%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 07:00:40 EDT 2022 % Result : Theorem 0.77s 1.00s % Output : Proof 0.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO196+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.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 : Fri Jun 17 18:23:36 EDT 2022 % 0.13/0.34 % CPUTime : % 0.77/1.00 (* PROOF-FOUND *) % 0.77/1.00 % SZS status Theorem % 0.77/1.00 (* BEGIN-PROOF *) % 0.77/1.00 % SZS output start Proof % 0.77/1.00 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines X Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point X Y) U))/\(~(apart_point_and_line (intersection_point X Y) V)))))->((~(apart_point_and_line (intersection_point U V) X))/\(~(apart_point_and_line (intersection_point U V) Y)))))))). % 0.77/1.00 Proof. % 0.77/1.00 assert (zenon_L1_ : forall (zenon_TU_q : zenon_U), (convergent_lines zenon_TU_q zenon_TU_q) -> False). % 0.77/1.00 do 1 intro. intros zenon_Hf. % 0.77/1.00 generalize (apart3 zenon_TU_q). zenon_intro zenon_H11. % 0.77/1.00 exact (zenon_H11 zenon_Hf). % 0.77/1.00 (* end of lemma zenon_L1_ *) % 0.77/1.00 assert (zenon_L2_ : forall (zenon_TV_v : zenon_U) (zenon_TU_q : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_q Y)->(~(apart_point_and_line (intersection_point zenon_TU_q Y) zenon_TU_q)))) -> (convergent_lines zenon_TU_q zenon_TV_v) -> (apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TU_q) -> False). % 0.77/1.00 do 2 intro. intros zenon_H12 zenon_H13 zenon_H14. % 0.77/1.00 generalize (zenon_H12 zenon_TV_v). zenon_intro zenon_H16. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.77/1.00 exact (zenon_H18 zenon_H13). % 0.77/1.00 exact (zenon_H17 zenon_H14). % 0.77/1.00 (* end of lemma zenon_L2_ *) % 0.77/1.00 assert (zenon_L3_ : forall (zenon_TY_bf : zenon_U) (zenon_TX_bg : zenon_U) (zenon_TV_v : zenon_U) (zenon_TU_q : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TU_q zenon_TV_v) (intersection_point zenon_TX_bg zenon_TY_bf))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) U)\/((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) V)\/((apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) U)\/(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) V))))))) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TV_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TU_q)) -> (~(apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TV_v)) -> (convergent_lines zenon_TU_q zenon_TV_v) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_q Y)->(~(apart_point_and_line (intersection_point zenon_TU_q Y) zenon_TU_q)))) -> (distinct_lines zenon_TU_q zenon_TV_v) -> (distinct_points (intersection_point zenon_TU_q zenon_TV_v) (intersection_point zenon_TX_bg zenon_TY_bf)) -> False). % 0.77/1.00 do 4 intro. intros zenon_H19 zenon_H1a zenon_H1b zenon_H1c zenon_H13 zenon_H12 zenon_H1d zenon_H1e. % 0.77/1.00 generalize (zenon_H19 zenon_TU_q). zenon_intro zenon_H21. % 0.77/1.00 generalize (zenon_H21 zenon_TV_v). zenon_intro zenon_H22. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.77/1.00 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 0.77/1.00 exact (zenon_H26 zenon_H1e). % 0.77/1.00 exact (zenon_H25 zenon_H1d). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H14 | zenon_intro zenon_H27 ]. % 0.77/1.00 apply (zenon_L2_ zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.77/1.00 exact (zenon_H1c zenon_H29). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.77/1.00 exact (zenon_H1b zenon_H2b). % 0.77/1.00 exact (zenon_H1a zenon_H2a). % 0.77/1.00 (* end of lemma zenon_L3_ *) % 0.77/1.00 assert (zenon_L4_ : forall (zenon_TY_bf : zenon_U) (zenon_TX_bg : zenon_U) (zenon_TV_v : zenon_U) (zenon_TU_q : zenon_U), (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TU_q zenon_TV_v) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) U)\/((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (forall Z : zenon_U, ((convergent_lines zenon_TU_q zenon_TV_v)->((convergent_lines zenon_TU_q Z)\/(convergent_lines zenon_TV_v Z)))) -> (convergent_lines zenon_TU_q zenon_TV_v) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TV_v Y)->((distinct_lines Y Z)\/(convergent_lines zenon_TV_v Z))))) -> (~(convergent_lines zenon_TV_v zenon_TV_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TV_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TU_q)) -> (~(apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TV_v)) -> (distinct_points (intersection_point zenon_TU_q zenon_TV_v) (intersection_point zenon_TX_bg zenon_TY_bf)) -> (~(distinct_lines zenon_TV_v zenon_TV_v)) -> False). % 0.77/1.00 do 4 intro. intros zenon_H2c zenon_H2d zenon_H13 zenon_H2e zenon_H2f zenon_H1a zenon_H1b zenon_H1c zenon_H1e zenon_H30. % 0.77/1.00 generalize (zenon_H2c (intersection_point zenon_TX_bg zenon_TY_bf)). zenon_intro zenon_H19. % 0.77/1.00 generalize (ci3 zenon_TU_q). zenon_intro zenon_H12. % 0.77/1.00 generalize (apart5 zenon_TU_q). zenon_intro zenon_H31. % 0.77/1.00 generalize (zenon_H31 zenon_TV_v). zenon_intro zenon_H32. % 0.77/1.00 generalize (zenon_H32 zenon_TV_v). zenon_intro zenon_H33. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H25 | zenon_intro zenon_H34 ]. % 0.77/1.00 generalize (zenon_H2d zenon_TU_q). zenon_intro zenon_H35. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H18 | zenon_intro zenon_H36 ]. % 0.77/1.00 exact (zenon_H18 zenon_H13). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_Hf | zenon_intro zenon_H37 ]. % 0.77/1.00 apply (zenon_L1_ zenon_TU_q); trivial. % 0.77/1.00 generalize (zenon_H2e zenon_TU_q). zenon_intro zenon_H38. % 0.77/1.00 generalize (zenon_H38 zenon_TV_v). zenon_intro zenon_H39. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.77/1.00 exact (zenon_H3b zenon_H37). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H1d | zenon_intro zenon_H3c ]. % 0.77/1.00 exact (zenon_H25 zenon_H1d). % 0.77/1.00 exact (zenon_H2f zenon_H3c). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H1d | zenon_intro zenon_H3d ]. % 0.77/1.00 apply (zenon_L3_ zenon_TY_bf zenon_TX_bg zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 exact (zenon_H30 zenon_H3d). % 0.77/1.00 (* end of lemma zenon_L4_ *) % 0.77/1.00 assert (zenon_L5_ : forall (zenon_TY_bf : zenon_U) (zenon_TX_bg : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bg Y)->(~(apart_point_and_line (intersection_point zenon_TX_bg Y) zenon_TX_bg)))) -> (convergent_lines zenon_TX_bg zenon_TY_bf) -> (apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TX_bg) -> False). % 0.77/1.00 do 2 intro. intros zenon_H3e zenon_H3f zenon_H40. % 0.77/1.00 generalize (zenon_H3e zenon_TY_bf). zenon_intro zenon_H41. