%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 07:01:08 EDT 2022 % Result : Theorem 0.49s 0.72s % Output : Proof 0.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO231+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n024.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 : Sat Jun 18 01:38:17 EDT 2022 % 0.12/0.34 % CPUTime : % 0.49/0.72 (* PROOF-FOUND *) % 0.49/0.72 % SZS status Theorem % 0.49/0.72 (* BEGIN-PROOF *) % 0.49/0.72 % SZS output start Proof % 0.49/0.72 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))))))). % 0.49/0.72 Proof. % 0.49/0.72 assert (zenon_L1_ : forall (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TM_bi)/\(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> False). % 0.49/0.72 do 1 intro. intros zenon_H20 zenon_H21. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.49/0.72 exact (zenon_H21 zenon_H24). % 0.49/0.72 (* end of lemma zenon_L1_ *) % 0.49/0.72 assert (zenon_L2_ : forall (zenon_TM_bi : zenon_U) (zenon_TL_bn : zenon_U), ((unequally_directed_lines zenon_TL_bn zenon_TM_bi)/\(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> False). % 0.49/0.72 do 2 intro. intros zenon_H25 zenon_H26. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.49/0.72 exact (zenon_H26 zenon_H28). % 0.49/0.72 (* end of lemma zenon_L2_ *) % 0.49/0.72 assert (zenon_L3_ : forall (zenon_TN_bs : zenon_U), ((unequally_directed_lines zenon_TN_bs zenon_TN_bs)/\(unequally_directed_lines zenon_TN_bs (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> False). % 0.49/0.72 do 1 intro. intros zenon_H2a zenon_H2b. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.49/0.72 exact (zenon_H2b zenon_H2e). % 0.49/0.72 (* end of lemma zenon_L3_ *) % 0.49/0.72 assert (zenon_L4_ : forall (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U), ((unequally_directed_lines zenon_TL_bn zenon_TN_bs)/\(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False). % 0.49/0.72 do 2 intro. intros zenon_H2f zenon_H30. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.49/0.72 exact (zenon_H30 zenon_H32). % 0.49/0.72 (* end of lemma zenon_L4_ *) % 0.49/0.72 assert (zenon_L5_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), ((unequally_directed_lines zenon_TN_bs zenon_TL_bn)/\(unequally_directed_lines zenon_TN_bs (reverse_line zenon_TL_bn))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> False). % 0.49/0.72 do 2 intro. intros zenon_H33 zenon_H30 zenon_H2b. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.49/0.72 generalize (oag7 zenon_TN_bs). zenon_intro zenon_H36. % 0.49/0.72 generalize (zenon_H36 zenon_TL_bn). zenon_intro zenon_H37. % 0.49/0.72 generalize (zenon_H37 zenon_TN_bs). zenon_intro zenon_H38. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.49/0.72 exact (zenon_H3c zenon_H35). % 0.49/0.72 exact (zenon_H3b zenon_H34). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H2a | zenon_intro zenon_H2f ]. % 0.49/0.72 apply (zenon_L3_ zenon_TN_bs); trivial. % 0.49/0.72 apply (zenon_L4_ zenon_TN_bs zenon_TL_bn); trivial. % 0.49/0.72 (* end of lemma zenon_L5_ *) % 0.49/0.72 assert (zenon_L6_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), (unequally_directed_lines zenon_TM_bi zenon_TN_bs) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (forall M : zenon_U, (forall N : zenon_U, (((unequally_directed_lines zenon_TM_bi M)/\(unequally_directed_lines zenon_TM_bi (reverse_line M)))->(((unequally_directed_lines zenon_TM_bi N)/\(unequally_directed_lines zenon_TM_bi (reverse_line N)))\/((unequally_directed_lines M N)/\(unequally_directed_lines M (reverse_line N))))))) -> False). % 0.49/0.72 do 3 intro. intros zenon_H3d zenon_H3e zenon_H26 zenon_H21 zenon_H3f zenon_H30 zenon_H2b zenon_H40. % 0.49/0.72 generalize (zenon_H40 zenon_TN_bs). zenon_intro zenon_H41. % 0.49/0.72 generalize (zenon_H40 zenon_TL_bn). zenon_intro zenon_H42. % 0.49/0.72 generalize (zenon_H41 zenon_TL_bn). zenon_intro zenon_H43. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.49/0.72 exact (zenon_H47 zenon_H3d). % 0.49/0.72 exact (zenon_H46 zenon_H3e). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H48 | zenon_intro zenon_H33 ]. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H3f. zenon_intro zenon_H49. % 0.49/0.72 generalize (zenon_H42 zenon_TM_bi). zenon_intro zenon_H4a. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.49/0.72 exact (zenon_H4e zenon_H3f). % 0.49/0.72 exact (zenon_H4d zenon_H49). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H20 | zenon_intro zenon_H25 ]. % 0.49/0.72 apply (zenon_L1_ zenon_TM_bi); trivial. % 0.49/0.72 apply (zenon_L2_ zenon_TM_bi zenon_TL_bn); trivial. % 0.49/0.72 apply (zenon_L5_ zenon_TL_bn zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L6_ *) % 0.49/0.72 assert (zenon_L7_ : forall (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U), (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> False). % 0.49/0.72 do 3 intro. intros zenon_H3f zenon_H3e zenon_H26 zenon_H21 zenon_H30 zenon_H2b zenon_H4f. % 0.49/0.72 generalize (oag7 zenon_TM_bi). zenon_intro zenon_H40. % 0.49/0.72 generalize (zenon_H4f zenon_TL_bn). zenon_intro zenon_H50. % 0.49/0.72 generalize (zenon_H50 zenon_TN_bs). zenon_intro zenon_H51. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H4e | zenon_intro zenon_H52 ]. % 0.49/0.72 exact (zenon_H4e zenon_H3f). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H3d | zenon_intro zenon_H32 ]. % 0.49/0.72 apply (zenon_L6_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 exact (zenon_H30 zenon_H32). % 0.49/0.72 (* end of lemma zenon_L7_ *) % 0.49/0.72 assert (zenon_L8_ : forall (zenon_TN_bs : zenon_U), ((unequally_directed_lines (reverse_line zenon_TN_bs) zenon_TN_bs)/\(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> False). % 0.49/0.72 do 1 intro. intros zenon_H53 zenon_H54. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.49/0.72 exact (zenon_H54 zenon_H55). % 0.49/0.72 (* end of lemma zenon_L8_ *) % 0.49/0.72 assert (zenon_L9_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), (unequally_directed_lines (reverse_line zenon_TN_bs) zenon_TL_bn) -> (unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TL_bn)) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False). % 0.49/0.72 do 2 intro. intros zenon_H57 zenon_H58 zenon_H54 zenon_H30. % 0.49/0.72 generalize (oag7 (reverse_line zenon_TN_bs)). zenon_intro zenon_H59. % 0.49/0.72 generalize (zenon_H59 zenon_TL_bn). zenon_intro zenon_H5a. % 0.49/0.72 generalize (zenon_H5a zenon_TN_bs). zenon_intro zenon_H5b. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 0.49/0.72 exact (zenon_H5f zenon_H57). % 0.49/0.72 exact (zenon_H5e zenon_H58). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H53 | zenon_intro zenon_H2f ]. % 0.49/0.72 apply (zenon_L8_ zenon_TN_bs); trivial. % 0.49/0.72 apply (zenon_L4_ zenon_TN_bs zenon_TL_bn); trivial. % 0.49/0.72 (* end of lemma zenon_L9_ *) % 0.49/0.72 assert (zenon_L10_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs))->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines (reverse_line zenon_TN_bs) N)))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TL_bn))) -> (unequally_directed_lines (reverse_line zenon_TN_bs) zenon_TL_bn) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False). % 0.49/0.72 do 3 intro. intros zenon_H60 zenon_H3e zenon_H4d zenon_H57 zenon_H54 zenon_H30. % 0.49/0.72 generalize (zenon_H60 (reverse_line zenon_TL_bn)). zenon_intro zenon_H61. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H46 | zenon_intro zenon_H62 ]. % 0.49/0.72 exact (zenon_H46 zenon_H3e). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H49 | zenon_intro zenon_H58 ]. % 0.49/0.72 exact (zenon_H4d zenon_H49). % 0.49/0.72 apply (zenon_L9_ zenon_TL_bn zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L10_ *) % 0.49/0.72 assert (zenon_L11_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TN_bs M)->((unequally_directed_lines zenon_TN_bs N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (unequally_directed_lines zenon_TN_bs zenon_TL_bn) -> False). % 0.49/0.72 do 2 intro. intros zenon_H63 zenon_H30 zenon_H2b zenon_H35. % 0.49/0.72 generalize (zenon_H63 zenon_TL_bn). zenon_intro zenon_H64. % 0.49/0.72 generalize (zenon_H64 zenon_TN_bs). zenon_intro zenon_H65. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H3c | zenon_intro zenon_H66 ]. % 0.49/0.72 exact (zenon_H3c zenon_H35). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H2e | zenon_intro zenon_H32 ]. % 0.49/0.72 exact (zenon_H2b zenon_H2e). % 0.49/0.72 exact (zenon_H30 zenon_H32). % 0.49/0.72 (* end of lemma zenon_L11_ *) % 0.49/0.72 assert (zenon_L12_ : forall (zenon_TM_bi : zenon_U) (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U), (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (unequally_directed_lines zenon_TM_bi zenon_TN_bs) -> False). % 0.49/0.72 do 3 intro. intros zenon_H2b zenon_H30 zenon_H3f zenon_H21 zenon_H26 zenon_H3e zenon_H3d. % 0.49/0.72 generalize (oag7 zenon_TM_bi). zenon_intro zenon_H40. % 0.49/0.72 apply (zenon_L6_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 (* end of lemma zenon_L12_ *) % 0.49/0.72 assert (zenon_L13_ : forall (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TN_bs : zenon_U), (unequally_directed_lines zenon_TN_bs zenon_TM_bi) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False). % 0.49/0.72 do 3 intro. intros zenon_H67 zenon_H30 zenon_H2b zenon_H21 zenon_H26 zenon_H3e. % 0.49/0.72 generalize (oag6 zenon_TN_bs). zenon_intro zenon_H63. % 0.49/0.72 generalize (zenon_H63 zenon_TM_bi). zenon_intro zenon_H68. % 0.49/0.72 generalize (zenon_H68 zenon_TL_bn). zenon_intro zenon_H69. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ]. % 0.49/0.72 exact (zenon_H6b zenon_H67). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H35 | zenon_intro zenon_H3f ]. % 0.49/0.72 apply (zenon_L11_ zenon_TL_bn zenon_TN_bs); trivial. % 0.49/0.72 generalize (zenon_H68 zenon_TN_bs). zenon_intro zenon_H6c. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H6b | zenon_intro zenon_H6d ]. % 0.49/0.72 exact (zenon_H6b zenon_H67). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H2e | zenon_intro zenon_H3d ]. % 0.49/0.72 exact (zenon_H2b zenon_H2e). % 0.49/0.72 apply (zenon_L12_ zenon_TM_bi zenon_TL_bn zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L13_ *) % 0.49/0.72 assert (zenon_L14_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi zenon_TN_bs)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines zenon_TN_bs N)))) -> (unequally_directed_lines zenon_TM_bi zenon_TN_bs) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False). % 0.49/0.72 do 3 intro. intros zenon_H6e zenon_H3d zenon_H21 zenon_H30 zenon_H2b zenon_H26 zenon_H3e. % 0.49/0.72 generalize (zenon_H6e zenon_TM_bi). zenon_intro zenon_H6f. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H47 | zenon_intro zenon_H70 ]. % 0.49/0.72 exact (zenon_H47 zenon_H3d). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H24 | zenon_intro zenon_H67 ]. % 0.49/0.72 exact (zenon_H21 zenon_H24). % 0.49/0.72 apply (zenon_L13_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L14_ *) % 0.49/0.72 assert (zenon_L15_ : forall (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TN_bs)/\(unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TN_bs)) -> False). % 0.49/0.72 do 2 intro. intros zenon_H71 zenon_H47. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H3d. zenon_intro zenon_H3e. % 0.49/0.72 exact (zenon_H47 zenon_H3d). % 0.49/0.72 (* end of lemma zenon_L15_ *) % 0.49/0.72 assert (zenon_L16_ : forall (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U) (zenon_TN_bs : zenon_U), ((unequally_directed_lines zenon_TN_bs zenon_TM_bi)/\(unequally_directed_lines zenon_TN_bs (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> False). % 0.49/0.72 do 3 intro. intros zenon_H72 zenon_H3e zenon_H26 zenon_H21 zenon_H2b zenon_H30. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H67. zenon_intro zenon_H73. % 0.49/0.72 apply (zenon_L13_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L16_ *) % 0.49/0.72 assert (zenon_L17_ : forall (zenon_TM_bi : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U), (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines (reverse_line zenon_TN_bs) (reverse_line zenon_TN_bs))) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TL_bn (reverse_line zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False). % 0.49/0.72 do 3 intro. intros zenon_H30 zenon_H2b zenon_H4f zenon_H54 zenon_H26 zenon_H31 zenon_H21 zenon_H3e. % 0.49/0.72 generalize (oag6 zenon_TL_bn). zenon_intro zenon_H74. % 0.49/0.72 generalize (oag7 zenon_TM_bi). zenon_intro zenon_H40. % 0.49/0.72 generalize (zenon_H40 zenon_TN_bs). zenon_intro zenon_H41. % 0.49/0.72 generalize (zenon_H41 zenon_TM_bi). zenon_intro zenon_H75. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H45 | zenon_intro zenon_H76 ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.49/0.72 generalize (zenon_H74 (reverse_line zenon_TN_bs)). zenon_intro zenon_H77. % 0.49/0.72 generalize (zenon_H4f (reverse_line zenon_TN_bs)). zenon_intro zenon_H60. % 0.49/0.72 generalize (zenon_H60 zenon_TM_bi). zenon_intro zenon_H78. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H46 | zenon_intro zenon_H79 ]. % 0.49/0.72 exact (zenon_H46 zenon_H3e). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H24 | zenon_intro zenon_H7a ]. % 0.49/0.72 exact (zenon_H21 zenon_H24). % 0.49/0.72 generalize (oag7 (reverse_line zenon_TN_bs)). zenon_intro zenon_H59. % 0.49/0.72 generalize (zenon_H59 zenon_TM_bi). zenon_intro zenon_H7b. % 0.49/0.72 generalize (zenon_H7b zenon_TN_bs). zenon_intro zenon_H7c. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7e | zenon_intro zenon_H7d ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ]. % 0.49/0.72 exact (zenon_H80 zenon_H7a). % 0.49/0.72 generalize (zenon_H77 (reverse_line zenon_TM_bi)). zenon_intro zenon_H81. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H81); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ]. % 0.49/0.72 exact (zenon_H83 zenon_H31). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H28 | zenon_intro zenon_H84 ]. % 0.49/0.72 exact (zenon_H26 zenon_H28). % 0.49/0.72 exact (zenon_H7f zenon_H84). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H53 | zenon_intro zenon_H71 ]. % 0.49/0.72 apply (zenon_L8_ zenon_TN_bs); trivial. % 0.49/0.72 apply (zenon_L15_ zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 exact (zenon_H46 zenon_H3e). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H76); [ zenon_intro zenon_H20 | zenon_intro zenon_H72 ]. % 0.49/0.72 apply (zenon_L1_ zenon_TM_bi); trivial. % 0.49/0.72 apply (zenon_L16_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L17_ *) % 0.49/0.72 assert (zenon_L18_ : forall (zenon_TL_bn : zenon_U), ((unequally_directed_lines (reverse_line zenon_TL_bn) zenon_TL_bn)/\(unequally_directed_lines (reverse_line zenon_TL_bn) (reverse_line zenon_TL_bn))) -> (~(unequally_directed_lines (reverse_line zenon_TL_bn) (reverse_line zenon_TL_bn))) -> False). % 0.49/0.72 do 1 intro. intros zenon_H85 zenon_H86. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87. % 0.49/0.72 exact (zenon_H86 zenon_H87). % 0.49/0.72 (* end of lemma zenon_L18_ *) % 0.49/0.72 assert (zenon_L19_ : forall (zenon_TN_bs : zenon_U) (zenon_TL_bn : zenon_U) (zenon_TM_bi : zenon_U), (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TN_bs)) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> False). % 0.49/0.72 do 3 intro. intros zenon_H4f zenon_H30 zenon_H47 zenon_H3f. % 0.49/0.72 generalize (zenon_H4f zenon_TL_bn). zenon_intro zenon_H50. % 0.49/0.72 generalize (zenon_H50 zenon_TN_bs). zenon_intro zenon_H51. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H4e | zenon_intro zenon_H52 ]. % 0.49/0.72 exact (zenon_H4e zenon_H3f). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H3d | zenon_intro zenon_H32 ]. % 0.49/0.72 exact (zenon_H47 zenon_H3d). % 0.49/0.72 exact (zenon_H30 zenon_H32). % 0.49/0.72 (* end of lemma zenon_L19_ *) % 0.49/0.72 assert (zenon_L20_ : forall (zenon_TL_bn : zenon_U) (zenon_TN_bs : zenon_U) (zenon_TM_bi : zenon_U), ((unequally_directed_lines zenon_TM_bi zenon_TN_bs)->((unequally_directed_lines zenon_TM_bi zenon_TM_bi)\/(unequally_directed_lines zenon_TN_bs zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi zenon_TL_bn) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines zenon_TM_bi M)->((unequally_directed_lines zenon_TM_bi N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines zenon_TL_bn zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TN_bs zenon_TN_bs)) -> (~(unequally_directed_lines zenon_TM_bi zenon_TM_bi)) -> (~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi))) -> (unequally_directed_lines zenon_TM_bi (reverse_line zenon_TN_bs)) -> False). % 0.49/0.72 do 3 intro. intros zenon_H6f zenon_H3f zenon_H4f zenon_H30 zenon_H2b zenon_H21 zenon_H26 zenon_H3e. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H47 | zenon_intro zenon_H70 ]. % 0.49/0.72 apply (zenon_L19_ zenon_TN_bs zenon_TL_bn zenon_TM_bi); trivial. % 0.49/0.72 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H24 | zenon_intro zenon_H67 ]. % 0.49/0.72 exact (zenon_H21 zenon_H24). % 0.49/0.72 apply (zenon_L13_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial. % 0.49/0.72 (* end of lemma zenon_L20_ *) % 0.49/0.72 apply NNPP. intro zenon_G. % 0.49/0.72 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_H89; idtac ]. % 0.49/0.72 elim zenon_H89. zenon_intro zenon_TL_bn. zenon_intro zenon_H8a. % 0.49/0.72 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, (((~(unequally_directed_lines zenon_TL_bn (reverse_line M)))/\(~(unequally_directed_lines zenon_TL_bn N)))->(~(unequally_directed_lines M (reverse_line N)))))) zenon_H8a); [ zenon_intro zenon_H8b; idtac ]. % 0.49/0.72 elim zenon_H8b. zenon_intro zenon_TM_bi. zenon_intro zenon_H8c. % 0.49/0.72 apply (zenon_notallex_s (fun N : zenon_U => (((~(unequally_directed_lines zenon_TL_bn (reverse_line zenon_TM_bi)))/\(~(unequally_directed_lines zenon_TL_bn N)))->(~(unequally_directed_lines zenon_TM_bi (reverse_line N))))) zenon_H8c); [ zenon_intro zenon_H8d; idtac ]. % 0.49/0.72 elim zenon_H8d. zenon_intro zenon_TN_bs. zenon_intro zenon_H8e. % 0.49/0.72 apply (zenon_notimply_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 0.49/0.72 apply zenon_H8f. zenon_intro zenon_H3e. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H26. zenon_intro zenon_H30. % 0.49/0.72 generalize (oag5 zenon_TN_bs). zenon_intro zenon_H2b. % 0.49/0.72 generalize (oag5 zenon_TM_bi). zenon_intro zenon_H21. % 0.49/0.72 generalize (oag5 zenon_TL_bn). zenon_intro zenon_H91. % 0.49/0.72 generalize (oag5 (reverse_line zenon_TN_bs)). zenon_intro zenon_H54. % 0.49/0.72 generalize (oag6 zenon_TM_bi). zenon_intro zenon_H4f. % 0.49/0.72 generalize (oag5 (reverse_line zenon_TL_bn)). zenon_intro zenon_H86. % 0.49/0.72 generalize (zenon_H4f (reverse_line zenon_TN_bs)). zenon_intro zenon_H60. % 0.49/0.72 generalize (zenon_H60 zenon_TL_bn). zenon_intro zenon_H92. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H46 | zenon_intro zenon_H93 ]. % 0.49/0.72 exact (zenon_H46 zenon_H3e). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H3f | zenon_intro zenon_H57 ]. % 0.49/0.72 apply (zenon_L7_ zenon_TN_bs zenon_TL_bn zenon_TM_bi); trivial. % 0.49/0.72 generalize (zenon_H4f (reverse_line zenon_TL_bn)). zenon_intro zenon_H94. % 0.49/0.72 generalize (zenon_H94 zenon_TM_bi). zenon_intro zenon_H95. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H4d | zenon_intro zenon_H96 ]. % 0.49/0.72 apply (zenon_L10_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 apply (zenon_or_s _ _ zenon_H96); [ zenon_intro zenon_H24 | zenon_intro zenon_H97 ]. % 0.49/0.72 exact (zenon_H21 zenon_H24). % 0.49/0.72 generalize (zenon_H94 zenon_TL_bn). zenon_intro zenon_H98. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H4d | zenon_intro zenon_H99 ]. % 0.49/0.72 apply (zenon_L10_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H3f | zenon_intro zenon_H88 ]. % 0.49/0.72 apply (zenon_L7_ zenon_TN_bs zenon_TL_bn zenon_TM_bi); trivial. % 0.49/0.72 generalize (zenon_H94 zenon_TN_bs). zenon_intro zenon_H9a. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H4d | zenon_intro zenon_H9b ]. % 0.49/0.72 apply (zenon_L10_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H3d | zenon_intro zenon_H9c ]. % 0.49/0.72 generalize (zenon_H4f zenon_TN_bs). zenon_intro zenon_H6e. % 0.49/0.72 apply (zenon_L14_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 generalize (zenon_H4f zenon_TN_bs). zenon_intro zenon_H6e. % 0.49/0.72 generalize (zenon_H4f zenon_TL_bn). zenon_intro zenon_H50. % 0.49/0.72 generalize (zenon_H6e zenon_TM_bi). zenon_intro zenon_H6f. % 0.49/0.72 generalize (zenon_H50 zenon_TL_bn). zenon_intro zenon_H9d. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_H9d); [ zenon_intro zenon_H4e | zenon_intro zenon_H9e ]. % 0.49/0.72 generalize (oag7 (reverse_line zenon_TL_bn)). zenon_intro zenon_H9f. % 0.49/0.72 generalize (zenon_H9f zenon_TM_bi). zenon_intro zenon_Ha0. % 0.49/0.72 generalize (zenon_H9f zenon_TN_bs). zenon_intro zenon_Ha1. % 0.49/0.72 generalize (zenon_Ha0 zenon_TL_bn). zenon_intro zenon_Ha2. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha5 ]. % 0.49/0.72 exact (zenon_Ha6 zenon_H97). % 0.49/0.72 generalize (zenon_Ha1 zenon_TM_bi). zenon_intro zenon_Ha7. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ]. % 0.49/0.72 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 0.49/0.72 exact (zenon_Hab zenon_H9c). % 0.49/0.72 generalize (oag6 (reverse_line zenon_TL_bn)). zenon_intro zenon_Hac. % 0.49/0.72 generalize (zenon_Hac zenon_TL_bn). zenon_intro zenon_Had. % 0.49/0.72 generalize (zenon_Had (reverse_line zenon_TN_bs)). zenon_intro zenon_Hae. % 0.49/0.72 apply (zenon_imply_s _ _ zenon_Hae); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Haf ]. % 0.49/0.72 exact (zenon_Hb0 zenon_H88). % 0.49/0.72 apply (zenon_or_s _ _ zenon_Haf); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H31 ]. % 0.49/0.72 exact (zenon_Haa zenon_Hb1). % 0.49/0.72 apply (zenon_L17_ zenon_TM_bi zenon_TN_bs zenon_TL_bn); trivial. % 0.49/0.72 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H72 ]. % 0.49/0.72 apply (zenon_and_s _ _ zenon_Hb2). zenon_intro zenon_H97. zenon_intro zenon_Hb3. % 0.49/0.72 exact (zenon_Ha5 zenon_Hb3). % 0.49/0.72 apply (zenon_L16_ zenon_TL_bn zenon_TM_bi zenon_TN_bs); trivial. % 0.49/0.72 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H85 | zenon_intro zenon_H48 ]. % 0.49/0.72 apply (zenon_L18_ zenon_TL_bn); trivial. % 0.49/0.72 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H3f. zenon_intro zenon_H49. % 0.49/0.72 exact (zenon_H4e zenon_H3f). % 0.49/0.72 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H3f | zenon_intro zenon_Hb4 ]. % 0.49/0.72 apply (zenon_L20_ zenon_TL_bn zenon_TN_bs zenon_TM_bi); trivial. % 0.49/0.72 exact (zenon_H91 zenon_Hb4). % 0.49/0.72 Qed. % 0.49/0.72 % SZS output end Proof % 0.49/0.72 (* END-PROOF *) % 0.49/0.72 nodes searched: 12921 % 0.49/0.72 max branch formulas: 1474 % 0.49/0.72 proof nodes created: 655 % 0.49/0.72 formulas created: 27116 % 0.49/0.72 %------------------------------------------------------------------------------