%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO202+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 07:00:45 EDT 2022 % Result : Theorem 0.38s 0.55s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO202+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n024.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 : Fri Jun 17 21:06:17 EDT 2022 % 0.12/0.34 % CPUTime : % 0.38/0.55 (* PROOF-FOUND *) % 0.38/0.55 % SZS status Theorem % 0.38/0.55 (* BEGIN-PROOF *) % 0.38/0.55 % SZS output start Proof % 0.38/0.55 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\(convergent_lines (line_connecting X Y) (line_connecting X Z))))->(~(distinct_points (intersection_point (line_connecting X Y) (line_connecting X Z)) X)))))). % 0.38/0.55 Proof. % 0.38/0.55 assert (zenon_L1_ : forall (zenon_TZ_u : zenon_U) (zenon_TY_v : zenon_U) (zenon_TX_w : zenon_U), (distinct_points (intersection_point (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w zenon_TZ_u)) zenon_TX_w) -> (convergent_lines (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w zenon_TZ_u)) -> (apart_point_and_line zenon_TZ_u (line_connecting zenon_TX_w zenon_TY_v)) -> (distinct_points zenon_TX_w zenon_TZ_u) -> (distinct_points zenon_TX_w zenon_TY_v) -> False). % 0.38/0.55 do 3 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13. % 0.38/0.55 generalize (ci1 zenon_TX_w). zenon_intro zenon_H17. % 0.38/0.55 generalize (ceq2 zenon_TZ_u). zenon_intro zenon_H18. % 0.40/0.55 generalize (ci2 zenon_TX_w). zenon_intro zenon_H19. % 0.40/0.55 generalize (zenon_H17 zenon_TY_v). zenon_intro zenon_H1a. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.40/0.55 exact (zenon_H1c zenon_H13). % 0.40/0.55 generalize (zenon_H17 zenon_TZ_u). zenon_intro zenon_H1d. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.40/0.55 exact (zenon_H1f zenon_H12). % 0.40/0.55 generalize (zenon_H19 zenon_TZ_u). zenon_intro zenon_H20. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H1f | zenon_intro zenon_H21 ]. % 0.40/0.55 exact (zenon_H1f zenon_H12). % 0.40/0.55 generalize (cu1 (intersection_point (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w zenon_TZ_u))). zenon_intro zenon_H22. % 0.40/0.55 generalize (zenon_H22 zenon_TX_w). zenon_intro zenon_H23. % 0.40/0.55 generalize (ci3 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H24. % 0.40/0.55 generalize (zenon_H18 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H25. % 0.40/0.55 generalize (zenon_H25 (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H26. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.40/0.55 exact (zenon_H28 zenon_H11). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.40/0.55 generalize (zenon_H23 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H2b. % 0.40/0.55 generalize (zenon_H2b (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H2c. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.40/0.55 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.40/0.55 exact (zenon_H30 zenon_Hf). % 0.40/0.55 exact (zenon_H2f zenon_H2a). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.40/0.55 generalize (zenon_H24 (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H33. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.40/0.55 exact (zenon_H35 zenon_H10). % 0.40/0.55 exact (zenon_H34 zenon_H32). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.40/0.55 generalize (ci4 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H38. % 0.40/0.55 generalize (zenon_H38 (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H39. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H35 | zenon_intro zenon_H3a ]. % 0.40/0.55 exact (zenon_H35 zenon_H10). % 0.40/0.55 exact (zenon_H3a zenon_H37). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.40/0.55 exact (zenon_H1b zenon_H3c). % 0.40/0.55 exact (zenon_H1e zenon_H3b). % 0.40/0.55 exact (zenon_H21 zenon_H29). % 0.40/0.55 (* end of lemma zenon_L1_ *) % 0.40/0.55 assert (zenon_L2_ : forall (zenon_TY_v : zenon_U) (zenon_TX_w : zenon_U), (forall Y : zenon_U, ((distinct_points zenon_TX_w Y)->(~(apart_point_and_line zenon_TX_w (line_connecting zenon_TX_w Y))))) -> (distinct_points zenon_TX_w zenon_TY_v) -> (apart_point_and_line zenon_TX_w (line_connecting zenon_TX_w zenon_TY_v)) -> False). % 0.40/0.55 do 2 intro. intros zenon_H17 zenon_H13 zenon_H3c. % 0.40/0.55 generalize (zenon_H17 zenon_TY_v). zenon_intro zenon_H1a. