%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO215+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 07:00:56 EDT 2022 % Result : Theorem 0.92s 1.10s % Output : Proof 0.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO215+1 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n026.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 : Sat Jun 18 00:51:39 EDT 2022 % 0.12/0.34 % CPUTime : % 0.92/1.10 (* PROOF-FOUND *) % 0.92/1.10 % SZS status Theorem % 0.92/1.10 (* BEGIN-PROOF *) % 0.92/1.10 % SZS output start Proof % 0.92/1.10 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((convergent_lines L M)->((unorthogonal_lines L N)\/(unorthogonal_lines M N)))))). % 0.92/1.10 Proof. % 0.92/1.10 assert (zenon_L1_ : forall (zenon_TL_bc : zenon_U) (zenon_TM_bd : zenon_U) (zenon_TN_be : zenon_U), (distinct_lines zenon_TN_be zenon_TM_bd) -> (~(unorthogonal_lines zenon_TN_be zenon_TL_bc)) -> (~(unorthogonal_lines zenon_TM_bd zenon_TL_bc)) -> (forall Y : zenon_U, ((convergent_lines zenon_TM_bd Y)->(~(apart_point_and_line (intersection_point zenon_TM_bd Y) zenon_TM_bd)))) -> (convergent_lines zenon_TM_bd zenon_TN_be) -> False). % 0.92/1.10 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19 zenon_H1a zenon_H1b. % 0.92/1.10 generalize (ci4 zenon_TM_bd). zenon_intro zenon_H1f. % 0.92/1.10 generalize (zenon_H1f zenon_TN_be). zenon_intro zenon_H20. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.92/1.10 exact (zenon_H22 zenon_H1b). % 0.92/1.10 generalize (zenon_H1a zenon_TN_be). zenon_intro zenon_H23. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H22 | zenon_intro zenon_H24 ]. % 0.92/1.10 exact (zenon_H22 zenon_H1b). % 0.92/1.10 generalize (ouo1 (intersection_point zenon_TM_bd zenon_TN_be)). zenon_intro zenon_H25. % 0.92/1.10 generalize (zenon_H25 zenon_TN_be). zenon_intro zenon_H26. % 0.92/1.10 generalize (zenon_H26 zenon_TM_bd). zenon_intro zenon_H27. % 0.92/1.10 generalize (zenon_H27 zenon_TL_bc). zenon_intro zenon_H28. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.92/1.10 exact (zenon_H2a zenon_H17). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.92/1.10 exact (zenon_H21 zenon_H2c). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.92/1.10 exact (zenon_H24 zenon_H2e). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.92/1.10 exact (zenon_H18 zenon_H30). % 0.92/1.10 exact (zenon_H19 zenon_H2f). % 0.92/1.10 (* end of lemma zenon_L1_ *) % 0.92/1.10 assert (zenon_L2_ : forall (zenon_TN_be : zenon_U) (zenon_TM_bd : zenon_U), ((convergent_lines zenon_TM_bd zenon_TN_be)/\(unorthogonal_lines zenon_TM_bd zenon_TN_be)) -> (~(unorthogonal_lines zenon_TM_bd zenon_TN_be)) -> False). % 0.92/1.10 do 2 intro. intros zenon_H31 zenon_H32. % 0.92/1.10 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H1b. zenon_intro zenon_H33. % 0.92/1.10 exact (zenon_H32 zenon_H33). % 0.92/1.10 (* end of lemma zenon_L2_ *) % 0.92/1.10 assert (zenon_L3_ : forall (zenon_TN_be : zenon_U) (zenon_TL_bc : zenon_U), ((convergent_lines zenon_TL_bc zenon_TN_be)/\(unorthogonal_lines zenon_TL_bc zenon_TN_be)) -> (~(unorthogonal_lines zenon_TL_bc zenon_TN_be)) -> False). % 0.92/1.10 do 2 intro. intros zenon_H34 zenon_H35. % 0.92/1.10 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.92/1.10 exact (zenon_H35 zenon_H36). % 0.92/1.10 (* end of lemma