%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n009.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 07:00:40 EDT 2022 % Result : Theorem 0.54s 0.73s % Output : Proof 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.14 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n009.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jun 18 04:46:23 EDT 2022 % 0.14/0.35 % CPUTime : % 0.54/0.73 (* PROOF-FOUND *) % 0.54/0.73 % SZS status Theorem % 0.54/0.73 (* BEGIN-PROOF *) % 0.54/0.73 % SZS output start Proof % 0.54/0.73 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Y X) Z)))))). % 0.54/0.73 Proof. % 0.54/0.73 assert (zenon_L1_ : forall (zenon_TX_bl : zenon_U), (convergent_lines zenon_TX_bl zenon_TX_bl) -> False). % 0.54/0.73 do 1 intro. intros zenon_H24. % 0.54/0.73 generalize (apart3 zenon_TX_bl). zenon_intro zenon_H26. % 0.54/0.73 exact (zenon_H26 zenon_H24). % 0.54/0.73 (* end of lemma zenon_L1_ *) % 0.54/0.73 assert (zenon_L2_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_bl : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bl Y)->(~(apart_point_and_line (intersection_point zenon_TX_bl Y) zenon_TX_bl)))) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) zenon_TX_bl) -> False). % 0.54/0.73 do 2 intro. intros zenon_H27 zenon_H28 zenon_H29. % 0.54/0.73 generalize (zenon_H27 zenon_TY_bq). zenon_intro zenon_H2b. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.54/0.73 exact (zenon_H2d zenon_H28). % 0.54/0.73 exact (zenon_H2c zenon_H29). % 0.54/0.73 (* end of lemma zenon_L2_ *) % 0.54/0.73 assert (zenon_L3_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_bl : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (~(convergent_lines zenon_TY_bq zenon_TX_bl)) -> False). % 0.54/0.73 do 2 intro. intros zenon_H2e zenon_H28 zenon_H2f. % 0.54/0.73 generalize (zenon_H2e zenon_TX_bl). zenon_intro zenon_H30. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H2d | zenon_intro zenon_H31 ]. % 0.54/0.73 exact (zenon_H2d zenon_H28). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H24 | zenon_intro zenon_H32 ]. % 0.54/0.73 apply (zenon_L1_ zenon_TX_bl); trivial. % 0.54/0.73 exact (zenon_H2f zenon_H32). % 0.54/0.73 (* end of lemma zenon_L3_ *) % 0.54/0.73 assert (zenon_L4_ : forall (zenon_TX_bl : zenon_U) (zenon_TY_bq : zenon_U), (apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) zenon_TX_bl) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> False). % 0.54/0.73 do 2 intro. intros zenon_H33 zenon_H28 zenon_H2e. % 0.54/0.73 generalize (ci4 zenon_TY_bq). zenon_intro zenon_H34. % 0.54/0.73 generalize (zenon_H34 zenon_TX_bl). zenon_intro zenon_H35. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H2f | zenon_intro zenon_H36 ]. % 0.54/0.73 apply (zenon_L3_ zenon_TY_bq zenon_TX_bl); trivial. % 0.54/0.73 exact (zenon_H36 zenon_H33). % 0.54/0.73 (* end of lemma zenon_L4_ *) % 0.54/0.73 assert (zenon_L5_ : forall (zenon_TX_bl : zenon_U) (zenon_TY_bq : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TY_bq Y)->(~(apart_point_and_line (intersection_point zenon_TY_bq Y) zenon_TY_bq)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) zenon_TY_bq) -> False). % 0.54/0.73 do 2 intro. intros zenon_H37 zenon_H2e zenon_H28 zenon_H38. % 0.54/0.73 generalize (zenon_H37 zenon_TX_bl). zenon_intro zenon_H39. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H2f | zenon_intro zenon_H3a ]. % 0.54/0.73 apply (zenon_L3_ zenon_TY_bq zenon_TX_bl); trivial. % 0.54/0.73 exact (zenon_H3a zenon_H38). % 0.54/0.73 (* end of lemma zenon_L5_ *) % 0.54/0.73 assert (zenon_L6_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_bl : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bl zenon_TY_bq) (intersection_point zenon_TY_bq zenon_TX_bl))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) U)\/((apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) V)\/((apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) U)\/(apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) V))))))) -> (forall Y : zenon_U, ((convergent_lines zenon_TY_bq Y)->(~(apart_point_and_line (intersection_point zenon_TY_bq Y) zenon_TY_bq)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> (~(apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) zenon_TY_bq)) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (forall Y : zenon_U, ((convergent_lines zenon_TX_bl Y)->(~(apart_point_and_line (intersection_point zenon_TX_bl Y) zenon_TX_bl)))) -> (distinct_lines zenon_TX_bl zenon_TY_bq) -> (distinct_points (intersection_point zenon_TX_bl zenon_TY_bq) (intersection_point zenon_TY_bq zenon_TX_bl)) -> False). % 0.54/0.73 do 2 intro. intros zenon_H3b zenon_H37 zenon_H2e zenon_H3c zenon_H28 zenon_H27 zenon_H3d zenon_H3e. % 0.54/0.73 generalize (zenon_H3b zenon_TX_bl). zenon_intro zenon_H3f. % 0.54/0.73 generalize (zenon_H3f zenon_TY_bq). zenon_intro zenon_H40. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.54/0.73 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.54/0.73 exact (zenon_H44 zenon_H3e). % 0.54/0.73 exact (zenon_H43 zenon_H3d). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H29 | zenon_intro zenon_H45 ]. % 0.54/0.73 apply (zenon_L2_ zenon_TY_bq zenon_TX_bl); trivial. % 0.54/0.73 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.54/0.73 exact (zenon_H3c zenon_H47). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H33 | zenon_intro zenon_H38 ]. % 0.54/0.73 apply (zenon_L4_ zenon_TX_bl zenon_TY_bq); trivial. % 0.54/0.73 apply (zenon_L5_ zenon_TX_bl zenon_TY_bq); trivial. % 0.54/0.73 (* end of lemma zenon_L6_ *) % 0.54/0.73 apply NNPP. intro zenon_G. % 0.54/0.73 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Y X) Z)))))) zenon_G); [ zenon_intro zenon_H48; idtac ]. % 0.54/0.73 elim zenon_H48. zenon_intro zenon_TX_bl. zenon_intro zenon_H49. % 0.54/0.73 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_bl Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_bl Z)))->((apart_point_and_line (intersection_point zenon_TX_bl Y) Z)->(apart_point_and_line (intersection_point Y zenon_TX_bl) Z))))) zenon_H49); [ zenon_intro zenon_H4a; idtac ]. % 0.54/0.73 elim zenon_H4a. zenon_intro zenon_TY_bq. zenon_intro zenon_H4b. % 0.54/0.73 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_bl zenon_TY_bq)/\((convergent_lines Z zenon_TY_bq)/\(convergent_lines zenon_TX_bl Z)))->((apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) Z)->(apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) Z)))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ]. % 0.54/0.73 elim zenon_H4c. zenon_intro zenon_TZ_cz. zenon_intro zenon_H4e. % 0.54/0.73 apply (zenon_notimply_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.54/0.73 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 0.54/0.73 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H28. zenon_intro zenon_H53. % 0.54/0.73 generalize (apart3 zenon_TY_bq). zenon_intro zenon_H54. % 0.54/0.73 generalize (ax6 