%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO194+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 1.69s 1.88s % Output : Proof 1.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO194+2 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n012.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 00:45:53 EDT 2022 % 0.13/0.34 % CPUTime : % 1.69/1.88 (* PROOF-FOUND *) % 1.69/1.88 % SZS status Theorem % 1.69/1.88 (* BEGIN-PROOF *) % 1.69/1.88 % SZS output start Proof % 1.69/1.88 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)))))). % 1.69/1.88 Proof. % 1.69/1.88 assert (zenon_L1_ : forall (zenon_TX_o : zenon_U), (convergent_lines zenon_TX_o zenon_TX_o) -> False). % 1.69/1.88 do 1 intro. intros zenon_Hd. % 1.69/1.88 generalize (apart3 zenon_TX_o). zenon_intro zenon_Hf. % 1.69/1.88 exact (zenon_Hf zenon_Hd). % 1.69/1.88 (* end of lemma zenon_L1_ *) % 1.69/1.88 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TX_o : zenon_U), (apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) zenon_TY_s) -> (convergent_lines zenon_TX_o zenon_TY_s) -> False). % 1.69/1.88 do 2 intro. intros zenon_H10 zenon_H11. % 1.69/1.88 generalize (con2 zenon_TX_o). zenon_intro zenon_H13. % 1.69/1.88 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14. % 1.69/1.88 generalize (apart1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H15. % 1.69/1.88 generalize (zenon_H14 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H16. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 1.69/1.88 exact (zenon_H18 zenon_H11). % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 1.69/1.88 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 1.69/1.88 exact (zenon_H1b zenon_H10). % 1.69/1.88 exact (zenon_H15 zenon_H19). % 1.69/1.88 (* end of lemma zenon_L2_ *) % 1.69/1.88 assert (zenon_L3_ : forall (zenon_TZ_bk : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_o : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) Z))))) -> (~(distinct_lines zenon_TY_s zenon_TY_s)) -> (convergent_lines zenon_TX_o zenon_TY_s) -> (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) zenon_TZ_bk)->((distinct_points (intersection_point zenon_TX_o zenon_TY_s) Z)\/(apart_point_and_line Z zenon_TZ_bk)))) -> (apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) zenon_TZ_bk) -> (~(apart_point_and_line (intersection_point zenon_TX_o zenon_TZ_bk) zenon_TY_s)) -> (distinct_lines zenon_TY_s zenon_TX_o) -> (convergent_lines zenon_TX_o zenon_TZ_bk) -> False). % 1.69/1.88 do 3 intro. intros zenon_H1d zenon_H1e zenon_H11 zenon_H1f zenon_H20 zenon_H21 zenon_H22 zenon_H23. % 1.69/1.88 generalize (zenon_H1d zenon_TY_s). zenon_intro zenon_H25. % 1.69/1.88 generalize (zenon_H25 zenon_TY_s). zenon_intro zenon_H26. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ]. % 1.69/1.88 generalize (apart1 (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H28. % 1.69/1.88 generalize (con2 zenon_TX_o). zenon_intro zenon_H13. % 1.69/1.88 generalize (zenon_H13 zenon_TZ_bk). zenon_intro zenon_H29. % 1.69/1.88 generalize (apart1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H15. % 1.69/1.88 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14. % 1.69/1.88 generalize (zenon_H14 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H16. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 1.69/1.88 exact (zenon_H18 zenon_H11). % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 1.69/1.88 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 1.69/1.88 generalize (zenon_H29 (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H2a. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 1.69/1.88 exact (zenon_H2c zenon_H23). % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 1.69/1.88 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 1.69/1.88 generalize (zenon_H1f (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H31. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 1.69/1.88 exact (zenon_H33 zenon_H20). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 1.69/1.88 generalize (cu1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H36. % 1.69/1.88 generalize (zenon_H36 (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H37. % 1.69/1.88 generalize (zenon_H37 zenon_TY_s). zenon_intro zenon_H38. % 1.69/1.88 generalize (zenon_H38 zenon_TX_o). zenon_intro zenon_H39. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 1.69/1.88 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 1.69/1.88 exact (zenon_H3d zenon_H35). % 1.69/1.88 exact (zenon_H3c zenon_H22). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H10 | zenon_intro zenon_H3e ]. % 1.69/1.88 exact (zenon_H1b zenon_H10). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 1.69/1.88 exact (zenon_H1c zenon_H40). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 1.69/1.88 exact (zenon_H21 zenon_H42). % 1.69/1.88 exact (zenon_H30 zenon_H41). % 1.69/1.88 exact (zenon_H2f zenon_H34). % 1.69/1.88 exact (zenon_H28 zenon_H2d). % 1.69/1.88 exact (zenon_H15 zenon_H19). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H43 | zenon_intro zenon_H10 ]. % 1.69/1.88 exact (zenon_H1e zenon_H43). % 1.69/1.88 apply (zenon_L2_ zenon_TY_s zenon_TX_o); trivial. % 1.69/1.88 (* end of lemma zenon_L3_ *) % 1.69/1.88 apply NNPP. intro zenon_G. % 1.69/1.88 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_H44; idtac ]. % 1.69/1.88 elim zenon_H44. zenon_intro zenon_TX_o. zenon_intro zenon_H45. % 1.69/1.88 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_o Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_o Z)))->((apart_point_and_line (intersection_point zenon_TX_o Y) Z)->(apart_point_and_line (intersection_point zenon_TX_o Z) Y))))) zenon_H45); [ zenon_intro zenon_H46; idtac ]. % 1.69/1.88 elim zenon_H46. zenon_intro zenon_TY_s. zenon_intro zenon_H47. % 1.69/1.88 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_o zenon_TY_s)/\((convergent_lines Z zenon_TY_s)/\(convergent_lines zenon_TX_o Z)))->((apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) Z)->(apart_point_and_line (intersection_point zenon_TX_o Z) zenon_TY_s)))) zenon_H47); [ zenon_intro zenon_H48; idtac ]. % 1.69/1.88 elim zenon_H48. zenon_intro zenon_TZ_bk. zenon_intro zenon_H49. % 1.69/1.88 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 1.69/1.88 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H20. zenon_intro zenon_H21. % 1.69/1.88 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H11. zenon_intro zenon_H4c. % 1.69/1.88 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4d. zenon_intro zenon_H23. % 1.69/1.88 generalize (apart2 zenon_TY_s). zenon_intro zenon_H1e. % 1.69/1.88 generalize (apart6 zenon_TX_o). zenon_intro zenon_H4e. % 1.69/1.88 generalize (zenon_H4e zenon_TY_s). zenon_intro zenon_H4f. % 1.69/1.88 generalize (ceq3 zenon_TY_s). zenon_intro zenon_H50. % 1.69/1.88 generalize (apart5 zenon_TY_s). zenon_intro zenon_H51. % 1.69/1.88 generalize (ceq2 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H1d. % 1.69/1.88 generalize (ceq1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H52. % 1.69/1.88 generalize (zenon_H52 zenon_TZ_bk). zenon_intro zenon_H1f. % 1.69/1.88 generalize (apart2 zenon_TX_o). zenon_intro zenon_H53. % 1.69/1.88 generalize (zenon_H51 zenon_TX_o). zenon_intro zenon_H54. % 1.69/1.88 generalize (zenon_H4f zenon_TX_o). zenon_intro zenon_H55. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H18 | zenon_intro zenon_H56 ]. % 1.69/1.88 exact (zenon_H18 zenon_H11). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_Hd | zenon_intro zenon_H57 ]. % 1.69/1.88 apply (zenon_L1_ zenon_TX_o); trivial. % 1.69/1.88 generalize (zenon_H54 zenon_TX_o). zenon_intro zenon_H58. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H3c | zenon_intro zenon_H59 ]. % 1.69/1.88 generalize (zenon_H50 zenon_TX_o). zenon_intro zenon_H5a. % 1.69/1.88 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H22 ]. % 1.69/1.88 exact (zenon_H5b zenon_H57). % 1.69/1.88 exact (zenon_H3c zenon_H22). % 1.69/1.88 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H22 | zenon_intro zenon_H5c ]. % 1.69/1.88 apply (zenon_L3_ zenon_TZ_bk zenon_TY_s zenon_TX_o); trivial. % 1.69/1.88 exact (zenon_H53 zenon_H5c). % 1.69/1.88 Qed. % 1.69/1.88 % SZS output end Proof % 1.69/1.88 (* END-PROOF *) % 1.69/1.88 nodes searched: 192423 % 1.69/1.88 max branch formulas: 3840 % 1.69/1.88 proof nodes created: 3482 % 1.69/1.88 formulas created: 218515 % 1.69/1.88 %------------------------------------------------------------------------------