H1b. apply refl_equal. % 0.92/1.07 (* end of lemma zenon_L3_ *) % 0.92/1.07 assert (zenon_L4_ : (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n2) (n5))) -> (less_than (n4) (n5)) -> False). % 0.92/1.07 do 0 intro. intros zenon_H7 zenon_Ha zenon_H8 zenon_H1c zenon_H1d. % 0.92/1.07 elim (classic ((~((n2) = (n4)))/\(~(less_than (n2) (n4))))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 0.92/1.07 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H9. % 0.92/1.07 apply (zenon_L2_); trivial. % 0.92/1.07 cut ((less_than (n4) (n5)) = (less_than (n2) (n5))). % 0.92/1.07 intro zenon_D_pnotp. % 0.92/1.07 apply zenon_H1c. % 0.92/1.07 rewrite <- zenon_D_pnotp. % 0.92/1.07 exact zenon_H1d. % 0.92/1.07 cut (((n5) = (n5))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.92/1.07 cut (((n4) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 0.92/1.07 congruence. % 0.92/1.07 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.92/1.07 apply zenon_H23. zenon_intro zenon_H24. % 0.92/1.07 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 0.92/1.07 cut (((n2) = (n2)) = ((n4) = (n2))). % 0.92/1.07 intro zenon_D_pnotp. % 0.92/1.07 apply zenon_H21. % 0.92/1.07 rewrite <- zenon_D_pnotp. % 0.92/1.07 exact zenon_H13. % 0.92/1.07 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 0.92/1.07 cut (((n2) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 0.92/1.07 congruence. % 0.92/1.07 exact (zenon_H20 zenon_H24). % 0.92/1.07 apply zenon_H14. apply refl_equal. % 0.92/1.07 apply zenon_H14. apply refl_equal. % 0.92/1.07 apply zenon_H22. zenon_intro zenon_H19. % 0.92/1.07 generalize (zenon_H8 (n2)). zenon_intro zenon_H15. % 0.92/1.07 generalize (zenon_H15 (n4)). zenon_intro zenon_H25. % 0.92/1.07 generalize (zenon_H25 (n5)). zenon_intro zenon_H26. % 0.92/1.07 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H9 | zenon_intro zenon_H27 ]. % 0.92/1.07 exact (zenon_H9 zenon_H19). % 0.92/1.07 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.92/1.07 exact (zenon_H29 zenon_H1d). % 0.92/1.07 exact (zenon_H1c zenon_H28). % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L4_ *) % 0.92/1.08 assert (zenon_L5_ : (~((n6) = (n6))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H2a. % 0.92/1.08 apply zenon_H2a. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L5_ *) % 0.92/1.08 assert (zenon_L6_ : (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n2) (n6))) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Ha zenon_H7 zenon_H1d zenon_H8 zenon_H2b zenon_H2c. % 0.92/1.08 elim (classic ((~((n2) = (n5)))/\(~(less_than (n2) (n5))))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H1c. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 cut ((less_than (n5) (n6)) = (less_than (n2) (n6))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H2b. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H2c. % 0.92/1.08 cut (((n6) = (n6))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.92/1.08 cut (((n5) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.92/1.08 apply zenon_H32. zenon_intro zenon_H33. % 0.92/1.08 elim (classic ((n2) = (n2))); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 0.92/1.08 cut (((n2) = (n2)) = ((n5) = (n2))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H30. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H13. % 0.92/1.08 cut (((n2) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 0.92/1.08 cut (((n2) = (n5))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_H2f zenon_H33). % 0.92/1.08 apply zenon_H14. apply refl_equal. % 0.92/1.08 apply zenon_H14. apply refl_equal. % 0.92/1.08 apply zenon_H31. zenon_intro zenon_H28. % 0.92/1.08 generalize (zenon_H8 (n2)). zenon_intro zenon_H15. % 0.92/1.08 generalize (zenon_H15 (n5)). zenon_intro zenon_H34. % 0.92/1.08 generalize (zenon_H34 (n6)). zenon_intro zenon_H35. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H1c | zenon_intro zenon_H36 ]. % 0.92/1.08 exact (zenon_H1c zenon_H28). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 exact (zenon_H2b zenon_H37). % 0.92/1.08 apply zenon_H2a. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L6_ *) % 0.92/1.08 assert (zenon_L7_ : (~((n3) = (n3))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H39. % 0.92/1.08 apply zenon_H39. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L7_ *) % 0.92/1.08 assert (zenon_L8_ : (less_than (n1) (n2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n1) (n3))) -> (less_than (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H3a zenon_H8 zenon_H3b zenon_H7. % 0.92/1.08 elim (classic ((~((n1) = (n2)))/\(~(less_than (n1) (n2))))); [ zenon_intro zenon_H3c | zenon_intro zenon_H3d ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.92/1.08 exact (zenon_H3e zenon_H3a). % 0.92/1.08 cut ((less_than (n2) (n3)) = (less_than (n1) (n3))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H3b. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H7. % 0.92/1.08 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 0.92/1.08 cut (((n2) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.92/1.08 apply zenon_H42. zenon_intro zenon_H43. % 0.92/1.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 0.92/1.08 cut (((n1) = (n1)) = ((n2) = (n1))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H40. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H44. % 0.92/1.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 0.92/1.08 cut (((n1) = (n2))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_H3f zenon_H43). % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H41. zenon_intro zenon_H3a. % 0.92/1.08 generalize (zenon_H8 (n1)). zenon_intro zenon_H46. % 0.92/1.08 generalize (zenon_H46 (n2)). zenon_intro zenon_H47. % 0.92/1.08 generalize (zenon_H47 (n3)). zenon_intro zenon_H48. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H3e | zenon_intro zenon_H49 ]. % 0.92/1.08 exact (zenon_H3e zenon_H3a). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_Hd | zenon_intro zenon_H4a ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 exact (zenon_H3b zenon_H4a). % 0.92/1.08 apply zenon_H39. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L8_ *) % 0.92/1.08 assert (zenon_L9_ : (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n1) (n4))) -> (less_than (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H3a zenon_H7 zenon_H8 zenon_H4b zenon_Ha. % 0.92/1.08 elim (classic ((~((n1) = (n3)))/\(~(less_than (n1) (n3))))); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H3b. % 0.92/1.08 apply (zenon_L8_); trivial. % 0.92/1.08 cut ((less_than (n3) (n4)) = (less_than (n1) (n4))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H4b. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_Ha. % 0.92/1.08 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.92/1.08 cut (((n3) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H4d); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.92/1.08 apply zenon_H51. zenon_intro zenon_H52. % 0.92/1.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 0.92/1.08 cut (((n1) = (n1)) = ((n3) = (n1))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H4f. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H44. % 0.92/1.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 0.92/1.08 cut (((n1) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_H4e zenon_H52). % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H50. zenon_intro zenon_H4a. % 0.92/1.08 generalize (zenon_H8 (n1)). zenon_intro zenon_H46. % 0.92/1.08 generalize (zenon_H46 (n3)). zenon_intro zenon_H53. % 0.92/1.08 generalize (zenon_H53 (n4)). zenon_intro zenon_H54. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H3b | zenon_intro zenon_H55 ]. % 0.92/1.08 exact (zenon_H3b zenon_H4a). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H1a | zenon_intro zenon_H56 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 exact (zenon_H4b zenon_H56). % 0.92/1.08 apply zenon_H6. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L9_ *) % 0.92/1.08 assert (zenon_L10_ : (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n1) (n5))) -> (less_than (n4) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7 zenon_H3a zenon_Ha zenon_H8 zenon_H57 zenon_H1d. % 0.92/1.08 elim (classic ((~((n1) = (n4)))/\(~(less_than (n1) (n4))))); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H4b. % 0.92/1.08 apply (zenon_L9_); trivial. % 0.92/1.08 cut ((less_than (n4) (n5)) = (less_than (n1) (n5))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H57. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H1d. % 0.92/1.08 cut (((n5) = (n5))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.92/1.08 cut (((n4) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.92/1.08 apply zenon_H5d. zenon_intro zenon_H5e. % 0.92/1.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 0.92/1.08 cut (((n1) = (n1)) = ((n4) = (n1))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H5b. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H44. % 0.92/1.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 0.92/1.08 cut (((n1) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_H5a zenon_H5e). % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H5c. zenon_intro zenon_H56. % 0.92/1.08 generalize (zenon_H8 (n1)). zenon_intro zenon_H46. % 0.92/1.08 generalize (zenon_H46 (n4)). zenon_intro zenon_H5f. % 0.92/1.08 generalize (zenon_H5f (n5)). zenon_intro zenon_H60. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H4b | zenon_intro zenon_H61 ]. % 0.92/1.08 exact (zenon_H4b zenon_H56). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H29 | zenon_intro zenon_H62 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 exact (zenon_H57 zenon_H62). % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L10_ *) % 0.92/1.08 assert (zenon_L11_ : (less_than (n3) (n4)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n3) (n5))) -> (less_than (n4) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Ha zenon_H8 zenon_H63 zenon_H1d. % 0.92/1.08 elim (classic ((~((n3) = (n4)))/\(~(less_than (n3) (n4))))); [ zenon_intro zenon_H64 | zenon_intro zenon_H65 ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H1a. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 cut ((less_than (n4) (n5)) = (less_than (n3) (n5))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H63. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H1d. % 0.92/1.08 cut (((n5) = (n5))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 0.92/1.08 cut (((n4) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 0.92/1.08 apply zenon_H69. zenon_intro zenon_H6a. % 0.92/1.08 elim (classic ((n3) = (n3))); [ zenon_intro zenon_H6b | zenon_intro zenon_H39 ]. % 0.92/1.08 cut (((n3) = (n3)) = ((n4) = (n3))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H67. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H6b. % 0.92/1.08 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 0.92/1.08 cut (((n3) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_H66 zenon_H6a). % 0.92/1.08 apply zenon_H39. apply refl_equal. % 0.92/1.08 apply zenon_H39. apply refl_equal. % 0.92/1.08 apply zenon_H68. zenon_intro zenon_Ha. % 0.92/1.08 generalize (zenon_H8 (n3)). zenon_intro zenon_H6c. % 0.92/1.08 generalize (zenon_H6c (n4)). zenon_intro zenon_H6d. % 0.92/1.08 generalize (zenon_H6d (n5)). zenon_intro zenon_H6e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H1a | zenon_intro zenon_H6f ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H29 | zenon_intro zenon_H70 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 exact (zenon_H63 zenon_H70). % 0.92/1.08 apply zenon_H1b. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L11_ *) % 0.92/1.08 assert (zenon_L12_ : (~(goal)) -> (goal) -> False). % 0.92/1.08 do 0 intro. intros zenon_G zenon_H71. % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L12_ *) % 0.92/1.08 assert (zenon_L13_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n3) (n5)) -> (red (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_H73 zenon_H74 zenon_H75. % 0.92/1.08 generalize (zenon_H72 (n3)). zenon_intro zenon_H76. % 0.92/1.08 generalize (zenon_H76 (n5)). zenon_intro zenon_H77. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H78 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 0.92/1.08 exact (zenon_H7a zenon_H75). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H79); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 0.92/1.08 exact (zenon_H7c zenon_H74). % 0.92/1.08 exact (zenon_H7b zenon_H73). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L13_ *) % 0.92/1.08 assert (zenon_L14_ : (forall C : zenon_U, (((red (n1) (n2))/\((red (n2) C)/\(red (n1) C)))->(goal))) -> (red (n1) (n2)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7d zenon_H7e zenon_H7f zenon_H73 zenon_G. % 0.92/1.08 generalize (zenon_H7d (n5)). zenon_intro zenon_H80. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 0.92/1.08 exact (zenon_H83 zenon_H7e). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H84 | zenon_intro zenon_H7b ]. % 0.92/1.08 exact (zenon_H84 zenon_H7f). % 0.92/1.08 exact (zenon_H7b zenon_H73). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L14_ *) % 0.92/1.08 assert (zenon_L15_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n2) (n5)) -> (red (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_H73 zenon_H7f zenon_H7e. % 0.92/1.08 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.08 apply (zenon_L14_); trivial. % 0.92/1.08 (* end of lemma zenon_L15_ *) % 0.92/1.08 assert (zenon_L16_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n3)) -> (red (n2) (n3)) -> (red (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_H75 zenon_H85 zenon_H7e. % 0.92/1.08 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.08 generalize (zenon_H7d (n3)). zenon_intro zenon_H86. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H87 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H83 | zenon_intro zenon_H88 ]. % 0.92/1.08 exact (zenon_H83 zenon_H7e). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H89 | zenon_intro zenon_H7a ]. % 0.92/1.08 exact (zenon_H89 zenon_H85). % 0.92/1.08 exact (zenon_H7a zenon_H75). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L16_ *) % 0.92/1.08 assert (zenon_L17_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (~(goal)) -> (green (n2) (n5)) -> (green (n3) (n5)) -> (green (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8a zenon_G zenon_H8b zenon_H8c zenon_H8d. % 0.92/1.08 generalize (zenon_H8a (n3)). zenon_intro zenon_H8e. % 0.92/1.08 generalize (zenon_H8e (n5)). zenon_intro zenon_H8f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H8f); [ zenon_intro zenon_H90 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H90); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 0.92/1.08 exact (zenon_H92 zenon_H8d). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H91); [ zenon_intro zenon_H94 | zenon_intro zenon_H93 ]. % 0.92/1.08 exact (zenon_H94 zenon_H8c). % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L17_ *) % 0.92/1.08 assert (zenon_L18_ : (green (n2) (n3)) -> (green (n3) (n5)) -> (green (n2) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8d zenon_H8c zenon_H8b zenon_G. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 apply (zenon_L17_); trivial. % 0.92/1.08 (* end of lemma zenon_L18_ *) % 0.92/1.08 assert (zenon_L19_ : ((less_than (n2) (n3))->((red (n2) (n3))\/(green (n2) (n3)))) -> (less_than (n2) (n3)) -> (red (n1) (n2)) -> (red (n1) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (green (n3) (n5)) -> (green (n2) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H95 zenon_H7 zenon_H7e zenon_H75 zenon_H72 zenon_H8c zenon_H8b zenon_G. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 apply (zenon_L16_); trivial. % 0.92/1.08 apply (zenon_L18_); trivial. % 0.92/1.08 (* end of lemma zenon_L19_ *) % 0.92/1.08 assert (zenon_L20_ : (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (less_than (n2) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n3)) -> (red (n1) (n2)) -> (green (n3) (n5)) -> (green (n2) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H97 zenon_H7 zenon_H72 zenon_G zenon_H75 zenon_H7e zenon_H8c zenon_H8b. % 0.92/1.08 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.08 apply (zenon_L19_); trivial. % 0.92/1.08 (* end of lemma zenon_L20_ *) % 0.92/1.08 assert (zenon_L21_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n1) (n2)) -> (less_than (n2) (n3)) -> (red (n1) (n3)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H7e zenon_H7 zenon_H75 zenon_H73 zenon_G zenon_Ha zenon_H1d. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 apply (zenon_L13_); trivial. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 apply (zenon_L15_); trivial. % 0.92/1.08 apply (zenon_L20_); trivial. % 0.92/1.08 (* end of lemma zenon_L21_ *) % 0.92/1.08 assert (zenon_L22_ : (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n1) (n6))) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H8 zenon_H9d zenon_H2c. % 0.92/1.08 elim (classic ((~((n1) = (n5)))/\(~(less_than (n1) (n5))))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H57. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 cut ((less_than (n5) (n6)) = (less_than (n1) (n6))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_H9d. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H2c. % 0.92/1.08 cut (((n6) = (n6))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.92/1.08 cut (((n5) = (n1))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha2 ]. % 0.92/1.08 apply zenon_Ha3. zenon_intro zenon_Ha4. % 0.92/1.08 elim (classic ((n1) = (n1))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 0.92/1.08 cut (((n1) = (n1)) = ((n5) = (n1))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_Ha1. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H44. % 0.92/1.08 cut (((n1) = (n1))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 0.92/1.08 cut (((n1) = (n5))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_Ha0 zenon_Ha4). % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_H45. apply refl_equal. % 0.92/1.08 apply zenon_Ha2. zenon_intro zenon_H62. % 0.92/1.08 generalize (zenon_H8 (n1)). zenon_intro zenon_H46. % 0.92/1.08 generalize (zenon_H46 (n5)). zenon_intro zenon_Ha5. % 0.92/1.08 generalize (zenon_Ha5 (n6)). zenon_intro zenon_Ha6. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Ha6); [ zenon_intro zenon_H57 | zenon_intro zenon_Ha7 ]. % 0.92/1.08 exact (zenon_H57 zenon_H62). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H38 | zenon_intro zenon_Ha8 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 exact (zenon_H9d zenon_Ha8). % 0.92/1.08 apply zenon_H2a. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L22_ *) % 0.92/1.08 assert (zenon_L23_ : (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n3) (n6))) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Ha zenon_H1d zenon_H8 zenon_Ha9 zenon_H2c. % 0.92/1.08 elim (classic ((~((n3) = (n5)))/\(~(less_than (n3) (n5))))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_Hac. zenon_intro zenon_H63. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 cut ((less_than (n5) (n6)) = (less_than (n3) (n6))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_Ha9. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H2c. % 0.92/1.08 cut (((n6) = (n6))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.92/1.08 cut (((n5) = (n3))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hab); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ]. % 0.92/1.08 apply zenon_Haf. zenon_intro zenon_Hb0. % 0.92/1.08 elim (classic ((n3) = (n3))); [ zenon_intro zenon_H6b | zenon_intro zenon_H39 ]. % 0.92/1.08 cut (((n3) = (n3)) = ((n5) = (n3))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_Had. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H6b. % 0.92/1.08 cut (((n3) = (n3))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 0.92/1.08 cut (((n3) = (n5))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_Hac zenon_Hb0). % 0.92/1.08 apply zenon_H39. apply refl_equal. % 0.92/1.08 apply zenon_H39. apply refl_equal. % 0.92/1.08 apply zenon_Hae. zenon_intro zenon_H70. % 0.92/1.08 generalize (zenon_H8 (n3)). zenon_intro zenon_H6c. % 0.92/1.08 generalize (zenon_H6c (n5)). zenon_intro zenon_Hb1. % 0.92/1.08 generalize (zenon_Hb1 (n6)). zenon_intro zenon_Hb2. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hb2); [ zenon_intro zenon_H63 | zenon_intro zenon_Hb3 ]. % 0.92/1.08 exact (zenon_H63 zenon_H70). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_H38 | zenon_intro zenon_Hb4 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 exact (zenon_Ha9 zenon_Hb4). % 0.92/1.08 apply zenon_H2a. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L23_ *) % 0.92/1.08 assert (zenon_L24_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n3) (n6)) -> (red (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_Hb5 zenon_Hb6 zenon_H75. % 0.92/1.08 generalize (zenon_H72 (n3)). zenon_intro zenon_H76. % 0.92/1.08 generalize (zenon_H76 (n6)). zenon_intro zenon_Hb7. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hb8); [ zenon_intro zenon_H7a | zenon_intro zenon_Hb9 ]. % 0.92/1.08 exact (zenon_H7a zenon_H75). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ]. % 0.92/1.08 exact (zenon_Hbb zenon_Hb6). % 0.92/1.08 exact (zenon_Hba zenon_Hb5). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L24_ *) % 0.92/1.08 assert (zenon_L25_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n2) (n6)) -> (red (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_Hb5 zenon_Hbc zenon_H7e. % 0.92/1.08 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.08 generalize (zenon_H7d (n6)). zenon_intro zenon_Hbd. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbe | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hbe); [ zenon_intro zenon_H83 | zenon_intro zenon_Hbf ]. % 0.92/1.08 exact (zenon_H83 zenon_H7e). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hba ]. % 0.92/1.08 exact (zenon_Hc0 zenon_Hbc). % 0.92/1.08 exact (zenon_Hba zenon_Hb5). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L25_ *) % 0.92/1.08 assert (zenon_L26_ : (forall C : zenon_U, (((green (n2) (n3))/\((green (n3) C)/\(green (n2) C)))->(goal))) -> (green (n2) (n3)) -> (green (n3) (n6)) -> (green (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8e zenon_H8d zenon_Hc1 zenon_Hc2 zenon_G. % 0.92/1.08 generalize (zenon_H8e (n6)). zenon_intro zenon_Hc3. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc3); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_H92 | zenon_intro zenon_Hc5 ]. % 0.92/1.08 exact (zenon_H92 zenon_H8d). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hc5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc6 ]. % 0.92/1.08 exact (zenon_Hc7 zenon_Hc1). % 0.92/1.08 exact (zenon_Hc6 zenon_Hc2). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L26_ *) % 0.92/1.08 assert (zenon_L27_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (~(goal)) -> (green (n2) (n6)) -> (green (n3) (n6)) -> (green (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8a zenon_G zenon_Hc2 zenon_Hc1 zenon_H8d. % 0.92/1.08 generalize (zenon_H8a (n3)). zenon_intro zenon_H8e. % 0.92/1.08 apply (zenon_L26_); trivial. % 0.92/1.08 (* end of lemma zenon_L27_ *) % 0.92/1.08 assert (zenon_L28_ : (green (n2) (n3)) -> (green (n3) (n6)) -> (green (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8d zenon_Hc1 zenon_Hc2 zenon_G. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 apply (zenon_L27_); trivial. % 0.92/1.08 (* end of lemma zenon_L28_ *) % 0.92/1.08 assert (zenon_L29_ : ((less_than (n2) (n3))->((red (n2) (n3))\/(green (n2) (n3)))) -> (less_than (n2) (n3)) -> (red (n1) (n2)) -> (red (n1) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (green (n3) (n6)) -> (green (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H95 zenon_H7 zenon_H7e zenon_H75 zenon_H72 zenon_Hc1 zenon_Hc2 zenon_G. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 apply (zenon_L16_); trivial. % 0.92/1.08 apply (zenon_L28_); trivial. % 0.92/1.08 (* end of lemma zenon_L29_ *) % 0.92/1.08 assert (zenon_L30_ : (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (less_than (n2) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n3)) -> (red (n1) (n2)) -> (green (n3) (n6)) -> (green (n2) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H97 zenon_H7 zenon_H72 zenon_G zenon_H75 zenon_H7e zenon_Hc1 zenon_Hc2. % 0.92/1.08 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.08 apply (zenon_L29_); trivial. % 0.92/1.08 (* end of lemma zenon_L30_ *) % 0.92/1.08 assert (zenon_L31_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n1) (n2)) -> (less_than (n2) (n3)) -> (red (n1) (n3)) -> (red (n1) (n6)) -> (~(goal)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H7e zenon_H7 zenon_H75 zenon_Hb5 zenon_G zenon_H1d zenon_Ha zenon_H2c. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 apply (zenon_L24_); trivial. % 0.92/1.08 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 apply (zenon_L25_); trivial. % 0.92/1.08 apply (zenon_L30_); trivial. % 0.92/1.08 (* end of lemma zenon_L31_ *) % 0.92/1.08 assert (zenon_L32_ : (red (n1) (n2)) -> (red (n2) (n3)) -> (red (n1) (n3)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7e zenon_H85 zenon_H75 zenon_G. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 apply (zenon_L16_); trivial. % 0.92/1.08 (* end of lemma zenon_L32_ *) % 0.92/1.08 assert (zenon_L33_ : (forall C : zenon_U, (((red (n1) (n2))/\((red (n2) C)/\(red (n1) C)))->(goal))) -> (red (n1) (n2)) -> (red (n2) (n4)) -> (red (n1) (n4)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7d zenon_H7e zenon_Hcc zenon_Hcd zenon_G. % 0.92/1.08 generalize (zenon_H7d (n4)). zenon_intro zenon_Hce. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hce); [ zenon_intro zenon_Hcf | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hcf); [ zenon_intro zenon_H83 | zenon_intro zenon_Hd0 ]. % 0.92/1.08 exact (zenon_H83 zenon_H7e). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd1 ]. % 0.92/1.08 exact (zenon_Hd2 zenon_Hcc). % 0.92/1.08 exact (zenon_Hd1 zenon_Hcd). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L33_ *) % 0.92/1.08 assert (zenon_L34_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n4)) -> (red (n2) (n4)) -> (red (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_Hcd zenon_Hcc zenon_H7e. % 0.92/1.08 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.08 apply (zenon_L33_); trivial. % 0.92/1.08 (* end of lemma zenon_L34_ *) % 0.92/1.08 assert (zenon_L35_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n4)) -> (red (n3) (n4)) -> (red (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_Hcd zenon_Hd3 zenon_H75. % 0.92/1.08 generalize (zenon_H72 (n3)). zenon_intro zenon_H76. % 0.92/1.08 generalize (zenon_H76 (n4)). zenon_intro zenon_Hd4. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd5 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hd5); [ zenon_intro zenon_H7a | zenon_intro zenon_Hd6 ]. % 0.92/1.08 exact (zenon_H7a zenon_H75). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hd1 ]. % 0.92/1.08 exact (zenon_Hd7 zenon_Hd3). % 0.92/1.08 exact (zenon_Hd1 zenon_Hcd). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L35_ *) % 0.92/1.08 assert (zenon_L36_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (~(goal)) -> (green (n2) (n4)) -> (green (n3) (n4)) -> (green (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8a zenon_G zenon_Hd8 zenon_Hd9 zenon_H8d. % 0.92/1.08 generalize (zenon_H8a (n3)). zenon_intro zenon_H8e. % 0.92/1.08 generalize (zenon_H8e (n4)). zenon_intro zenon_Hda. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hda); [ zenon_intro zenon_Hdb | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hdb); [ zenon_intro zenon_H92 | zenon_intro zenon_Hdc ]. % 0.92/1.08 exact (zenon_H92 zenon_H8d). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hdc); [ zenon_intro zenon_Hde | zenon_intro zenon_Hdd ]. % 0.92/1.08 exact (zenon_Hde zenon_Hd9). % 0.92/1.08 exact (zenon_Hdd zenon_Hd8). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L36_ *) % 0.92/1.08 assert (zenon_L37_ : (green (n2) (n3)) -> (green (n2) (n4)) -> (red (n1) (n3)) -> (red (n1) (n4)) -> (~(goal)) -> (less_than (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8d zenon_Hd8 zenon_H75 zenon_Hcd zenon_G zenon_Ha. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.08 apply (zenon_L35_); trivial. % 0.92/1.08 apply (zenon_L36_); trivial. % 0.92/1.08 (* end of lemma zenon_L37_ *) % 0.92/1.08 assert (zenon_L38_ : (less_than (n4) (n5)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(less_than (n4) (n6))) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H1d zenon_H8 zenon_He1 zenon_H2c. % 0.92/1.08 elim (classic ((~((n4) = (n5)))/\(~(less_than (n4) (n5))))); [ zenon_intro zenon_He2 | zenon_intro zenon_He3 ]. % 0.92/1.08 apply (zenon_and_s _ _ zenon_He2). zenon_intro zenon_He4. zenon_intro zenon_H29. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 cut ((less_than (n5) (n6)) = (less_than (n4) (n6))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_He1. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_H2c. % 0.92/1.08 cut (((n6) = (n6))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.92/1.08 cut (((n5) = (n4))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 0.92/1.08 congruence. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_He3); [ zenon_intro zenon_He7 | zenon_intro zenon_He6 ]. % 0.92/1.08 apply zenon_He7. zenon_intro zenon_He8. % 0.92/1.08 elim (classic ((n4) = (n4))); [ zenon_intro zenon_He9 | zenon_intro zenon_H6 ]. % 0.92/1.08 cut (((n4) = (n4)) = ((n5) = (n4))). % 0.92/1.08 intro zenon_D_pnotp. % 0.92/1.08 apply zenon_He5. % 0.92/1.08 rewrite <- zenon_D_pnotp. % 0.92/1.08 exact zenon_He9. % 0.92/1.08 cut (((n4) = (n4))); [idtac | apply NNPP; zenon_intro zenon_H6]. % 0.92/1.08 cut (((n4) = (n5))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 0.92/1.08 congruence. % 0.92/1.08 exact (zenon_He4 zenon_He8). % 0.92/1.08 apply zenon_H6. apply refl_equal. % 0.92/1.08 apply zenon_H6. apply refl_equal. % 0.92/1.08 apply zenon_He6. zenon_intro zenon_H1d. % 0.92/1.08 generalize (zenon_H8 (n4)). zenon_intro zenon_Hea. % 0.92/1.08 generalize (zenon_Hea (n5)). zenon_intro zenon_Heb. % 0.92/1.08 generalize (zenon_Heb (n6)). zenon_intro zenon_Hec. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hec); [ zenon_intro zenon_H29 | zenon_intro zenon_Hed ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hed); [ zenon_intro zenon_H38 | zenon_intro zenon_Hee ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 exact (zenon_He1 zenon_Hee). % 0.92/1.08 apply zenon_H2a. apply refl_equal. % 0.92/1.08 (* end of lemma zenon_L38_ *) % 0.92/1.08 assert (zenon_L39_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n4) B)/\((red B C)/\(red (n4) C)))->(goal)))) -> (~(goal)) -> (red (n4) (n6)) -> (red (n5) (n6)) -> (red (n4) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hef zenon_G zenon_Hf0 zenon_Hf1 zenon_Hf2. % 0.92/1.08 generalize (zenon_Hef (n5)). zenon_intro zenon_Hf3. % 0.92/1.08 generalize (zenon_Hf3 (n6)). zenon_intro zenon_Hf4. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hf6 ]. % 0.92/1.08 exact (zenon_Hf7 zenon_Hf2). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_Hf6); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hf8 ]. % 0.92/1.08 exact (zenon_Hf9 zenon_Hf1). % 0.92/1.08 exact (zenon_Hf8 zenon_Hf0). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L39_ *) % 0.92/1.08 assert (zenon_L40_ : (red (n4) (n5)) -> (red (n5) (n6)) -> (red (n4) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hf2 zenon_Hf1 zenon_Hf0 zenon_G. % 0.92/1.08 generalize (red_clique (n4)). zenon_intro zenon_Hef. % 0.92/1.08 apply (zenon_L39_); trivial. % 0.92/1.08 (* end of lemma zenon_L40_ *) % 0.92/1.08 assert (zenon_L41_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n5) B)->((red (n5) B)\/(green (n5) B)))) -> (less_than (n5) (n6)) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (~(goal)) -> (~(green (n4) (n6))) -> (~(green (n5) (n6))) -> (~(green (n4) (n5))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H1d zenon_Hfa zenon_H2c zenon_Hfb zenon_G zenon_Hfc zenon_Hfd zenon_Hfe. % 0.92/1.08 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.08 generalize (zenon_Hfa (n6)). zenon_intro zenon_H102. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H102); [ zenon_intro zenon_H38 | zenon_intro zenon_H103 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H104 ]. % 0.92/1.08 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.08 apply (zenon_L38_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.08 apply (zenon_L40_); trivial. % 0.92/1.08 exact (zenon_Hfc zenon_H107). % 0.92/1.08 exact (zenon_Hfd zenon_H104). % 0.92/1.08 exact (zenon_Hfe zenon_H101). % 0.92/1.08 (* end of lemma zenon_L41_ *) % 0.92/1.08 assert (zenon_L42_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (~(goal)) -> (~(green (n4) (n6))) -> (~(green (n5) (n6))) -> (~(green (n4) (n5))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H1d zenon_H2c zenon_G zenon_Hfc zenon_Hfd zenon_Hfe. % 0.92/1.08 generalize (partition (n5)). zenon_intro zenon_Hfa. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 apply (zenon_L41_); trivial. % 0.92/1.08 (* end of lemma zenon_L42_ *) % 0.92/1.08 assert (zenon_L43_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n1) (n6)) -> (~(goal)) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (green (n1) (n4)) -> (green (n1) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H108 zenon_G zenon_H2c zenon_H1d zenon_H109 zenon_H10a. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (zenon_H10b (n5)). zenon_intro zenon_H10c. % 0.92/1.08 generalize (zenon_H10b (n4)). zenon_intro zenon_H10d. % 0.92/1.08 generalize (zenon_H10c (n6)). zenon_intro zenon_H10e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H10e); [ zenon_intro zenon_H10f | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H10f); [ zenon_intro zenon_H111 | zenon_intro zenon_H110 ]. % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H110); [ zenon_intro zenon_Hfd | zenon_intro zenon_H112 ]. % 0.92/1.08 generalize (zenon_H10d (n6)). zenon_intro zenon_H113. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H113); [ zenon_intro zenon_H114 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H114); [ zenon_intro zenon_H116 | zenon_intro zenon_H115 ]. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_Hfc | zenon_intro zenon_H112 ]. % 0.92/1.08 generalize (zenon_H10d (n5)). zenon_intro zenon_H117. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H118 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H118); [ zenon_intro zenon_H116 | zenon_intro zenon_H119 ]. