%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 07:00:28 EDT 2022 % Result : Theorem 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n021.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 10:53:16 EDT 2022 % 0.13/0.34 % CPUTime : % 0.46/0.64 (* PROOF-FOUND *) % 0.46/0.64 % SZS status Theorem % 0.46/0.64 (* BEGIN-PROOF *) % 0.46/0.64 % SZS output start Proof % 0.46/0.64 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Y (line_connecting X Z))))))). % 0.46/0.64 Proof. % 0.46/0.64 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TZ_s : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points zenon_TZ_s Y)->((distinct_points zenon_TZ_s Z)\/(distinct_points Y Z))))) -> (~(distinct_points zenon_TX_r zenon_TZ_s)) -> (~(distinct_points zenon_TZ_s zenon_TZ_s)) -> (distinct_points zenon_TZ_s zenon_TX_r) -> False). % 0.46/0.64 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10. % 0.46/0.64 generalize (zenon_Hd zenon_TX_r). zenon_intro zenon_H13. % 0.46/0.64 generalize (zenon_H13 zenon_TZ_s). zenon_intro zenon_H14. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.46/0.64 exact (zenon_H16 zenon_H10). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.46/0.64 exact (zenon_Hf zenon_H18). % 0.46/0.64 exact (zenon_He zenon_H17). % 0.46/0.64 (* end of lemma zenon_L1_ *) % 0.46/0.64 assert (zenon_L2_ : forall (zenon_TY_bi : zenon_U) (zenon_TX_r : zenon_U) (zenon_TZ_s : zenon_U), (distinct_points zenon_TZ_s zenon_TX_r) -> (~(distinct_points zenon_TZ_s zenon_TZ_s)) -> (distinct_points zenon_TX_r zenon_TY_bi) -> (~(apart_point_and_line zenon_TX_r (line_connecting zenon_TX_r zenon_TY_bi))) -> (~(apart_point_and_line zenon_TY_bi (line_connecting zenon_TX_r zenon_TY_bi))) -> (~(apart_point_and_line zenon_TY_bi (line_connecting zenon_TX_r zenon_TZ_s))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_r zenon_TY_bi)/\(distinct_lines U V))->((apart_point_and_line zenon_TX_r U)\/((apart_point_and_line zenon_TX_r V)\/((apart_point_and_line zenon_TY_bi U)\/(apart_point_and_line zenon_TY_bi V))))))) -> (apart_point_and_line zenon_TZ_s (line_connecting zenon_TX_r zenon_TY_bi)) -> (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_s (line_connecting zenon_TX_r zenon_TY_bi))->((distinct_lines (line_connecting zenon_TX_r zenon_TY_bi) Z)\/(apart_point_and_line zenon_TZ_s Z)))) -> (forall Z : zenon_U, ((distinct_points zenon_TX_r zenon_TZ_s)->((apart_point_and_line Z (line_connecting zenon_TX_r zenon_TZ_s))->((distinct_points Z zenon_TX_r)/\(distinct_points Z zenon_TZ_s))))) -> (~(distinct_points zenon_TX_r zenon_TX_r)) -> False). % 0.46/0.64 do 3 intro. intros zenon_H10 zenon_Hf zenon_H19 zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H1e zenon_H1f zenon_H20 zenon_H21. % 0.46/0.64 generalize (zenon_H20 zenon_TX_r). zenon_intro zenon_H23. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_He | zenon_intro zenon_H24 ]. % 0.46/0.64 generalize (apart4 zenon_TZ_s). zenon_intro zenon_Hd. % 0.46/0.64 apply (zenon_L1_ zenon_TX_r zenon_TZ_s); trivial. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.46/0.64 generalize (apart4 zenon_TZ_s). zenon_intro zenon_Hd. % 0.46/0.64 generalize (zenon_H20 zenon_TZ_s). zenon_intro zenon_H27. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_He | zenon_intro zenon_H28 ]. % 0.46/0.64 apply (zenon_L1_ zenon_TX_r zenon_TZ_s); trivial. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.46/0.64 generalize (zenon_H1f (line_connecting zenon_TX_r zenon_TZ_s)). zenon_intro zenon_H2b. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.46/0.64 exact (zenon_H2d zenon_H1e). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.46/0.64 generalize (zenon_H1d (line_connecting zenon_TX_r zenon_TY_bi)). zenon_intro zenon_H30. % 0.46/0.64 generalize (zenon_H30 (line_connecting zenon_TX_r zenon_TZ_s)). zenon_intro zenon_H31. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 0.46/0.64 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.46/0.64 exact (zenon_H35 zenon_H19). % 0.46/0.64 exact (zenon_H34 zenon_H2f). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.46/0.64 exact (zenon_H1a zenon_H37). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.46/0.64 exact (zenon_H26 zenon_H39). % 0.46/0.64 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.46/0.64 exact (zenon_H1b zenon_H3b). % 0.46/0.64 exact (zenon_H1c zenon_H3a). % 0.46/0.64 exact (zenon_H2a zenon_H2e). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H10. zenon_intro zenon_H18. % 0.46/0.64 exact (zenon_Hf zenon_H18). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H3c. zenon_intro zenon_H17. % 0.46/0.64 exact (zenon_H21 zenon_H3c). % 0.46/0.64 (* end of lemma zenon_L2_ *) % 0.46/0.64 apply NNPP. intro zenon_G. % 0.46/0.64 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Y (line_connecting X Z))))))) zenon_G); [ zenon_intro zenon_H3d; idtac ]. % 0.46/0.64 elim zenon_H3d. zenon_intro zenon_TX_r. zenon_intro zenon_H3e. % 0.46/0.64 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((distinct_points zenon_TX_r Y)->((apart_point_and_line Z (line_connecting zenon_TX_r Y))->(apart_point_and_line Y (line_connecting zenon_TX_r Z)))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.46/0.64 elim zenon_H3f. zenon_intro zenon_TY_bi. zenon_intro zenon_H40. % 0.46/0.64 apply (zenon_notallex_s (fun Z : zenon_U => ((distinct_points zenon_TX_r zenon_TY_bi)->((apart_point_and_line Z (line_connecting zenon_TX_r zenon_TY_bi))->(apart_point_and_line zenon_TY_bi (line_connecting zenon_TX_r Z))))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.46/0.64 elim zenon_H41. zenon_intro zenon_TZ_s. zenon_intro zenon_H42. % 0.46/0.64 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H19. zenon_intro zenon_H43. % 0.46/0.64 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H1e. zenon_intro zenon_H1c. % 0.46/0.64 generalize (apart1 zenon_TY_bi). zenon_intro zenon_H44. % 0.46/0.64 generalize (cu1 zenon_TX_r). zenon_intro zenon_H45. % 0.46/0.64 generalize (zenon_H45 zenon_TY_bi). zenon_intro zenon_H1d. % 0.46/0.64 generalize (con1 zenon_TX_r). zenon_intro zenon_H46. % 0.46/0.64 generalize (apart1 zenon_TX_r). zenon_intro zenon_H21. % 0.46/0.64 generalize (zenon_H46 zenon_TY_bi). zenon_intro zenon_H47. % 0.46/0.64 generalize (ceq2 zenon_TZ_s). zenon_intro zenon_H48. % 0.46/0.64 generalize (zenon_H47 zenon_TY_bi). zenon_intro zenon_H49. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H35 | zenon_intro zenon_H4a ]. % 0.46/0.64 exact (zenon_H35 zenon_H19). % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H1b | zenon_intro zenon_H4b ]. % 0.46/0.64 generalize (zenon_H47 zenon_TX_r). zenon_intro zenon_H4c. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H35 | zenon_intro zenon_H4d ]. % 0.46/0.64 exact (zenon_H35 zenon_H19). % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H1a | zenon_intro zenon_H4e ]. % 0.46/0.64 generalize (zenon_H48 (line_connecting zenon_TX_r zenon_TY_bi)). zenon_intro zenon_H1f. % 0.46/0.64 generalize (apart1 zenon_TZ_s). zenon_intro zenon_Hf. % 0.46/0.64 generalize (zenon_H46 zenon_TZ_s). zenon_intro zenon_H20. % 0.46/0.64 generalize (zenon_H47 zenon_TZ_s). zenon_intro zenon_H4f. % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H35 | zenon_intro zenon_H50 ]. % 0.46/0.64 exact (zenon_H35 zenon_H19). % 0.46/0.64 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H2d | zenon_intro zenon_H51 ]. % 0.46/0.64 exact (zenon_H2d zenon_H1e). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H10. zenon_intro zenon_H52. % 0.46/0.64 apply (zenon_L2_ zenon_TY_bi zenon_TX_r zenon_TZ_s); trivial. % 0.46/0.64 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H3c. zenon_intro zenon_H19. % 0.46/0.64 exact (zenon_H21 zenon_H3c). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H54. zenon_intro zenon_H53. % 0.46/0.64 exact (zenon_H44 zenon_H53). % 0.46/0.64 Qed. % 0.46/0.64 % SZS output end Proof % 0.46/0.64 (* END-PROOF *) % 0.46/0.64 nodes searched: 6802 % 0.46/0.64 max branch formulas: 1461 % 0.46/0.64 proof nodes created: 672 % 0.46/0.64 formulas created: 17440 % 0.46/0.64 %------------------------------------------------------------------------------