%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 07:00:26 EDT 2022 % Result : Theorem 0.60s 0.78s % Output : Proof 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n003.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 00:58:42 EDT 2022 % 0.12/0.33 % CPUTime : % 0.60/0.78 (* PROOF-FOUND *) % 0.60/0.78 % SZS status Theorem % 0.60/0.78 (* BEGIN-PROOF *) % 0.60/0.78 % SZS output start Proof % 0.60/0.78 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)))->((distinct_lines (line_connecting X Y) (line_connecting Z X))/\(distinct_lines (line_connecting X Y) (line_connecting Z Y))))))). % 0.60/0.78 Proof. % 0.60/0.78 assert (zenon_L1_ : forall (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TY_v zenon_TX_u)/\(distinct_lines U V))->((apart_point_and_line zenon_TY_v U)\/((apart_point_and_line zenon_TY_v V)\/((apart_point_and_line zenon_TX_u U)\/(apart_point_and_line zenon_TX_u V))))))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TY_v zenon_TX_u))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TX_u zenon_TY_v))) -> (~(apart_point_and_line zenon_TY_v (line_connecting zenon_TY_v zenon_TX_u))) -> (~(apart_point_and_line zenon_TY_v (line_connecting zenon_TX_u zenon_TY_v))) -> (distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting zenon_TY_v zenon_TX_u)) -> (distinct_points zenon_TY_v zenon_TX_u) -> False). % 0.60/0.78 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13. % 0.60/0.78 generalize (zenon_Hd (line_connecting zenon_TX_u zenon_TY_v)). zenon_intro zenon_H16. % 0.60/0.78 generalize (zenon_H16 (line_connecting zenon_TY_v zenon_TX_u)). zenon_intro zenon_H17. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 exact (zenon_H1a zenon_H12). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H18); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.60/0.78 exact (zenon_H11 zenon_H1d). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.60/0.78 exact (zenon_H10 zenon_H1f). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.60/0.78 exact (zenon_Hf zenon_H21). % 0.60/0.78 exact (zenon_He zenon_H20). % 0.60/0.78 (* end of lemma zenon_L1_ *) % 0.60/0.78 assert (zenon_L2_ : forall (zenon_TZ_bl : zenon_U) (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TY_v zenon_TX_u)->((apart_point_and_line Z (line_connecting zenon_TY_v zenon_TX_u))->((distinct_points Z zenon_TY_v)/\(distinct_points Z zenon_TX_u))))) -> (distinct_points zenon_TY_v zenon_TX_u) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TY_v zenon_TX_u)) -> (~(distinct_points zenon_TZ_bl zenon_TX_u)) -> False). % 0.60/0.78 do 3 intro. intros zenon_H22 zenon_H13 zenon_H23 zenon_H24. % 0.60/0.78 generalize (zenon_H22 zenon_TZ_bl). zenon_intro zenon_H26. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.60/0.78 exact (zenon_H29 zenon_H23). % 0.60/0.78 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.60/0.78 exact (zenon_H24 zenon_H2a). % 0.60/0.78 (* end of lemma zenon_L2_ *) % 0.60/0.78 assert (zenon_L3_ : forall (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U) (zenon_TZ_bl : zenon_U), (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v))->((distinct_lines (line_connecting zenon_TX_u zenon_TY_v) Z)\/(apart_point_and_line zenon_TZ_bl Z)))) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v)) -> (~(distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting zenon_TZ_bl zenon_TX_u))) -> (~(apart_point_and_line zenon_TZ_bl (line_connecting zenon_TZ_bl zenon_TX_u))) -> False). % 0.60/0.78 do 3 intro. intros zenon_H2c zenon_H2d zenon_H2e zenon_H2f. % 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TZ_bl zenon_TX_u)). zenon_intro zenon_H30. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.60/0.78 exact (zenon_H32 zenon_H2d). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.60/0.78 exact (zenon_H2e zenon_H34). % 0.60/0.78 exact (zenon_H2f zenon_H33). % 0.60/0.78 (* end of lemma zenon_L3_ *) % 0.60/0.78 assert (zenon_L4_ : forall (zenon_TX_u : zenon_U) (zenon_TZ_bl : zenon_U), ((distinct_points zenon_TZ_bl zenon_TZ_bl)/\(distinct_points zenon_TZ_bl zenon_TX_u)) -> (~(distinct_points zenon_TZ_bl zenon_TZ_bl)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H35 zenon_H36. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H2a. % 0.60/0.78 exact (zenon_H36 zenon_H37). % 0.60/0.78 (* end of lemma zenon_L4_ *) % 0.60/0.78 assert (zenon_L5_ : forall (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U), ((distinct_points zenon_TX_u zenon_TY_v)/\(distinct_points zenon_TX_u zenon_TX_u)) -> (~(distinct_points zenon_TX_u zenon_TX_u)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H38 zenon_H39. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 0.60/0.78 exact (zenon_H39 zenon_H3a). % 0.60/0.78 (* end of lemma zenon_L5_ *) % 0.60/0.78 assert (zenon_L6_ : forall (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), ((distinct_points zenon_TY_v zenon_TY_v)/\(distinct_points zenon_TY_v zenon_TX_u)) -> (~(distinct_points zenon_TY_v zenon_TY_v)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H3c zenon_H3d. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H13. % 0.60/0.78 exact (zenon_H3d zenon_H3e). % 0.60/0.78 (* end of lemma zenon_L6_ *) % 0.60/0.78 assert (zenon_L7_ : forall (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U), ((distinct_points zenon_TX_u zenon_TX_u)/\(distinct_points zenon_TX_u zenon_TY_v)) -> (~(distinct_points zenon_TX_u zenon_TX_u)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H3f zenon_H39. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H3a. zenon_intro zenon_H3b. % 0.60/0.78 exact (zenon_H39 zenon_H3a). % 0.60/0.78 (* end of lemma zenon_L7_ *) % 0.60/0.78 assert (zenon_L8_ : forall (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), ((distinct_points zenon_TY_v zenon_TX_u)/\(distinct_points zenon_TY_v zenon_TY_v)) -> (~(distinct_points zenon_TY_v zenon_TY_v)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H40 zenon_H3d. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H13. zenon_intro zenon_H3e. % 0.60/0.78 exact (zenon_H3d zenon_H3e). % 0.60/0.78 (* end of lemma zenon_L8_ *) % 0.60/0.78 assert (zenon_L9_ : forall (zenon_TZ_bl : zenon_U) (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TY_v zenon_TX_u)->((apart_point_and_line Z (line_connecting zenon_TY_v zenon_TX_u))->((distinct_points Z zenon_TY_v)/\(distinct_points Z zenon_TX_u))))) -> (distinct_points zenon_TY_v zenon_TX_u) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TY_v zenon_TX_u)) -> (~(distinct_points zenon_TZ_bl zenon_TY_v)) -> False). % 0.60/0.78 do 3 intro. intros zenon_H22 zenon_H13 zenon_H23 zenon_H41. % 0.60/0.78 generalize (zenon_H22 zenon_TZ_bl). zenon_intro zenon_H26. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.60/0.78 exact (zenon_H29 zenon_H23). % 0.60/0.78 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.60/0.78 exact (zenon_H41 zenon_H2b). % 0.60/0.78 (* end of lemma zenon_L9_ *) % 0.60/0.78 assert (zenon_L10_ : forall (zenon_TY_v : zenon_U) (zenon_TZ_bl : zenon_U), ((distinct_points zenon_TZ_bl zenon_TZ_bl)/\(distinct_points zenon_TZ_bl zenon_TY_v)) -> (~(distinct_points zenon_TZ_bl zenon_TZ_bl)) -> False). % 0.60/0.78 do 2 intro. intros zenon_H42 zenon_H36. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H37. zenon_intro zenon_H2b. % 0.60/0.78 exact (zenon_H36 zenon_H37). % 0.60/0.78 (* end of lemma zenon_L10_ *) % 0.60/0.78 assert (zenon_L11_ : forall (zenon_TZ_bl : zenon_U) (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U), (~(distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting zenon_TZ_bl zenon_TY_v))) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v)) -> (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v))->((distinct_lines (line_connecting zenon_TX_u zenon_TY_v) Z)\/(apart_point_and_line zenon_TZ_bl Z)))) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TY_v zenon_TX_u)) -> (distinct_points zenon_TY_v zenon_TX_u) -> (forall Z : zenon_U, ((distinct_points zenon_TY_v zenon_TX_u)->((apart_point_and_line Z (line_connecting zenon_TY_v zenon_TX_u))->((distinct_points Z zenon_TY_v)/\(distinct_points Z zenon_TX_u))))) -> False). % 0.60/0.78 do 3 intro. intros zenon_H43 zenon_H2d zenon_H2c zenon_H23 zenon_H13 zenon_H22. % 0.60/0.78 generalize (con1 zenon_TZ_bl). zenon_intro zenon_H44. % 0.60/0.78 generalize (apart1 zenon_TZ_bl). zenon_intro zenon_H36. % 0.60/0.78 generalize (zenon_H44 zenon_TY_v). zenon_intro zenon_H45. % 0.60/0.78 generalize (zenon_H45 zenon_TZ_bl). zenon_intro zenon_H46. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H41 | zenon_intro zenon_H47 ]. % 0.60/0.78 apply (zenon_L9_ zenon_TZ_bl zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H42 ]. % 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TZ_bl zenon_TY_v)). zenon_intro zenon_H49. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H32 | zenon_intro zenon_H4a ]. % 0.60/0.78 exact (zenon_H32 zenon_H2d). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.60/0.78 exact (zenon_H43 zenon_H4c). % 0.60/0.78 exact (zenon_H48 zenon_H4b). % 0.60/0.78 apply (zenon_L10_ zenon_TY_v zenon_TZ_bl); trivial. % 0.60/0.78 (* end of lemma zenon_L11_ *) % 0.60/0.78 apply NNPP. intro zenon_G. % 0.60/0.78 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)))->((distinct_lines (line_connecting X Y) (line_connecting Z X))/\(distinct_lines (line_connecting X Y) (line_connecting Z Y))))))) zenon_G); [ zenon_intro zenon_H4d; idtac ]. % 0.60/0.78 elim zenon_H4d. zenon_intro zenon_TX_u. zenon_intro zenon_H4e. % 0.60/0.78 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_u Y)/\(apart_point_and_line Z (line_connecting zenon_TX_u Y)))->((distinct_lines (line_connecting zenon_TX_u Y) (line_connecting Z zenon_TX_u))/\(distinct_lines (line_connecting zenon_TX_u Y) (line_connecting Z Y)))))) zenon_H4e); [ zenon_intro zenon_H4f; idtac ]. % 0.60/0.78 elim zenon_H4f. zenon_intro zenon_TY_v. zenon_intro zenon_H50. % 0.60/0.78 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_u zenon_TY_v)/\(apart_point_and_line Z (line_connecting zenon_TX_u zenon_TY_v)))->((distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting Z zenon_TX_u))/\(distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting Z zenon_TY_v))))) zenon_H50); [ zenon_intro zenon_H51; idtac ]. % 0.60/0.78 elim zenon_H51. zenon_intro zenon_TZ_bl. zenon_intro zenon_H52. % 0.60/0.78 apply (zenon_notimply_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 0.60/0.78 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H3b. zenon_intro zenon_H2d. % 0.60/0.78 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H2e | zenon_intro zenon_H43 ]. % 0.60/0.78 generalize (apart1 zenon_TY_v). zenon_intro zenon_H3d. % 0.60/0.78 generalize (con1 zenon_TY_v). zenon_intro zenon_H55. % 0.60/0.78 generalize (apart4 zenon_TX_u). zenon_intro zenon_H56. % 0.60/0.78 generalize (zenon_H56 zenon_TY_v). zenon_intro zenon_H57. % 0.60/0.78 generalize (con1 zenon_TX_u). zenon_intro zenon_H58. % 0.60/0.78 generalize (apart1 zenon_TX_u). zenon_intro zenon_H39. % 0.60/0.78 generalize (zenon_H58 zenon_TY_v). zenon_intro zenon_H59. % 0.60/0.78 generalize (zenon_H55 zenon_TX_u). zenon_intro zenon_H22. % 0.60/0.78 generalize (ceq2 zenon_TZ_bl). zenon_intro zenon_H5a. % 0.60/0.78 generalize (zenon_H59 zenon_TY_v). zenon_intro zenon_H5b. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.60/0.78 exact (zenon_H5d zenon_H3b). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H11 | zenon_intro zenon_H40 ]. % 0.60/0.78 generalize (zenon_H59 zenon_TX_u). zenon_intro zenon_H5e. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5d | zenon_intro zenon_H5f ]. % 0.60/0.78 exact (zenon_H5d zenon_H3b). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_Hf | zenon_intro zenon_H3f ]. % 0.60/0.78 generalize (zenon_H57 zenon_TX_u). zenon_intro zenon_H60. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H5d | zenon_intro zenon_H61 ]. % 0.60/0.78 exact (zenon_H5d zenon_H3b). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H3a | zenon_intro zenon_H13 ]. % 0.60/0.78 exact (zenon_H39 zenon_H3a). % 0.60/0.78 generalize (zenon_H22 zenon_TY_v). zenon_intro zenon_H62. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H1b | zenon_intro zenon_H63 ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H10 | zenon_intro zenon_H3c ]. % 0.60/0.78 generalize (cu1 zenon_TY_v). zenon_intro zenon_H64. % 0.60/0.78 generalize (zenon_H22 zenon_TX_u). zenon_intro zenon_H65. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H1b | zenon_intro zenon_H66 ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_He | zenon_intro zenon_H38 ]. % 0.60/0.78 generalize (zenon_H64 zenon_TX_u). zenon_intro zenon_Hd. % 0.60/0.78 generalize (zenon_H5a (line_connecting zenon_TX_u zenon_TY_v)). zenon_intro zenon_H2c. % 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TY_v zenon_TX_u)). zenon_intro zenon_H67. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H32 | zenon_intro zenon_H68 ]. % 0.60/0.78 exact (zenon_H32 zenon_H2d). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H12 | zenon_intro zenon_H23 ]. % 0.60/0.78 apply (zenon_L1_ zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 generalize (con1 zenon_TZ_bl). zenon_intro zenon_H44. % 0.60/0.78 generalize (apart1 zenon_TZ_bl). zenon_intro zenon_H36. % 0.60/0.78 generalize (zenon_H44 zenon_TX_u). zenon_intro zenon_H69. % 0.60/0.78 generalize (zenon_H69 zenon_TZ_bl). zenon_intro zenon_H6a. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H24 | zenon_intro zenon_H6b ]. % 0.60/0.78 apply (zenon_L2_ zenon_TZ_bl zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ]. % 0.60/0.78 apply (zenon_L3_ zenon_TY_v zenon_TX_u zenon_TZ_bl); trivial. % 0.60/0.78 apply (zenon_L4_ zenon_TX_u zenon_TZ_bl); trivial. % 0.60/0.78 apply (zenon_L5_ zenon_TY_v zenon_TX_u); trivial. % 0.60/0.78 apply (zenon_L6_ zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 apply (zenon_L7_ zenon_TY_v zenon_TX_u); trivial. % 0.60/0.78 apply (zenon_L8_ zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 generalize (apart1 zenon_TY_v). zenon_intro zenon_H3d. % 0.60/0.78 generalize (con1 zenon_TY_v). zenon_intro zenon_H55. % 0.60/0.78 generalize (apart4 zenon_TX_u). zenon_intro zenon_H56. % 0.60/0.78 generalize (zenon_H56 zenon_TY_v). zenon_intro zenon_H57. % 0.60/0.78 generalize (con1 zenon_TX_u). zenon_intro zenon_H58. % 0.60/0.78 generalize (apart1 zenon_TX_u). zenon_intro zenon_H39. % 0.60/0.78 generalize (zenon_H58 zenon_TY_v). zenon_intro zenon_H59. % 0.60/0.78 generalize (zenon_H55 zenon_TX_u). zenon_intro zenon_H22. % 0.60/0.78 generalize (ceq2 zenon_TZ_bl). zenon_intro zenon_H5a. % 0.60/0.78 generalize (zenon_H59 zenon_TY_v). zenon_intro zenon_H5b. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.60/0.78 exact (zenon_H5d zenon_H3b). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H11 | zenon_intro zenon_H40 ]. % 0.60/0.78 generalize (zenon_H59 zenon_TX_u). zenon_intro zenon_H5e. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5d | zenon_intro zenon_H5f ]. % 0.60/0.78 exact (zenon_H5d zenon_H3b). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_Hf | zenon_intro zenon_H3f ]. % 0.60/0.78 generalize (zenon_H57 zenon_TX_u). zenon_intro zenon_H60. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H5d | zenon_intro zenon_H61 ]. % 0.60/0.78 exact (zenon_H5d zenon_H3b). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H3a | zenon_intro zenon_H13 ]. % 0.60/0.78 exact (zenon_H39 zenon_H3a). % 0.60/0.78 generalize (zenon_H22 zenon_TY_v). zenon_intro zenon_H62. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H1b | zenon_intro zenon_H63 ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H10 | zenon_intro zenon_H3c ]. % 0.60/0.78 generalize (cu1 zenon_TY_v). zenon_intro zenon_H64. % 0.60/0.78 generalize (zenon_H22 zenon_TX_u). zenon_intro zenon_H65. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H1b | zenon_intro zenon_H66 ]. % 0.60/0.78 exact (zenon_H1b zenon_H13). % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_He | zenon_intro zenon_H38 ]. % 0.60/0.78 generalize (zenon_H64 zenon_TX_u). zenon_intro zenon_Hd. % 0.60/0.78 generalize (zenon_H5a (line_connecting zenon_TX_u zenon_TY_v)). zenon_intro zenon_H2c. % 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TY_v zenon_TX_u)). zenon_intro zenon_H67. % 0.60/0.78 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H32 | zenon_intro zenon_H68 ]. % 0.60/0.78 exact (zenon_H32 zenon_H2d). % 0.60/0.78 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H12 | zenon_intro zenon_H23 ]. % 0.60/0.78 apply (zenon_L1_ zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 apply (zenon_L11_ zenon_TZ_bl zenon_TY_v zenon_TX_u); trivial. % 0.60/0.78 apply (zenon_L5_ zenon_TY_v zenon_TX_u); trivial. % 0.60/0.78 apply (zenon_L6_ zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 apply (zenon_L7_ zenon_TY_v zenon_TX_u); trivial. % 0.60/0.78 apply (zenon_L8_ zenon_TX_u zenon_TY_v); trivial. % 0.60/0.78 Qed. % 0.60/0.78 % SZS output end Proof % 0.60/0.78 (* END-PROOF *) % 0.60/0.78 nodes searched: 19034 % 0.60/0.78 max branch formulas: 1557 % 0.60/0.78 proof nodes created: 1664 % 0.60/0.78 formulas created: 32381 % 0.60/0.78 %------------------------------------------------------------------------------