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.77/1.00 exact (zenon_H43 zenon_H3f). % 0.77/1.00 exact (zenon_H42 zenon_H40). % 0.77/1.00 (* end of lemma zenon_L5_ *) % 0.77/1.00 assert (zenon_L6_ : forall (zenon_TV_v : zenon_U) (zenon_TU_q : zenon_U), (apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TV_v) -> (convergent_lines zenon_TU_q zenon_TV_v) -> False). % 0.77/1.00 do 2 intro. intros zenon_H29 zenon_H13. % 0.77/1.00 generalize (ci4 zenon_TU_q). zenon_intro zenon_H44. % 0.77/1.00 generalize (zenon_H44 zenon_TV_v). zenon_intro zenon_H45. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H18 | zenon_intro zenon_H1c ]. % 0.77/1.00 exact (zenon_H18 zenon_H13). % 0.77/1.00 exact (zenon_H1c zenon_H29). % 0.77/1.00 (* end of lemma zenon_L6_ *) % 0.77/1.00 assert (zenon_L7_ : forall (zenon_TV_v : zenon_U) (zenon_TU_q : zenon_U) (zenon_TY_bf : zenon_U) (zenon_TX_bg : zenon_U), (convergent_lines zenon_TX_bg zenon_TY_bf) -> (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TY_bf)->((distinct_points (intersection_point zenon_TU_q zenon_TV_v) Z)\/(apart_point_and_line Z zenon_TY_bf)))) -> (apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TY_bf) -> (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TU_q zenon_TV_v) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) U)\/((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (forall Z : zenon_U, ((convergent_lines zenon_TU_q zenon_TV_v)->((convergent_lines zenon_TU_q Z)\/(convergent_lines zenon_TV_v Z)))) -> (convergent_lines zenon_TU_q zenon_TV_v) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TV_v Y)->((distinct_lines Y Z)\/(convergent_lines zenon_TV_v Z))))) -> (~(convergent_lines zenon_TV_v zenon_TV_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TV_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TU_q)) -> (~(distinct_lines zenon_TV_v zenon_TV_v)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) Z))))) -> False). % 0.77/1.00 do 4 intro. intros zenon_H3f zenon_H46 zenon_H47 zenon_H2c zenon_H2d zenon_H13 zenon_H2e zenon_H2f zenon_H1a zenon_H1b zenon_H30 zenon_H48. % 0.77/1.00 generalize (ci4 zenon_TX_bg). zenon_intro zenon_H49. % 0.77/1.00 generalize (zenon_H48 zenon_TV_v). zenon_intro zenon_H4a. % 0.77/1.00 generalize (zenon_H49 zenon_TY_bf). zenon_intro zenon_H4b. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H43 | zenon_intro zenon_H4c ]. % 0.77/1.00 exact (zenon_H43 zenon_H3f). % 0.77/1.00 generalize (zenon_H4a zenon_TV_v). zenon_intro zenon_H4d. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H1c | zenon_intro zenon_H4e ]. % 0.77/1.00 generalize (zenon_H46 (intersection_point zenon_TX_bg zenon_TY_bf)). zenon_intro zenon_H4f. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.77/1.00 exact (zenon_H51 zenon_H47). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H1e | zenon_intro zenon_H52 ]. % 0.77/1.00 apply (zenon_L4_ zenon_TY_bf zenon_TX_bg zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 exact (zenon_H4c zenon_H52). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3d | zenon_intro zenon_H29 ]. % 0.77/1.00 exact (zenon_H30 zenon_H3d). % 0.77/1.00 apply (zenon_L6_ zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 (* end of lemma zenon_L7_ *) % 0.77/1.00 assert (zenon_L8_ : forall (zenon_TY_bf : zenon_U) (zenon_TX_bg : zenon_U) (zenon_TV_v : zenon_U) (zenon_TU_q : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) Z))))) -> (~(distinct_lines zenon_TV_v zenon_TV_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TU_q)) -> (~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TV_v)) -> (~(convergent_lines zenon_TV_v zenon_TV_v)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TV_v Y)->((distinct_lines Y Z)\/(convergent_lines zenon_TV_v Z))))) -> (convergent_lines zenon_TU_q zenon_TV_v) -> (forall Z : zenon_U, ((convergent_lines zenon_TU_q zenon_TV_v)->((convergent_lines zenon_TU_q Z)\/(convergent_lines zenon_TV_v Z)))) -> (apart_point_and_line (intersection_point zenon_TU_q zenon_TV_v) zenon_TY_bf) -> (convergent_lines zenon_TX_bg zenon_TY_bf) -> False). % 0.77/1.00 do 4 intro. intros zenon_H48 zenon_H30 zenon_H1b zenon_H1a zenon_H2f zenon_H2e zenon_H13 zenon_H2d zenon_H47 zenon_H3f. % 0.77/1.00 generalize (ceq1 (intersection_point zenon_TU_q zenon_TV_v)). zenon_intro zenon_H53. % 0.77/1.00 generalize (zenon_H53 zenon_TY_bf). zenon_intro zenon_H46. % 0.77/1.00 generalize (cu1 (intersection_point zenon_TU_q zenon_TV_v)). zenon_intro zenon_H2c. % 0.77/1.00 apply (zenon_L7_ zenon_TV_v zenon_TU_q zenon_TY_bf zenon_TX_bg); trivial. % 0.77/1.00 (* end of lemma zenon_L8_ *) % 0.77/1.00 apply NNPP. intro zenon_G. % 0.77/1.00 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines X Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point X Y) U))/\(~(apart_point_and_line (intersection_point X Y) V)))))->((~(apart_point_and_line (intersection_point U V) X))/\(~(apart_point_and_line (intersection_point U V) Y)))))))) zenon_G); [ zenon_intro zenon_H54; idtac ]. % 0.77/1.00 elim zenon_H54. zenon_intro zenon_TX_bg. zenon_intro zenon_H55. % 0.77/1.00 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines zenon_TX_bg Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point zenon_TX_bg Y) U))/\(~(apart_point_and_line (intersection_point zenon_TX_bg Y) V)))))->((~(apart_point_and_line (intersection_point U V) zenon_TX_bg))/\(~(apart_point_and_line (intersection_point U V) Y))))))) zenon_H55); [ zenon_intro zenon_H56; idtac ]. % 0.77/1.00 elim zenon_H56. zenon_intro zenon_TY_bf. zenon_intro zenon_H57. % 0.77/1.00 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((convergent_lines zenon_TX_bg zenon_TY_bf)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) U))/\(~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) V)))))->((~(apart_point_and_line (intersection_point U V) zenon_TX_bg))/\(~(apart_point_and_line (intersection_point U V) zenon_TY_bf)))))) zenon_H57); [ zenon_intro zenon_H58; idtac ]. % 0.77/1.00 elim zenon_H58. zenon_intro zenon_TU_q. zenon_intro zenon_H59. % 0.77/1.00 apply (zenon_notallex_s (fun V : zenon_U => (((convergent_lines zenon_TX_bg zenon_TY_bf)/\((convergent_lines zenon_TU_q V)/\((~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) zenon_TU_q))/\(~(apart_point_and_line (intersection_point zenon_TX_bg zenon_TY_bf) V)))))->((~(apart_point_and_line (intersection_point zenon_TU_q V) zenon_TX_bg))/\(~(apart_point_and_line (intersection_point zenon_TU_q V) zenon_TY_bf))))) zenon_H59); [ zenon_intro zenon_H5a; idtac ]. % 0.77/1.00 elim zenon_H5a. zenon_intro zenon_TV_v. zenon_intro zenon_H5b. % 0.77/1.00 apply (zenon_notimply_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 0.77/1.00 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H3f. zenon_intro zenon_H5e. % 0.77/1.00 