zenon_L3_ *) % 0.92/1.10 assert (zenon_L4_ : forall (zenon_TN_be : zenon_U) (zenon_TL_bc : zenon_U) (zenon_TM_bd : zenon_U), (forall N : zenon_U, (((convergent_lines zenon_TM_bd zenon_TL_bc)/\(unorthogonal_lines zenon_TM_bd zenon_TL_bc))->(((convergent_lines zenon_TM_bd N)/\(unorthogonal_lines zenon_TM_bd N))\/((convergent_lines zenon_TL_bc N)/\(unorthogonal_lines zenon_TL_bc N))))) -> (convergent_lines zenon_TM_bd zenon_TL_bc) -> (distinct_lines zenon_TN_be zenon_TM_bd) -> (~(unorthogonal_lines zenon_TN_be zenon_TL_bc)) -> (forall Y : zenon_U, ((convergent_lines zenon_TM_bd Y)->(~(apart_point_and_line (intersection_point zenon_TM_bd Y) zenon_TM_bd)))) -> (convergent_lines zenon_TM_bd zenon_TN_be) -> (~(unorthogonal_lines zenon_TM_bd zenon_TN_be)) -> (~(unorthogonal_lines zenon_TL_bc zenon_TN_be)) -> False). % 0.92/1.10 do 3 intro. intros zenon_H38 zenon_H39 zenon_H17 zenon_H18 zenon_H1a zenon_H1b zenon_H32 zenon_H35. % 0.92/1.10 generalize (zenon_H38 zenon_TN_be). zenon_intro zenon_H3a. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.92/1.10 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3d | zenon_intro zenon_H19 ]. % 0.92/1.10 exact (zenon_H3d zenon_H39). % 0.92/1.10 apply (zenon_L1_ zenon_TL_bc zenon_TM_bd zenon_TN_be); trivial. % 0.92/1.10 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H31 | zenon_intro zenon_H34 ]. % 0.92/1.10 apply (zenon_L2_ zenon_TN_be zenon_TM_bd); trivial. % 0.92/1.10 apply (zenon_L3_ zenon_TN_be zenon_TL_bc); trivial. % 0.92/1.10 (* end of lemma zenon_L4_ *) % 0.92/1.10 assert (zenon_L5_ : forall (zenon_TN_be : zenon_U), ((convergent_lines zenon_TN_be zenon_TN_be)/\(unorthogonal_lines zenon_TN_be zenon_TN_be)) -> (~(convergent_lines zenon_TN_be zenon_TN_be)) -> False). % 0.92/1.10 do 1 intro. intros zenon_H3e zenon_H3f. % 0.92/1.10 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40. % 0.92/1.10 exact (zenon_H3f zenon_H41). % 0.92/1.10 (* end of lemma zenon_L5_ *) % 0.92/1.10 apply NNPP. intro zenon_G. % 0.92/1.10 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((convergent_lines L M)->((unorthogonal_lines L N)\/(unorthogonal_lines M N)))))) zenon_G); [ zenon_intro zenon_H42; idtac ]. % 0.92/1.10 elim zenon_H42. zenon_intro zenon_TL_bc. zenon_intro zenon_H43. % 0.92/1.10 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((convergent_lines zenon_TL_bc M)->((unorthogonal_lines zenon_TL_bc N)\/(unorthogonal_lines M N))))) zenon_H43); [ zenon_intro zenon_H44; idtac ]. % 0.92/1.10 elim zenon_H44. zenon_intro zenon_TM_bd. zenon_intro zenon_H45. % 0.92/1.10 apply (zenon_notallex_s (fun N : zenon_U => ((convergent_lines zenon_TL_bc zenon_TM_bd)->((unorthogonal_lines zenon_TL_bc N)\/(unorthogonal_lines zenon_TM_bd N)))) zenon_H45); [ zenon_intro zenon_H46; idtac ]. % 0.92/1.10 elim zenon_H46. zenon_intro zenon_TN_be. zenon_intro zenon_H47. % 0.92/1.10 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.92/1.10 apply (zenon_notor_s _ _ zenon_H48). zenon_intro zenon_H35. zenon_intro zenon_H32. % 0.92/1.10 generalize (apart3 zenon_TM_bd). zenon_intro zenon_H4a. % 0.92/1.10 generalize (occu1 zenon_TL_bc). zenon_intro zenon_H4b. % 0.92/1.10 generalize (occu1 zenon_TM_bd). zenon_intro zenon_H4c. % 0.92/1.10 generalize (ax6 zenon_TL_bc). zenon_intro zenon_H4d. % 0.92/1.10 generalize (ci3 zenon_TM_bd). zenon_intro