%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO255+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 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 07:01:21 EDT 2022 % Result : Theorem 0.76s 0.97s % Output : Proof 0.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO255+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 16:06:53 EDT 2022 % 0.12/0.33 % CPUTime : % 0.76/0.97 (* PROOF-FOUND *) % 0.76/0.97 % SZS status Theorem % 0.76/0.97 (* BEGIN-PROOF *) % 0.76/0.97 % SZS output start Proof % 0.76/0.97 Theorem con : (forall L : zenon_U, (forall A : zenon_U, (forall B : zenon_U, (((line L)/\(distinct_points A B))->(~((before_on_line L A B)/\(before_on_line L B A))))))). % 0.76/0.97 Proof. % 0.76/0.97 assert (zenon_L1_ : forall (zenon_TL_bi : zenon_U), (line zenon_TL_bi) -> (~(line (reverse_line zenon_TL_bi))) -> False). % 0.76/0.97 do 1 intro. intros zenon_H20 zenon_H21. % 0.76/0.97 generalize (oagco4 zenon_TL_bi). zenon_intro zenon_H23. % 0.76/0.97 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.76/0.97 exact (zenon_H25 zenon_H20). % 0.76/0.97 exact (zenon_H21 zenon_H24). % 0.76/0.97 (* end of lemma zenon_L1_ *) % 0.76/0.97 assert (zenon_L2_ : forall (zenon_TB_bq : zenon_U) (zenon_TA_br : zenon_U) (zenon_TL_bi : zenon_U), (forall N : zenon_U, ((unequally_directed_lines (reverse_line zenon_TL_bi) (line_connecting zenon_TA_br zenon_TB_bq))->((unequally_directed_lines (reverse_line zenon_TL_bi) N)\/(unequally_directed_lines (line_connecting zenon_TA_br zenon_TB_bq) N)))) -> (unequally_directed_lines (reverse_line zenon_TL_bi) (line_connecting zenon_TA_br zenon_TB_bq)) -> (~(unequally_directed_lines (reverse_line zenon_TL_bi) (reverse_line (line_connecting zenon_TB_bq zenon_TA_br)))) -> (~(unequally_directed_lines (line_connecting zenon_TA_br zenon_TB_bq) (reverse_line (line_connecting zenon_TB_bq zenon_TA_br)))) -> False). % 0.76/0.97 do 3 intro. intros zenon_H26 zenon_H27 zenon_H28 zenon_H29. % 0.76/0.97 generalize (zenon_H26 (reverse_line (line_connecting zenon_TB_bq zenon_TA_br))). zenon_intro zenon_H2c. % 0.76/0.97 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.76/0.97 exact (zenon_H2e zenon_H27). % 0.76/0.97 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.76/0.97 exact (zenon_H28 zenon_H30). % 0.76/0.97 exact (zenon_H29 zenon_H2f). % 0.76/0.97 (* end of lemma zenon_L2_ *) % 0.76/0.97 assert (zenon_L3_ : forall (zenon_TL_bi : zenon_U), ((unequally_directed_lines (reverse_line zenon_TL_bi) zenon_TL_bi)/\(unequally_directed_lines (reverse_line zenon_TL_bi) (reverse_line zenon_TL_bi))) -> (~(unequally_directed_lines (reverse_line zenon_TL_bi) (reverse_line zenon_TL_bi))) -> False). % 0.76/0.97 do 1 intro. intros zenon_H31 zenon_H32. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.76/0.97 exact (zenon_H32 zenon_H33). % 0.76/0.97 (* end of lemma zenon_L3_ *) % 0.76/0.97 assert (zenon_L4_ : forall (zenon_TL_bi : zenon_U) (zenon_TA_br : zenon_U) (zenon_TB_bq : zenon_U), (forall N : zenon_U, ((unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) zenon_TL_bi)->((unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) N)\/(unequally_directed_lines zenon_TL_bi N)))) -> (unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) zenon_TL_bi) -> (~(unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) (line_connecting zenon_TB_bq zenon_TA_br))) -> (~(unequally_directed_lines zenon_TL_bi (line_connecting zenon_TB_bq zenon_TA_br))) -> False). % 0.76/0.97 do 3 intro. intros zenon_H35 zenon_H36 zenon_H37 zenon_H38. % 0.76/0.97 generalize (zenon_H35 (line_connecting zenon_TB_bq zenon_TA_br)). zenon_intro zenon_H39. % 0.76/0.97 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.76/0.97 exact (zenon_H3b zenon_H36). % 0.76/0.97 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.76/0.97 exact (zenon_H37 zenon_H3d). % 0.76/0.97 exact (zenon_H38 