%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 07:00:33 EDT 2022 % Result : Theorem 0.14s 0.45s % Output : Proof 0.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0. % 0.00/0.10 % Command : run_zenon %s %d % 0.10/0.28 % Computer : n032.cluster.edu % 0.10/0.28 % Model : x86_64 x86_64 % 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.28 % Memory : 8042.1875MB % 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.28 % CPULimit : 300 % 0.10/0.28 % WCLimit : 600 % 0.10/0.28 % DateTime : Sat Jun 18 05:08:31 EDT 2022 % 0.10/0.29 % CPUTime : % 0.14/0.45 (* PROOF-FOUND *) % 0.14/0.45 % SZS status Theorem % 0.14/0.45 (* BEGIN-PROOF *) % 0.14/0.45 % SZS output start Proof % 0.14/0.45 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((distinct_points U V)/\((incident_point_and_line X (line_connecting U V))/\(incident_point_and_line Y (line_connecting U V)))))->((incident_point_and_line U (line_connecting X Y))/\(incident_point_and_line V (line_connecting X Y)))))))). % 0.14/0.45 Proof. % 0.14/0.45 assert (zenon_L1_ : forall (zenon_TV_br : zenon_U) (zenon_TU_bs : zenon_U) (zenon_TY_bt : zenon_U) (zenon_TX_bu : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bu zenon_TY_bt)/\(distinct_lines U V))->((apart_point_and_line zenon_TX_bu U)\/((apart_point_and_line zenon_TX_bu V)\/((apart_point_and_line zenon_TY_bt U)\/(apart_point_and_line zenon_TY_bt V))))))) -> (~(apart_point_and_line zenon_TY_bt (line_connecting zenon_TU_bs zenon_TV_br))) -> (~(apart_point_and_line zenon_TY_bt (line_connecting zenon_TX_bu zenon_TY_bt))) -> (~(apart_point_and_line zenon_TX_bu (line_connecting zenon_TU_bs zenon_TV_br))) -> (~(apart_point_and_line zenon_TX_bu (line_connecting zenon_TX_bu zenon_TY_bt))) -> (distinct_lines (line_connecting zenon_TX_bu zenon_TY_bt) (line_connecting zenon_TU_bs zenon_TV_br)) -> (distinct_points zenon_TX_bu zenon_TY_bt) -> False). % 0.14/0.45 do 4 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27 zenon_H28 zenon_H29 zenon_H2a. % 0.14/0.45 generalize (zenon_H24 (line_connecting zenon_TX_bu zenon_TY_bt)). zenon_intro zenon_H2f. % 0.14/0.45 generalize (zenon_H2f (line_connecting zenon_TU_bs zenon_TV_br)). zenon_intro zenon_H30. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.14/0.45 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.14/0.45 exact (zenon_H34 zenon_H2a). % 0.14/0.45 exact (zenon_H33 zenon_H29). % 0.14/0.45 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.14/0.45 exact (zenon_H28 zenon_H36). % 0.14/0.45 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.14/0.45 exact (zenon_H27 zenon_H38). % 0.14/0.45 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.14/0.45 exact (zenon_H26 zenon_H3a). % 0.14/0.45 exact (zenon_H25 zenon_H39). % 0.14/0.45 (* end of lemma zenon_L1_ *) % 0.14/0.45 apply NNPP. intro zenon_G. % 0.14/0.45 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((distinct_points U V)/\((incident_point_and_line X (line_connecting U V))/\(incident_point_and_line Y (line_connecting U V)))))->((incident_point_and_line U (line_connecting X Y))/\(incident_point_and_line V (line_connecting X Y)))))))) zenon_G); [ zenon_intro zenon_H3b; idtac ]. % 0.14/0.45 elim zenon_H3b. zenon_intro zenon_TX_bu. zenon_intro zenon_H3c. % 0.14/0.45 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bu Y)/\((distinct_points