zenon_TX_bl). zenon_intro zenon_H55. % 0.54/0.73 generalize (ci3 zenon_TY_bq). zenon_intro zenon_H37. % 0.54/0.73 generalize (zenon_H55 zenon_TY_bq). zenon_intro zenon_H2e. % 0.54/0.73 generalize (ceq3 zenon_TY_bq). zenon_intro zenon_H56. % 0.54/0.73 generalize (ceq2 (intersection_point zenon_TX_bl zenon_TY_bq)). zenon_intro zenon_H57. % 0.54/0.73 generalize (zenon_H57 zenon_TY_bq). zenon_intro zenon_H58. % 0.54/0.73 generalize (ceq1 (intersection_point zenon_TX_bl zenon_TY_bq)). zenon_intro zenon_H59. % 0.54/0.73 generalize (zenon_H59 zenon_TZ_cz). zenon_intro zenon_H5a. % 0.54/0.73 generalize (zenon_H5a (intersection_point zenon_TY_bq zenon_TX_bl)). zenon_intro zenon_H5b. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.54/0.73 exact (zenon_H5d zenon_H52). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H3e | zenon_intro zenon_H5e ]. % 0.54/0.73 generalize (cu1 (intersection_point zenon_TX_bl zenon_TY_bq)). zenon_intro zenon_H5f. % 0.54/0.73 generalize (zenon_H58 zenon_TY_bq). zenon_intro zenon_H60. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H3c | zenon_intro zenon_H61 ]. % 0.54/0.73 generalize (zenon_H5f (intersection_point zenon_TY_bq zenon_TX_bl)). zenon_intro zenon_H3b. % 0.54/0.73 generalize (ci3 zenon_TX_bl). zenon_intro zenon_H27. % 0.54/0.73 generalize (apart2 zenon_TY_bq). zenon_intro zenon_H62. % 0.54/0.73 generalize (apart5 zenon_TX_bl). zenon_intro zenon_H63. % 0.54/0.73 generalize (zenon_H63 zenon_TY_bq). zenon_intro zenon_H64. % 0.54/0.73 generalize (zenon_H64 zenon_TY_bq). zenon_intro zenon_H65. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H43 | zenon_intro zenon_H66 ]. % 0.54/0.73 generalize (zenon_H2e zenon_TX_bl). zenon_intro zenon_H30. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H2d | zenon_intro zenon_H31 ]. % 0.54/0.73 exact (zenon_H2d zenon_H28). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H24 | zenon_intro zenon_H32 ]. % 0.54/0.73 apply (zenon_L1_ zenon_TX_bl); trivial. % 0.54/0.73 generalize (zenon_H56 zenon_TX_bl). zenon_intro zenon_H67. % 0.54/0.73 generalize (zenon_H67 zenon_TY_bq). zenon_intro zenon_H68. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H2f | zenon_intro zenon_H69 ]. % 0.54/0.73 exact (zenon_H2f zenon_H32). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H3d | zenon_intro zenon_H6a ]. % 0.54/0.73 exact (zenon_H43 zenon_H3d). % 0.54/0.73 exact (zenon_H54 zenon_H6a). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H3d | zenon_intro zenon_H6b ]. % 0.54/0.73 apply (zenon_L6_ zenon_TY_bq zenon_TX_bl); trivial. % 0.54/0.73 exact (zenon_H62 zenon_H6b). % 0.54/0.73 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H6b | zenon_intro zenon_H47 ]. % 0.54/0.73 generalize (apart2 zenon_TY_bq). zenon_intro zenon_H62. % 0.54/0.73 exact (zenon_H62 zenon_H6b). % 0.54/0.73 generalize (ci4 zenon_TX_bl). zenon_intro zenon_H6c. % 0.54/0.73 generalize (zenon_H6c zenon_TY_bq). zenon_intro zenon_H6d. % 0.54/0.73 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H2d | zenon_intro zenon_H3c ]. % 0.54/0.73 exact (zenon_H2d zenon_H28). % 0.54/0.73 exact (zenon_H3c zenon_H47). % 0.54/0.73 exact (zenon_H51 zenon_H5e). % 0.54/0.73 Qed. % 0.54/0.73 % SZS output end Proof % 0.54/0.73 (* END-PROOF *) % 0.54/0.73 nodes searched: 10791 % 0.54/0.73 max branch formulas: 1926 % 0.54/0.73 proof nodes created: 644 % 0.54/0.73 formulas created: 33973 % 0.54/0.73 %------------------------------------------------------------------------------