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_Hfe | zenon_intro zenon_H111 ]. % 0.92/1.08 apply (zenon_L42_); trivial. % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L43_ *) % 0.92/1.08 assert (zenon_L44_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (red (n1) (n2)) -> (red (n1) (n3)) -> (~(goal)) -> (less_than (n5) (n6)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H7e zenon_H75 zenon_G zenon_H2c zenon_H11a. % 0.92/1.08 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.08 apply (zenon_L21_); trivial. % 0.92/1.08 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.08 apply (zenon_L22_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.08 apply (zenon_L31_); trivial. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.08 apply (zenon_L9_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 apply (zenon_L32_); trivial. % 0.92/1.08 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.08 apply (zenon_L2_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.08 apply (zenon_L34_); trivial. % 0.92/1.08 apply (zenon_L37_); trivial. % 0.92/1.08 apply (zenon_L43_); trivial. % 0.92/1.08 (* end of lemma zenon_L44_ *) % 0.92/1.08 assert (zenon_L45_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n4) (n5)) -> (red (n1) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_H73 zenon_Hf2 zenon_Hcd. % 0.92/1.08 generalize (zenon_H72 (n4)). zenon_intro zenon_H123. % 0.92/1.08 generalize (zenon_H123 (n5)). zenon_intro zenon_H124. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H124); [ zenon_intro zenon_H125 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H125); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H126 ]. % 0.92/1.08 exact (zenon_Hd1 zenon_Hcd). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H126); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H7b ]. % 0.92/1.08 exact (zenon_Hf7 zenon_Hf2). % 0.92/1.08 exact (zenon_H7b zenon_H73). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L45_ *) % 0.92/1.08 assert (zenon_L46_ : (forall C : zenon_U, (((green (n3) (n4))/\((green (n4) C)/\(green (n3) C)))->(goal))) -> (green (n3) (n4)) -> (green (n4) (n5)) -> (green (n3) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H127 zenon_Hd9 zenon_H101 zenon_H8c zenon_G. % 0.92/1.08 generalize (zenon_H127 (n5)). zenon_intro zenon_H128. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H128); [ zenon_intro zenon_H129 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H129); [ zenon_intro zenon_Hde | zenon_intro zenon_H12a ]. % 0.92/1.08 exact (zenon_Hde zenon_Hd9). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H12a); [ zenon_intro zenon_Hfe | zenon_intro zenon_H94 ]. % 0.92/1.08 exact (zenon_Hfe zenon_H101). % 0.92/1.08 exact (zenon_H94 zenon_H8c). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L46_ *) % 0.92/1.08 assert (zenon_L47_ : (green (n3) (n4)) -> (green (n4) (n5)) -> (green (n3) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hd9 zenon_H101 zenon_H8c zenon_G. % 0.92/1.08 generalize (green_clique (n3)). zenon_intro zenon_H12b. % 0.92/1.08 generalize (zenon_H12b (n4)). zenon_intro zenon_H127. % 0.92/1.08 apply (zenon_L46_); trivial. % 0.92/1.08 (* end of lemma zenon_L47_ *) % 0.92/1.08 assert (zenon_L48_ : (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n1) (n4)) -> (green (n3) (n4)) -> (green (n3) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hfb zenon_H1d zenon_H72 zenon_G zenon_H73 zenon_Hcd zenon_Hd9 zenon_H8c. % 0.92/1.08 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.08 apply (zenon_L45_); trivial. % 0.92/1.08 apply (zenon_L47_); trivial. % 0.92/1.08 (* end of lemma zenon_L48_ *) % 0.92/1.08 assert (zenon_L49_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n1) (n3)) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (red (n1) (n4)) -> (green (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H98 zenon_H1d zenon_Ha zenon_H72 zenon_G zenon_H73 zenon_H75 zenon_Hfb zenon_Hcd zenon_Hd9. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 apply (zenon_L13_); trivial. % 0.92/1.08 apply (zenon_L48_); trivial. % 0.92/1.08 (* end of lemma zenon_L49_ *) % 0.92/1.08 assert (zenon_L50_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n5) (n6)) -> (red (n1) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_Hb5 zenon_Hf1 zenon_H73. % 0.92/1.08 generalize (zenon_H72 (n5)). zenon_intro zenon_H12c. % 0.92/1.08 generalize (zenon_H12c (n6)). zenon_intro zenon_H12d. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H12d); [ zenon_intro zenon_H12e | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H12e); [ zenon_intro zenon_H7b | zenon_intro zenon_H12f ]. % 0.92/1.08 exact (zenon_H7b zenon_H73). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H12f); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hba ]. % 0.92/1.08 exact (zenon_Hf9 zenon_Hf1). % 0.92/1.08 exact (zenon_Hba zenon_Hb5). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L50_ *) % 0.92/1.08 assert (zenon_L51_ : (green (n3) (n5)) -> (green (n5) (n6)) -> (green (n3) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8c zenon_H104 zenon_Hc1 zenon_G. % 0.92/1.08 generalize (green_clique (n3)). zenon_intro zenon_H12b. % 0.92/1.08 generalize (zenon_H12b (n5)). zenon_intro zenon_H130. % 0.92/1.08 generalize (zenon_H130 (n6)). zenon_intro zenon_H131. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H131); [ zenon_intro zenon_H132 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H132); [ zenon_intro zenon_H94 | zenon_intro zenon_H133 ]. % 0.92/1.08 exact (zenon_H94 zenon_H8c). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H133); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hc7 ]. % 0.92/1.08 exact (zenon_Hfd zenon_H104). % 0.92/1.08 exact (zenon_Hc7 zenon_Hc1). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L51_ *) % 0.92/1.08 assert (zenon_L52_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n3)) -> (green (n3) (n5)) -> (green (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H98 zenon_H2c zenon_Ha zenon_H1d zenon_H72 zenon_G zenon_Hb5 zenon_H75 zenon_H8c zenon_H104. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 apply (zenon_L24_); trivial. % 0.92/1.08 apply (zenon_L51_); trivial. % 0.92/1.08 (* end of lemma zenon_L52_ *) % 0.92/1.08 assert (zenon_L53_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n5)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (red (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H2c zenon_H72 zenon_G zenon_Hb5 zenon_H73 zenon_H1d zenon_Ha zenon_H75. % 0.92/1.08 generalize (partition (n5)). zenon_intro zenon_Hfa. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_Hfa (n6)). zenon_intro zenon_H102. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H102); [ zenon_intro zenon_H38 | zenon_intro zenon_H103 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H104 ]. % 0.92/1.08 apply (zenon_L50_); trivial. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 apply (zenon_L13_); trivial. % 0.92/1.08 apply (zenon_L52_); trivial. % 0.92/1.08 (* end of lemma zenon_L53_ *) % 0.92/1.08 assert (zenon_L54_ : (red (n2) (n4)) -> (red (n4) (n5)) -> (red (n2) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hcc zenon_Hf2 zenon_H7f zenon_G. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (zenon_H134 (n4)). zenon_intro zenon_H135. % 0.92/1.08 generalize (zenon_H135 (n5)). zenon_intro zenon_H136. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H136); [ zenon_intro zenon_H137 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H137); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H138 ]. % 0.92/1.08 exact (zenon_Hd2 zenon_Hcc). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H84 ]. % 0.92/1.08 exact (zenon_Hf7 zenon_Hf2). % 0.92/1.08 exact (zenon_H84 zenon_H7f). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L54_ *) % 0.92/1.08 assert (zenon_L55_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(green (n2) (n4))) -> (~(green (n4) (n5))) -> (~(goal)) -> (red (n2) (n5)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hdd zenon_Hfe zenon_G zenon_H7f zenon_H1d zenon_H7 zenon_Ha zenon_H97. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.08 apply (zenon_L2_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.08 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.08 apply (zenon_L54_); trivial. % 0.92/1.08 exact (zenon_Hfe zenon_H101). % 0.92/1.08 exact (zenon_Hdd zenon_Hd8). % 0.92/1.08 (* end of lemma zenon_L55_ *) % 0.92/1.08 assert (zenon_L56_ : (((green (n1) (n4))/\((green (n4) (n5))/\(green (n1) (n5))))->(goal)) -> (green (n1) (n5)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(green (n2) (n5))) -> (~(green (n2) (n4))) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (green (n1) (n4)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H117 zenon_H10a zenon_H8 zenon_H93 zenon_Hdd zenon_Ha zenon_H7 zenon_H1d zenon_H109 zenon_G. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H118 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H118); [ zenon_intro zenon_H116 | zenon_intro zenon_H119 ]. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_Hfe | zenon_intro zenon_H111 ]. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 apply (zenon_L55_); trivial. % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L56_ *) % 0.92/1.08 assert (zenon_L57_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n1) (n5)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (~(goal)) -> (green (n1) (n4)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H10a zenon_H1d zenon_H7 zenon_Ha zenon_G zenon_H109 zenon_H139. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.08 generalize (zenon_H10b (n4)). zenon_intro zenon_H10d. % 0.92/1.08 generalize (zenon_H13a (n5)). zenon_intro zenon_H13b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H13b); [ zenon_intro zenon_H13c | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H13c); [ zenon_intro zenon_H13e | zenon_intro zenon_H13d ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H13d); [ zenon_intro zenon_H93 | zenon_intro zenon_H111 ]. % 0.92/1.08 generalize (zenon_H13a (n4)). zenon_intro zenon_H13f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H140 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H140); [ zenon_intro zenon_H13e | zenon_intro zenon_H141 ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H141); [ zenon_intro zenon_Hdd | zenon_intro zenon_H116 ]. % 0.92/1.08 generalize (zenon_H10d (n5)). zenon_intro zenon_H117. % 0.92/1.08 apply (zenon_L56_); trivial. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L57_ *) % 0.92/1.08 assert (zenon_L58_ : ((less_than (n1) (n5))->((red (n1) (n5))\/(green (n1) (n5)))) -> (less_than (n1) (n2)) -> (red (n1) (n3)) -> (red (n1) (n6)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n5) (n6)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (~(goal)) -> (green (n1) (n4)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H11b zenon_H3a zenon_H75 zenon_Hb5 zenon_H72 zenon_H2c zenon_H8 zenon_H1d zenon_H7 zenon_Ha zenon_G zenon_H109 zenon_H139. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.08 apply (zenon_L53_); trivial. % 0.92/1.08 apply (zenon_L57_); trivial. % 0.92/1.08 (* end of lemma zenon_L58_ *) % 0.92/1.08 assert (zenon_L59_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (~(goal)) -> (red (n2) (n6)) -> (red (n4) (n6)) -> (red (n2) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H134 zenon_G zenon_Hbc zenon_Hf0 zenon_Hcc. % 0.92/1.08 generalize (zenon_H134 (n4)). zenon_intro zenon_H135. % 0.92/1.08 generalize (zenon_H135 (n6)). zenon_intro zenon_H142. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H142); [ zenon_intro zenon_H143 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H143); [ zenon_intro zenon_Hd2 | zenon_intro zenon_H144 ]. % 0.92/1.08 exact (zenon_Hd2 zenon_Hcc). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H144); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hc0 ]. % 0.92/1.08 exact (zenon_Hf8 zenon_Hf0). % 0.92/1.08 exact (zenon_Hc0 zenon_Hbc). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L59_ *) % 0.92/1.08 assert (zenon_L60_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (red (n2) (n4)) -> (~(goal)) -> (~(green (n4) (n6))) -> (~(green (n2) (n6))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H97 zenon_H2c zenon_Ha zenon_H7 zenon_H1d zenon_Hfb zenon_Hcc zenon_G zenon_Hfc zenon_Hc6. % 0.92/1.08 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.08 apply (zenon_L38_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 apply (zenon_L59_); trivial. % 0.92/1.08 exact (zenon_Hfc zenon_H107). % 0.92/1.08 exact (zenon_Hc6 zenon_Hc2). % 0.92/1.08 (* end of lemma zenon_L60_ *) % 0.92/1.08 assert (zenon_L61_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(green (n2) (n4))) -> (~(green (n2) (n6))) -> (~(green (n4) (n6))) -> (~(goal)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hdd zenon_Hc6 zenon_Hfc zenon_G zenon_H1d zenon_H2c zenon_H97 zenon_H7 zenon_Ha. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.08 apply (zenon_L2_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.08 apply (zenon_L60_); trivial. % 0.92/1.08 exact (zenon_Hdd zenon_Hd8). % 0.92/1.08 (* end of lemma zenon_L61_ *) % 0.92/1.08 assert (zenon_L62_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (~(goal)) -> (~(green (n4) (n6))) -> (~(green (n2) (n6))) -> (~(green (n2) (n4))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Ha zenon_H7 zenon_H2c zenon_H1d zenon_G zenon_Hfc zenon_Hc6 zenon_Hdd. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 apply (zenon_L61_); trivial. % 0.92/1.08 (* end of lemma zenon_L62_ *) % 0.92/1.08 assert (zenon_L63_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n1) (n6)) -> (~(goal)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (green (n1) (n4)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H108 zenon_G zenon_H1d zenon_H2c zenon_H7 zenon_Ha zenon_H109 zenon_H139. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.08 generalize (zenon_H10b (n4)). zenon_intro zenon_H10d. % 0.92/1.08 generalize (zenon_H13a (n6)). zenon_intro zenon_H145. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H146 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H146); [ zenon_intro zenon_H13e | zenon_intro zenon_H147 ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H112 ]. % 0.92/1.08 generalize (zenon_H10d (n6)). zenon_intro zenon_H113. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H113); [ zenon_intro zenon_H114 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H114); [ zenon_intro zenon_H116 | zenon_intro zenon_H115 ]. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_Hfc | zenon_intro zenon_H112 ]. % 0.92/1.08 generalize (zenon_H13a (n4)). zenon_intro zenon_H13f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H140 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H140); [ zenon_intro zenon_H13e | zenon_intro zenon_H141 ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H141); [ zenon_intro zenon_Hdd | zenon_intro zenon_H116 ]. % 0.92/1.08 apply (zenon_L62_); trivial. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L63_ *) % 0.92/1.08 assert (zenon_L64_ : ((less_than (n1) (n6))->((red (n1) (n6))\/(green (n1) (n6)))) -> (red (n1) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(goal)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (green (n1) (n4)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H11d zenon_H75 zenon_H72 zenon_H3a zenon_H11a zenon_H8 zenon_G zenon_H1d zenon_H2c zenon_H7 zenon_Ha zenon_H109 zenon_H139. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.08 apply (zenon_L22_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.08 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.08 apply (zenon_L58_); trivial. % 0.92/1.08 apply (zenon_L63_); trivial. % 0.92/1.08 (* end of lemma zenon_L64_ *) % 0.92/1.08 assert (zenon_L65_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n3)) -> (green (n1) (n4)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H11a zenon_H72 zenon_G zenon_H75 zenon_H109 zenon_H139. % 0.92/1.08 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.08 apply (zenon_L64_); trivial. % 0.92/1.08 (* end of lemma zenon_L65_ *) % 0.92/1.08 assert (zenon_L66_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n4) (n6)) -> (red (n1) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H72 zenon_G zenon_Hb5 zenon_Hf0 zenon_Hcd. % 0.92/1.08 generalize (zenon_H72 (n4)). zenon_intro zenon_H123. % 0.92/1.08 generalize (zenon_H123 (n6)). zenon_intro zenon_H148. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H148); [ zenon_intro zenon_H149 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H149); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H14a ]. % 0.92/1.08 exact (zenon_Hd1 zenon_Hcd). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H14a); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hba ]. % 0.92/1.08 exact (zenon_Hf8 zenon_Hf0). % 0.92/1.08 exact (zenon_Hba zenon_Hb5). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L66_ *) % 0.92/1.08 assert (zenon_L67_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n3) B)/\((green B C)/\(green (n3) C)))->(goal)))) -> (~(goal)) -> (green (n3) (n6)) -> (green (n4) (n6)) -> (green (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H12b zenon_G zenon_Hc1 zenon_H107 zenon_Hd9. % 0.92/1.08 generalize (zenon_H12b (n4)). zenon_intro zenon_H127. % 0.92/1.08 generalize (zenon_H127 (n6)). zenon_intro zenon_H14b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H14b); [ zenon_intro zenon_H14c | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H14c); [ zenon_intro zenon_Hde | zenon_intro zenon_H14d ]. % 0.92/1.08 exact (zenon_Hde zenon_Hd9). