%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO234+1 : TPTP v8.1.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 07:01:10 EDT 2022 % Result : Theorem 0.60s 0.78s % Output : Proof 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO234+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n008.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 06:16:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.60/0.78 (* PROOF-FOUND *) % 0.60/0.78 % SZS status Theorem % 0.60/0.78 (* BEGIN-PROOF *) % 0.60/0.78 % SZS output start Proof % 0.60/0.78 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines L (reverse_line M))->((unequally_directed_lines L N)\/(unequally_directed_lines M (reverse_line N))))))). % 0.60/0.78 Proof. % 0.60/0.78 assert (zenon_L1_ : forall (zenon_TM_bi : zenon_U), ((unequally_directed_lines (reverse_line zenon_TM_bi) zenon_TM_bi)/\(unequally_directed_lines (reverse_line zenon_TM_bi) (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines (reverse_line zenon_TM_bi) (reverse_line zenon_TM_bi))) -> False). % 0.60/0.78 do 1 intro. intros zenon_H20 zenon_H21. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.60/0.78 exact (zenon_H21 zenon_H23). % 0.60/0.78 (* end of lemma zenon_L1_ *) % 0.60/0.78 assert (zenon_L2_ : forall (zenon_TN_bn : zenon_U), ((unequally_directed_lines zenon_TN_bn zenon_TN_bn)/\(unequally_directed_lines zenon_TN_bn (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TN_bn zenon_TN_bn)) -> False). % 0.60/0.78 do 1 intro. intros zenon_H25 zenon_H26. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.60/0.78 exact (zenon_H26 zenon_H29). % 0.60/0.78 (* end of lemma zenon_L2_ *) % 0.60/0.78 assert (zenon_L3_ : forall (zenon_TN_bn : zenon_U) (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TN_bn)/\(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> False). % 0.60/0.78 do 2 intro. intros zenon_H2a zenon_H2b. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.60/0.78 exact (zenon_H2b zenon_H2c). % 0.60/0.78 (* end of lemma zenon_L3_ *) % 0.60/0.78 assert (zenon_L4_ : forall (zenon_TM_bi : zenon_U) (zenon_TN_bn : zenon_U), ((unequally_directed_lines zenon_TN_bn zenon_TM_bi)/\(unequally_directed_lines zenon_TN_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TN_bn zenon_TN_bn)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H2e zenon_H2b zenon_H26. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.60/0.78 generalize (oag7 zenon_TN_bn). zenon_intro zenon_H31. % 0.60/0.78 generalize (zenon_H31 zenon_TM_bi). zenon_intro zenon_H32. % 0.60/0.78 generalize (zenon_H32 zenon_TN_bn). zenon_intro zenon_H33. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.60/0.78 exact (zenon_H37 zenon_H30). % 0.60/0.78 exact (zenon_H36 zenon_H2f). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H25 | zenon_intro zenon_H2a ]. % 0.60/0.78 apply (zenon_L2_ zenon_TN_bn); trivial. % 0.60/0.78 apply (zenon_L3_ zenon_TN_bn zenon_TM_bi); trivial. % 0.60/0.78 (* end of lemma zenon_L4_ *) % 0.60/0.78 assert (zenon_L5_ : forall (zenon_TN_bn : zenon_U) (zenon_TM_bi : zenon_U), (unequally_directed_lines (reverse_line zenon_TM_bi) zenon_TN_bn) -> (unequally_directed_lines (reverse_line zenon_TM_bi) (reverse_line zenon_TN_bn)) -> (~(unequally_directed_lines (reverse_line zenon_TM_bi) (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TN_bn zenon_TN_bn)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H38 zenon_H39 zenon_H21 zenon_H2b zenon_H26. % 0.60/0.78 generalize (oag7 (reverse_line zenon_TM_bi)). zenon_intro zenon_H3a. % 0.60/0.78 generalize (zenon_H3a zenon_TN_bn). zenon_intro zenon_H3b. % 0.60/0.78 generalize (zenon_H3b zenon_TM_bi). zenon_intro zenon_H3c. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.60/0.78 exact (zenon_H40 zenon_H38). % 0.60/0.78 exact (zenon_H3f zenon_H39). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H20 | zenon_intro zenon_H2e ]. % 0.60/0.78 apply (zenon_L1_ zenon_TM_bi); trivial. % 0.60/0.78 apply (zenon_L4_ zenon_TM_bi zenon_TN_bn); trivial. % 0.60/0.78 (* end of lemma zenon_L5_ *) % 0.60/0.78 assert (zenon_L6_ : forall (zenon_TN_bn : zenon_U), ((unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TN_bn)/\(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TN_bn))) -> False). % 0.60/0.78 do 1 intro. intros zenon_H41 zenon_H42. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.60/0.78 exact (zenon_H42 zenon_H43). % 0.60/0.78 (* end of lemma zenon_L6_ *) % 0.60/0.78 assert (zenon_L7_ : forall (zenon_TN_bn : zenon_U) (zenon_TL_ct : zenon_U), ((unequally_directed_lines zenon_TL_ct zenon_TN_bn)/\(unequally_directed_lines zenon_TL_ct (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H45 zenon_H46. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.60/0.78 exact (zenon_H46 zenon_H49). % 0.60/0.78 (* end of lemma zenon_L7_ *) % 0.60/0.78 assert (zenon_L8_ : forall (zenon_TL_ct : zenon_U) (zenon_TN_bn : zenon_U), (forall N : zenon_U, (((unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TL_ct)/\(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TL_ct)))->(((unequally_directed_lines (reverse_line zenon_TN_bn) N)/\(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line N)))\/((unequally_directed_lines zenon_TL_ct N)/\(unequally_directed_lines zenon_TL_ct (reverse_line N)))))) -> (unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TL_ct) -> (unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TL_ct)) -> (~(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H4a zenon_H4b zenon_H4c zenon_H42 zenon_H46. % 0.60/0.78 generalize (zenon_H4a zenon_TN_bn). zenon_intro zenon_H4d. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.60/0.78 exact (zenon_H51 zenon_H4b). % 0.60/0.78 exact (zenon_H50 zenon_H4c). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H41 | zenon_intro zenon_H45 ]. % 0.60/0.78 apply (zenon_L6_ zenon_TN_bn); trivial. % 0.60/0.78 apply (zenon_L7_ zenon_TN_bn zenon_TL_ct); trivial. % 0.60/0.78 (* end of lemma zenon_L8_ *) % 0.60/0.78 assert (zenon_L9_ : forall (zenon_TL_ct : zenon_U) (zenon_TN_bn : zenon_U), ((unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TL_ct)/\(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TL_ct))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> (~(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TN_bn))) -> (unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TL_ct) -> (forall N : zenon_U, (((unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TL_ct)/\(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TL_ct)))->(((unequally_directed_lines (reverse_line zenon_TN_bn) N)/\(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line N)))\/((unequally_directed_lines zenon_TL_ct N)/\(unequally_directed_lines zenon_TL_ct (reverse_line N)))))) -> False). % 0.60/0.78 do 2 intro. intros zenon_H52 zenon_H46 zenon_H42 zenon_H4b zenon_H4a. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H4b. zenon_intro zenon_H4c. % 0.60/0.78 apply (zenon_L8_ zenon_TL_ct zenon_TN_bn); trivial. % 0.60/0.78 (* end of lemma zenon_L9_ *) % 0.60/0.78 assert (zenon_L10_ : forall (zenon_TL_ct : zenon_U), ((unequally_directed_lines zenon_TL_ct zenon_TL_ct)/\(unequally_directed_lines zenon_TL_ct (reverse_line zenon_TL_ct))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TL_ct)) -> False). % 0.60/0.78 do 1 intro. intros zenon_H53 zenon_H54. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.60/0.78 exact (zenon_H54 zenon_H56). % 0.60/0.78 (* end of lemma zenon_L10_ *) % 0.60/0.78 assert (zenon_L11_ : forall (zenon_TL_ct : zenon_U) (zenon_TN_bn : zenon_U), (unequally_directed_lines (reverse_line zenon_TN_bn) zenon_TL_ct) -> (~(unequally_directed_lines zenon_TL_ct (reverse_line zenon_TL_ct))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> (~(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TL_ct)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H4b zenon_H57 zenon_H46 zenon_H42 zenon_H54. % 0.60/0.78 generalize (oag7 (reverse_line zenon_TN_bn)). zenon_intro zenon_H58. % 0.60/0.78 generalize (zenon_H58 zenon_TL_ct). zenon_intro zenon_H4a. % 0.60/0.78 generalize (zenon_H4a zenon_TL_ct). zenon_intro zenon_H59. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H4f | zenon_intro zenon_H5a ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.60/0.78 exact (zenon_H51 zenon_H4b). % 0.60/0.78 generalize (oag6 (reverse_line zenon_TN_bn)). zenon_intro zenon_H5b. % 0.60/0.78 generalize (zenon_H5b zenon_TL_ct). zenon_intro zenon_H5c. % 0.60/0.78 generalize (zenon_H5c (reverse_line zenon_TL_ct)). zenon_intro zenon_H5d. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H51 | zenon_intro zenon_H5e ]. % 0.60/0.78 exact (zenon_H51 zenon_H4b). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H4c | zenon_intro zenon_H55 ]. % 0.60/0.78 exact (zenon_H50 zenon_H4c). % 0.60/0.78 exact (zenon_H57 zenon_H55). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H52 | zenon_intro zenon_H53 ]. % 0.60/0.78 apply (zenon_L9_ zenon_TL_ct zenon_TN_bn); trivial. % 0.60/0.78 apply (zenon_L10_ zenon_TL_ct); trivial. % 0.60/0.78 (* end of lemma zenon_L11_ *) % 0.60/0.78 assert (zenon_L12_ : forall (zenon_TL_ct : zenon_U) (zenon_TN_bn : zenon_U) (zenon_TM_bi : zenon_U), (~(unequally_directed_lines (reverse_line zenon_TM_bi) (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TN_bn zenon_TN_bn)) -> (~(unequally_directed_lines zenon_TL_ct zenon_TL_ct)) -> (~(unequally_directed_lines zenon_TL_ct (reverse_line zenon_TL_ct))) -> (~(unequally_directed_lines (reverse_line zenon_TN_bn) (reverse_line zenon_TN_bn))) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TL_ct M)->((unequally_directed_lines zenon_TL_ct N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> (unequally_directed_lines zenon_TL_ct (reverse_line zenon_TM_bi)) -> False). % 0.60/0.78 do 3 intro. intros zenon_H21 zenon_H2b zenon_H26 zenon_H54 zenon_H57 zenon_H42 zenon_H5f zenon_H46 zenon_H60. % 0.60/0.78 generalize (zenon_H5f (reverse_line zenon_TM_bi)). zenon_intro zenon_H61. % 0.60/0.78 generalize (zenon_H61 zenon_TN_bn). zenon_intro zenon_H62. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.60/0.78 exact (zenon_H64 zenon_H60). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H49 | zenon_intro zenon_H38 ]. % 0.60/0.78 exact (zenon_H46 zenon_H49). % 0.60/0.78 generalize (zenon_H5f (reverse_line zenon_TN_bn)). zenon_intro zenon_H65. % 0.60/0.78 generalize (zenon_H65 zenon_TL_ct). zenon_intro zenon_H66. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.60/0.78 generalize (zenon_H61 (reverse_line zenon_TN_bn)). zenon_intro zenon_H69. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H64 | zenon_intro zenon_H6a ]. % 0.60/0.78 exact (zenon_H64 zenon_H60). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H48 | zenon_intro zenon_H39 ]. % 0.60/0.78 exact (zenon_H68 zenon_H48). % 0.60/0.78 apply (zenon_L5_ zenon_TN_bn zenon_TM_bi); trivial. % 0.60/0.78 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H56 | zenon_intro zenon_H4b ]. % 0.60/0.78 exact (zenon_H54 zenon_H56). % 0.60/0.78 apply (zenon_L11_ zenon_TL_ct zenon_TN_bn); trivial. % 0.60/0.78 (* end of lemma zenon_L12_ *) % 0.60/0.78 assert (zenon_L13_ : forall (zenon_TN_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TL_ct : zenon_U), (forall N : zenon_U, (((unequally_directed_lines zenon_TL_ct zenon_TM_bi)/\(unequally_directed_lines zenon_TL_ct (reverse_line zenon_TM_bi)))->(((unequally_directed_lines zenon_TL_ct N)/\(unequally_directed_lines zenon_TL_ct (reverse_line N)))\/((unequally_directed_lines zenon_TM_bi N)/\(unequally_directed_lines zenon_TM_bi (reverse_line N)))))) -> (unequally_directed_lines zenon_TL_ct zenon_TM_bi) -> (unequally_directed_lines zenon_TL_ct (reverse_line zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> False). % 0.60/0.78 do 3 intro. intros zenon_H6b zenon_H6c zenon_H60 zenon_H46 zenon_H2b. % 0.60/0.78 generalize (zenon_H6b zenon_TN_bn). zenon_intro zenon_H6d. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H70 | zenon_intro zenon_H64 ]. % 0.60/0.78 exact (zenon_H70 zenon_H6c). % 0.60/0.78 exact (zenon_H64 zenon_H60). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H6e); [ zenon_intro zenon_H45 | zenon_intro zenon_H2a ]. % 0.60/0.78 apply (zenon_L7_ zenon_TN_bn zenon_TL_ct); trivial. % 0.60/0.78 apply (zenon_L3_ zenon_TN_bn zenon_TM_bi); trivial. % 0.60/0.78 (* end of lemma zenon_L13_ *) % 0.60/0.78 assert (zenon_L14_ : forall (zenon_TN_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TL_ct : zenon_U), (unequally_directed_lines zenon_TL_ct zenon_TM_bi) -> (unequally_directed_lines zenon_TL_ct (reverse_line zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> False). % 0.60/0.78 do 3 intro. intros zenon_H6c zenon_H60 zenon_H46 zenon_H2b. % 0.60/0.78 generalize (oag7 zenon_TL_ct). zenon_intro zenon_H71. % 0.60/0.78 generalize (zenon_H71 zenon_TM_bi). zenon_intro zenon_H6b. % 0.60/0.78 apply (zenon_L13_ zenon_TN_bn zenon_TM_bi zenon_TL_ct); trivial. % 0.60/0.78 (* end of lemma zenon_L14_ *) % 0.60/0.78 assert (zenon_L15_ : forall (zenon_TN_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TL_ct : zenon_U), (forall N : zenon_U, ((unequally_directed_lines (reverse_line zenon_TL_ct) zenon_TM_bi)->((unequally_directed_lines (reverse_line zenon_TL_ct) N)\/(unequally_directed_lines zenon_TM_bi N)))) -> (unequally_directed_lines (reverse_line zenon_TL_ct) zenon_TM_bi) -> (~(unequally_directed_lines (reverse_line zenon_TL_ct) (reverse_line zenon_TN_bn))) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bn))) -> False). % 0.60/0.78 do 3 intro. intros zenon_H72 zenon_H73 zenon_H74 zenon_H2b. % 0.60/0.78 generalize (zenon_H72 (reverse_line zenon_TN_bn)). zenon_intro zenon_H75. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 0.60/0.78 exact (zenon_H77 zenon_H73). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H78 | zenon_intro zenon_H2c ]. % 0.60/0.78 exact (zenon_H74 zenon_H78). % 0.60/0.78 exact (zenon_H2b zenon_H2c). % 0.60/0.78 (* end of lemma zenon_L15_ *) % 0.60/0.78 assert (zenon_L16_ : forall (zenon_TL_ct : zenon_U), ((unequally_directed_lines (reverse_line zenon_TL_ct) zenon_TL_ct)/\(unequally_directed_lines (reverse_line zenon_TL_ct) (reverse_line zenon_TL_ct))) -> (~(unequally_directed_lines (reverse_line zenon_TL_ct) (reverse_line zenon_TL_ct))) -> False). % 0.60/0.78 do 1 intro. intros zenon_H79 zenon_H7a. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 0.60/0.78 exact (zenon_H7a zenon_H7b). % 0.60/0.78 (* end of lemma zenon_L16_ *) % 0.60/0.78 assert (zenon_L17_ : forall (zenon_TL_ct : zenon_U) (zenon_TN_bn : zenon_U), ((unequally_directed_lines zenon_TN_bn zenon_TL_ct)/\(unequally_directed_lines zenon_TN_bn (reverse_line zenon_TL_ct))) -> (~(unequally_directed_lines zenon_TL_ct zenon_TN_bn)) -> (~(unequally_directed_lines zenon_TN_bn zenon_TN_bn)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H7d zenon_H46 zenon_H26. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 0.60/0.78 generalize (oag7 zenon_TN_bn). zenon_intro zenon_H31. % 0.60/0.78 generalize (zenon_H31 zenon_TL_ct). zenon_intro zenon_H80. % 0.60/0.78 generalize (zenon_H80 zenon_TN_bn). zenon_intro zenon_H81. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 0.60/0.78 exact (zenon_H85 zenon_H7f). % 0.60/0.78 exact (zenon_H84 zenon_H7e). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H25 | zenon_intro zenon_H45 ]. % 0.60/0.78 apply (zenon_L2_ zenon_TN_bn); trivial. % 0.60/0.78 apply (zenon_L7_ zenon_TN_bn zenon_TL_ct); trivial. % 0.60/0.78 (* end of lemma zenon_L17_ *) % 0.60/0.78 apply NNPP. intro zenon_G. % 0.60/0.78 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines L (reverse_line M))->((unequally_directed_lines L N)\/(unequally_directed_lines M (reverse_line N))))))) zenon_G); [ zenon_intro zenon_H86; idtac ]. % 0.60/0.78 elim zenon_H86. zenon_intro zenon_TL_ct. zenon_intro zenon_H87. % 0.60/0.78 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unequally_directed_lines zenon_TL_ct (reverse_line M))->((unequally_directed_lines zenon_TL_ct N)\/(unequally_directed_lines M (reverse_line N)))))) zenon_H87); [ zenon_intro zenon_H88; idtac ]. % 0.60/0.78 elim zenon_H88. zenon_intro zenon_TM_bi. zenon_intro zenon_H89. % 0.60/0.78 apply (zenon_notallex_s (fun N : zenon_U => ((unequally_directed_lines zenon_TL_ct (reverse_line zenon_TM_bi))->((unequally_directed_lines zenon_TL_ct N)\/(unequally_directed_lines zenon_TM_bi (reverse_line N))))) zenon_H89); [ zenon_intro zenon_H8a; idtac ]. % 0.60/0.78 elim zenon_H8a. zenon_intro zenon_TN_bn. zenon_intro zenon_H8b. % 0.60/0.78 apply (zenon_notimply_s _ _ zenon_H8b). zenon_intro zenon_H60. zenon_intro zenon_H8c. % 0.60/0.78 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H46. zenon_intro zenon_H2b. % 0.60/0.78 generalize (oag5 zenon_TN_bn). zenon_intro zenon_H26. % 0.60/0.78 generalize (oag5 zenon_TL_ct). zenon_intro zenon_H54. % 0.60/0.78 generalize (oag6 zenon_TL_ct). zenon_intro zenon_H5f. % 0.60/0.78 generalize (oag5 (reverse_line zenon_TL_ct)). zenon_intro zenon_H7a. % 0.60/0.78 generalize (oag5 (reverse_line zenon_TN_bn)). zenon_intro zenon_H42. % 0.60/0.78 generalize (oag5 (reverse_line zenon_TM_bi)). zenon_intro zenon_H21. % 0.60/0.78 generalize (zenon_H5f (reverse_line zenon_TL_ct)). zenon_intro zenon_H8d. % 0.60/0.78 generalize (zenon_H8d zenon_TN_bn). zenon_intro zenon_H8e. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H57 | zenon_intro zenon_H8f ]. % 0.60/0.78 apply (zenon_L12_ zenon_TL_ct zenon_TN_bn zenon_TM_bi); trivial. % 0.60/0.78 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H49 | zenon_intro zenon_H90 ]. % 0.60/0.78 exact (zenon_H46 zenon_H49). % 0.60/0.78 generalize (zenon_H8d zenon_TM_bi). zenon_intro zenon_H91. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H57 | zenon_intro zenon_H92 ]. % 0.60/0.78 apply (zenon_L12_ zenon_TL_ct zenon_TN_bn zenon_TM_bi); trivial. % 0.60/0.78 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H6c | zenon_intro zenon_H73 ]. % 0.60/0.78 apply (zenon_L14_ zenon_TN_bn zenon_TM_bi zenon_TL_ct); trivial. % 0.60/0.78 generalize (oag7 (reverse_line zenon_TL_ct)). zenon_intro zenon_H93. % 0.60/0.78 generalize (zenon_H93 zenon_TN_bn). zenon_intro zenon_H94. % 0.60/0.78 generalize (zenon_H94 zenon_TL_ct). zenon_intro zenon_H95. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H98 | zenon_intro zenon_H74 ]. % 0.60/0.78 exact (zenon_H98 zenon_H90). % 0.60/0.78 generalize (oag6 (reverse_line zenon_TL_ct)). zenon_intro zenon_H99. % 0.60/0.78 generalize (zenon_H99 zenon_TM_bi). zenon_intro zenon_H72. % 0.60/0.78 apply (zenon_L15_ zenon_TN_bn zenon_TM_bi zenon_TL_ct); trivial. % 0.60/0.78 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H79 | zenon_intro zenon_H7d ]. % 0.60/0.78 apply (zenon_L16_ zenon_TL_ct); trivial. % 0.60/0.78 apply (zenon_L17_ zenon_TL_ct zenon_TN_bn); trivial. % 0.60/0.78 Qed. % 0.60/0.78 % SZS output end Proof % 0.60/0.78 (* END-PROOF *) % 0.60/0.78 nodes searched: 20897 % 0.60/0.78 max branch formulas: 1621 % 0.60/0.78 proof nodes created: 1040 % 0.60/0.78 formulas created: 38342 % 0.60/0.78 %------------------------------------------------------------------------------