zenon_H3c). % 0.76/0.97 (* end of lemma zenon_L4_ *) % 0.76/0.97 assert (zenon_L5_ : forall (zenon_TL_bi : zenon_U) (zenon_TA_br : zenon_U) (zenon_TB_bq : zenon_U), (forall M : zenon_U, (forall N : zenon_U, ((unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) M)->((unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) N)\/(unequally_directed_lines M N))))) -> (unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) zenon_TL_bi) -> (~(unequally_directed_lines zenon_TL_bi (line_connecting zenon_TB_bq zenon_TA_br))) -> False). % 0.76/0.97 do 3 intro. intros zenon_H3e zenon_H36 zenon_H38. % 0.76/0.97 generalize (zenon_H3e zenon_TL_bi). zenon_intro zenon_H35. % 0.76/0.97 generalize (oag5 (line_connecting zenon_TB_bq zenon_TA_br)). zenon_intro zenon_H37. % 0.76/0.97 apply (zenon_L4_ zenon_TL_bi zenon_TA_br zenon_TB_bq); trivial. % 0.76/0.97 (* end of lemma zenon_L5_ *) % 0.76/0.97 assert (zenon_L6_ : forall (zenon_TA_br : zenon_U) (zenon_TB_bq : zenon_U) (zenon_TL_bi : zenon_U), (~(unequally_directed_lines zenon_TL_bi (line_connecting zenon_TB_bq zenon_TA_br))) -> (unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) zenon_TL_bi) -> False). % 0.76/0.97 do 3 intro. intros zenon_H38 zenon_H36. % 0.76/0.97 generalize (oag6 (line_connecting zenon_TB_bq zenon_TA_br)). zenon_intro zenon_H3e. % 0.76/0.97 apply (zenon_L5_ zenon_TL_bi zenon_TA_br zenon_TB_bq); trivial. % 0.76/0.97 (* end of lemma zenon_L6_ *) % 0.76/0.97 assert (zenon_L7_ : forall (zenon_TL_bi : zenon_U) (zenon_TA_br : zenon_U) (zenon_TB_bq : zenon_U), ((unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) zenon_TL_bi)/\(unequally_directed_lines (line_connecting zenon_TB_bq zenon_TA_br) (reverse_line zenon_TL_bi))) -> (~(unequally_directed_lines zenon_TL_bi (line_connecting zenon_TB_bq zenon_TA_br))) -> False). % 0.76/0.97 do 3 intro. intros zenon_H3f zenon_H38. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H36. zenon_intro zenon_H40. % 0.76/0.97 apply (zenon_L6_ zenon_TA_br zenon_TB_bq zenon_TL_bi); trivial. % 0.76/0.97 (* end of lemma zenon_L7_ *) % 0.76/0.97 apply NNPP. intro zenon_G. % 0.76/0.97 apply (zenon_notallex_s (fun L : zenon_U => (forall A : zenon_U, (forall B : zenon_U, (((line L)/\(distinct_points A B))->(~((before_on_line L A B)/\(before_on_line L B A))))))) zenon_G); [ zenon_intro zenon_H41; idtac ]. % 0.76/0.97 elim zenon_H41. zenon_intro zenon_TL_bi. zenon_intro zenon_H42. % 0.76/0.97 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((line zenon_TL_bi)/\(distinct_points A B))->(~((before_on_line zenon_TL_bi A B)/\(before_on_line zenon_TL_bi B A)))))) zenon_H42); [ zenon_intro zenon_H43; idtac ]. % 0.76/0.97 elim zenon_H43. zenon_intro zenon_TA_br. zenon_intro zenon_H44. % 0.76/0.97 apply (zenon_notallex_s (fun B : zenon_U => (((line zenon_TL_bi)/\(distinct_points zenon_TA_br B))->(~((before_on_line zenon_TL_bi zenon_TA_br B)/\(before_on_line zenon_TL_bi B zenon_TA_br))))) zenon_H44); [ zenon_intro zenon_H45; idtac ]. % 0.76/0.97 elim zenon_H45. zenon_intro zenon_TB_bq. zenon_intro zenon_H46. % 0.76/0.97 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.76/0.97 apply zenon_H47. zenon_intro zenon_H49. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H20. zenon_intro zenon_H4c. % 0.76/0.97 generalize (bf_def zenon_TL_bi). zenon_intro zenon_H4d. % 0.76/0.97 generalize (zenon_H4d zenon_TA_br). zenon_intro zenon_H4e. % 0.76/0.97 generalize (zenon_H4e zenon_TB_bq). zenon_intro zenon_H4f. % 0.76/0.97 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H4b; zenon_intro zenon_H50 ]. % 0.76/0.97 exact (zenon_H52 zenon_H4b). % 0.76/0.97 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H4c. zenon_intro zenon_H53. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H55. zenon_intro zenon_H54. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H57. zenon_intro zenon_H56. % 0.76/0.97 generalize (bf_def zenon_TL_bi). zenon_intro zenon_H4d. % 0.76/0.97 generalize (zenon_H4d zenon_TB_bq). zenon_intro zenon_H58. % 0.76/0.97 generalize (zenon_H58 zenon_TA_br). zenon_intro zenon_H59. % 0.76/0.97 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H5c; zenon_intro zenon_H5b | zenon_intro zenon_H4a; zenon_intro zenon_H5a ]. % 0.76/0.97 exact (zenon_H5c zenon_H4a). % 0.76/0.97 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H57. zenon_intro zenon_H5f. % 0.76/0.97 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H55. zenon_intro zenon_H38. % 0.76/0.97 generalize (oagco9 zenon_TA_br). zenon_intro zenon_H60. % 0.76/0.97 generalize (zenon_H60 zenon_TB_bq). zenon_intro zenon_H29. % 0.76/0.97 generalize (oag5 (reverse_line zenon_TL_bi)). zenon_intro zenon_H32. % 0.76/0.97 generalize (oag8 (reverse_line zenon_TL_bi)). zenon_intro zenon_H61. % 0.76/0.97 generalize (zenon_H61 zenon_TL_bi). zenon_intro zenon_H62. % 0.76/0.97 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.76/0.97 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H21 | zenon_intro zenon_H25 ]. % 0.76/0.97 apply (zenon_L1_ zenon_TL_bi); trivial. % 0.76/0.97 exact (zenon_H25 zenon_H20). % 0.76/0.97 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.81/0.97 generalize (oag7 (reverse_line zenon_TL_bi)). zenon_intro zenon_H65. % 0.81/0.97 generalize (oag6 (reverse_line zenon_TL_bi)). zenon_intro zenon_H66. % 0.81/0.97 generalize (zenon_H66 zenon_TL_bi). zenon_intro zenon_H67. % 0.81/0.97 generalize (zenon_H67 (reverse_line zenon_TL_bi)). zenon_intro zenon_H68. % 0.81/0.97 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 0.81/0.97 exact (zenon_H6a zenon_H34). % 0.81/0.97 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H33 | zenon_intro zenon_H6b ]. % 0.81/0.97 exact (zenon_H32 zenon_H33). % 0.81/0.97 generalize (oag6 zenon_TL_bi). zenon_intro zenon_H6c. % 0.81/0.97 generalize (zenon_H6c (reverse_line zenon_TL_bi)). zenon_intro zenon_H6d. % 0.81/0.97 generalize (zenon_H6d (line_connecting zenon_TA_br zenon_TB_bq)). zenon_intro zenon_H6e. % 0.81/0.97 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H70 | zenon_intro zenon_H6f ]. % 0.81/0.97 exact (zenon_H70 zenon_H6b). % 0.81/0.97 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H71 | zenon_intro zenon_H27 ]. % 0.81/0.97 exact (zenon_H56 zenon_H71). % 0.81/0.97 generalize (zenon_H67 (line_connecting zenon_TB_bq zenon_TA_br)). zenon_intro zenon_H72. % 0.81/0.97 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H6a | zenon_intro zenon_H73 ]. % 0.81/0.97 exact (zenon_H6a zenon_H34). % 0.81/0.97 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H74 | zenon_intro zenon_H3c ]. % 0.81/0.97 generalize (zenon_H65 (line_connecting zenon_TB_bq zenon_TA_br)). zenon_intro zenon_H75. % 0.81/0.97 generalize (zenon_H66 (line_connecting zenon_TA_br zenon_TB_bq)). zenon_intro zenon_H26. % 0.81/0.97 generalize (zenon_H75 zenon_TL_bi). zenon_intro zenon_H76. % 0.81/0.97 apply (zenon_imply_s _ _ zenon_H76); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 0.81/0.97 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H28 ]. % 0.81/0.97 exact (zenon_H79 zenon_H74). % 0.81/0.97 apply (zenon_L2_ zenon_TB_bq zenon_TA_br zenon_TL_bi); trivial. % 0.81/0.97 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H31 | zenon_intro zenon_H3f ]. % 0.81/0.97 apply (zenon_L3_ zenon_TL_bi); trivial. % 0.81/0.97 apply (zenon_L7_ zenon_TL_bi zenon_TA_br zenon_TB_bq); trivial. % 0.81/0.97 exact (zenon_H38 zenon_H3c). % 0.81/0.97 exact (zenon_H32 zenon_H33). % 0.81/0.97 Qed. % 0.81/0.97 % SZS output end Proof % 0.81/0.98 (* END-PROOF *) % 0.81/0.98 nodes searched: 35958 % 0.81/0.98 max branch formulas: 5634 % 0.81/0.98 proof nodes created: 1187 % 0.81/0.98 formulas created: 100755 % 0.81/0.98 %------------------------------------------------------------------------------