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.40/0.55 exact (zenon_H1c zenon_H13). % 0.40/0.55 exact (zenon_H1b zenon_H3c). % 0.40/0.55 (* end of lemma zenon_L2_ *) % 0.40/0.55 assert (zenon_L3_ : forall (zenon_TY_v : zenon_U) (zenon_TX_w : zenon_U), (apart_point_and_line zenon_TX_w (line_connecting zenon_TX_w zenon_TY_v)) -> (distinct_points zenon_TX_w zenon_TY_v) -> False). % 0.40/0.55 do 2 intro. intros zenon_H3c zenon_H13. % 0.40/0.55 generalize (ci1 zenon_TX_w). zenon_intro zenon_H17. % 0.40/0.55 apply (zenon_L2_ zenon_TY_v zenon_TX_w); trivial. % 0.40/0.55 (* end of lemma zenon_L3_ *) % 0.40/0.55 apply NNPP. intro zenon_G. % 0.40/0.55 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\(convergent_lines (line_connecting X Y) (line_connecting X Z))))->(~(distinct_points (intersection_point (line_connecting X Y) (line_connecting X Z)) X)))))) zenon_G); [ zenon_intro zenon_H3d; idtac ]. % 0.40/0.55 elim zenon_H3d. zenon_intro zenon_TX_w. zenon_intro zenon_H3e. % 0.40/0.55 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_w Y)/\((distinct_points zenon_TX_w Z)/\(convergent_lines (line_connecting zenon_TX_w Y) (line_connecting zenon_TX_w Z))))->(~(distinct_points (intersection_point (line_connecting zenon_TX_w Y) (line_connecting zenon_TX_w Z)) zenon_TX_w))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.40/0.55 elim zenon_H3f. zenon_intro zenon_TY_v. zenon_intro zenon_H40. % 0.40/0.55 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_w zenon_TY_v)/\((distinct_points zenon_TX_w Z)/\(convergent_lines (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w Z))))->(~(distinct_points (intersection_point (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w Z)) zenon_TX_w)))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.40/0.55 elim zenon_H41. zenon_intro zenon_TZ_u. zenon_intro zenon_H42. % 0.40/0.55 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.40/0.55 apply zenon_H43. zenon_intro zenon_Hf. % 0.40/0.55 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H13. zenon_intro zenon_H45. % 0.40/0.55 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H12. zenon_intro zenon_H10. % 0.40/0.55 generalize (apart4 zenon_TX_w). zenon_intro zenon_H46. % 0.40/0.55 generalize (apart1 zenon_TX_w). zenon_intro zenon_H47. % 0.40/0.55 generalize (zenon_H46 zenon_TZ_u). zenon_intro zenon_H48. % 0.40/0.55 generalize (zenon_H48 zenon_TX_w). zenon_intro zenon_H49. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H1f | zenon_intro zenon_H4a ]. % 0.40/0.55 exact (zenon_H1f zenon_H12). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.40/0.55 exact (zenon_H47 zenon_H4c). % 0.40/0.55 generalize (cu1 zenon_TZ_u). zenon_intro zenon_H4d. % 0.40/0.55 generalize (zenon_H4d zenon_TX_w). zenon_intro zenon_H4e. % 0.40/0.55 generalize (ceq3 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H4f. % 0.40/0.55 generalize (zenon_H4f (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H50. % 0.40/0.55 generalize (apart3 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H51. % 0.40/0.55 generalize (zenon_H50 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H52. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H35 | zenon_intro zenon_H53 ]. % 0.40/0.55 exact (zenon_H35 zenon_H10). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.40/0.55 generalize (zenon_H4e (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H56. % 0.40/0.55 generalize (zenon_H56 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H57. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.40/0.55 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.40/0.55 exact (zenon_H5b zenon_H4b). % 0.40/0.55 exact (zenon_H5a zenon_H55). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H29 | zenon_intro zenon_H5c ]. % 0.40/0.55 generalize (ci2 zenon_TX_w). zenon_intro zenon_H19. % 0.40/0.55 generalize (zenon_H19 zenon_TZ_u). zenon_intro zenon_H20. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H1f | zenon_intro zenon_H21 ]. % 0.40/0.55 exact (zenon_H1f zenon_H12). % 0.40/0.55 exact (zenon_H21 zenon_H29). % 0.40/0.55 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H11 | zenon_intro zenon_H5d ]. % 0.40/0.55 apply (zenon_L1_ zenon_TZ_u zenon_TY_v zenon_TX_w); trivial. % 0.40/0.55 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H3b | zenon_intro zenon_H3c ]. % 0.40/0.55 generalize (ci1 zenon_TX_w). zenon_intro zenon_H17. % 0.40/0.55 generalize (zenon_H17 zenon_TZ_u). zenon_intro zenon_H1d. % 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.40/0.55 exact (zenon_H1f zenon_H12). % 0.40/0.55 exact (zenon_H1e zenon_H3b). % 0.40/0.55 apply (zenon_L3_ zenon_TY_v zenon_TX_w); trivial. % 0.40/0.55 exact (zenon_H51 zenon_H54). % 0.40/0.55 Qed. % 0.40/0.55 % SZS output end Proof % 0.40/0.55 (* END-PROOF *) % 0.40/0.55 nodes searched: 1790 % 0.40/0.55 max branch formulas: 789 % 0.40/0.55 proof nodes created: 198 % 0.40/0.55 formulas created: 6999 % 0.40/0.55 %------------------------------------------------------------------------------