U V)/\((incident_point_and_line zenon_TX_bu (line_connecting U V))/\(incident_point_and_line Y (line_connecting U V)))))->((incident_point_and_line U (line_connecting zenon_TX_bu Y))/\(incident_point_and_line V (line_connecting zenon_TX_bu Y))))))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ]. % 0.14/0.45 elim zenon_H3d. zenon_intro zenon_TY_bt. zenon_intro zenon_H3e. % 0.14/0.45 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bu zenon_TY_bt)/\((distinct_points U V)/\((incident_point_and_line zenon_TX_bu (line_connecting U V))/\(incident_point_and_line zenon_TY_bt (line_connecting U V)))))->((incident_point_and_line U (line_connecting zenon_TX_bu zenon_TY_bt))/\(incident_point_and_line V (line_connecting zenon_TX_bu zenon_TY_bt)))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.14/0.45 elim zenon_H3f. zenon_intro zenon_TU_bs. zenon_intro zenon_H40. % 0.14/0.45 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bu zenon_TY_bt)/\((distinct_points zenon_TU_bs V)/\((incident_point_and_line zenon_TX_bu (line_connecting zenon_TU_bs V))/\(incident_point_and_line zenon_TY_bt (line_connecting zenon_TU_bs V)))))->((incident_point_and_line zenon_TU_bs (line_connecting zenon_TX_bu zenon_TY_bt))/\(incident_point_and_line V (line_connecting zenon_TX_bu zenon_TY_bt))))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.14/0.45 elim zenon_H41. zenon_intro zenon_TV_br. zenon_intro zenon_H42. % 0.14/0.45 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.14/0.45 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H2a. zenon_intro zenon_H45. % 0.14/0.45 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H47. zenon_intro zenon_H46. % 0.14/0.45 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.14/0.45 generalize (a4 zenon_TX_bu). zenon_intro zenon_H4a. % 0.14/0.45 generalize (zenon_H4a (line_connecting zenon_TU_bs zenon_TV_br)). zenon_intro zenon_H4b. % 0.14/0.45 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4d; zenon_intro zenon_H4c | zenon_intro zenon_H49; zenon_intro zenon_H27 ]. % 0.14/0.45 exact (zenon_H4d zenon_H49). % 0.14/0.45 generalize (a4 zenon_TY_bt). zenon_intro zenon_H4e. % 0.14/0.45 generalize (zenon_H4e (line_connecting zenon_TU_bs zenon_TV_br)). zenon_intro zenon_H4f. % 0.14/0.45 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H51; zenon_intro zenon_H50 | zenon_intro zenon_H48; zenon_intro zenon_H25 ]. % 0.14/0.45 exact (zenon_H51 zenon_H48). % 0.14/0.45 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.14/0.45 generalize (a4 zenon_TU_bs). zenon_intro zenon_H54. % 0.14/0.45 generalize (zenon_H54 (line_connecting zenon_TX_bu zenon_TY_bt)). zenon_intro zenon_H55. % 0.14/0.45 apply (zenon_equiv_s _ _ zenon_H55); [ zenon_intro zenon_H53; zenon_intro zenon_H58 | zenon_intro zenon_H57; zenon_intro zenon_H56 ]. % 0.14/0.45 apply zenon_H58. zenon_intro zenon_H59. % 0.14/0.45 generalize (cu1 zenon_TX_bu). zenon_intro zenon_H5a. % 0.14/0.45 generalize (ci1 zenon_TX_bu). zenon_intro zenon_H5b. % 0.14/0.45 generalize (zenon_H5a zenon_TY_bt). zenon_intro zenon_H24. % 0.14/0.45 generalize (ci2 zenon_TX_bu). zenon_intro zenon_H5c. % 0.14/0.45 generalize (zenon_H5b zenon_TY_bt). zenon_intro zenon_H5d. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H34 | zenon_intro zenon_H28 ]. % 0.14/0.45 exact (zenon_H34 zenon_H2a). % 0.14/0.45 generalize (zenon_H5c zenon_TY_bt). zenon_intro zenon_H5e. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H34 | zenon_intro zenon_H26 ]. % 0.14/0.45 exact (zenon_H34 zenon_H2a). % 0.14/0.45 generalize (ceq2 zenon_TU_bs). zenon_intro zenon_H5f. % 0.14/0.45 generalize (zenon_H5f (line_connecting zenon_TX_bu zenon_TY_bt)). zenon_intro zenon_H60. % 0.14/0.45 generalize (ci1 zenon_TU_bs). zenon_intro zenon_H61. % 0.14/0.45 generalize (zenon_H61 zenon_TV_br). zenon_intro zenon_H62. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.14/0.45 exact (zenon_H64 zenon_H47). % 0.14/0.45 generalize (zenon_H60 (line_connecting zenon_TU_bs zenon_TV_br)). zenon_intro zenon_H65. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H56 | zenon_intro zenon_H66 ]. % 0.14/0.45 exact (zenon_H56 zenon_H59). % 0.14/0.45 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H29 | zenon_intro zenon_H67 ]. % 0.14/0.45 apply (zenon_L1_ zenon_TV_br zenon_TU_bs zenon_TY_bt zenon_TX_bu); trivial. % 0.14/0.45 exact (zenon_H63 zenon_H67). % 0.14/0.45 exact (zenon_H53 zenon_H57). % 0.14/0.45 generalize (a4 zenon_TV_br). zenon_intro zenon_H68. % 0.14/0.45 generalize (zenon_H68 (line_connecting zenon_TX_bu zenon_TY_bt)). zenon_intro zenon_H69. % 0.14/0.45 apply (zenon_equiv_s _ _ zenon_H69); [ zenon_intro zenon_H52; zenon_intro zenon_H6c | zenon_intro zenon_H6b; zenon_intro zenon_H6a ]. % 0.14/0.45 apply zenon_H6c. zenon_intro zenon_H6d. % 0.14/0.45 generalize (cu1 zenon_TX_bu). zenon_intro zenon_H5a. % 0.14/0.45 generalize (ci1 zenon_TX_bu). zenon_intro zenon_H5b. % 0.14/0.45 generalize (zenon_H5a zenon_TY_bt). zenon_intro zenon_H24. % 0.14/0.45 generalize (ci2 zenon_TX_bu). zenon_intro zenon_H5c. % 0.14/0.45 generalize (zenon_H5b zenon_TY_bt). zenon_intro zenon_H5d. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H34 | zenon_intro zenon_H28 ]. % 0.14/0.45 exact (zenon_H34 zenon_H2a). % 0.14/0.45 generalize (zenon_H5c zenon_TY_bt). zenon_intro zenon_H5e. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H34 | zenon_intro zenon_H26 ]. % 0.14/0.45 exact (zenon_H34 zenon_H2a). % 0.14/0.45 generalize (ceq2 zenon_TV_br). zenon_intro zenon_H6e. % 0.14/0.45 generalize (zenon_H6e (line_connecting zenon_TX_bu zenon_TY_bt)). zenon_intro zenon_H6f. % 0.14/0.45 generalize (ci2 zenon_TU_bs). zenon_intro zenon_H70. % 0.14/0.45 generalize (zenon_H70 zenon_TV_br). zenon_intro zenon_H71. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H64 | zenon_intro zenon_H72 ]. % 0.14/0.45 exact (zenon_H64 zenon_H47). % 0.14/0.45 generalize (zenon_H6f (line_connecting zenon_TU_bs zenon_TV_br)). zenon_intro zenon_H73. % 0.14/0.45 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H6a | zenon_intro zenon_H74 ]. % 0.14/0.45 exact (zenon_H6a zenon_H6d). % 0.14/0.45 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H29 | zenon_intro zenon_H75 ]. % 0.14/0.45 apply (zenon_L1_ zenon_TV_br zenon_TU_bs zenon_TY_bt zenon_TX_bu); trivial. % 0.14/0.45 exact (zenon_H72 zenon_H75). % 0.14/0.45 exact (zenon_H52 zenon_H6b). % 0.14/0.45 Qed. % 0.14/0.45 % SZS output end Proof % 0.14/0.45 (* END-PROOF *) % 0.14/0.45 nodes searched: 3148 % 0.14/0.45 max branch formulas: 976 % 0.14/0.45 proof nodes created: 249 % 0.14/0.45 formulas created: 10410 % 0.14/0.45 %------------------------------------------------------------------------------