%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO194+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n007.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 07:00:38 EDT 2022 % Result : Theorem 0.46s 0.62s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO194+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.14 % Command : run_zenon %s %d % 0.15/0.36 % Computer : n007.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Sat Jun 18 11:12:28 EDT 2022 % 0.15/0.36 % CPUTime : % 0.46/0.62 (* PROOF-FOUND *) % 0.46/0.62 % SZS status Theorem % 0.46/0.62 (* BEGIN-PROOF *) % 0.46/0.62 % SZS output start Proof % 0.46/0.62 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 X Z) Y)))))). % 0.46/0.62 Proof. % 0.46/0.62 assert (zenon_L1_ : forall (zenon_TY_r : zenon_U) (zenon_TX_s : zenon_U), (apart_point_and_line (intersection_point zenon_TX_s zenon_TY_r) zenon_TY_r) -> (convergent_lines zenon_TX_s zenon_TY_r) -> False). % 0.46/0.62 do 2 intro. intros zenon_Hf zenon_H10. % 0.46/0.62 generalize (ci4 zenon_TX_s). zenon_intro zenon_H13. % 0.46/0.62 generalize (zenon_H13 zenon_TY_r). zenon_intro zenon_H14. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.46/0.62 exact (zenon_H16 zenon_H10). % 0.46/0.62 exact (zenon_H15 zenon_Hf). % 0.46/0.62 (* end of lemma zenon_L1_ *) % 0.46/0.62 assert (zenon_L2_ : forall (zenon_TY_r : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_s Y)->(~(apart_point_and_line (intersection_point zenon_TX_s Y) zenon_TX_s)))) -> (convergent_lines zenon_TX_s zenon_TY_r) -> (apart_point_and_line (intersection_point zenon_TX_s zenon_TY_r) zenon_TX_s) -> False). % 0.46/0.62 do 2 intro. intros zenon_H17 zenon_H10 zenon_H18. % 0.46/0.62 generalize (zenon_H17 zenon_TY_r). zenon_intro zenon_H19. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H16 | zenon_intro zenon_H1a ]. % 0.46/0.62 exact (zenon_H16 zenon_H10). % 0.46/0.62 exact (zenon_H1a zenon_H18). % 0.46/0.62 (* end of lemma zenon_L2_ *) % 0.46/0.62 assert (zenon_L3_ : forall (zenon_TY_r : zenon_U) (zenon_TX_s : zenon_U), (apart_point_and_line (intersection_point zenon_TX_s zenon_TY_r) zenon_TX_s) -> (convergent_lines zenon_TX_s zenon_TY_r) -> False). % 0.46/0.62 do 2 intro. intros zenon_H18 zenon_H10. % 0.46/0.62 generalize (ci3 zenon_TX_s). zenon_intro zenon_H17. % 0.46/0.62 apply (zenon_L2_ zenon_TY_r zenon_TX_s); trivial. % 0.46/0.62 (* end of lemma zenon_L3_ *) % 0.46/0.62 assert (zenon_L4_ : forall (zenon_TY_r : zenon_U) (zenon_TZ_bd : zenon_U), (apart_point_and_line (intersection_point zenon_TZ_bd zenon_TY_r) zenon_TY_r) -> (convergent_lines zenon_TZ_bd zenon_TY_r) -> False). % 0.46/0.62 do 2 intro. intros zenon_H1b zenon_H1c. % 0.46/0.62 generalize (ci4 zenon_TZ_bd). zenon_intro zenon_H1e. % 0.46/0.62 generalize (zenon_H1e zenon_TY_r). zenon_intro zenon_H1f. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.46/0.62 exact (zenon_H21 zenon_H1c). % 0.46/0.62 exact (zenon_H20 zenon_H1b). % 0.46/0.62 (* end of lemma zenon_L4_ *) % 0.46/0.62 assert (zenon_L5_ : forall (zenon_TZ_bd : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_s Y)->(~(apart_point_and_line (intersection_point zenon_TX_s Y) zenon_TX_s)))) -> (convergent_lines zenon_TX_s zenon_TZ_bd) -> (apart_point_and_line (intersection_point zenon_TX_s zenon_TZ_bd) zenon_TX_s) -> False). % 0.46/0.62 do 2 intro. intros zenon_H17 zenon_H22 zenon_H23. % 0.46/0.62 generalize (zenon_H17 zenon_TZ_bd). zenon_intro zenon_H24. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.46/0.62 exact (zenon_H26 zenon_H22). % 0.46/0.62 exact (zenon_H25 zenon_H23). % 0.46/0.62 (* end of lemma zenon_L5_ *) % 0.46/0.62 assert (zenon_L6_ : forall (zenon_TX_s : zenon_U) (zenon_TY_r : zenon_U) (zenon_TZ_bd : zenon_U), (convergent_lines zenon_TZ_bd zenon_TY_r) -> (~(distinct_lines zenon_TY_r zenon_TY_r)) -> (apart_point_and_line (intersection_point zenon_TZ_bd zenon_TY_r) zenon_TX_s) -> (distinct_lines zenon_TY_r zenon_TZ_bd) -> (~(apart_point_and_line (intersection_point zenon_TZ_bd zenon_TY_r) zenon_TZ_bd)) -> (~(apart_point_and_line (intersection_point zenon_TX_s zenon_TZ_bd) zenon_TY_r)) -> (convergent_lines zenon_TX_s zenon_TZ_bd) -> (~(distinct_lines zenon_TZ_bd zenon_TZ_bd)) -> False). % 0.46/0.62 do 3 intro. intros zenon_H1c zenon_H27 zenon_H28 zenon_H29 zenon_H2a zenon_H2b zenon_H22 zenon_H2c. % 0.46/0.62 generalize (ci3 zenon_TX_s). zenon_intro zenon_H17. % 0.46/0.62 generalize (ceq2 (intersection_point zenon_TZ_bd zenon_TY_r)). zenon_intro zenon_H2d. % 0.46/0.62 generalize (apart2 zenon_TX_s). zenon_intro zenon_H2e. % 0.46/0.62 generalize (ceq1 (intersection_point zenon_TZ_bd zenon_TY_r)). zenon_intro zenon_H2f. % 0.46/0.62 generalize (zenon_H2f zenon_TX_s). zenon_intro zenon_H30. % 0.46/0.62 generalize (cu1 (intersection_point zenon_TZ_bd zenon_TY_r)). zenon_intro zenon_H31. % 0.46/0.62 generalize (zenon_H2d zenon_TY_r). zenon_intro zenon_H32. % 0.46/0.62 generalize (zenon_H32 zenon_TY_r). zenon_intro zenon_H33. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H20 | zenon_intro zenon_H34 ]. % 0.46/0.62 generalize (ceq2 (intersection_point zenon_TX_s zenon_TZ_bd)). zenon_intro zenon_H35. % 0.46/0.62 generalize (zenon_H35 zenon_TZ_bd). zenon_intro zenon_H36. % 0.46/0.62 generalize (zenon_H35 zenon_TX_s). zenon_intro zenon_H37. % 0.46/0.62 generalize (zenon_H36 zenon_TZ_bd). zenon_intro zenon_H38. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.46/0.62 generalize (zenon_H37 zenon_TX_s). zenon_intro zenon_H3b. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H25 | zenon_intro zenon_H3c ]. % 0.46/0.62 generalize (zenon_H30 (intersection_point zenon_TX_s zenon_TZ_bd)). zenon_intro zenon_H3d. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 0.46/0.62 exact (zenon_H3f zenon_H28). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H23 ]. % 0.46/0.62 generalize (zenon_H31 (intersection_point zenon_TX_s zenon_TZ_bd)). zenon_intro zenon_H41. % 0.46/0.62 generalize (zenon_H41 zenon_TY_r). zenon_intro zenon_H42. % 0.46/0.62 generalize (zenon_H42 zenon_TZ_bd). zenon_intro zenon_H43. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.46/0.62 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.46/0.62 exact (zenon_H47 zenon_H40). % 0.46/0.62 exact (zenon_H46 zenon_H29). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H1b | zenon_intro zenon_H48 ]. % 0.46/0.62 exact (zenon_H20 zenon_H1b). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.46/0.62 exact (zenon_H2a zenon_H4a). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.46/0.62 exact (zenon_H2b zenon_H4c). % 0.46/0.62 exact (zenon_H3a zenon_H4b). % 0.46/0.62 exact (zenon_H25 zenon_H23). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H4d | zenon_intro zenon_H23 ]. % 0.46/0.62 exact (zenon_H2e zenon_H4d). % 0.46/0.62 apply (zenon_L5_ zenon_TZ_bd zenon_TX_s); trivial. % 0.46/0.62 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H4e | zenon_intro zenon_H4b ]. % 0.46/0.62 exact (zenon_H2c zenon_H4e). % 0.46/0.62 generalize (ci4 zenon_TX_s). zenon_intro zenon_H13. % 0.46/0.62 generalize (zenon_H13 zenon_TZ_bd). zenon_intro zenon_H4f. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H26 | zenon_intro zenon_H3a ]. % 0.46/0.62 exact (zenon_H26 zenon_H22). % 0.46/0.62 exact (zenon_H3a zenon_H4b). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H50 | zenon_intro zenon_H1b ]. % 0.46/0.62 exact (zenon_H27 zenon_H50). % 0.46/0.62 apply (zenon_L4_ zenon_TY_r zenon_TZ_bd); trivial. % 0.46/0.62 (* end of lemma zenon_L6_ *) % 0.46/0.62 apply NNPP. intro zenon_G. % 0.46/0.62 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 X Z) Y)))))) zenon_G); [ zenon_intro zenon_H51; idtac ]. % 0.46/0.62 elim zenon_H51. zenon_intro zenon_TX_s. zenon_intro zenon_H52. % 0.46/0.62 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_s Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_s Z)))->((apart_point_and_line (intersection_point zenon_TX_s Y) Z)->(apart_point_and_line (intersection_point zenon_TX_s Z) Y))))) zenon_H52); [ zenon_intro zenon_H53; idtac ]. % 0.46/0.62 elim zenon_H53. zenon_intro zenon_TY_r. zenon_intro zenon_H54. % 0.46/0.62 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_s zenon_TY_r)/\((convergent_lines Z zenon_TY_r)/\(convergent_lines zenon_TX_s Z)))->((apart_point_and_line (intersection_point zenon_TX_s zenon_TY_r) Z)->(apart_point_and_line (intersection_point zenon_TX_s Z) zenon_TY_r)))) zenon_H54); [ zenon_intro zenon_H55; idtac ]. % 0.46/0.62 elim zenon_H55. zenon_intro zenon_TZ_bd. zenon_intro zenon_H56. % 0.46/0.62 apply (zenon_notimply_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 0.46/0.62 apply (zenon_notimply_s _ _ zenon_H57). zenon_intro zenon_H59. zenon_intro zenon_H2b. % 0.46/0.62 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H10. zenon_intro zenon_H5a. % 0.46/0.62 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H1c. zenon_intro zenon_H22. % 0.46/0.62 generalize (ci3 zenon_TZ_bd). zenon_intro zenon_H5b. % 0.46/0.62 generalize (apart3 zenon_TZ_bd). zenon_intro zenon_H5c. % 0.46/0.62 generalize (zenon_H5b zenon_TY_r). zenon_intro zenon_H5d. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H21 | zenon_intro zenon_H2a ]. % 0.46/0.62 exact (zenon_H21 zenon_H1c). % 0.46/0.62 generalize (ceq3 zenon_TX_s). zenon_intro zenon_H5e. % 0.46/0.62 generalize (ceq3 zenon_TZ_bd). zenon_intro zenon_H5f. % 0.46/0.62 generalize (zenon_H5e zenon_TY_r). zenon_intro zenon_H60. % 0.46/0.62 generalize (zenon_H5f zenon_TY_r). zenon_intro zenon_H61. % 0.46/0.62 generalize (zenon_H61 zenon_TZ_bd). zenon_intro zenon_H62. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H21 | zenon_intro zenon_H63 ]. % 0.46/0.62 exact (zenon_H21 zenon_H1c). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H29 | zenon_intro zenon_H64 ]. % 0.46/0.62 generalize (apart2 zenon_TZ_bd). zenon_intro zenon_H2c. % 0.46/0.62 generalize (ceq1 (intersection_point zenon_TX_s zenon_TY_r)). zenon_intro zenon_H65. % 0.46/0.62 generalize (zenon_H65 zenon_TZ_bd). zenon_intro zenon_H66. % 0.46/0.62 generalize (zenon_H66 (intersection_point zenon_TZ_bd zenon_TY_r)). zenon_intro zenon_H67. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 0.46/0.62 exact (zenon_H69 zenon_H59). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H4a ]. % 0.46/0.62 generalize (cu1 (intersection_point zenon_TX_s zenon_TY_r)). zenon_intro zenon_H6b. % 0.46/0.62 generalize (zenon_H6b (intersection_point zenon_TZ_bd zenon_TY_r)). zenon_intro zenon_H6c. % 0.46/0.62 generalize (apart2 zenon_TY_r). zenon_intro zenon_H27. % 0.46/0.62 generalize (zenon_H6c zenon_TY_r). zenon_intro zenon_H6d. % 0.46/0.62 generalize (apart3 zenon_TX_s). zenon_intro zenon_H6e. % 0.46/0.62 generalize (zenon_H60 zenon_TX_s). zenon_intro zenon_H6f. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H16 | zenon_intro zenon_H70 ]. % 0.46/0.62 exact (zenon_H16 zenon_H10). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H72 | zenon_intro zenon_H71 ]. % 0.46/0.62 generalize (zenon_H6d zenon_TX_s). zenon_intro zenon_H73. % 0.46/0.62 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 0.46/0.62 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 0.46/0.62 exact (zenon_H77 zenon_H6a). % 0.46/0.62 exact (zenon_H76 zenon_H72). % 0.46/0.62 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_Hf | zenon_intro zenon_H78 ]. % 0.46/0.62 apply (zenon_L1_ zenon_TY_r zenon_TX_s); trivial. % 0.46/0.62 apply (zenon_or_s _ _ zenon_H78); [ zenon_intro zenon_H18 | zenon_intro zenon_H79 ]. % 0.46/0.62 apply (zenon_L3_ zenon_TY_r zenon_TX_s); trivial. % 0.46/0.62 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H1b | zenon_intro zenon_H28 ]. % 0.46/0.62 apply (zenon_L4_ zenon_TY_r zenon_TZ_bd); trivial. % 0.46/0.62 apply (zenon_L6_ zenon_TX_s zenon_TY_r zenon_TZ_bd); trivial. % 0.46/0.62 exact (zenon_H6e zenon_H71). % 0.46/0.62 exact (zenon_H2a zenon_H4a). % 0.46/0.62 exact (zenon_H5c zenon_H64). % 0.46/0.62 Qed. % 0.46/0.62 % SZS output end Proof % 0.46/0.62 (* END-PROOF *) % 0.46/0.62 nodes searched: 3722 % 0.46/0.62 max branch formulas: 1202 % 0.46/0.62 proof nodes created: 394 % 0.46/0.62 formulas created: 13933 % 0.46/0.62 %------------------------------------------------------------------------------