%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n023.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 07:00:42 EDT 2022 % Result : Theorem 2.12s 2.35s % Output : Proof 2.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n023.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 07:32:34 EDT 2022 % 0.12/0.34 % CPUTime : % 2.12/2.35 (* PROOF-FOUND *) % 2.12/2.35 % SZS status Theorem % 2.12/2.35 (* BEGIN-PROOF *) % 2.12/2.35 % SZS output start Proof % 2.12/2.35 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)))))). % 2.12/2.35 Proof. % 2.12/2.35 assert (zenon_L1_ : forall (zenon_TY_u : zenon_U) (zenon_TZ_v : zenon_U) (zenon_TX_w : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TY_u)->((distinct_points (intersection_point zenon_TX_w zenon_TZ_v) Z)\/(apart_point_and_line Z zenon_TY_u)))) -> (apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TY_u) -> (distinct_lines zenon_TZ_v zenon_TX_w) -> (~(apart_point_and_line (intersection_point zenon_TX_w zenon_TY_u) zenon_TZ_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TZ_v)) -> (convergent_lines zenon_TX_w zenon_TZ_v) -> (convergent_lines zenon_TX_w zenon_TY_u) -> False). % 2.12/2.35 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13. % 2.12/2.35 generalize (con2 zenon_TX_w). zenon_intro zenon_H17. % 2.12/2.35 generalize (zenon_H17 zenon_TY_u). zenon_intro zenon_H18. % 2.12/2.35 generalize (apart1 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H19. % 2.12/2.35 generalize (zenon_H18 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H1a. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 2.12/2.35 exact (zenon_H1c zenon_H13). % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 2.12/2.35 apply (zenon_notor_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 2.12/2.35 generalize (zenon_H17 zenon_TZ_v). zenon_intro zenon_H21. % 2.12/2.35 generalize (apart1 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H22. % 2.12/2.35 generalize (zenon_Hd (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H23. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 2.12/2.35 exact (zenon_H25 zenon_He). % 2.12/2.35 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 2.12/2.35 generalize (apart4 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H28. % 2.12/2.35 generalize (zenon_H21 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H29. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 2.12/2.35 exact (zenon_H2b zenon_H12). % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.12/2.35 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H2e. zenon_intro zenon_H11. % 2.12/2.35 generalize (zenon_H28 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H2f. % 2.12/2.35 generalize (zenon_H2f (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H30. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 2.12/2.35 exact (zenon_H32 zenon_H27). % 2.12/2.35 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2c | zenon_intro zenon_H33 ]. % 2.12/2.35 exact (zenon_H22 zenon_H2c). % 2.12/2.35 generalize (cu1 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H34. % 2.12/2.35 generalize (zenon_H34 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H35. % 2.12/2.35 generalize (zenon_H35 zenon_TZ_v). zenon_intro zenon_H36. % 2.12/2.35 generalize (zenon_H36 zenon_TX_w). zenon_intro zenon_H37. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 2.12/2.35 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 2.12/2.35 exact (zenon_H3b zenon_H33). % 2.12/2.35 exact (zenon_H3a zenon_Hf). % 2.12/2.35 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 2.12/2.35 exact (zenon_H10 zenon_H3d). % 2.12/2.35 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 2.12/2.35 exact (zenon_H20 zenon_H3f). % 2.12/2.35 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 2.12/2.35 exact (zenon_H11 zenon_H41). % 2.12/2.35 exact (zenon_H2e zenon_H40). % 2.12/2.35 exact (zenon_H22 zenon_H2c). % 2.12/2.35 exact (zenon_H1f zenon_H26). % 2.12/2.35 exact (zenon_H19 zenon_H1d). % 2.12/2.35 (* end of lemma zenon_L1_ *) % 2.12/2.35 assert (zenon_L2_ : forall (zenon_TX_w : zenon_U), (distinct_lines zenon_TX_w zenon_TX_w) -> False). % 2.12/2.35 do 1 intro. intros zenon_H42. % 2.12/2.35 generalize (apart2 zenon_TX_w). zenon_intro zenon_H43. % 2.12/2.35 exact (zenon_H43 zenon_H42). % 2.12/2.35 (* end of lemma zenon_L2_ *) % 2.12/2.35 assert (zenon_L3_ : forall (zenon_TZ_v : zenon_U) (zenon_TX_w : zenon_U), (apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TZ_v) -> (convergent_lines zenon_TX_w zenon_TZ_v) -> False). % 2.12/2.35 do 2 intro. intros zenon_H41 zenon_H12. % 2.12/2.35 generalize (con2 zenon_TX_w). zenon_intro zenon_H17. % 2.12/2.35 generalize (apart1 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H22. % 2.12/2.35 generalize (zenon_H17 zenon_TZ_v). zenon_intro zenon_H21. % 2.12/2.35 generalize (zenon_H21 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H29. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 2.12/2.35 exact (zenon_H2b zenon_H12). % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.12/2.35 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H2e. zenon_intro zenon_H11. % 2.12/2.35 exact (zenon_H11 zenon_H41). % 2.12/2.35 exact (zenon_H22 zenon_H2c). % 2.12/2.35 (* end of lemma zenon_L3_ *) % 2.12/2.35 apply NNPP. intro zenon_G. % 2.12/2.35 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 ]. % 2.12/2.35 elim zenon_H44. zenon_intro zenon_TX_w. zenon_intro zenon_H45. % 2.12/2.35 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_w Y)/\((convergent_lines Z Y)/\((convergent_lines zenon_TX_w Z)/\(~(apart_point_and_line (intersection_point zenon_TX_w Y) Z)))))->(~(apart_point_and_line (intersection_point zenon_TX_w Z) Y))))) zenon_H45); [ zenon_intro zenon_H46; idtac ]. % 2.12/2.35 elim zenon_H46. zenon_intro zenon_TY_u. zenon_intro zenon_H47. % 2.12/2.35 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_w zenon_TY_u)/\((convergent_lines Z zenon_TY_u)/\((convergent_lines zenon_TX_w Z)/\(~(apart_point_and_line (intersection_point zenon_TX_w zenon_TY_u) Z)))))->(~(apart_point_and_line (intersection_point zenon_TX_w Z) zenon_TY_u)))) zenon_H47); [ zenon_intro zenon_H48; idtac ]. % 2.12/2.35 elim zenon_H48. zenon_intro zenon_TZ_v. zenon_intro zenon_H49. % 2.12/2.35 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 2.12/2.35 apply zenon_H4a. zenon_intro zenon_He. % 2.12/2.35 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H13. zenon_intro zenon_H4c. % 2.12/2.35 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 2.12/2.35 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H12. zenon_intro zenon_H10. % 2.12/2.35 generalize (apart2 zenon_TZ_v). zenon_intro zenon_H4f. % 2.12/2.35 generalize (apart6 zenon_TX_w). zenon_intro zenon_H50. % 2.12/2.35 generalize (ceq3 zenon_TZ_v). zenon_intro zenon_H51. % 2.12/2.35 generalize (zenon_H50 zenon_TZ_v). zenon_intro zenon_H52. % 2.12/2.35 generalize (ceq2 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H53. % 2.12/2.35 generalize (ceq1 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H54. % 2.12/2.35 generalize (zenon_H54 zenon_TY_u). zenon_intro zenon_Hd. % 2.12/2.35 generalize (ceq3 zenon_TX_w). zenon_intro zenon_H55. % 2.12/2.35 generalize (zenon_H53 zenon_TZ_v). zenon_intro zenon_H56. % 2.12/2.35 generalize (zenon_H56 zenon_TZ_v). zenon_intro zenon_H57. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H11 | zenon_intro zenon_H58 ]. % 2.12/2.35 generalize (zenon_H55 zenon_TX_w). zenon_intro zenon_H59. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5a | zenon_intro zenon_H42 ]. % 2.12/2.35 generalize (zenon_H51 zenon_TX_w). zenon_intro zenon_H5b. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5c | zenon_intro zenon_Hf ]. % 2.12/2.35 generalize (zenon_H52 zenon_TX_w). zenon_intro zenon_H5d. % 2.12/2.35 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H2b | zenon_intro zenon_H5e ]. % 2.12/2.35 exact (zenon_H2b zenon_H12). % 2.12/2.35 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 2.12/2.35 exact (zenon_H5a zenon_H60). % 2.12/2.35 exact (zenon_H5c zenon_H5f). % 2.12/2.35 apply (zenon_L1_ zenon_TY_u zenon_TZ_v zenon_TX_w); trivial. % 2.12/2.35 apply (zenon_L2_ zenon_TX_w); trivial. % 2.12/2.35 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H61 | zenon_intro zenon_H41 ]. % 2.12/2.35 exact (zenon_H4f zenon_H61). % 2.12/2.35 apply (zenon_L3_ zenon_TZ_v zenon_TX_w); trivial. % 2.12/2.35 Qed. % 2.12/2.35 % SZS output end Proof % 2.12/2.35 (* END-PROOF *) % 2.12/2.35 nodes searched: 214783 % 2.12/2.35 max branch formulas: 4717 % 2.12/2.35 proof nodes created: 4379 % 2.12/2.35 formulas created: 224151 % 2.12/2.35 %------------------------------------------------------------------------------