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H14d); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hc7 ]. % 0.92/1.08 exact (zenon_Hfc zenon_H107). % 0.92/1.08 exact (zenon_Hc7 zenon_Hc1). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L67_ *) % 0.92/1.08 assert (zenon_L68_ : (green (n3) (n4)) -> (green (n4) (n6)) -> (green (n3) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hd9 zenon_H107 zenon_Hc1 zenon_G. % 0.92/1.08 generalize (green_clique (n3)). zenon_intro zenon_H12b. % 0.92/1.08 apply (zenon_L67_); trivial. % 0.92/1.08 (* end of lemma zenon_L68_ *) % 0.92/1.08 assert (zenon_L69_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n4)) -> (green (n3) (n4)) -> (green (n3) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hfb zenon_H2c zenon_H1d zenon_H72 zenon_G zenon_Hb5 zenon_Hcd zenon_Hd9 zenon_Hc1. % 0.92/1.08 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.08 apply (zenon_L38_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.08 apply (zenon_L66_); trivial. % 0.92/1.08 apply (zenon_L68_); trivial. % 0.92/1.08 (* end of lemma zenon_L69_ *) % 0.92/1.08 assert (zenon_L70_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n3)) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (red (n1) (n4)) -> (green (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H98 zenon_H2c zenon_Ha zenon_H1d zenon_H72 zenon_G zenon_Hb5 zenon_H75 zenon_Hfb zenon_Hcd zenon_Hd9. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 apply (zenon_L24_); trivial. % 0.92/1.08 apply (zenon_L69_); trivial. % 0.92/1.08 (* end of lemma zenon_L70_ *) % 0.92/1.08 assert (zenon_L71_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (red (n1) (n6)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (red (n1) (n3)) -> (red (n1) (n4)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hfb zenon_Hb5 zenon_H1d zenon_H2c zenon_H75 zenon_Hcd zenon_G zenon_H72 zenon_Ha. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.08 apply (zenon_L35_); trivial. % 0.92/1.08 apply (zenon_L70_); trivial. % 0.92/1.08 (* end of lemma zenon_L71_ *) % 0.92/1.08 assert (zenon_L72_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n4)) -> (red (n1) (n3)) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (red (n1) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Ha zenon_H72 zenon_G zenon_Hcd zenon_H75 zenon_H2c zenon_H1d zenon_Hb5. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 apply (zenon_L71_); trivial. % 0.92/1.08 (* end of lemma zenon_L72_ *) % 0.92/1.08 assert (zenon_L73_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (~(goal)) -> (red (n2) (n6)) -> (red (n5) (n6)) -> (red (n2) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H134 zenon_G zenon_Hbc zenon_Hf1 zenon_H7f. % 0.92/1.08 generalize (zenon_H134 (n5)). zenon_intro zenon_H14e. % 0.92/1.08 generalize (zenon_H14e (n6)). zenon_intro zenon_H14f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H14f); [ zenon_intro zenon_H150 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H150); [ zenon_intro zenon_H84 | zenon_intro zenon_H151 ]. % 0.92/1.08 exact (zenon_H84 zenon_H7f). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H151); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hc0 ]. % 0.92/1.08 exact (zenon_Hf9 zenon_Hf1). % 0.92/1.08 exact (zenon_Hc0 zenon_Hbc). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L73_ *) % 0.92/1.08 assert (zenon_L74_ : (red (n2) (n5)) -> (red (n5) (n6)) -> (red (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7f zenon_Hf1 zenon_Hbc zenon_G. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 apply (zenon_L73_); trivial. % 0.92/1.08 (* end of lemma zenon_L74_ *) % 0.92/1.08 assert (zenon_L75_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n6)) -> (green (n5) (n6)) -> (green (n1) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H108 zenon_H104 zenon_H10a. % 0.92/1.08 generalize (zenon_H10b (n5)). zenon_intro zenon_H10c. % 0.92/1.08 generalize (zenon_H10c (n6)). zenon_intro zenon_H10e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H10e); [ zenon_intro zenon_H10f | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H10f); [ zenon_intro zenon_H111 | zenon_intro zenon_H110 ]. % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H110); [ zenon_intro zenon_Hfd | zenon_intro zenon_H112 ]. % 0.92/1.08 exact (zenon_Hfd zenon_H104). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L75_ *) % 0.92/1.08 assert (zenon_L76_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n6)) -> (green (n2) (n6)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H108 zenon_Hc2 zenon_H139. % 0.92/1.08 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.08 generalize (zenon_H13a (n6)). zenon_intro zenon_H145. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H145); [ zenon_intro zenon_H146 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H146); [ zenon_intro zenon_H13e | zenon_intro zenon_H147 ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H147); [ zenon_intro zenon_Hc6 | zenon_intro zenon_H112 ]. % 0.92/1.08 exact (zenon_Hc6 zenon_Hc2). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L76_ *) % 0.92/1.08 assert (zenon_L77_ : (green (n1) (n2)) -> (green (n2) (n6)) -> (green (n1) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H139 zenon_Hc2 zenon_H108 zenon_G. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 apply (zenon_L76_); trivial. % 0.92/1.08 (* end of lemma zenon_L77_ *) % 0.92/1.08 assert (zenon_L78_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n5)) -> (green (n2) (n5)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H10a zenon_H8b zenon_H139. % 0.92/1.08 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.08 generalize (zenon_H13a (n5)). zenon_intro zenon_H13b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H13b); [ zenon_intro zenon_H13c | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H13c); [ zenon_intro zenon_H13e | zenon_intro zenon_H13d ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H13d); [ zenon_intro zenon_H93 | zenon_intro zenon_H111 ]. % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L78_ *) % 0.92/1.08 assert (zenon_L79_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (green (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n5) (n6)) -> (red (n1) (n3)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H139 zenon_H11a zenon_H2c zenon_H75 zenon_G. % 0.92/1.08 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.08 apply (zenon_L9_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.08 apply (zenon_L35_); trivial. % 0.92/1.08 apply (zenon_L49_); trivial. % 0.92/1.08 apply (zenon_L65_); trivial. % 0.92/1.08 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.08 apply (zenon_L22_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.08 apply (zenon_L9_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.08 apply (zenon_L72_); trivial. % 0.92/1.08 apply (zenon_L58_); trivial. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (partition (n5)). zenon_intro zenon_Hfa. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 generalize (zenon_Hfa (n6)). zenon_intro zenon_H102. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H102); [ zenon_intro zenon_H38 | zenon_intro zenon_H103 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H104 ]. % 0.92/1.08 apply (zenon_L74_); trivial. % 0.92/1.08 apply (zenon_L75_); trivial. % 0.92/1.08 apply (zenon_L77_); trivial. % 0.92/1.08 apply (zenon_L78_); trivial. % 0.92/1.08 (* end of lemma zenon_L79_ *) % 0.92/1.08 assert (zenon_L80_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n1) (n2)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (red (n1) (n3)) -> (~(goal)) -> (less_than (n5) (n6)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H3a zenon_H1d zenon_H7 zenon_Ha zenon_H75 zenon_G zenon_H2c zenon_H11a. % 0.92/1.08 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.08 exact (zenon_H3e zenon_H3a). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.08 apply (zenon_L44_); trivial. % 0.92/1.08 apply (zenon_L79_); trivial. % 0.92/1.08 (* end of lemma zenon_L80_ *) % 0.92/1.08 assert (zenon_L81_ : (red (n1) (n2)) -> (red (n2) (n4)) -> (red (n1) (n4)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7e zenon_Hcc zenon_Hcd zenon_G. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 apply (zenon_L34_); trivial. % 0.92/1.08 (* end of lemma zenon_L81_ *) % 0.92/1.08 assert (zenon_L82_ : (red (n1) (n2)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H7e zenon_H7f zenon_H73 zenon_G. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 apply (zenon_L15_); trivial. % 0.92/1.08 (* end of lemma zenon_L82_ *) % 0.92/1.08 assert (zenon_L83_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n5)) -> (green (n4) (n5)) -> (green (n1) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H10a zenon_H101 zenon_H109. % 0.92/1.08 generalize (zenon_H10b (n4)). zenon_intro zenon_H10d. % 0.92/1.08 generalize (zenon_H10d (n5)). zenon_intro zenon_H117. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H117); [ zenon_intro zenon_H118 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H118); [ zenon_intro zenon_H116 | zenon_intro zenon_H119 ]. % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H119); [ zenon_intro zenon_Hfe | zenon_intro zenon_H111 ]. % 0.92/1.08 exact (zenon_Hfe zenon_H101). % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L83_ *) % 0.92/1.08 assert (zenon_L84_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (red (n1) (n2)) -> (red (n2) (n5)) -> (~(goal)) -> (red (n2) (n4)) -> (green (n1) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H11a zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H7e zenon_H7f zenon_G zenon_Hcc zenon_H109. % 0.92/1.08 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.08 apply (zenon_L82_); trivial. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.08 apply (zenon_L54_); trivial. % 0.92/1.08 apply (zenon_L83_); trivial. % 0.92/1.08 (* end of lemma zenon_L84_ *) % 0.92/1.08 assert (zenon_L85_ : (forall C : zenon_U, (((red (n2) (n3))/\((red (n3) C)/\(red (n2) C)))->(goal))) -> (red (n2) (n3)) -> (red (n3) (n4)) -> (red (n2) (n4)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H154 zenon_H85 zenon_Hd3 zenon_Hcc zenon_G. % 0.92/1.08 generalize (zenon_H154 (n4)). zenon_intro zenon_H155. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H155); [ zenon_intro zenon_H156 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H156); [ zenon_intro zenon_H89 | zenon_intro zenon_H157 ]. % 0.92/1.08 exact (zenon_H89 zenon_H85). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H157); [ zenon_intro zenon_Hd7 | zenon_intro zenon_Hd2 ]. % 0.92/1.08 exact (zenon_Hd7 zenon_Hd3). % 0.92/1.08 exact (zenon_Hd2 zenon_Hcc). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L85_ *) % 0.92/1.08 assert (zenon_L86_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n4)) -> (green (n3) (n4)) -> (green (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H109 zenon_Hd9 zenon_H158. % 0.92/1.08 generalize (zenon_H10b (n3)). zenon_intro zenon_H159. % 0.92/1.08 generalize (zenon_H159 (n4)). zenon_intro zenon_H15a. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H15a); [ zenon_intro zenon_H15b | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H15b); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 0.92/1.08 exact (zenon_H15d zenon_H158). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_Hde | zenon_intro zenon_H116 ]. % 0.92/1.08 exact (zenon_Hde zenon_Hd9). % 0.92/1.08 exact (zenon_H116 zenon_H109). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L86_ *) % 0.92/1.08 assert (zenon_L87_ : (less_than (n3) (n4)) -> (red (n2) (n3)) -> (red (n2) (n4)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n4)) -> (green (n1) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_Ha zenon_H85 zenon_Hcc zenon_G zenon_H10b zenon_H109 zenon_H158 zenon_H134. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_H134 (n3)). zenon_intro zenon_H154. % 0.92/1.08 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.08 apply (zenon_L85_); trivial. % 0.92/1.08 apply (zenon_L86_); trivial. % 0.92/1.08 (* end of lemma zenon_L87_ *) % 0.92/1.08 assert (zenon_L88_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (green (n1) (n3)) -> (green (n1) (n4)) -> (~(goal)) -> (red (n2) (n4)) -> (red (n2) (n3)) -> (less_than (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H134 zenon_H158 zenon_H109 zenon_G zenon_Hcc zenon_H85 zenon_Ha. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 apply (zenon_L87_); trivial. % 0.92/1.08 (* end of lemma zenon_L88_ *) % 0.92/1.08 assert (zenon_L89_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n2) (n3)) -> (red (n2) (n4)) -> (green (n1) (n4)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (~(goal)) -> (red (n1) (n5)) -> (red (n1) (n2)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H85 zenon_Hcc zenon_H109 zenon_H1d zenon_Ha zenon_G zenon_H73 zenon_H7e zenon_H3a zenon_H7 zenon_H11a. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.08 apply (zenon_L8_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.08 apply (zenon_L21_); trivial. % 0.92/1.08 apply (zenon_L88_); trivial. % 0.92/1.08 (* end of lemma zenon_L89_ *) % 0.92/1.08 assert (zenon_L90_ : (green (n1) (n2)) -> (green (n2) (n5)) -> (green (n1) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H139 zenon_H8b zenon_H10a zenon_G. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 apply (zenon_L78_); trivial. % 0.92/1.08 (* end of lemma zenon_L90_ *) % 0.92/1.08 assert (zenon_L91_ : ((less_than (n1) (n2))->((red (n1) (n2))\/(green (n1) (n2)))) -> (less_than (n1) (n2)) -> (red (n1) (n3)) -> (red (n2) (n3)) -> (green (n2) (n5)) -> (green (n1) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H152 zenon_H3a zenon_H75 zenon_H85 zenon_H8b zenon_H10a zenon_G. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.08 exact (zenon_H3e zenon_H3a). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.08 apply (zenon_L32_); trivial. % 0.92/1.08 apply (zenon_L90_); trivial. % 0.92/1.08 (* end of lemma zenon_L91_ *) % 0.92/1.08 assert (zenon_L92_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (red (n1) (n2)) -> (red (n2) (n4)) -> (~(goal)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (red (n2) (n3)) -> ((less_than (n1) (n2))->((red (n1) (n2))\/(green (n1) (n2)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Ha zenon_H3a zenon_H7 zenon_H7e zenon_Hcc zenon_G zenon_H97 zenon_H1d zenon_H11a zenon_H85 zenon_H152. % 0.92/1.08 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.08 apply (zenon_L9_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.08 apply (zenon_L81_); trivial. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 apply (zenon_L84_); trivial. % 0.92/1.08 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.08 apply (zenon_L89_); trivial. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.08 apply (zenon_L8_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.08 apply (zenon_L91_); trivial. % 0.92/1.08 apply (zenon_L88_); trivial. % 0.92/1.08 (* end of lemma zenon_L92_ *) % 0.92/1.08 assert (zenon_L93_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (~(goal)) -> (red (n2) (n4)) -> (red (n3) (n4)) -> (red (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H134 zenon_G zenon_Hcc zenon_Hd3 zenon_H85. % 0.92/1.08 generalize (zenon_H134 (n3)). zenon_intro zenon_H154. % 0.92/1.08 apply (zenon_L85_); trivial. % 0.92/1.08 (* end of lemma zenon_L93_ *) % 0.92/1.08 assert (zenon_L94_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (~(goal)) -> (red (n2) (n6)) -> (red (n3) (n6)) -> (red (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H134 zenon_G zenon_Hbc zenon_Hb6 zenon_H85. % 0.92/1.08 generalize (zenon_H134 (n3)). zenon_intro zenon_H154. % 0.92/1.08 generalize (zenon_H154 (n6)). zenon_intro zenon_H160. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H160); [ zenon_intro zenon_H161 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H161); [ zenon_intro zenon_H89 | zenon_intro zenon_H162 ]. % 0.92/1.08 exact (zenon_H89 zenon_H85). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H162); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc0 ]. % 0.92/1.08 exact (zenon_Hbb zenon_Hb6). % 0.92/1.08 exact (zenon_Hc0 zenon_Hbc). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L94_ *) % 0.92/1.08 assert (zenon_L95_ : (red (n2) (n3)) -> (red (n3) (n6)) -> (red (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H85 zenon_Hb6 zenon_Hbc zenon_G. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 apply (zenon_L94_); trivial. % 0.92/1.08 (* end of lemma zenon_L95_ *) % 0.92/1.08 assert (zenon_L96_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n3) (n6)) -> (green (n3) (n4)) -> (red (n1) (n4)) -> (red (n1) (n6)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hc1 zenon_Hd9 zenon_Hcd zenon_Hb5 zenon_G zenon_H72 zenon_H1d zenon_H2c. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 apply (zenon_L69_); trivial. % 0.92/1.08 (* end of lemma zenon_L96_ *) % 0.92/1.08 assert (zenon_L97_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (red (n2) (n3)) -> (red (n2) (n6)) -> (~(goal)) -> (green (n3) (n4)) -> (red (n1) (n4)) -> (red (n1) (n6)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H98 zenon_H2c zenon_Ha zenon_H1d zenon_H85 zenon_Hbc zenon_G zenon_Hd9 zenon_Hcd zenon_Hb5 zenon_H72. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 apply (zenon_L95_); trivial. % 0.92/1.08 apply (zenon_L96_); trivial. % 0.92/1.08 (* end of lemma zenon_L97_ *) % 0.92/1.08 assert (zenon_L98_ : (red (n2) (n3)) -> (red (n3) (n5)) -> (red (n2) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H85 zenon_H74 zenon_H7f zenon_G. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (zenon_H134 (n3)). zenon_intro zenon_H154. % 0.92/1.08 generalize (zenon_H154 (n5)). zenon_intro zenon_H163. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H163); [ zenon_intro zenon_H164 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H164); [ zenon_intro zenon_H89 | zenon_intro zenon_H165 ]. % 0.92/1.08 exact (zenon_H89 zenon_H85). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H165); [ zenon_intro zenon_H7c | zenon_intro zenon_H84 ]. % 0.92/1.08 exact (zenon_H7c zenon_H74). % 0.92/1.08 exact (zenon_H84 zenon_H7f). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L98_ *) % 0.92/1.08 assert (zenon_L99_ : (green (n2) (n6)) -> (red (n1) (n5)) -> (red (n1) (n6)) -> (~(goal)) -> (less_than (n5) (n6)) -> (green (n2) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hc2 zenon_H73 zenon_Hb5 zenon_G zenon_H2c zenon_H8b zenon_H8a. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (zenon_H8a (n5)). zenon_intro zenon_H166. % 0.92/1.08 generalize (partition (n5)). zenon_intro zenon_Hfa. % 0.92/1.08 generalize (zenon_H166 (n6)). zenon_intro zenon_H167. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H167); [ zenon_intro zenon_H168 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H168); [ zenon_intro zenon_H93 | zenon_intro zenon_H169 ]. % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H169); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hc6 ]. % 0.92/1.08 generalize (zenon_Hfa (n6)). zenon_intro zenon_H102. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H102); [ zenon_intro zenon_H38 | zenon_intro zenon_H103 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H104 ]. % 0.92/1.08 apply (zenon_L50_); trivial. % 0.92/1.08 exact (zenon_Hfd zenon_H104). % 0.92/1.08 exact (zenon_Hc6 zenon_Hc2). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L99_ *) % 0.92/1.08 assert (zenon_L100_ : (green (n2) (n5)) -> (less_than (n5) (n6)) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n5)) -> (green (n2) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8b zenon_H2c zenon_G zenon_Hb5 zenon_H73 zenon_Hc2. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 apply (zenon_L99_); trivial. % 0.92/1.08 (* end of lemma zenon_L100_ *) % 0.92/1.08 assert (zenon_L101_ : ((less_than (n3) (n4))->((red (n3) (n4))\/(green (n3) (n4)))) -> (less_than (n3) (n4)) -> (red (n2) (n3)) -> (red (n2) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n1) (n4)) -> (green (n3) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hdf zenon_Ha zenon_H85 zenon_Hcc zenon_H134 zenon_Hfb zenon_H1d zenon_H72 zenon_G zenon_H73 zenon_Hcd zenon_H8c. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.08 apply (zenon_L93_); trivial. % 0.92/1.08 apply (zenon_L48_); trivial. % 0.92/1.08 (* end of lemma zenon_L101_ *) % 0.92/1.08 assert (zenon_L102_ : (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n3) (n4)) -> (~(goal)) -> (red (n2) (n4)) -> (red (n2) (n3)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (red (n1) (n5)) -> (red (n1) (n4)) -> (green (n3) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H98 zenon_Ha zenon_G zenon_Hcc zenon_H85 zenon_H1d zenon_H72 zenon_H73 zenon_Hcd zenon_H8c. % 0.92/1.08 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 apply (zenon_L101_); trivial. % 0.92/1.08 (* end of lemma zenon_L102_ *) % 0.92/1.08 assert (zenon_L103_ : (forall C : zenon_U, (((green (n1) (n2))/\((green (n2) C)/\(green (n1) C)))->(goal))) -> (green (n1) (n2)) -> (green (n2) (n3)) -> (green (n1) (n3)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H13a zenon_H139 zenon_H8d zenon_H158 zenon_G. % 0.92/1.08 generalize (zenon_H13a (n3)). zenon_intro zenon_H16a. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H16a); [ zenon_intro zenon_H16b | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H16b); [ zenon_intro zenon_H13e | zenon_intro zenon_H16c ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H16c); [ zenon_intro zenon_H92 | zenon_intro zenon_H15d ]. % 0.92/1.08 exact (zenon_H92 zenon_H8d). % 0.92/1.08 exact (zenon_H15d zenon_H158). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L103_ *) % 0.92/1.08 assert (zenon_L104_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n3)) -> (green (n2) (n3)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H158 zenon_H8d zenon_H139. % 0.92/1.08 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.08 apply (zenon_L103_); trivial. % 0.92/1.08 (* end of lemma zenon_L104_ *) % 0.92/1.08 assert (zenon_L105_ : (green (n1) (n2)) -> (green (n2) (n3)) -> (green (n1) (n3)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H139 zenon_H8d zenon_H158 zenon_G. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 apply (zenon_L104_); trivial. % 0.92/1.08 (* end of lemma zenon_L105_ *) % 0.92/1.08 assert (zenon_L106_ : (forall C : zenon_U, (((green (n2) (n4))/\((green (n4) C)/\(green (n2) C)))->(goal))) -> (green (n2) (n4)) -> (green (n4) (n5)) -> (green (n2) (n5)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H16d zenon_Hd8 zenon_H101 zenon_H8b zenon_G. % 0.92/1.08 generalize (zenon_H16d (n5)). zenon_intro zenon_H16e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H16e); [ zenon_intro zenon_H16f | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H16f); [ zenon_intro zenon_Hdd | zenon_intro zenon_H170 ]. % 0.92/1.08 exact (zenon_Hdd zenon_Hd8). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H170); [ zenon_intro zenon_Hfe | zenon_intro zenon_H93 ]. % 0.92/1.08 exact (zenon_Hfe zenon_H101). % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L106_ *) % 0.92/1.08 assert (zenon_L107_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (~(goal)) -> (green (n2) (n5)) -> (green (n4) (n5)) -> (green (n2) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8a zenon_G zenon_H8b zenon_H101 zenon_Hd8. % 0.92/1.08 generalize (zenon_H8a (n4)). zenon_intro zenon_H16d. % 0.92/1.08 apply (zenon_L106_); trivial. % 0.92/1.08 (* end of lemma zenon_L107_ *) % 0.92/1.08 assert (zenon_L108_ : (green (n2) (n4)) -> (green (n2) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (red (n1) (n4)) -> (red (n1) (n5)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n4) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hd8 zenon_H8b zenon_H8a zenon_Hcd zenon_H73 zenon_G zenon_H72 zenon_H1d. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.08 apply (zenon_L45_); trivial. % 0.92/1.08 apply (zenon_L107_); trivial. % 0.92/1.08 (* end of lemma zenon_L108_ *) % 0.92/1.08 assert (zenon_L109_ : (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n5)) -> (red (n1) (n4)) -> (green (n2) (n5)) -> (green (n2) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H1d zenon_H72 zenon_G zenon_H73 zenon_Hcd zenon_H8b zenon_Hd8. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 apply (zenon_L108_); trivial. % 0.92/1.08 (* end of lemma zenon_L109_ *) % 0.92/1.08 assert (zenon_L110_ : (green (n2) (n4)) -> (green (n2) (n5)) -> (red (n1) (n4)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n4) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hd8 zenon_H8b zenon_Hcd zenon_H73 zenon_G zenon_H1d. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 apply (zenon_L109_); trivial. % 0.92/1.08 (* end of lemma zenon_L110_ *) % 0.92/1.08 assert (zenon_L111_ : (forall C : zenon_U, (((green (n2) (n4))/\((green (n4) C)/\(green (n2) C)))->(goal))) -> (green (n2) (n4)) -> (green (n4) (n6)) -> (green (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H16d zenon_Hd8 zenon_H107 zenon_Hc2 zenon_G. % 0.92/1.08 generalize (zenon_H16d (n6)). zenon_intro zenon_H171. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H171); [ zenon_intro zenon_H172 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H172); [ zenon_intro zenon_Hdd | zenon_intro zenon_H173 ]. % 0.92/1.08 exact (zenon_Hdd zenon_Hd8). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H173); [ zenon_intro zenon_Hfc | zenon_intro zenon_Hc6 ]. % 0.92/1.08 exact (zenon_Hfc zenon_H107). % 0.92/1.08 exact (zenon_Hc6 zenon_Hc2). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L111_ *) % 0.92/1.08 assert (zenon_L112_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (~(goal)) -> (green (n2) (n6)) -> (green (n4) (n6)) -> (green (n2) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8a zenon_G zenon_Hc2 zenon_H107 zenon_Hd8. % 0.92/1.08 generalize (zenon_H8a (n4)). zenon_intro zenon_H16d. % 0.92/1.08 apply (zenon_L111_); trivial. % 0.92/1.08 (* end of lemma zenon_L112_ *) % 0.92/1.08 assert (zenon_L113_ : (green (n2) (n4)) -> (green (n4) (n6)) -> (green (n2) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hd8 zenon_H107 zenon_Hc2 zenon_G. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 apply (zenon_L112_); trivial. % 0.92/1.08 (* end of lemma zenon_L113_ *) % 0.92/1.08 assert (zenon_L114_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n4) B)->((red (n4) B)\/(green (n4) B)))) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n4)) -> (green (n2) (n4)) -> (green (n2) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hfb zenon_H2c zenon_H1d zenon_H72 zenon_G zenon_Hb5 zenon_Hcd zenon_Hd8 zenon_Hc2. % 0.92/1.08 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.08 apply (zenon_L38_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.08 apply (zenon_L66_); trivial. % 0.92/1.08 apply (zenon_L113_); trivial. % 0.92/1.08 (* end of lemma zenon_L114_ *) % 0.92/1.08 assert (zenon_L115_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n2) (n6)) -> (green (n2) (n4)) -> (red (n1) (n4)) -> (red (n1) (n6)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hc2 zenon_Hd8 zenon_Hcd zenon_Hb5 zenon_G zenon_H72 zenon_H1d zenon_H2c. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 apply (zenon_L114_); trivial. % 0.92/1.08 (* end of lemma zenon_L115_ *) % 0.92/1.08 assert (zenon_L116_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n4)) -> (green (n2) (n4)) -> (green (n2) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H2c zenon_H1d zenon_G zenon_Hb5 zenon_Hcd zenon_Hd8 zenon_Hc2. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 apply (zenon_L115_); trivial. % 0.92/1.08 (* end of lemma zenon_L116_ *) % 0.92/1.08 assert (zenon_L117_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (red (n1) (n2)) -> (red (n1) (n4)) -> (~(goal)) -> (~(green (n2) (n4))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H72 zenon_Ha zenon_H7 zenon_H7e zenon_Hcd zenon_G zenon_Hdd. % 0.92/1.08 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.08 apply (zenon_L2_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.08 apply (zenon_L33_); trivial. % 0.92/1.08 exact (zenon_Hdd zenon_Hd8). % 0.92/1.08 (* end of lemma zenon_L117_ *) % 0.92/1.08 assert (zenon_L118_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (red (n1) (n5)) -> (~(goal)) -> (red (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (red (n1) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H1d zenon_H8a zenon_H73 zenon_G zenon_H7e zenon_H7 zenon_Ha zenon_H72 zenon_Hcd. % 0.92/1.08 generalize (zenon_H72 (n4)). zenon_intro zenon_H123. % 0.92/1.08 generalize (zenon_H123 (n5)). zenon_intro zenon_H124. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H124); [ zenon_intro zenon_H125 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H125); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H126 ]. % 0.92/1.08 exact (zenon_Hd1 zenon_Hcd). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H126); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H7b ]. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.08 exact (zenon_H29 zenon_H1d). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.08 exact (zenon_Hf7 zenon_Hf2). % 0.92/1.08 generalize (zenon_H8a (n4)). zenon_intro zenon_H16d. % 0.92/1.08 generalize (zenon_H16d (n5)). zenon_intro zenon_H16e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H16e); [ zenon_intro zenon_H16f | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H16f); [ zenon_intro zenon_Hdd | zenon_intro zenon_H170 ]. % 0.92/1.08 apply (zenon_L117_); trivial. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H170); [ zenon_intro zenon_Hfe | zenon_intro zenon_H93 ]. % 0.92/1.08 exact (zenon_Hfe zenon_H101). % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.08 generalize (zenon_H7d (n5)). zenon_intro zenon_H80. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 0.92/1.08 exact (zenon_H83 zenon_H7e). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H84 | zenon_intro zenon_H7b ]. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 exact (zenon_H84 zenon_H7f). % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 exact (zenon_H7b zenon_H73). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H7b zenon_H73). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L118_ *) % 0.92/1.08 assert (zenon_L119_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (less_than (n4) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (red (n1) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n3)) -> (green (n2) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H11a zenon_H3a zenon_H1d zenon_H73 zenon_G zenon_H7 zenon_Ha zenon_Hcd zenon_H10b zenon_H158 zenon_H8d. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.08 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.08 exact (zenon_H3e zenon_H3a). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.08 apply (zenon_L118_); trivial. % 0.92/1.08 apply (zenon_L104_); trivial. % 0.92/1.08 (* end of lemma zenon_L119_ *) % 0.92/1.08 assert (zenon_L120_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (~(goal)) -> (red (n1) (n4)) -> (red (n1) (n6)) -> (red (n1) (n5)) -> (green (n1) (n2)) -> (green (n1) (n3)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Ha zenon_H7 zenon_H2c zenon_H1d zenon_G zenon_Hcd zenon_Hb5 zenon_H73 zenon_H139 zenon_H158 zenon_H11a zenon_H3a. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.08 apply (zenon_L2_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.08 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.08 exact (zenon_H1a zenon_Ha). % 0.92/1.08 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 apply (zenon_L93_); trivial. % 0.92/1.08 apply (zenon_L97_); trivial. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 apply (zenon_L98_); trivial. % 0.92/1.08 apply (zenon_L100_); trivial. % 0.92/1.08 apply (zenon_L102_); trivial. % 0.92/1.08 apply (zenon_L105_); trivial. % 0.92/1.08 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 apply (zenon_L98_); trivial. % 0.92/1.08 apply (zenon_L110_); trivial. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 apply (zenon_L95_); trivial. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (partition (n5)). zenon_intro zenon_Hfa. % 0.92/1.08 generalize (zenon_Hfa (n6)). zenon_intro zenon_H102. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H102); [ zenon_intro zenon_H38 | zenon_intro zenon_H103 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H104 ]. % 0.92/1.08 apply (zenon_L73_); trivial. % 0.92/1.08 apply (zenon_L51_); trivial. % 0.92/1.08 apply (zenon_L109_); trivial. % 0.92/1.08 apply (zenon_L116_); trivial. % 0.92/1.08 apply (zenon_L119_); trivial. % 0.92/1.08 (* end of lemma zenon_L120_ *) % 0.92/1.08 assert (zenon_L121_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n1) (n6)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (red (n1) (n2)) -> (red (n1) (n4)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_Hb5 zenon_H1d zenon_H2c zenon_H97 zenon_H7e zenon_Hcd zenon_G zenon_H72 zenon_H7 zenon_Ha. % 0.92/1.08 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.08 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.08 apply (zenon_L2_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.08 apply (zenon_L34_); trivial. % 0.92/1.08 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 apply (zenon_L25_); trivial. % 0.92/1.08 apply (zenon_L114_); trivial. % 0.92/1.08 (* end of lemma zenon_L121_ *) % 0.92/1.08 assert (zenon_L122_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (less_than (n2) (n3)) -> (red (n2) (n3)) -> (~(goal)) -> (~(green (n2) (n5))) -> (~(green (n3) (n5))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H98 zenon_H1d zenon_Ha zenon_H97 zenon_H7 zenon_H85 zenon_G zenon_H93 zenon_H94. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.08 apply (zenon_L4_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.08 apply (zenon_L98_); trivial. % 0.92/1.08 exact (zenon_H93 zenon_H8b). % 0.92/1.08 exact (zenon_H94 zenon_H8c). % 0.92/1.08 (* end of lemma zenon_L122_ *) % 0.92/1.08 assert (zenon_L123_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (~(goal)) -> (~(green (n2) (n5))) -> (~(green (n3) (n5))) -> (~(green (n2) (n3))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H7 zenon_H1d zenon_Ha zenon_G zenon_H93 zenon_H94 zenon_H92. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.08 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 apply (zenon_L122_); trivial. % 0.92/1.08 exact (zenon_H92 zenon_H8d). % 0.92/1.08 (* end of lemma zenon_L123_ *) % 0.92/1.08 assert (zenon_L124_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n5)) -> (~(goal)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (green (n1) (n3)) -> (forall C : zenon_U, (((green (n1) (n2))/\((green (n2) C)/\(green (n1) C)))->(goal))) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H10b zenon_H10a zenon_G zenon_Ha zenon_H1d zenon_H7 zenon_H158 zenon_H13a zenon_H139. % 0.92/1.08 generalize (zenon_H10b (n3)). zenon_intro zenon_H159. % 0.92/1.08 generalize (zenon_H13a (n3)). zenon_intro zenon_H16a. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H16a); [ zenon_intro zenon_H16b | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H16b); [ zenon_intro zenon_H13e | zenon_intro zenon_H16c ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H16c); [ zenon_intro zenon_H92 | zenon_intro zenon_H15d ]. % 0.92/1.08 generalize (zenon_H13a (n5)). zenon_intro zenon_H13b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H13b); [ zenon_intro zenon_H13c | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H13c); [ zenon_intro zenon_H13e | zenon_intro zenon_H13d ]. % 0.92/1.08 exact (zenon_H13e zenon_H139). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H13d); [ zenon_intro zenon_H93 | zenon_intro zenon_H111 ]. % 0.92/1.08 generalize (zenon_H159 (n5)). zenon_intro zenon_H174. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H174); [ zenon_intro zenon_H175 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H175); [ zenon_intro zenon_H15d | zenon_intro zenon_H176 ]. % 0.92/1.08 exact (zenon_H15d zenon_H158). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H176); [ zenon_intro zenon_H94 | zenon_intro zenon_H111 ]. % 0.92/1.08 apply (zenon_L123_); trivial. % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 exact (zenon_H15d zenon_H158). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L124_ *) % 0.92/1.08 assert (zenon_L125_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n1) (n5)) -> (~(goal)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (green (n1) (n3)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H10a zenon_G zenon_Ha zenon_H1d zenon_H7 zenon_H158 zenon_H139. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.08 apply (zenon_L124_); trivial. % 0.92/1.08 (* end of lemma zenon_L125_ *) % 0.92/1.08 assert (zenon_L126_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n3) B)/\((red B C)/\(red (n3) C)))->(goal)))) -> (~(goal)) -> (red (n3) (n6)) -> (red (n5) (n6)) -> (red (n3) (n5)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H177 zenon_G zenon_Hb6 zenon_Hf1 zenon_H74. % 0.92/1.08 generalize (zenon_H177 (n5)). zenon_intro zenon_H178. % 0.92/1.08 generalize (zenon_H178 (n6)). zenon_intro zenon_H179. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H179); [ zenon_intro zenon_H17a | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H17a); [ zenon_intro zenon_H7c | zenon_intro zenon_H17b ]. % 0.92/1.08 exact (zenon_H7c zenon_H74). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H17b); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hbb ]. % 0.92/1.08 exact (zenon_Hf9 zenon_Hf1). % 0.92/1.08 exact (zenon_Hbb zenon_Hb6). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L126_ *) % 0.92/1.08 assert (zenon_L127_ : (red (n3) (n5)) -> (red (n5) (n6)) -> (red (n3) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H74 zenon_Hf1 zenon_Hb6 zenon_G. % 0.92/1.08 generalize (red_clique (n3)). zenon_intro zenon_H177. % 0.92/1.08 apply (zenon_L126_); trivial. % 0.92/1.08 (* end of lemma zenon_L127_ *) % 0.92/1.08 assert (zenon_L128_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (red (n5) (n6)) -> (red (n3) (n6)) -> (~(goal)) -> (~(green (n3) (n5))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H98 zenon_H1d zenon_Ha zenon_Hf1 zenon_Hb6 zenon_G zenon_H94. % 0.92/1.08 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.08 apply (zenon_L11_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.08 apply (zenon_L127_); trivial. % 0.92/1.08 exact (zenon_H94 zenon_H8c). % 0.92/1.08 (* end of lemma zenon_L128_ *) % 0.92/1.08 assert (zenon_L129_ : (forall C : zenon_U, (((green (n1) (n3))/\((green (n3) C)/\(green (n1) C)))->(goal))) -> (green (n1) (n3)) -> (green (n3) (n6)) -> (green (n1) (n6)) -> (~(goal)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H159 zenon_H158 zenon_Hc1 zenon_H108 zenon_G. % 0.92/1.08 generalize (zenon_H159 (n6)). zenon_intro zenon_H17c. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H17c); [ zenon_intro zenon_H17d | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H17d); [ zenon_intro zenon_H15d | zenon_intro zenon_H17e ]. % 0.92/1.08 exact (zenon_H15d zenon_H158). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H17e); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H112 ]. % 0.92/1.08 exact (zenon_Hc7 zenon_Hc1). % 0.92/1.08 exact (zenon_H112 zenon_H108). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 (* end of lemma zenon_L129_ *) % 0.92/1.08 assert (zenon_L130_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n6)) -> (green (n3) (n6)) -> (green (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H10b zenon_G zenon_H108 zenon_Hc1 zenon_H158. % 0.92/1.08 generalize (zenon_H10b (n3)). zenon_intro zenon_H159. % 0.92/1.08 apply (zenon_L129_); trivial. % 0.92/1.08 (* end of lemma zenon_L130_ *) % 0.92/1.08 assert (zenon_L131_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (~(goal)) -> (green (n1) (n6)) -> (green (n1) (n5)) -> (green (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H1d zenon_G zenon_H108 zenon_H10a zenon_H158. % 0.92/1.08 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 generalize (zenon_H10b (n3)). zenon_intro zenon_H159. % 0.92/1.08 generalize (zenon_H159 (n5)). zenon_intro zenon_H174. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H174); [ zenon_intro zenon_H175 | zenon_intro zenon_H71 ]. % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H175); [ zenon_intro zenon_H15d | zenon_intro zenon_H176 ]. % 0.92/1.08 exact (zenon_H15d zenon_H158). % 0.92/1.08 apply (zenon_notand_s _ _ zenon_H176); [ zenon_intro zenon_H94 | zenon_intro zenon_H111 ]. % 0.92/1.08 generalize (partition (n5)). zenon_intro zenon_Hfa. % 0.92/1.08 generalize (zenon_Hfa (n6)). zenon_intro zenon_H102. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H102); [ zenon_intro zenon_H38 | zenon_intro zenon_H103 ]. % 0.92/1.08 exact (zenon_H38 zenon_H2c). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hf1 | zenon_intro zenon_H104 ]. % 0.92/1.08 apply (zenon_L128_); trivial. % 0.92/1.08 apply (zenon_L75_); trivial. % 0.92/1.08 exact (zenon_H111 zenon_H10a). % 0.92/1.08 exact (zenon_G zenon_H71). % 0.92/1.08 apply (zenon_L130_); trivial. % 0.92/1.08 (* end of lemma zenon_L131_ *) % 0.92/1.08 assert (zenon_L132_ : ((less_than (n1) (n6))->((red (n1) (n6))\/(green (n1) (n6)))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (red (n1) (n4)) -> (less_than (n2) (n3)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (~(goal)) -> (green (n1) (n5)) -> (green (n1) (n3)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H11d zenon_H11a zenon_H3a zenon_H97 zenon_Hcd zenon_H7 zenon_H8 zenon_H2c zenon_Ha zenon_H1d zenon_G zenon_H10a zenon_H158. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.08 apply (zenon_L22_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.08 exact (zenon_H3e zenon_H3a). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.08 apply (zenon_L121_); trivial. % 0.92/1.08 apply (zenon_L125_); trivial. % 0.92/1.08 apply (zenon_L131_); trivial. % 0.92/1.08 (* end of lemma zenon_L132_ *) % 0.92/1.08 assert (zenon_L133_ : ((less_than (n1) (n3))->((red (n1) (n3))\/(green (n1) (n3)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> (~(goal)) -> (red (n1) (n4)) -> (red (n1) (n6)) -> (green (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> ((less_than (n1) (n6))->((red (n1) (n6))\/(green (n1) (n6)))) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H15e zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H2c zenon_G zenon_Hcd zenon_Hb5 zenon_H139 zenon_H11a zenon_H11d zenon_H97. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.08 apply (zenon_L8_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.08 apply (zenon_L79_); trivial. % 0.92/1.08 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.08 apply (zenon_L10_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.08 apply (zenon_L120_); trivial. % 0.92/1.08 apply (zenon_L132_); trivial. % 0.92/1.08 (* end of lemma zenon_L133_ *) % 0.92/1.08 assert (zenon_L134_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n1) (n3)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (red (n1) (n5)) -> (red (n1) (n6)) -> (~(goal)) -> (less_than (n5) (n6)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H75 zenon_Ha zenon_H1d zenon_H73 zenon_Hb5 zenon_G zenon_H2c. % 0.92/1.08 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.08 apply (zenon_L53_); trivial. % 0.92/1.08 (* end of lemma zenon_L134_ *) % 0.92/1.08 assert (zenon_L135_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n2) (n3)) -> (red (n2) (n4)) -> (green (n1) (n4)) -> (less_than (n5) (n6)) -> (~(goal)) -> (red (n1) (n6)) -> (red (n1) (n5)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.08 do 0 intro. intros zenon_H8 zenon_H85 zenon_Hcc zenon_H109 zenon_H2c zenon_G zenon_Hb5 zenon_H73 zenon_H1d zenon_Ha zenon_H3a zenon_H7 zenon_H11a. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.08 apply (zenon_L8_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.08 apply (zenon_L134_); trivial. % 0.92/1.08 apply (zenon_L88_); trivial. % 0.92/1.08 (* end of lemma zenon_L135_ *) % 0.92/1.08 assert (zenon_L136_ : ((less_than (n2) (n3))->((red (n2) (n3))\/(green (n2) (n3)))) -> (less_than (n2) (n3)) -> (green (n1) (n6)) -> (red (n2) (n6)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n3)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_H95 zenon_H7 zenon_H108 zenon_Hbc zenon_H1d zenon_Ha zenon_H2c zenon_H8 zenon_H10b zenon_G zenon_H158 zenon_H139. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.08 exact (zenon_Hd zenon_H7). % 0.92/1.08 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.08 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.08 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.08 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.08 apply (zenon_L23_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.08 apply (zenon_L94_); trivial. % 0.92/1.08 apply (zenon_L130_); trivial. % 0.92/1.08 apply (zenon_L104_); trivial. % 0.92/1.08 (* end of lemma zenon_L136_ *) % 0.92/1.08 assert (zenon_L137_ : ((less_than (n2) (n6))->((red (n2) (n6))\/(green (n2) (n6)))) -> (green (n1) (n3)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> ((less_than (n2) (n3))->((red (n2) (n3))\/(green (n2) (n3)))) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n6)) -> (green (n1) (n2)) -> False). % 0.92/1.08 do 0 intro. intros zenon_Hca zenon_H158 zenon_H8 zenon_H2c zenon_Ha zenon_H1d zenon_H7 zenon_H95 zenon_H10b zenon_G zenon_H108 zenon_H139. % 0.92/1.08 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.08 apply (zenon_L6_); trivial. % 0.92/1.08 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.08 apply (zenon_L136_); trivial. % 0.92/1.08 apply (zenon_L76_); trivial. % 0.92/1.08 (* end of lemma zenon_L137_ *) % 0.92/1.08 assert (zenon_L138_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> ((less_than (n2) (n3))->((red (n2) (n3))\/(green (n2) (n3)))) -> (green (n1) (n3)) -> (green (n1) (n6)) -> ((less_than (n2) (n6))->((red (n2) (n6))\/(green (n2) (n6)))) -> (red (n2) (n3)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (~(goal)) -> (red (n2) (n4)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_H95 zenon_H158 zenon_H108 zenon_Hca zenon_H85 zenon_H11a zenon_H1d zenon_H97 zenon_G zenon_Hcc zenon_H7 zenon_Ha zenon_H3a. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L92_); trivial. % 0.92/1.09 apply (zenon_L137_); trivial. % 0.92/1.09 (* end of lemma zenon_L138_ *) % 0.92/1.09 assert (zenon_L139_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n1) (n6)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (red (n1) (n3)) -> (red (n1) (n4)) -> (~(goal)) -> (less_than (n3) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_Hb5 zenon_H1d zenon_H2c zenon_H75 zenon_Hcd zenon_G zenon_Ha. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 apply (zenon_L72_); trivial. % 0.92/1.09 (* end of lemma zenon_L139_ *) % 0.92/1.09 assert (zenon_L140_ : ((less_than (n1) (n3))->((red (n1) (n3))\/(green (n1) (n3)))) -> (red (n1) (n6)) -> ((less_than (n1) (n6))->((red (n1) (n6))\/(green (n1) (n6)))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (red (n1) (n4)) -> (less_than (n2) (n3)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (~(goal)) -> (green (n1) (n5)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H15e zenon_Hb5 zenon_H11d zenon_H11a zenon_H3a zenon_H97 zenon_Hcd zenon_H7 zenon_H8 zenon_H2c zenon_Ha zenon_H1d zenon_G zenon_H10a. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L139_); trivial. % 0.92/1.09 apply (zenon_L132_); trivial. % 0.92/1.09 (* end of lemma zenon_L140_ *) % 0.92/1.09 assert (zenon_L141_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (red (n4) (n5)) -> (~(goal)) -> (~(green (n3) (n4))) -> (~(green (n3) (n5))) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n3) B)/\((red B C)/\(red (n3) C)))->(goal)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_Ha zenon_Hf2 zenon_G zenon_Hde zenon_H94 zenon_H177. % 0.92/1.09 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.09 generalize (zenon_H177 (n4)). zenon_intro zenon_H17f. % 0.92/1.09 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.09 apply (zenon_L11_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.09 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.09 exact (zenon_H1a zenon_Ha). % 0.92/1.09 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.09 generalize (zenon_H17f (n5)). zenon_intro zenon_H180. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H180); [ zenon_intro zenon_H181 | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H181); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H182 ]. % 0.92/1.09 exact (zenon_Hd7 zenon_Hd3). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H182); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H7c ]. % 0.92/1.09 exact (zenon_Hf7 zenon_Hf2). % 0.92/1.09 exact (zenon_H7c zenon_H74). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 exact (zenon_Hde zenon_Hd9). % 0.92/1.09 exact (zenon_H94 zenon_H8c). % 0.92/1.09 (* end of lemma zenon_L141_ *) % 0.92/1.09 assert (zenon_L142_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(green (n3) (n5))) -> (~(green (n3) (n4))) -> (~(goal)) -> (red (n4) (n5)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H94 zenon_Hde zenon_G zenon_Hf2 zenon_Ha zenon_H1d. % 0.92/1.09 generalize (red_clique (n3)). zenon_intro zenon_H177. % 0.92/1.09 apply (zenon_L141_); trivial. % 0.92/1.09 (* end of lemma zenon_L142_ *) % 0.92/1.09 assert (zenon_L143_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n4)) -> (green (n1) (n5)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (red (n4) (n5)) -> (~(goal)) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H10b zenon_H109 zenon_H10a zenon_H1d zenon_Ha zenon_Hf2 zenon_G zenon_H158. % 0.92/1.09 generalize (zenon_H10b (n3)). zenon_intro zenon_H159. % 0.92/1.09 generalize (zenon_H159 (n4)). zenon_intro zenon_H15a. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15a); [ zenon_intro zenon_H15b | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H15b); [ zenon_intro zenon_H15d | zenon_intro zenon_H15c ]. % 0.92/1.09 exact (zenon_H15d zenon_H158). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H15c); [ zenon_intro zenon_Hde | zenon_intro zenon_H116 ]. % 0.92/1.09 generalize (zenon_H159 (n5)). zenon_intro zenon_H174. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H174); [ zenon_intro zenon_H175 | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H175); [ zenon_intro zenon_H15d | zenon_intro zenon_H176 ]. % 0.92/1.09 exact (zenon_H15d zenon_H158). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H176); [ zenon_intro zenon_H94 | zenon_intro zenon_H111 ]. % 0.92/1.09 apply (zenon_L142_); trivial. % 0.92/1.09 exact (zenon_H111 zenon_H10a). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 exact (zenon_H116 zenon_H109). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 (* end of lemma zenon_L143_ *) % 0.92/1.09 assert (zenon_L144_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n1) (n3)) -> (~(goal)) -> (less_than (n3) (n4)) -> (green (n1) (n5)) -> (green (n1) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (less_than (n4) (n5)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H158 zenon_G zenon_Ha zenon_H10a zenon_H109 zenon_H10b zenon_H1d. % 0.92/1.09 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.09 generalize (zenon_Hfb (n5)). zenon_intro zenon_Hff. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hff); [ zenon_intro zenon_H29 | zenon_intro zenon_H100 ]. % 0.92/1.09 exact (zenon_H29 zenon_H1d). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H101 ]. % 0.92/1.09 apply (zenon_L143_); trivial. % 0.92/1.09 apply (zenon_L83_); trivial. % 0.92/1.09 (* end of lemma zenon_L144_ *) % 0.92/1.09 assert (zenon_L145_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (green (n1) (n3)) -> (~(goal)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (green (n1) (n5)) -> ((less_than (n1) (n3))->((red (n1) (n3))\/(green (n1) (n3)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H158 zenon_G zenon_H11a zenon_H97 zenon_H10a zenon_H15e. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L140_); trivial. % 0.92/1.09 apply (zenon_L144_); trivial. % 0.92/1.09 apply (zenon_L131_); trivial. % 0.92/1.09 (* end of lemma zenon_L145_ *) % 0.92/1.09 assert (zenon_L146_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> (red (n2) (n4)) -> (~(goal)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (red (n2) (n3)) -> ((less_than (n1) (n3))->((red (n1) (n3))\/(green (n1) (n3)))) -> ((less_than (n2) (n3))->((red (n2) (n3))\/(green (n2) (n3)))) -> (green (n1) (n3)) -> ((less_than (n2) (n6))->((red (n2) (n6))\/(green (n2) (n6)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H2c zenon_Hcc zenon_G zenon_H97 zenon_H11a zenon_H85 zenon_H15e zenon_H95 zenon_H158 zenon_Hca. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L92_); trivial. % 0.92/1.09 apply (zenon_L133_); trivial. % 0.92/1.09 apply (zenon_L135_); trivial. % 0.92/1.09 apply (zenon_L138_); trivial. % 0.92/1.09 apply (zenon_L145_); trivial. % 0.92/1.09 (* end of lemma zenon_L146_ *) % 0.92/1.09 assert (zenon_L147_ : (green (n1) (n3)) -> (green (n2) (n3)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H158 zenon_H8d zenon_H7f zenon_H73 zenon_G zenon_H3a zenon_H11a. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L15_); trivial. % 0.92/1.09 apply (zenon_L105_); trivial. % 0.92/1.09 (* end of lemma zenon_L147_ *) % 0.92/1.09 assert (zenon_L148_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n2) (n3)) -> (green (n2) (n5)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (red (n1) (n3)) -> (red (n1) (n5)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H8d zenon_H8b zenon_H8a zenon_H75 zenon_H73 zenon_G zenon_H72 zenon_Ha zenon_H1d. % 0.92/1.09 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.09 generalize (zenon_H98 (n5)). zenon_intro zenon_H99. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H63 | zenon_intro zenon_H9a ]. % 0.92/1.09 apply (zenon_L11_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H74 | zenon_intro zenon_H8c ]. % 0.92/1.09 apply (zenon_L13_); trivial. % 0.92/1.09 apply (zenon_L17_); trivial. % 0.92/1.09 (* end of lemma zenon_L148_ *) % 0.92/1.09 assert (zenon_L149_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n2) (n3)) -> (green (n2) (n5)) -> (red (n1) (n3)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H8d zenon_H8b zenon_H75 zenon_H73 zenon_G zenon_Ha zenon_H1d. % 0.92/1.09 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 apply (zenon_L148_); trivial. % 0.92/1.09 (* end of lemma zenon_L149_ *) % 0.92/1.09 assert (zenon_L150_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n2) (n3)) -> (green (n1) (n3)) -> (red (n1) (n4)) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (~(goal)) -> (red (n1) (n5)) -> (less_than (n4) (n5)) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H8d zenon_H158 zenon_Hcd zenon_Ha zenon_H7 zenon_G zenon_H73 zenon_H1d zenon_H3a zenon_H11a. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 apply (zenon_L119_); trivial. % 0.92/1.09 (* end of lemma zenon_L150_ *) % 0.92/1.09 assert (zenon_L151_ : ((less_than (n1) (n3))->((red (n1) (n3))\/(green (n1) (n3)))) -> (green (n2) (n5)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n2) (n3)) -> (red (n1) (n4)) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (~(goal)) -> (red (n1) (n5)) -> (less_than (n4) (n5)) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H15e zenon_H8b zenon_H8 zenon_H8d zenon_Hcd zenon_Ha zenon_H7 zenon_G zenon_H73 zenon_H1d zenon_H3a zenon_H11a. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L149_); trivial. % 0.92/1.09 apply (zenon_L150_); trivial. % 0.92/1.09 (* end of lemma zenon_L151_ *) % 0.92/1.09 assert (zenon_L152_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (green (n2) (n3)) -> (green (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (red (n1) (n4)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H7 zenon_H3a zenon_H8d zenon_H8b zenon_H73 zenon_G zenon_Ha zenon_H1d zenon_Hcd zenon_H11a. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_L151_); trivial. % 0.92/1.09 (* end of lemma zenon_L152_ *) % 0.92/1.09 assert (zenon_L153_ : (red (n1) (n2)) -> (red (n2) (n6)) -> (red (n1) (n6)) -> (~(goal)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H7e zenon_Hbc zenon_Hb5 zenon_G. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 apply (zenon_L25_); trivial. % 0.92/1.09 (* end of lemma zenon_L153_ *) % 0.92/1.09 assert (zenon_L154_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(green (n4) (n6))) -> (red (n2) (n4)) -> (red (n2) (n6)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n2) B)/\((red B C)/\(red (n2) C)))->(goal)))) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_Hfc zenon_Hcc zenon_Hbc zenon_G zenon_H134 zenon_H1d zenon_H2c. % 0.92/1.09 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.09 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.09 apply (zenon_L38_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.09 apply (zenon_L59_); trivial. % 0.92/1.09 exact (zenon_Hfc zenon_H107). % 0.92/1.09 (* end of lemma zenon_L154_ *) % 0.92/1.09 assert (zenon_L155_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (red (n1) (n2)) -> (red (n2) (n6)) -> (~(goal)) -> (red (n2) (n4)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H11a zenon_H2c zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H7e zenon_Hbc zenon_G zenon_Hcc zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L153_); trivial. % 0.92/1.09 generalize (red_clique (n2)). zenon_intro zenon_H134. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (zenon_H10b (n4)). zenon_intro zenon_H10d. % 0.92/1.09 generalize (zenon_H10d (n6)). zenon_intro zenon_H113. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H113); [ zenon_intro zenon_H114 | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H114); [ zenon_intro zenon_H116 | zenon_intro zenon_H115 ]. % 0.92/1.09 exact (zenon_H116 zenon_H109). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_Hfc | zenon_intro zenon_H112 ]. % 0.92/1.09 apply (zenon_L154_); trivial. % 0.92/1.09 exact (zenon_H112 zenon_H108). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 (* end of lemma zenon_L155_ *) % 0.92/1.09 assert (zenon_L156_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (red (n1) (n5)) -> (red (n1) (n6)) -> (~(goal)) -> (less_than (n5) (n6)) -> (green (n1) (n2)) -> (green (n2) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H11a zenon_H7 zenon_H3a zenon_Ha zenon_H1d zenon_H73 zenon_Hb5 zenon_G zenon_H2c zenon_H139 zenon_H8d. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L134_); trivial. % 0.92/1.09 apply (zenon_L105_); trivial. % 0.92/1.09 (* end of lemma zenon_L156_ *) % 0.92/1.09 assert (zenon_L157_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (red (n1) (n6)) -> (~(goal)) -> (less_than (n5) (n6)) -> (green (n1) (n2)) -> (green (n2) (n3)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H11a zenon_Hb5 zenon_G zenon_H2c zenon_H139 zenon_H8d zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 apply (zenon_L156_); trivial. % 0.92/1.09 apply (zenon_L57_); trivial. % 0.92/1.09 (* end of lemma zenon_L157_ *) % 0.92/1.09 assert (zenon_L158_ : ((less_than (n1) (n6))->((red (n1) (n6))\/(green (n1) (n6)))) -> (green (n2) (n3)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(goal)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (green (n1) (n4)) -> (green (n1) (n2)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H11d zenon_H8d zenon_H11a zenon_H3a zenon_H8 zenon_G zenon_H1d zenon_H2c zenon_H7 zenon_Ha zenon_H109 zenon_H139. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L157_); trivial. % 0.92/1.09 apply (zenon_L63_); trivial. % 0.92/1.09 (* end of lemma zenon_L158_ *) % 0.92/1.09 assert (zenon_L159_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (~(goal)) -> (green (n1) (n2)) -> (green (n2) (n3)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H11a zenon_G zenon_H139 zenon_H8d zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_L158_); trivial. % 0.92/1.09 (* end of lemma zenon_L159_ *) % 0.92/1.09 assert (zenon_L160_ : (red (n3) (n4)) -> (red (n4) (n6)) -> (red (n3) (n6)) -> (~(goal)) -> False). % 0.92/1.09 do 0 intro. intros zenon_Hd3 zenon_Hf0 zenon_Hb6 zenon_G. % 0.92/1.09 generalize (red_clique (n3)). zenon_intro zenon_H177. % 0.92/1.09 generalize (zenon_H177 (n4)). zenon_intro zenon_H17f. % 0.92/1.09 generalize (zenon_H17f (n6)). zenon_intro zenon_H183. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H183); [ zenon_intro zenon_H184 | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H184); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H185 ]. % 0.92/1.09 exact (zenon_Hd7 zenon_Hd3). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H185); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hbb ]. % 0.92/1.09 exact (zenon_Hf8 zenon_Hf0). % 0.92/1.09 exact (zenon_Hbb zenon_Hb6). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 (* end of lemma zenon_L160_ *) % 0.92/1.09 assert (zenon_L161_ : (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (less_than (n3) (n4)) -> (red (n4) (n6)) -> (red (n3) (n6)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n4)) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H98 zenon_Ha zenon_Hf0 zenon_Hb6 zenon_G zenon_H10b zenon_H109 zenon_H158. % 0.92/1.09 generalize (zenon_H98 (n4)). zenon_intro zenon_Hdf. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hdf); [ zenon_intro zenon_H1a | zenon_intro zenon_He0 ]. % 0.92/1.09 exact (zenon_H1a zenon_Ha). % 0.92/1.09 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd9 ]. % 0.92/1.09 apply (zenon_L160_); trivial. % 0.92/1.09 apply (zenon_L86_); trivial. % 0.92/1.09 (* end of lemma zenon_L161_ *) % 0.92/1.09 assert (zenon_L162_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (green (n1) (n6)) -> (green (n1) (n3)) -> (green (n1) (n4)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (red (n4) (n6)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H108 zenon_H158 zenon_H109 zenon_H10b zenon_G zenon_Hf0 zenon_H1d zenon_Ha zenon_H2c. % 0.92/1.09 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.09 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.09 apply (zenon_L23_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.09 apply (zenon_L161_); trivial. % 0.92/1.09 apply (zenon_L130_); trivial. % 0.92/1.09 (* end of lemma zenon_L162_ *) % 0.92/1.09 assert (zenon_L163_ : (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (~(goal)) -> (green (n1) (n6)) -> (green (n4) (n6)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H10b zenon_G zenon_H108 zenon_H107 zenon_H109. % 0.92/1.09 generalize (zenon_H10b (n4)). zenon_intro zenon_H10d. % 0.92/1.09 generalize (zenon_H10d (n6)). zenon_intro zenon_H113. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H113); [ zenon_intro zenon_H114 | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H114); [ zenon_intro zenon_H116 | zenon_intro zenon_H115 ]. % 0.92/1.09 exact (zenon_H116 zenon_H109). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H115); [ zenon_intro zenon_Hfc | zenon_intro zenon_H112 ]. % 0.92/1.09 exact (zenon_Hfc zenon_H107). % 0.92/1.09 exact (zenon_H112 zenon_H108). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 (* end of lemma zenon_L163_ *) % 0.92/1.09 assert (zenon_L164_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n4)) -> (green (n1) (n3)) -> (green (n1) (n6)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_Ha zenon_G zenon_H10b zenon_H109 zenon_H158 zenon_H108 zenon_H1d zenon_H2c. % 0.92/1.09 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.09 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.09 apply (zenon_L38_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.09 apply (zenon_L162_); trivial. % 0.92/1.09 apply (zenon_L163_); trivial. % 0.92/1.09 (* end of lemma zenon_L164_ *) % 0.92/1.09 assert (zenon_L165_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (green (n1) (n6)) -> (green (n1) (n3)) -> (green (n2) (n3)) -> (green (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> ((less_than (n1) (n3))->((red (n1) (n3))\/(green (n1) (n3)))) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_H108 zenon_H158 zenon_H8d zenon_H8b zenon_H73 zenon_G zenon_H1d zenon_H11a zenon_H15e zenon_H7 zenon_H3a zenon_Ha. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L151_); trivial. % 0.92/1.09 apply (zenon_L164_); trivial. % 0.92/1.09 (* end of lemma zenon_L165_ *) % 0.92/1.09 assert (zenon_L166_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (red (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (red (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H73 zenon_G zenon_H7e zenon_H7 zenon_Ha zenon_Hcd. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.09 apply (zenon_L118_); trivial. % 0.92/1.09 (* end of lemma zenon_L166_ *) % 0.92/1.09 assert (zenon_L167_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (~(goal)) -> (red (n1) (n2)) -> (red (n1) (n4)) -> (less_than (n5) (n6)) -> (green (n1) (n6)) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H11a zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_G zenon_H7e zenon_Hcd zenon_H2c zenon_H108 zenon_H158. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 apply (zenon_L166_); trivial. % 0.92/1.09 apply (zenon_L131_); trivial. % 0.92/1.09 (* end of lemma zenon_L167_ *) % 0.92/1.09 assert (zenon_L168_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (green (n1) (n6)) -> (green (n1) (n3)) -> (green (n1) (n4)) -> (~(goal)) -> (less_than (n3) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_H1d zenon_H108 zenon_H158 zenon_H109 zenon_G zenon_Ha. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 apply (zenon_L164_); trivial. % 0.92/1.09 (* end of lemma zenon_L168_ *) % 0.92/1.09 assert (zenon_L169_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n4) (n5)) -> (~(goal)) -> (red (n1) (n2)) -> (less_than (n5) (n6)) -> (green (n1) (n6)) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_Ha zenon_H3a zenon_H7 zenon_H11a zenon_H1d zenon_G zenon_H7e zenon_H2c zenon_H108 zenon_H158. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L167_); trivial. % 0.92/1.09 apply (zenon_L168_); trivial. % 0.92/1.09 (* end of lemma zenon_L169_ *) % 0.92/1.09 assert (zenon_L170_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (red (n1) (n2)) -> (red (n2) (n3)) -> (~(goal)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (green (n1) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H7 zenon_H3a zenon_H7e zenon_H85 zenon_G zenon_Ha zenon_H11a zenon_H1d zenon_H2c zenon_H108. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L32_); trivial. % 0.92/1.09 apply (zenon_L169_); trivial. % 0.92/1.09 (* end of lemma zenon_L170_ *) % 0.92/1.09 assert (zenon_L171_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (~(goal)) -> (red (n1) (n4)) -> (red (n1) (n2)) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (red (n1) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_Ha zenon_H7 zenon_H72 zenon_G zenon_Hcd zenon_H7e zenon_H2c zenon_H1d zenon_Hb5. % 0.92/1.09 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.09 apply (zenon_L121_); trivial. % 0.92/1.09 (* end of lemma zenon_L171_ *) % 0.92/1.09 assert (zenon_L172_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (red (n1) (n6)) -> (less_than (n4) (n5)) -> (less_than (n5) (n6)) -> (red (n1) (n2)) -> (red (n1) (n4)) -> (~(goal)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_Hb5 zenon_H1d zenon_H2c zenon_H7e zenon_Hcd zenon_G zenon_H7 zenon_Ha. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 apply (zenon_L171_); trivial. % 0.92/1.09 (* end of lemma zenon_L172_ *) % 0.92/1.09 assert (zenon_L173_ : ((less_than (n1) (n6))->((red (n1) (n6))\/(green (n1) (n6)))) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (~(goal)) -> (red (n1) (n2)) -> (red (n1) (n4)) -> (less_than (n5) (n6)) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H11d zenon_H8 zenon_H11a zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_G zenon_H7e zenon_Hcd zenon_H2c zenon_H158. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L172_); trivial. % 0.92/1.09 apply (zenon_L167_); trivial. % 0.92/1.09 (* end of lemma zenon_L173_ *) % 0.92/1.09 assert (zenon_L174_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (red (n1) (n2)) -> (red (n1) (n4)) -> (~(goal)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H7e zenon_Hcd zenon_G zenon_H11a zenon_H158. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_L173_); trivial. % 0.92/1.09 (* end of lemma zenon_L174_ *) % 0.92/1.09 assert (zenon_L175_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (red (n1) (n2)) -> (~(goal)) -> (less_than (n5) (n6)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (green (n1) (n6)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H7 zenon_H3a zenon_H1d zenon_Ha zenon_H7e zenon_G zenon_H2c zenon_H11a zenon_H108 zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L44_); trivial. % 0.92/1.09 apply (zenon_L168_); trivial. % 0.92/1.09 (* end of lemma zenon_L175_ *) % 0.92/1.09 assert (zenon_L176_ : (green (n1) (n2)) -> (green (n2) (n4)) -> (green (n1) (n4)) -> (~(goal)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H139 zenon_Hd8 zenon_H109 zenon_G. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (zenon_H10b (n2)). zenon_intro zenon_H13a. % 0.92/1.09 generalize (zenon_H13a (n4)). zenon_intro zenon_H13f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H13f); [ zenon_intro zenon_H140 | zenon_intro zenon_H71 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H140); [ zenon_intro zenon_H13e | zenon_intro zenon_H141 ]. % 0.92/1.09 exact (zenon_H13e zenon_H139). % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H141); [ zenon_intro zenon_Hdd | zenon_intro zenon_H116 ]. % 0.92/1.09 exact (zenon_Hdd zenon_Hd8). % 0.92/1.09 exact (zenon_H116 zenon_H109). % 0.92/1.09 exact (zenon_G zenon_H71). % 0.92/1.09 (* end of lemma zenon_L176_ *) % 0.92/1.09 assert (zenon_L177_ : (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (red (n2) (n6)) -> (red (n1) (n6)) -> (~(goal)) -> (green (n2) (n4)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H11a zenon_H3a zenon_Hbc zenon_Hb5 zenon_G zenon_Hd8 zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L153_); trivial. % 0.92/1.09 apply (zenon_L176_); trivial. % 0.92/1.09 (* end of lemma zenon_L177_ *) % 0.92/1.09 assert (zenon_L178_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (~(goal)) -> (green (n1) (n6)) -> (green (n1) (n3)) -> (green (n1) (n2)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_G zenon_H108 zenon_H158 zenon_H139 zenon_H1d zenon_H7 zenon_Ha zenon_H2c. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.09 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.09 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.09 apply (zenon_L137_); trivial. % 0.92/1.09 (* end of lemma zenon_L178_ *) % 0.92/1.09 assert (zenon_L179_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (green (n1) (n3)) -> (green (n1) (n6)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H7 zenon_H1d zenon_H158 zenon_H108 zenon_H7f zenon_H73 zenon_G zenon_H3a zenon_H11a. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L15_); trivial. % 0.92/1.09 apply (zenon_L178_); trivial. % 0.92/1.09 (* end of lemma zenon_L179_ *) % 0.92/1.09 assert (zenon_L180_ : (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (green (n2) (n4)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H11a zenon_H3a zenon_H7f zenon_H73 zenon_G zenon_Hd8 zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L82_); trivial. % 0.92/1.09 apply (zenon_L176_); trivial. % 0.92/1.09 (* end of lemma zenon_L180_ *) % 0.92/1.09 assert (zenon_L181_ : ((less_than (n1) (n4))->((red (n1) (n4))\/(green (n1) (n4)))) -> (green (n1) (n3)) -> (green (n2) (n6)) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n3) (n4)) -> (less_than (n5) (n6)) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (green (n2) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H11f zenon_H158 zenon_Hc2 zenon_H1d zenon_H7 zenon_Ha zenon_H2c zenon_H8 zenon_H11a zenon_H3a zenon_H7f zenon_H73 zenon_G zenon_Hd8. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L116_); trivial. % 0.92/1.09 apply (zenon_L179_); trivial. % 0.92/1.09 apply (zenon_L180_); trivial. % 0.92/1.09 (* end of lemma zenon_L181_ *) % 0.92/1.09 assert (zenon_L182_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (green (n1) (n4)) -> (green (n1) (n5)) -> (less_than (n3) (n4)) -> (~(goal)) -> (green (n1) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H109 zenon_H10a zenon_Ha zenon_G zenon_H158. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 apply (zenon_L144_); trivial. % 0.92/1.09 (* end of lemma zenon_L182_ *) % 0.92/1.09 assert (zenon_L183_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n3) B)->((red (n3) B)\/(green (n3) B)))) -> (red (n4) (n6)) -> (~(goal)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n1) B)/\((green B C)/\(green (n1) C)))->(goal)))) -> (green (n1) (n4)) -> (green (n1) (n3)) -> (forall B : zenon_U, (forall C : zenon_U, (((green (n2) B)/\((green B C)/\(green (n2) C)))->(goal)))) -> (green (n2) (n6)) -> (green (n2) (n3)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H1d zenon_H98 zenon_Hf0 zenon_G zenon_H10b zenon_H109 zenon_H158 zenon_H8a zenon_Hc2 zenon_H8d. % 0.92/1.09 generalize (zenon_H98 (n6)). zenon_intro zenon_Hc8. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc9 ]. % 0.92/1.09 apply (zenon_L23_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hc1 ]. % 0.92/1.09 apply (zenon_L161_); trivial. % 0.92/1.09 apply (zenon_L27_); trivial. % 0.92/1.09 (* end of lemma zenon_L183_ *) % 0.92/1.09 assert (zenon_L184_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n4) (n5)) -> (less_than (n3) (n4)) -> (~(goal)) -> (green (n1) (n4)) -> (green (n1) (n3)) -> (green (n2) (n6)) -> (green (n2) (n3)) -> (green (n2) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_H1d zenon_Ha zenon_G zenon_H109 zenon_H158 zenon_Hc2 zenon_H8d zenon_Hd8. % 0.92/1.09 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.09 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.09 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.09 apply (zenon_L38_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.09 apply (zenon_L183_); trivial. % 0.92/1.09 apply (zenon_L113_); trivial. % 0.92/1.09 (* end of lemma zenon_L184_ *) % 0.92/1.09 assert (zenon_L185_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n5) (n6)) -> (less_than (n3) (n4)) -> (less_than (n1) (n2)) -> (less_than (n2) (n3)) -> (less_than (n4) (n5)) -> (green (n1) (n3)) -> (green (n1) (n5)) -> (~(goal)) -> (red (n1) (n4)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H2c zenon_Ha zenon_H3a zenon_H7 zenon_H1d zenon_H158 zenon_H10a zenon_G zenon_Hcd zenon_H97 zenon_H11a. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_L132_); trivial. % 0.92/1.09 (* end of lemma zenon_L185_ *) % 0.92/1.09 assert (zenon_L186_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (green (n2) (n3)) -> (green (n1) (n3)) -> (~(goal)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n5) (n6)) -> (green (n2) (n6)) -> (green (n2) (n4)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H8d zenon_H158 zenon_G zenon_H11a zenon_H2c zenon_Hc2 zenon_Hd8 zenon_H97. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L150_); trivial. % 0.92/1.09 apply (zenon_L184_); trivial. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L185_); trivial. % 0.92/1.09 apply (zenon_L184_); trivial. % 0.92/1.09 (* end of lemma zenon_L186_ *) % 0.92/1.09 assert (zenon_L187_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (green (n2) (n3)) -> (green (n2) (n4)) -> (red (n1) (n4)) -> (~(goal)) -> (less_than (n3) (n4)) -> (less_than (n4) (n5)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n5) (n6)) -> (green (n2) (n6)) -> (forall B : zenon_U, ((less_than (n2) B)->((red (n2) B)\/(green (n2) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H7 zenon_H3a zenon_H8d zenon_Hd8 zenon_Hcd zenon_G zenon_Ha zenon_H1d zenon_H11a zenon_H2c zenon_Hc2 zenon_H97. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L37_); trivial. % 0.92/1.09 apply (zenon_L186_); trivial. % 0.92/1.09 (* end of lemma zenon_L187_ *) % 0.92/1.09 assert (zenon_L188_ : (forall B : zenon_U, (forall C : zenon_U, (((red (n1) B)/\((red B C)/\(red (n1) C)))->(goal)))) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n1) (n2)) -> (red (n2) (n5)) -> (red (n1) (n5)) -> (~(goal)) -> (green (n1) (n6)) -> (green (n2) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H72 zenon_H11a zenon_H3a zenon_H7f zenon_H73 zenon_G zenon_H108 zenon_Hc2. % 0.92/1.09 generalize (zenon_H72 (n2)). zenon_intro zenon_H7d. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L14_); trivial. % 0.92/1.09 apply (zenon_L76_); trivial. % 0.92/1.09 (* end of lemma zenon_L188_ *) % 0.92/1.09 assert (zenon_L189_ : (green (n2) (n6)) -> (green (n1) (n6)) -> (~(goal)) -> (red (n1) (n5)) -> (red (n2) (n5)) -> (less_than (n1) (n2)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> False). % 0.92/1.09 do 0 intro. intros zenon_Hc2 zenon_H108 zenon_G zenon_H73 zenon_H7f zenon_H3a zenon_H11a. % 0.92/1.09 generalize (red_clique (n1)). zenon_intro zenon_H72. % 0.92/1.09 apply (zenon_L188_); trivial. % 0.92/1.09 (* end of lemma zenon_L189_ *) % 0.92/1.09 assert (zenon_L190_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (green (n2) (n6)) -> (green (n1) (n6)) -> (~(goal)) -> (red (n2) (n5)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (less_than (n5) (n6)) -> (green (n1) (n4)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_Hc2 zenon_H108 zenon_G zenon_H7f zenon_H11a zenon_H2c zenon_H109. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 apply (zenon_L189_); trivial. % 0.92/1.09 apply (zenon_L43_); trivial. % 0.92/1.09 (* end of lemma zenon_L190_ *) % 0.92/1.09 assert (zenon_L191_ : (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z)))))) -> (less_than (n4) (n5)) -> (less_than (n2) (n3)) -> (less_than (n1) (n2)) -> (less_than (n3) (n4)) -> (forall B : zenon_U, ((less_than (n1) B)->((red (n1) B)\/(green (n1) B)))) -> (green (n2) (n3)) -> (green (n2) (n5)) -> (~(goal)) -> (less_than (n5) (n6)) -> (green (n1) (n4)) -> (green (n2) (n6)) -> (green (n1) (n6)) -> False). % 0.92/1.09 do 0 intro. intros zenon_H8 zenon_H1d zenon_H7 zenon_H3a zenon_Ha zenon_H11a zenon_H8d zenon_H8b zenon_G zenon_H2c zenon_H109 zenon_Hc2 zenon_H108. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L149_); trivial. % 0.92/1.09 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.09 generalize (green_clique (n1)). zenon_intro zenon_H10b. % 0.92/1.09 generalize (partition (n4)). zenon_intro zenon_Hfb. % 0.92/1.09 generalize (partition (n3)). zenon_intro zenon_H98. % 0.92/1.09 generalize (zenon_Hfb (n6)). zenon_intro zenon_H105. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H105); [ zenon_intro zenon_He1 | zenon_intro zenon_H106 ]. % 0.92/1.09 apply (zenon_L38_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H107 ]. % 0.92/1.09 apply (zenon_L183_); trivial. % 0.92/1.09 apply (zenon_L163_); trivial. % 0.92/1.09 apply (zenon_L43_); trivial. % 0.92/1.09 (* end of lemma zenon_L191_ *) % 0.92/1.09 apply NNPP. intro zenon_G. % 0.92/1.09 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((less_than x y)->((less_than y z)->(less_than x z))))))); [ zenon_intro zenon_H8 | zenon_intro zenon_H186 ]. % 0.92/1.09 apply (zenon_and_s _ _ ordering). zenon_intro zenon_H3a. zenon_intro zenon_H187. % 0.92/1.09 apply (zenon_and_s _ _ zenon_H187). zenon_intro zenon_H7. zenon_intro zenon_H188. % 0.92/1.09 apply (zenon_and_s _ _ zenon_H188). zenon_intro zenon_Ha. zenon_intro zenon_H189. % 0.92/1.09 apply (zenon_and_s _ _ zenon_H189). zenon_intro zenon_H1d. zenon_intro zenon_H2c. % 0.92/1.09 generalize (partition (n2)). zenon_intro zenon_H97. % 0.92/1.09 generalize (zenon_H97 (n4)). zenon_intro zenon_H121. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H121); [ zenon_intro zenon_H9 | zenon_intro zenon_H122 ]. % 0.92/1.09 apply (zenon_L2_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hd8 ]. % 0.92/1.09 generalize (partition (n1)). zenon_intro zenon_H11a. % 0.92/1.09 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.09 apply (zenon_L6_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L80_); trivial. % 0.92/1.09 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.09 exact (zenon_Hd zenon_H7). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.09 apply (zenon_L146_); trivial. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.09 apply (zenon_L4_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.09 apply (zenon_L147_); trivial. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L152_); trivial. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 apply (zenon_L155_); trivial. % 0.92/1.09 apply (zenon_L159_); trivial. % 0.92/1.09 apply (zenon_L145_); trivial. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L80_); trivial. % 0.92/1.09 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.09 exact (zenon_Hd zenon_H7). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.09 apply (zenon_L146_); trivial. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.09 apply (zenon_L4_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.09 apply (zenon_L147_); trivial. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L100_); trivial. % 0.92/1.09 apply (zenon_L165_); trivial. % 0.92/1.09 apply (zenon_L145_); trivial. % 0.92/1.09 generalize (partition (n1)). zenon_intro zenon_H11a. % 0.92/1.09 generalize (zenon_H97 (n6)). zenon_intro zenon_Hca. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H2b | zenon_intro zenon_Hcb ]. % 0.92/1.09 apply (zenon_L6_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hc2 ]. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.09 exact (zenon_Hd zenon_H7). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L153_); trivial. % 0.92/1.09 apply (zenon_L170_); trivial. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 apply (zenon_L153_); trivial. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L37_); trivial. % 0.92/1.09 apply (zenon_L174_); trivial. % 0.92/1.09 apply (zenon_L175_); trivial. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_L133_); trivial. % 0.92/1.09 apply (zenon_L177_); trivial. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L80_); trivial. % 0.92/1.09 apply (zenon_L178_); trivial. % 0.92/1.09 generalize (zenon_H11a (n2)). zenon_intro zenon_H152. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H152); [ zenon_intro zenon_H3e | zenon_intro zenon_H153 ]. % 0.92/1.09 exact (zenon_H3e zenon_H3a). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H7e | zenon_intro zenon_H139 ]. % 0.92/1.09 generalize (zenon_H97 (n3)). zenon_intro zenon_H95. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_Hd | zenon_intro zenon_H96 ]. % 0.92/1.09 exact (zenon_Hd zenon_H7). % 0.92/1.09 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H8d ]. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.09 apply (zenon_L4_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L172_); trivial. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L31_); trivial. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 apply (zenon_L181_); trivial. % 0.92/1.09 apply (zenon_L182_); trivial. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L116_); trivial. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L44_); trivial. % 0.92/1.09 generalize (green_clique (n2)). zenon_intro zenon_H8a. % 0.92/1.09 generalize (zenon_H11a (n5)). zenon_intro zenon_H11b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11b); [ zenon_intro zenon_H57 | zenon_intro zenon_H11c ]. % 0.92/1.09 apply (zenon_L10_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11c); [ zenon_intro zenon_H73 | zenon_intro zenon_H10a ]. % 0.92/1.09 apply (zenon_L99_); trivial. % 0.92/1.09 apply (zenon_L182_); trivial. % 0.92/1.09 apply (zenon_L170_); trivial. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L187_); trivial. % 0.92/1.09 generalize (zenon_H11a (n3)). zenon_intro zenon_H15e. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H15e); [ zenon_intro zenon_H3b | zenon_intro zenon_H15f ]. % 0.92/1.09 apply (zenon_L8_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H75 | zenon_intro zenon_H158 ]. % 0.92/1.09 apply (zenon_L31_); trivial. % 0.92/1.09 apply (zenon_L184_); trivial. % 0.92/1.09 generalize (zenon_H97 (n5)). zenon_intro zenon_H9b. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H1c | zenon_intro zenon_H9c ]. % 0.92/1.09 apply (zenon_L4_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H9c); [ zenon_intro zenon_H7f | zenon_intro zenon_H8b ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L187_); trivial. % 0.92/1.09 apply (zenon_L190_); trivial. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L187_); trivial. % 0.92/1.09 apply (zenon_L191_); trivial. % 0.92/1.09 generalize (zenon_H11a (n6)). zenon_intro zenon_H11d. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11d); [ zenon_intro zenon_H9d | zenon_intro zenon_H11e ]. % 0.92/1.09 apply (zenon_L22_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H108 ]. % 0.92/1.09 generalize (zenon_H11a (n4)). zenon_intro zenon_H11f. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H4b | zenon_intro zenon_H120 ]. % 0.92/1.09 apply (zenon_L9_); trivial. % 0.92/1.09 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_Hcd | zenon_intro zenon_H109 ]. % 0.92/1.09 apply (zenon_L116_); trivial. % 0.92/1.09 apply (zenon_L176_); trivial. % 0.92/1.09 apply (zenon_L77_); trivial. % 0.92/1.09 apply zenon_H186. zenon_intro zenon_Tx_pe. apply NNPP. zenon_intro zenon_H18b. % 0.92/1.09 apply zenon_H18b. zenon_intro zenon_Ty_pg. apply NNPP. zenon_intro zenon_H18d. % 0.92/1.09 apply zenon_H18d. zenon_intro zenon_Tz_pi. apply NNPP. zenon_intro zenon_H18f. % 0.92/1.09 apply (zenon_notimply_s _ _ zenon_H18f). zenon_intro zenon_H191. zenon_intro zenon_H190. % 0.92/1.09 apply (zenon_notimply_s _ _ zenon_H190). zenon_intro zenon_H193. zenon_intro zenon_H192. % 0.92/1.09 generalize (less_than_transitive zenon_Tx_pe). zenon_intro zenon_H194. % 0.92/1.09 generalize (zenon_H194 zenon_Ty_pg). zenon_intro zenon_H195. % 0.92/1.09 generalize (zenon_H195 zenon_Tz_pi). zenon_intro zenon_H196. % 0.92/1.09 apply (zenon_imply_s _ _ zenon_H196); [ zenon_intro zenon_H198 | zenon_intro zenon_H197 ]. % 0.92/1.09 apply (zenon_notand_s _ _ zenon_H198); [ zenon_intro zenon_H19a | zenon_intro zenon_H199 ]. % 0.92/1.09 exact (zenon_H19a zenon_H191). % 0.92/1.09 exact (zenon_H199 zenon_H193). % 0.92/1.09 exact (zenon_H192 zenon_H197). % 0.92/1.09 Qed. % 0.92/1.09 % SZS output end Proof % 0.92/1.09 (* END-PROOF *) % 0.92/1.09 nodes searched: 54148 % 0.92/1.09 max branch formulas: 983 % 0.92/1.09 proof nodes created: 4515 % 0.92/1.09 formulas created: 64715 % 0.92/1.09 %------------------------------------------------------------------------------