zenon_H1a. % 0.92/1.10 generalize (zenon_H4d zenon_TM_bd). zenon_intro zenon_H4e. % 0.92/1.10 generalize (zenon_H4b zenon_TN_be). zenon_intro zenon_H4f. % 0.92/1.10 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.92/1.10 generalize (zenon_H4c zenon_TN_be). zenon_intro zenon_H50. % 0.92/1.10 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H1b | zenon_intro zenon_H33 ]. % 0.92/1.10 generalize (zenon_H4d zenon_TN_be). zenon_intro zenon_H51. % 0.92/1.10 generalize (apart3 zenon_TN_be). zenon_intro zenon_H3f. % 0.92/1.10 generalize (ceq3 zenon_TM_bd). zenon_intro zenon_H52. % 0.92/1.10 generalize (zenon_H52 zenon_TN_be). zenon_intro zenon_H53. % 0.92/1.10 generalize (ax6 zenon_TN_be). zenon_intro zenon_H54. % 0.92/1.10 generalize (zenon_H53 zenon_TM_bd). zenon_intro zenon_H55. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H22 | zenon_intro zenon_H56 ]. % 0.92/1.10 exact (zenon_H22 zenon_H1b). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H17 | zenon_intro zenon_H57 ]. % 0.92/1.10 generalize (apart3 zenon_TL_bc). zenon_intro zenon_H58. % 0.92/1.10 generalize (zenon_H4e zenon_TL_bc). zenon_intro zenon_H59. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.92/1.10 exact (zenon_H5b zenon_H49). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H39 ]. % 0.92/1.10 exact (zenon_H58 zenon_H5c). % 0.92/1.10 generalize (oac1 zenon_TM_bd). zenon_intro zenon_H5d. % 0.92/1.10 generalize (oac1 zenon_TN_be). zenon_intro zenon_H5e. % 0.92/1.10 generalize (zenon_H54 zenon_TL_bc). zenon_intro zenon_H5f. % 0.92/1.10 generalize (zenon_H5f zenon_TL_bc). zenon_intro zenon_H60. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H62 | zenon_intro zenon_H61 ]. % 0.92/1.10 generalize (zenon_H51 zenon_TL_bc). zenon_intro zenon_H63. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 0.92/1.10 exact (zenon_H65 zenon_H37). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_H5c | zenon_intro zenon_H66 ]. % 0.92/1.10 exact (zenon_H58 zenon_H5c). % 0.92/1.10 exact (zenon_H62 zenon_H66). % 0.92/1.10 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H66 | zenon_intro zenon_H5c ]. % 0.92/1.10 generalize (zenon_H5e zenon_TL_bc). zenon_intro zenon_H67. % 0.92/1.10 generalize (zenon_H5d zenon_TL_bc). zenon_intro zenon_H38. % 0.92/1.10 generalize (zenon_H67 zenon_TN_be). zenon_intro zenon_H68. % 0.92/1.10 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 0.92/1.10 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H62 | zenon_intro zenon_H18 ]. % 0.92/1.10 exact (zenon_H62 zenon_H66). % 0.92/1.10 apply (zenon_L4_ zenon_TN_be zenon_TL_bc zenon_TM_bd); trivial. % 0.92/1.10 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H3e | zenon_intro zenon_H34 ]. % 0.92/1.10 apply (zenon_L5_ zenon_TN_be); trivial. % 0.92/1.10 apply (zenon_L3_ zenon_TN_be zenon_TL_bc); trivial. % 0.92/1.10 exact (zenon_H58 zenon_H5c). % 0.92/1.10 exact (zenon_H4a zenon_H57). % 0.92/1.10 exact (zenon_H32 zenon_H33). % 0.92/1.10 exact (zenon_H35 zenon_H36). % 0.92/1.10 Qed. % 0.92/1.10 % SZS output end Proof % 0.92/1.10 (* END-PROOF *) % 0.92/1.10 nodes searched: 59076 % 0.92/1.10 max branch formulas: 6306 % 0.92/1.10 proof nodes created: 2242 % 0.92/1.10 formulas created: 130750 % 0.92/1.10 %------------------------------------------------------------------------------