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H13. zenon_intro zenon_H5f. % 0.77/1.00 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.77/1.00 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 0.77/1.00 apply zenon_H61. zenon_intro zenon_H62. % 0.77/1.00 generalize (ci3 zenon_TX_bg). zenon_intro zenon_H3e. % 0.77/1.00 generalize (ax6 zenon_TU_q). zenon_intro zenon_H63. % 0.77/1.00 generalize (apart3 zenon_TV_v). zenon_intro zenon_H2f. % 0.77/1.00 generalize (zenon_H63 zenon_TV_v). zenon_intro zenon_H2d. % 0.77/1.00 generalize (ceq3 zenon_TV_v). zenon_intro zenon_H2e. % 0.77/1.00 generalize (apart2 zenon_TV_v). zenon_intro zenon_H30. % 0.77/1.00 generalize (ceq2 (intersection_point zenon_TU_q zenon_TV_v)). zenon_intro zenon_H48. % 0.77/1.00 generalize (ceq1 (intersection_point zenon_TU_q zenon_TV_v)). zenon_intro zenon_H53. % 0.77/1.00 generalize (zenon_H53 zenon_TX_bg). zenon_intro zenon_H64. % 0.77/1.00 generalize (cu1 (intersection_point zenon_TU_q zenon_TV_v)). zenon_intro zenon_H2c. % 0.77/1.00 generalize (zenon_H48 zenon_TV_v). zenon_intro zenon_H4a. % 0.77/1.00 generalize (zenon_H4a zenon_TV_v). zenon_intro zenon_H4d. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H1c | zenon_intro zenon_H4e ]. % 0.77/1.00 generalize (apart2 zenon_TX_bg). zenon_intro zenon_H65. % 0.77/1.00 generalize (ceq2 (intersection_point zenon_TX_bg zenon_TY_bf)). zenon_intro zenon_H66. % 0.77/1.00 generalize (zenon_H66 zenon_TX_bg). zenon_intro zenon_H67. % 0.77/1.00 generalize (zenon_H67 zenon_TX_bg). zenon_intro zenon_H68. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H42 | zenon_intro zenon_H69 ]. % 0.77/1.00 generalize (zenon_H64 (intersection_point zenon_TX_bg zenon_TY_bf)). zenon_intro zenon_H6a. % 0.77/1.00 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.77/1.00 exact (zenon_H6c zenon_H62). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H6b); [ zenon_intro zenon_H1e | zenon_intro zenon_H40 ]. % 0.77/1.00 apply (zenon_L4_ zenon_TY_bf zenon_TX_bg zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 exact (zenon_H42 zenon_H40). % 0.77/1.00 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H6d | zenon_intro zenon_H40 ]. % 0.77/1.00 exact (zenon_H65 zenon_H6d). % 0.77/1.00 apply (zenon_L5_ zenon_TY_bf zenon_TX_bg); trivial. % 0.77/1.00 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H3d | zenon_intro zenon_H29 ]. % 0.77/1.00 exact (zenon_H30 zenon_H3d). % 0.77/1.00 apply (zenon_L6_ zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 apply zenon_H60. zenon_intro zenon_H47. % 0.77/1.00 generalize (ax6 zenon_TU_q). zenon_intro zenon_H63. % 0.77/1.00 generalize (apart3 zenon_TV_v). zenon_intro zenon_H2f. % 0.77/1.00 generalize (zenon_H63 zenon_TV_v). zenon_intro zenon_H2d. % 0.77/1.00 generalize (ceq3 zenon_TV_v). zenon_intro zenon_H2e. % 0.77/1.00 generalize (apart2 zenon_TV_v). zenon_intro zenon_H30. % 0.77/1.00 generalize (ceq2 (intersection_point zenon_TU_q zenon_TV_v)). zenon_intro zenon_H48. % 0.77/1.00 apply (zenon_L8_ zenon_TY_bf zenon_TX_bg zenon_TV_v zenon_TU_q); trivial. % 0.77/1.00 Qed. % 0.77/1.00 % SZS output end Proof % 0.77/1.00 (* END-PROOF *) % 0.77/1.00 nodes searched: 33831 % 0.77/1.00 max branch formulas: 3833 % 0.77/1.00 proof nodes created: 1835 % 0.77/1.00 formulas created: 102029 % 0.77/1.00 %------------------------------------------------------------------------------