%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO255+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 07:01:22 EDT 2022 % Result : Theorem 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO255+3 : TPTP v8.1.0. Released v4.0.0. % 0.04/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 14:36:08 EDT 2022 % 0.12/0.33 % CPUTime : % 0.46/0.64 (* PROOF-FOUND *) % 0.46/0.64 % SZS status Theorem % 0.46/0.64 (* BEGIN-PROOF *) % 0.46/0.64 % SZS output start Proof % 0.46/0.64 Theorem con : (forall L : zenon_U, (forall A : zenon_U, (forall B : zenon_U, (~((before_on_line L A B)/\(before_on_line L B A)))))). % 0.46/0.64 Proof. % 0.46/0.64 assert (zenon_L1_ : forall (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U), ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (line_connecting zenon_TB_bn zenon_TA_bo))/\(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> False). % 0.46/0.64 do 2 intro. intros zenon_H25 zenon_H26. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.46/0.64 exact (zenon_H26 zenon_H29). % 0.46/0.64 (* end of lemma zenon_L1_ *) % 0.46/0.64 assert (zenon_L2_ : forall (zenon_TA_bo : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TL_bt : zenon_U), ((unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))/\(unequally_directed_lines zenon_TL_bt (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H2b zenon_H2c. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 0.46/0.64 exact (zenon_H2c zenon_H2f). % 0.46/0.64 (* end of lemma zenon_L2_ *) % 0.46/0.64 assert (zenon_L3_ : forall (zenon_TL_bt : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U), (unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) zenon_TL_bt) -> (unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line zenon_TL_bt)) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H30 zenon_H31 zenon_H26 zenon_H2c. % 0.46/0.64 generalize (ax7_basics (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H32. % 0.46/0.64 generalize (zenon_H32 zenon_TL_bt). zenon_intro zenon_H33. % 0.46/0.64 generalize (zenon_H33 (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H34. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.46/0.64 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.46/0.64 exact (zenon_H38 zenon_H30). % 0.46/0.64 exact (zenon_H37 zenon_H31). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H25 | zenon_intro zenon_H2b ]. % 0.46/0.64 apply (zenon_L1_ zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 apply (zenon_L2_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 (* end of lemma zenon_L3_ *) % 0.46/0.64 assert (zenon_L4_ : forall (zenon_TL_bt : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U), ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) zenon_TL_bt)/\(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line zenon_TL_bt))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H39 zenon_H2c zenon_H26. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H30. zenon_intro zenon_H31. % 0.46/0.64 apply (zenon_L3_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 (* end of lemma zenon_L4_ *) % 0.46/0.64 assert (zenon_L5_ : forall (zenon_TL_bt : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U), (forall M : zenon_U, (forall N : zenon_U, (((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) M)/\(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line M)))->(((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) N)/\(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line N)))\/((unequally_directed_lines M N)/\(unequally_directed_lines M (reverse_line N))))))) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line zenon_TL_bt))) -> (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) M)->((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) N)\/(unequally_directed_lines M N))))) -> (forall M : zenon_U, ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) M)\/(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line M)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))) -> (unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) zenon_TL_bt) -> (forall N : zenon_U, ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) zenon_TL_bt)->((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) N)\/(unequally_directed_lines zenon_TL_bt N)))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H32 zenon_H26 zenon_H2c zenon_H37 zenon_H3a zenon_H3b zenon_H3c zenon_H30 zenon_H3d. % 0.46/0.64 generalize (zenon_H32 (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H3e. % 0.46/0.64 generalize (zenon_H3e zenon_TL_bt). zenon_intro zenon_H3f. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 0.46/0.64 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.46/0.64 generalize (zenon_H3d (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H44. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H38 | zenon_intro zenon_H45 ]. % 0.46/0.64 exact (zenon_H38 zenon_H30). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.46/0.64 exact (zenon_H43 zenon_H47). % 0.46/0.64 exact (zenon_H3c zenon_H46). % 0.46/0.64 generalize (zenon_H3b (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H48. % 0.46/0.64 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H47 | zenon_intro zenon_H49 ]. % 0.46/0.64 generalize (zenon_H3a (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H4a. % 0.46/0.64 generalize (zenon_H4a (reverse_line zenon_TL_bt)). zenon_intro zenon_H4b. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4c ]. % 0.46/0.64 exact (zenon_H43 zenon_H47). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H31 | zenon_intro zenon_H31 ]. % 0.46/0.64 exact (zenon_H37 zenon_H31). % 0.46/0.64 exact (zenon_H37 zenon_H31). % 0.46/0.64 exact (zenon_H42 zenon_H49). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H39 | zenon_intro zenon_H39 ]. % 0.46/0.64 apply (zenon_L4_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 apply (zenon_L4_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 (* end of lemma zenon_L5_ *) % 0.46/0.64 assert (zenon_L6_ : forall (zenon_TL_bt : zenon_U), ((unequally_directed_lines zenon_TL_bt zenon_TL_bt)/\(unequally_directed_lines zenon_TL_bt (reverse_line zenon_TL_bt))) -> (~(unequally_directed_lines zenon_TL_bt zenon_TL_bt)) -> False). % 0.46/0.64 do 1 intro. intros zenon_H4d zenon_H4e. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.46/0.64 exact (zenon_H4e zenon_H50). % 0.46/0.64 (* end of lemma zenon_L6_ *) % 0.46/0.64 assert (zenon_L7_ : forall (zenon_TA_bo : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TL_bt : zenon_U), (forall N : zenon_U, ((unequally_directed_lines zenon_TL_bt zenon_TL_bt)->((unequally_directed_lines zenon_TL_bt N)\/(unequally_directed_lines zenon_TL_bt N)))) -> (unequally_directed_lines zenon_TL_bt zenon_TL_bt) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H51 zenon_H50 zenon_H2c. % 0.46/0.64 generalize (zenon_H51 (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H52. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H4e | zenon_intro zenon_H53 ]. % 0.46/0.64 exact (zenon_H4e zenon_H50). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H2f | zenon_intro zenon_H2f ]. % 0.46/0.64 exact (zenon_H2c zenon_H2f). % 0.46/0.64 exact (zenon_H2c zenon_H2f). % 0.46/0.64 (* end of lemma zenon_L7_ *) % 0.46/0.64 assert (zenon_L8_ : forall (zenon_TA_bo : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TL_bt : zenon_U), (unequally_directed_lines zenon_TL_bt zenon_TL_bt) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H50 zenon_H2c. % 0.46/0.64 generalize (ax6_basics zenon_TL_bt). zenon_intro zenon_H54. % 0.46/0.64 generalize (zenon_H54 zenon_TL_bt). zenon_intro zenon_H51. % 0.46/0.64 apply (zenon_L7_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 (* end of lemma zenon_L8_ *) % 0.46/0.64 assert (zenon_L9_ : forall (zenon_TA_bo : zenon_U) (zenon_TB_bn : zenon_U), ((unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (line_connecting zenon_TA_bo zenon_TB_bn))/\(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> (~(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> False). % 0.46/0.64 do 2 intro. intros zenon_H55 zenon_H56. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 0.46/0.64 exact (zenon_H56 zenon_H57). % 0.46/0.64 (* end of lemma zenon_L9_ *) % 0.46/0.64 assert (zenon_L10_ : forall (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U) (zenon_TL_bt : zenon_U), ((unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))/\(unequally_directed_lines zenon_TL_bt (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H59 zenon_H3c. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H46. zenon_intro zenon_H5a. % 0.46/0.64 exact (zenon_H3c zenon_H46). % 0.46/0.64 (* end of lemma zenon_L10_ *) % 0.46/0.64 assert (zenon_L11_ : forall (zenon_TL_bt : zenon_U) (zenon_TA_bo : zenon_U) (zenon_TB_bn : zenon_U), (unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) zenon_TL_bt) -> (unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line zenon_TL_bt)) -> (~(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H5b zenon_H5c zenon_H56 zenon_H3c. % 0.46/0.64 generalize (ax7_basics (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H5d. % 0.46/0.64 generalize (zenon_H5d zenon_TL_bt). zenon_intro zenon_H5e. % 0.46/0.64 generalize (zenon_H5e (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H5f. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 0.46/0.64 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 0.46/0.64 exact (zenon_H63 zenon_H5b). % 0.46/0.64 exact (zenon_H62 zenon_H5c). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H60); [ zenon_intro zenon_H55 | zenon_intro zenon_H59 ]. % 0.46/0.64 apply (zenon_L9_ zenon_TA_bo zenon_TB_bn); trivial. % 0.46/0.64 apply (zenon_L10_ zenon_TB_bn zenon_TA_bo zenon_TL_bt); trivial. % 0.46/0.64 (* end of lemma zenon_L11_ *) % 0.46/0.64 assert (zenon_L12_ : forall (zenon_TL_bt : zenon_U) (zenon_TA_bo : zenon_U) (zenon_TB_bn : zenon_U), ((unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) zenon_TL_bt)/\(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line zenon_TL_bt))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))) -> (~(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H64 zenon_H3c zenon_H56. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H5b. zenon_intro zenon_H5c. % 0.46/0.64 apply (zenon_L11_ zenon_TL_bt zenon_TA_bo zenon_TB_bn); trivial. % 0.46/0.64 (* end of lemma zenon_L12_ *) % 0.46/0.64 assert (zenon_L13_ : forall (zenon_TL_bt : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U), (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) M)->((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) N)\/(unequally_directed_lines M N))))) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) zenon_TL_bt)) -> (unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (line_connecting zenon_TB_bn zenon_TA_bo)) -> (unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line zenon_TL_bt)) -> (~(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))) -> (~(unequally_directed_lines zenon_TL_bt zenon_TL_bt)) -> False). % 0.46/0.64 do 3 intro. intros zenon_H3a zenon_H38 zenon_H2a zenon_H5c zenon_H56 zenon_H3c zenon_H4e. % 0.46/0.64 generalize (ax6_basics (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H65. % 0.46/0.64 generalize (zenon_H65 zenon_TL_bt). zenon_intro zenon_H66. % 0.46/0.64 generalize (zenon_H66 zenon_TL_bt). zenon_intro zenon_H67. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H63 | zenon_intro zenon_H68 ]. % 0.46/0.64 generalize (zenon_H3a (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H69. % 0.46/0.64 generalize (zenon_H69 zenon_TL_bt). zenon_intro zenon_H6a. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.46/0.64 exact (zenon_H6c zenon_H2a). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H30 | zenon_intro zenon_H5b ]. % 0.46/0.64 exact (zenon_H38 zenon_H30). % 0.46/0.64 exact (zenon_H63 zenon_H5b). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H5b | zenon_intro zenon_H50 ]. % 0.46/0.64 apply (zenon_L11_ zenon_TL_bt zenon_TA_bo zenon_TB_bn); trivial. % 0.46/0.64 exact (zenon_H4e zenon_H50). % 0.46/0.64 (* end of lemma zenon_L13_ *) % 0.46/0.64 assert (zenon_L14_ : forall (zenon_TL_bt : zenon_U) (zenon_TB_bn : zenon_U) (zenon_TA_bo : zenon_U), (forall M : zenon_U, ((unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) M)\/(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line M)))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TB_bn zenon_TA_bo))) -> (~(unequally_directed_lines zenon_TL_bt (line_connecting zenon_TA_bo zenon_TB_bn))) -> (~(unequally_directed_lines (line_connecting zenon_TB_bn zenon_TA_bo) (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn)))) -> (unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line zenon_TL_bt)) -> (~(unequally_directed_lines (line_connecting zenon_TA_bo zenon_TB_bn) (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo)))) -> False). % 0.46/0.64 do 3 intro. intros zenon_H3b zenon_H2c zenon_H3c zenon_H56 zenon_H31 zenon_H26. % 0.46/0.64 generalize (zenon_H3b (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H6d. % 0.46/0.64 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.46/0.64 generalize (ax6_basics (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H3a. % 0.46/0.64 generalize (zenon_H3a zenon_TL_bt). zenon_intro zenon_H3d. % 0.46/0.64 generalize (zenon_H3d zenon_TL_bt). zenon_intro zenon_H6e. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H38 | zenon_intro zenon_H6f ]. % 0.46/0.64 generalize (ax6_basics zenon_TL_bt). zenon_intro zenon_H54. % 0.46/0.64 generalize (zenon_H54 zenon_TL_bt). zenon_intro zenon_H51. % 0.46/0.64 generalize (zenon_H51 zenon_TL_bt). zenon_intro zenon_H70. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H4e | zenon_intro zenon_H71 ]. % 0.46/0.64 generalize (ax8_basics (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H72. % 0.46/0.64 generalize (zenon_H72 zenon_TL_bt). zenon_intro zenon_H73. % 0.46/0.64 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 0.46/0.64 generalize (ax6_basics (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H65. % 0.46/0.64 generalize (zenon_H65 zenon_TL_bt). zenon_intro zenon_H66. % 0.46/0.64 generalize (zenon_H66 (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H74. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H74); [ zenon_intro zenon_H63 | zenon_intro zenon_H75 ]. % 0.46/0.64 exact (zenon_H63 zenon_H5b). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H76 | zenon_intro zenon_H2f ]. % 0.46/0.64 generalize (zenon_H65 (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H77. % 0.46/0.64 generalize (ax7_basics (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H5d. % 0.46/0.64 generalize (zenon_H5d zenon_TL_bt). zenon_intro zenon_H5e. % 0.46/0.64 generalize (zenon_H5e zenon_TL_bt). zenon_intro zenon_H78. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H61 | zenon_intro zenon_H79 ]. % 0.46/0.64 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 0.46/0.64 exact (zenon_H63 zenon_H5b). % 0.46/0.64 generalize (zenon_H77 (reverse_line zenon_TL_bt)). zenon_intro zenon_H7a. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 0.46/0.64 exact (zenon_H7c zenon_H76). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H5c | zenon_intro zenon_H5c ]. % 0.46/0.64 exact (zenon_H62 zenon_H5c). % 0.46/0.64 exact (zenon_H62 zenon_H5c). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H64 | zenon_intro zenon_H4d ]. % 0.46/0.64 apply (zenon_L12_ zenon_TL_bt zenon_TA_bo zenon_TB_bn); trivial. % 0.46/0.64 apply (zenon_L6_ zenon_TL_bt); trivial. % 0.46/0.64 exact (zenon_H2c zenon_H2f). % 0.46/0.64 apply (zenon_L13_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H50 | zenon_intro zenon_H50 ]. % 0.46/0.64 apply (zenon_L7_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 apply (zenon_L7_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H30 | zenon_intro zenon_H50 ]. % 0.46/0.64 apply (zenon_L3_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 apply (zenon_L8_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 exact (zenon_H26 zenon_H29). % 0.46/0.64 (* end of lemma zenon_L14_ *) % 0.46/0.64 apply NNPP. intro zenon_G. % 0.46/0.64 apply (zenon_notallex_s (fun L : zenon_U => (forall A : zenon_U, (forall B : zenon_U, (~((before_on_line L A B)/\(before_on_line L B A)))))) zenon_G); [ zenon_intro zenon_H7d; idtac ]. % 0.46/0.64 elim zenon_H7d. zenon_intro zenon_TL_bt. zenon_intro zenon_H7e. % 0.46/0.64 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (~((before_on_line zenon_TL_bt A B)/\(before_on_line zenon_TL_bt B A))))) zenon_H7e); [ zenon_intro zenon_H7f; idtac ]. % 0.46/0.64 elim zenon_H7f. zenon_intro zenon_TA_bo. zenon_intro zenon_H80. % 0.46/0.64 apply (zenon_notallex_s (fun B : zenon_U => (~((before_on_line zenon_TL_bt zenon_TA_bo B)/\(before_on_line zenon_TL_bt B zenon_TA_bo)))) zenon_H80); [ zenon_intro zenon_H81; idtac ]. % 0.46/0.64 elim zenon_H81. zenon_intro zenon_TB_bn. zenon_intro zenon_H82. % 0.46/0.64 apply zenon_H82. zenon_intro zenon_H83. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84. % 0.46/0.64 generalize (ax4_defns zenon_TL_bt). zenon_intro zenon_H86. % 0.46/0.64 generalize (zenon_H86 zenon_TA_bo). zenon_intro zenon_H87. % 0.46/0.64 generalize (zenon_H87 zenon_TB_bn). zenon_intro zenon_H88. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_H88); [ zenon_intro zenon_H8b; zenon_intro zenon_H8a | zenon_intro zenon_H85; zenon_intro zenon_H89 ]. % 0.46/0.64 exact (zenon_H8b zenon_H85). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 0.46/0.64 generalize (a4_defns zenon_TL_bt). zenon_intro zenon_H92. % 0.46/0.64 generalize (zenon_H92 (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H93. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H95; zenon_intro zenon_H94 | zenon_intro zenon_H90; zenon_intro zenon_H3c ]. % 0.46/0.64 exact (zenon_H95 zenon_H90). % 0.46/0.64 generalize (ax4_defns zenon_TL_bt). zenon_intro zenon_H86. % 0.46/0.64 generalize (zenon_H86 zenon_TB_bn). zenon_intro zenon_H96. % 0.46/0.64 generalize (zenon_H96 zenon_TA_bo). zenon_intro zenon_H97. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_H97); [ zenon_intro zenon_H9a; zenon_intro zenon_H99 | zenon_intro zenon_H84; zenon_intro zenon_H98 ]. % 0.46/0.64 exact (zenon_H9a zenon_H84). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H98). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H91. zenon_intro zenon_H9d. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H9d). zenon_intro zenon_H8f. zenon_intro zenon_H9e. % 0.46/0.64 generalize (a4_defns zenon_TL_bt). zenon_intro zenon_H92. % 0.46/0.64 generalize (zenon_H92 (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_H9f. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_Ha1; zenon_intro zenon_Ha0 | zenon_intro zenon_H9e; zenon_intro zenon_H2c ]. % 0.46/0.64 exact (zenon_Ha1 zenon_H9e). % 0.46/0.64 generalize (ax9_cons_objs zenon_TA_bo). zenon_intro zenon_Ha2. % 0.46/0.64 generalize (zenon_Ha2 zenon_TB_bn). zenon_intro zenon_Ha3. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_Ha3); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Ha4 ]. % 0.46/0.64 exact (zenon_Ha5 zenon_H8d). % 0.46/0.64 generalize (a4_defns (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_Ha6. % 0.46/0.64 generalize (zenon_Ha6 (reverse_line (line_connecting zenon_TB_bn zenon_TA_bo))). zenon_intro zenon_Ha7. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9; zenon_intro zenon_Ha8 | zenon_intro zenon_Ha4; zenon_intro zenon_H26 ]. % 0.46/0.64 exact (zenon_Ha9 zenon_Ha4). % 0.46/0.64 generalize (ax9_cons_objs zenon_TB_bn). zenon_intro zenon_Haa. % 0.46/0.64 generalize (zenon_Haa zenon_TA_bo). zenon_intro zenon_Hab. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_Had | zenon_intro zenon_Hac ]. % 0.46/0.64 exact (zenon_Had zenon_H9c). % 0.46/0.64 generalize (a4_defns (line_connecting zenon_TB_bn zenon_TA_bo)). zenon_intro zenon_Hae. % 0.46/0.64 generalize (zenon_Hae (reverse_line (line_connecting zenon_TA_bo zenon_TB_bn))). zenon_intro zenon_Haf. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_Haf); [ zenon_intro zenon_Hb1; zenon_intro zenon_Hb0 | zenon_intro zenon_Hac; zenon_intro zenon_H56 ]. % 0.46/0.64 exact (zenon_Hb1 zenon_Hac). % 0.46/0.64 generalize (ax8_basics (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H3b. % 0.46/0.64 generalize (zenon_H3b zenon_TL_bt). zenon_intro zenon_Hb2. % 0.46/0.64 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_H30 | zenon_intro zenon_H31 ]. % 0.46/0.64 generalize (ax6_basics (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H3a. % 0.46/0.64 generalize (zenon_H3a zenon_TL_bt). zenon_intro zenon_H3d. % 0.46/0.64 generalize (ax6_basics zenon_TL_bt). zenon_intro zenon_H54. % 0.46/0.64 generalize (zenon_H54 zenon_TL_bt). zenon_intro zenon_H51. % 0.46/0.64 generalize (zenon_H51 zenon_TL_bt). zenon_intro zenon_H70. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H4e | zenon_intro zenon_H71 ]. % 0.46/0.64 generalize (ax7_basics (line_connecting zenon_TA_bo zenon_TB_bn)). zenon_intro zenon_H32. % 0.46/0.64 generalize (zenon_H32 zenon_TL_bt). zenon_intro zenon_H33. % 0.46/0.64 generalize (zenon_H33 zenon_TL_bt). zenon_intro zenon_Hb3. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb4 ]. % 0.46/0.64 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.46/0.64 exact (zenon_H38 zenon_H30). % 0.46/0.64 apply (zenon_L5_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H39 | zenon_intro zenon_H4d ]. % 0.46/0.64 apply (zenon_L4_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 apply (zenon_L6_ zenon_TL_bt); trivial. % 0.46/0.64 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H50 | zenon_intro zenon_H50 ]. % 0.46/0.64 apply (zenon_L8_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 apply (zenon_L8_ zenon_TA_bo zenon_TB_bn zenon_TL_bt); trivial. % 0.46/0.64 apply (zenon_L14_ zenon_TL_bt zenon_TB_bn zenon_TA_bo); trivial. % 0.46/0.64 Qed. % 0.46/0.64 % SZS output end Proof % 0.46/0.64 (* END-PROOF *) % 0.46/0.64 nodes searched: 9906 % 0.46/0.64 max branch formulas: 1396 % 0.46/0.64 proof nodes created: 543 % 0.46/0.64 formulas created: 25692 % 0.46/0.64 %------------------------------------------------------------------------------