%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 07:00:32 EDT 2022 % Result : Theorem 0.20s 0.54s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO186+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n005.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 : Fri Jun 17 15:34:53 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.54 (* PROOF-FOUND *) % 0.20/0.54 % SZS status Theorem % 0.20/0.54 (* BEGIN-PROOF *) % 0.20/0.54 % SZS output start Proof % 0.20/0.54 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((incident_point_and_line X U)/\(incident_point_and_line X V))))->(equal_points X (intersection_point U V))))))). % 0.20/0.54 Proof. % 0.20/0.54 assert (zenon_L1_ : forall (zenon_TV_bm : zenon_U) (zenon_TU_bn : zenon_U), (apart_point_and_line (intersection_point zenon_TU_bn zenon_TV_bm) zenon_TV_bm) -> (convergent_lines zenon_TU_bn zenon_TV_bm) -> False). % 0.20/0.54 do 2 intro. intros zenon_H24 zenon_H25. % 0.20/0.54 generalize (ci4 zenon_TU_bn). zenon_intro zenon_H28. % 0.20/0.54 generalize (zenon_H28 zenon_TV_bm). zenon_intro zenon_H29. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.20/0.54 exact (zenon_H2b zenon_H25). % 0.20/0.54 exact (zenon_H2a zenon_H24). % 0.20/0.54 (* end of lemma zenon_L1_ *) % 0.20/0.54 assert (zenon_L2_ : forall (zenon_TV_bm : zenon_U) (zenon_TU_bn : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_bn Y)->(~(apart_point_and_line (intersection_point zenon_TU_bn Y) zenon_TU_bn)))) -> (convergent_lines zenon_TU_bn zenon_TV_bm) -> (apart_point_and_line (intersection_point zenon_TU_bn zenon_TV_bm) zenon_TU_bn) -> False). % 0.20/0.54 do 2 intro. intros zenon_H2c zenon_H25 zenon_H2d. % 0.20/0.54 generalize (zenon_H2c zenon_TV_bm). zenon_intro zenon_H2e. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2b | zenon_intro zenon_H2f ]. % 0.20/0.54 exact (zenon_H2b zenon_H25). % 0.20/0.54 exact (zenon_H2f zenon_H2d). % 0.20/0.54 (* end of lemma zenon_L2_ *) % 0.20/0.54 apply NNPP. intro zenon_G. % 0.20/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((incident_point_and_line X U)/\(incident_point_and_line X V))))->(equal_points X (intersection_point U V))))))) zenon_G); [ zenon_intro zenon_H30; idtac ]. % 0.20/0.54 elim zenon_H30. zenon_intro zenon_TX_bx. zenon_intro zenon_H32. % 0.20/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bx Y)/\((convergent_lines U V)/\((incident_point_and_line zenon_TX_bx U)/\(incident_point_and_line zenon_TX_bx V))))->(equal_points zenon_TX_bx (intersection_point U V)))))) zenon_H32); [ zenon_intro zenon_H33; idtac ]. % 0.20/0.54 elim zenon_H33. zenon_intro zenon_TY_ca. zenon_intro zenon_H35. % 0.20/0.54 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bx zenon_TY_ca)/\((convergent_lines U V)/\((incident_point_and_line zenon_TX_bx U)/\(incident_point_and_line zenon_TX_bx V))))->(equal_points zenon_TX_bx (intersection_point U V))))) zenon_H35); [ zenon_intro zenon_H36; idtac ]. % 0.20/0.54 elim zenon_H36. zenon_intro zenon_TU_bn. zenon_intro zenon_H37. % 0.20/0.54 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bx zenon_TY_ca)/\((convergent_lines zenon_TU_bn V)/\((incident_point_and_line zenon_TX_bx zenon_TU_bn)/\(incident_point_and_line zenon_TX_bx V))))->(equal_points zenon_TX_bx (intersection_point zenon_TU_bn V)))) zenon_H37); [ zenon_intro zenon_H38; idtac ]. % 0.20/0.54 elim zenon_H38. zenon_intro zenon_TV_bm. zenon_intro zenon_H39. % 0.20/0.54 apply (zenon_notimply_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H25. zenon_intro zenon_H3e. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.20/0.54 generalize (a4 zenon_TX_bx). zenon_intro zenon_H41. % 0.20/0.54 generalize (zenon_H41 zenon_TU_bn). zenon_intro zenon_H42. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H45; zenon_intro zenon_H44 | zenon_intro zenon_H40; zenon_intro zenon_H43 ]. % 0.20/0.54 exact (zenon_H45 zenon_H40). % 0.20/0.54 generalize (a4 zenon_TX_bx). zenon_intro zenon_H41. % 0.20/0.54 generalize (zenon_H41 zenon_TV_bm). zenon_intro zenon_H46. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H49; zenon_intro zenon_H48 | zenon_intro zenon_H3f; zenon_intro zenon_H47 ]. % 0.20/0.54 exact (zenon_H49 zenon_H3f). % 0.20/0.54 generalize (ax1 zenon_TX_bx). zenon_intro zenon_H4a. % 0.20/0.54 generalize (zenon_H4a (intersection_point zenon_TU_bn zenon_TV_bm)). zenon_intro zenon_H4b. % 0.20/0.54 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H3a; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ]. % 0.20/0.54 apply zenon_H4e. zenon_intro zenon_H4f. % 0.20/0.54 generalize (ceq3 zenon_TU_bn). zenon_intro zenon_H50. % 0.20/0.54 generalize (zenon_H50 zenon_TV_bm). zenon_intro zenon_H51. % 0.20/0.54 generalize (apart4 zenon_TX_bx). zenon_intro zenon_H52. % 0.20/0.54 generalize (apart1 zenon_TX_bx). zenon_intro zenon_H53. % 0.20/0.54 generalize (zenon_H52 (intersection_point zenon_TU_bn zenon_TV_bm)). zenon_intro zenon_H54. % 0.20/0.54 generalize (zenon_H54 zenon_TX_bx). zenon_intro zenon_H55. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H4c | zenon_intro zenon_H56 ]. % 0.20/0.54 exact (zenon_H4c zenon_H4f). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ]. % 0.20/0.54 exact (zenon_H53 zenon_H58). % 0.20/0.54 generalize (cu1 (intersection_point zenon_TU_bn zenon_TV_bm)). zenon_intro zenon_H59. % 0.20/0.54 generalize (zenon_H59 zenon_TX_bx). zenon_intro zenon_H5a. % 0.20/0.54 generalize (ci3 zenon_TU_bn). zenon_intro zenon_H2c. % 0.20/0.54 generalize (apart3 zenon_TU_bn). zenon_intro zenon_H5b. % 0.20/0.54 generalize (zenon_H51 zenon_TU_bn). zenon_intro zenon_H5c. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H2b | zenon_intro zenon_H5d ]. % 0.20/0.54 exact (zenon_H2b zenon_H25). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 0.20/0.54 generalize (zenon_H5a zenon_TV_bm). zenon_intro zenon_H60. % 0.20/0.54 generalize (zenon_H60 zenon_TU_bn). zenon_intro zenon_H61. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 0.20/0.54 exact (zenon_H65 zenon_H57). % 0.20/0.54 exact (zenon_H64 zenon_H5f). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H24 | zenon_intro zenon_H66 ]. % 0.20/0.54 apply (zenon_L1_ zenon_TV_bm zenon_TU_bn); trivial. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H2d | zenon_intro zenon_H67 ]. % 0.20/0.54 apply (zenon_L2_ zenon_TV_bm zenon_TU_bn); trivial. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 0.20/0.54 exact (zenon_H47 zenon_H69). % 0.20/0.54 exact (zenon_H43 zenon_H68). % 0.20/0.54 exact (zenon_H5b zenon_H5e). % 0.20/0.54 exact (zenon_H3a zenon_H4d). % 0.20/0.54 Qed. % 0.20/0.54 % SZS output end Proof % 0.20/0.54 (* END-PROOF *) % 0.20/0.54 nodes searched: 2099 % 0.20/0.54 max branch formulas: 863 % 0.20/0.54 proof nodes created: 190 % 0.20/0.54 formulas created: 7136 % 0.20/0.54 %------------------------------------------------------------------------------