%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 2.88s 3.08s % Output : Proof 2.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO196+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.32 % Computer : n006.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.32 % CPULimit : 300 % 0.12/0.32 % WCLimit : 600 % 0.12/0.32 % DateTime : Sat Jun 18 04:10:10 EDT 2022 % 0.12/0.32 % CPUTime : % 2.88/3.08 (* PROOF-FOUND *) % 2.88/3.08 % SZS status Theorem % 2.88/3.08 (* BEGIN-PROOF *) % 2.88/3.08 % SZS output start Proof % 2.88/3.08 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)))))))). % 2.88/3.08 Proof. % 2.88/3.08 assert (zenon_L1_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TU_x zenon_TV_w) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) U)\/((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (distinct_points (intersection_point zenon_TU_x zenon_TV_w) (intersection_point zenon_TX_v zenon_TY_u)) -> (distinct_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> False). % 2.88/3.08 do 4 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13. % 2.88/3.08 generalize (zenon_Hd (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H18. % 2.88/3.08 generalize (zenon_H18 zenon_TU_x). zenon_intro zenon_H19. % 2.88/3.08 generalize (zenon_H19 zenon_TV_w). zenon_intro zenon_H1a. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 2.88/3.08 apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 2.88/3.08 exact (zenon_H1e zenon_He). % 2.88/3.08 exact (zenon_H1d zenon_Hf). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 2.88/3.08 exact (zenon_H10 zenon_H20). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 2.88/3.08 exact (zenon_H11 zenon_H22). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 2.88/3.08 exact (zenon_H12 zenon_H24). % 2.88/3.08 exact (zenon_H13 zenon_H23). % 2.88/3.08 (* end of lemma zenon_L1_ *) % 2.88/3.08 assert (zenon_L2_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (convergent_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w)) -> (distinct_lines zenon_TU_x zenon_TV_w) -> (distinct_points (intersection_point zenon_TU_x zenon_TV_w) (intersection_point zenon_TX_v zenon_TY_u)) -> False). % 2.88/3.08 do 4 intro. intros zenon_H25 zenon_H13 zenon_H12 zenon_H11 zenon_Hf zenon_He. % 2.88/3.08 generalize (con2 zenon_TU_x). zenon_intro zenon_H26. % 2.88/3.08 generalize (zenon_H26 zenon_TV_w). zenon_intro zenon_H27. % 2.88/3.08 generalize (cu1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_Hd. % 2.88/3.08 generalize (apart1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H28. % 2.88/3.08 generalize (zenon_H27 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H29. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 2.88/3.08 exact (zenon_H2b zenon_H25). % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.88/3.08 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H10. zenon_intro zenon_H11. % 2.88/3.08 apply (zenon_L1_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 exact (zenon_H28 zenon_H2c). % 2.88/3.08 (* end of lemma zenon_L2_ *) % 2.88/3.08 assert (zenon_L3_ : forall (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w) -> (convergent_lines zenon_TU_x zenon_TV_w) -> False). % 2.88/3.08 do 2 intro. intros zenon_H22 zenon_H25. % 2.88/3.08 generalize (apart1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H28. % 2.88/3.08 generalize (con2 zenon_TU_x). zenon_intro zenon_H26. % 2.88/3.08 generalize (zenon_H26 zenon_TV_w). zenon_intro zenon_H27. % 2.88/3.08 generalize (zenon_H27 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H29. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 2.88/3.08 exact (zenon_H2b zenon_H25). % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.88/3.08 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H10. zenon_intro zenon_H11. % 2.88/3.08 exact (zenon_H11 zenon_H22). % 2.88/3.08 exact (zenon_H28 zenon_H2c). % 2.88/3.08 (* end of lemma zenon_L3_ *) % 2.88/3.08 assert (zenon_L4_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U), (apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TY_u) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_v zenon_TY_u)->(((apart_point_and_line Z zenon_TX_v)\/(apart_point_and_line Z zenon_TY_u))->(distinct_points Z (intersection_point zenon_TX_v zenon_TY_u))))) -> False). % 2.88/3.08 do 2 intro. intros zenon_H2e zenon_H2f zenon_H30. % 2.88/3.08 generalize (apart1 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H31. % 2.88/3.08 generalize (zenon_H30 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H32. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 2.88/3.08 exact (zenon_H34 zenon_H2f). % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 2.88/3.08 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 2.88/3.08 exact (zenon_H37 zenon_H2e). % 2.88/3.08 exact (zenon_H31 zenon_H35). % 2.88/3.08 (* end of lemma zenon_L4_ *) % 2.88/3.08 assert (zenon_L5_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U), (apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TY_u) -> (convergent_lines zenon_TX_v zenon_TY_u) -> False). % 2.88/3.08 do 2 intro. intros zenon_H2e zenon_H2f. % 2.88/3.08 generalize (con2 zenon_TX_v). zenon_intro zenon_H39. % 2.88/3.08 generalize (zenon_H39 zenon_TY_u). zenon_intro zenon_H30. % 2.88/3.08 apply (zenon_L4_ zenon_TY_u zenon_TX_v); trivial. % 2.88/3.08 (* end of lemma zenon_L5_ *) % 2.88/3.08 assert (zenon_L6_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TU_x)->((distinct_points (intersection_point zenon_TU_x zenon_TV_w) (intersection_point zenon_TX_v zenon_TY_u))\/(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x))) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (~(distinct_lines zenon_TY_u zenon_TY_u)) -> (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u) -> (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u)->((distinct_points (intersection_point zenon_TU_x zenon_TV_w) Z)\/(apart_point_and_line Z zenon_TY_u)))) -> (distinct_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (convergent_lines zenon_TU_x zenon_TV_w) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> False). % 2.88/3.08 do 4 intro. intros zenon_H3a zenon_H2f zenon_H3b zenon_H3c zenon_H3d zenon_Hf zenon_H11 zenon_H13 zenon_H25 zenon_H12. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H10 | zenon_intro zenon_H3e ]. % 2.88/3.08 generalize (ceq2 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H3f. % 2.88/3.08 generalize (zenon_H3f zenon_TY_u). zenon_intro zenon_H40. % 2.88/3.08 generalize (zenon_H40 zenon_TY_u). zenon_intro zenon_H41. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H37 | zenon_intro zenon_H42 ]. % 2.88/3.08 generalize (zenon_H3d (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H43. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 2.88/3.08 exact (zenon_H45 zenon_H3c). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_He | zenon_intro zenon_H2e ]. % 2.88/3.08 generalize (cu1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_Hd. % 2.88/3.08 apply (zenon_L1_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 exact (zenon_H37 zenon_H2e). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H46 | zenon_intro zenon_H2e ]. % 2.88/3.08 exact (zenon_H3b zenon_H46). % 2.88/3.08 apply (zenon_L5_ zenon_TY_u zenon_TX_v); trivial. % 2.88/3.08 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_He | zenon_intro zenon_H24 ]. % 2.88/3.08 apply (zenon_L2_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 exact (zenon_H12 zenon_H24). % 2.88/3.08 (* end of lemma zenon_L6_ *) % 2.88/3.08 assert (zenon_L7_ : forall (zenon_TX_v : zenon_U) (zenon_TY_u : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Y)->((distinct_points (intersection_point zenon_TU_x zenon_TV_w) Z)\/(apart_point_and_line Z Y))))) -> (~(distinct_lines zenon_TV_w zenon_TV_w)) -> (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(distinct_lines zenon_TY_u zenon_TY_u)) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (convergent_lines zenon_TU_x zenon_TV_w) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Z))))) -> False). % 2.88/3.08 do 4 intro. intros zenon_H47 zenon_H48 zenon_H3c zenon_H13 zenon_H12 zenon_H3b zenon_H2f zenon_H25 zenon_H49. % 2.88/3.08 generalize (zenon_H47 zenon_TY_u). zenon_intro zenon_H3d. % 2.88/3.08 generalize (zenon_H49 zenon_TV_w). zenon_intro zenon_H4a. % 2.88/3.08 generalize (zenon_H47 zenon_TU_x). zenon_intro zenon_H4b. % 2.88/3.08 generalize (zenon_H4a zenon_TV_w). zenon_intro zenon_H4c. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H11 | zenon_intro zenon_H4d ]. % 2.88/3.08 generalize (zenon_H4b (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H3a. % 2.88/3.08 generalize (ceq3 zenon_TU_x). zenon_intro zenon_H4e. % 2.88/3.08 generalize (zenon_H4e zenon_TV_w). zenon_intro zenon_H4f. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H2b | zenon_intro zenon_Hf ]. % 2.88/3.08 exact (zenon_H2b zenon_H25). % 2.88/3.08 apply (zenon_L6_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H50 | zenon_intro zenon_H22 ]. % 2.88/3.08 exact (zenon_H48 zenon_H50). % 2.88/3.08 apply (zenon_L3_ zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 (* end of lemma zenon_L7_ *) % 2.88/3.08 assert (zenon_L8_ : forall (zenon_TY_u : zenon_U) (zenon_TX_v : zenon_U) (zenon_TV_w : zenon_U) (zenon_TU_x : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) Z))))) -> (convergent_lines zenon_TU_x zenon_TV_w) -> (convergent_lines zenon_TX_v zenon_TY_u) -> (~(distinct_lines zenon_TY_u zenon_TY_u)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x)) -> (~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TV_w)) -> (apart_point_and_line (intersection_point zenon_TU_x zenon_TV_w) zenon_TY_u) -> (~(distinct_lines zenon_TV_w zenon_TV_w)) -> False). % 2.88/3.08 do 4 intro. intros zenon_H49 zenon_H25 zenon_H2f zenon_H3b zenon_H12 zenon_H13 zenon_H3c zenon_H48. % 2.88/3.08 generalize (ceq1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H47. % 2.88/3.08 apply (zenon_L7_ zenon_TX_v zenon_TY_u zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 (* end of lemma zenon_L8_ *) % 2.88/3.08 apply NNPP. intro zenon_G. % 2.88/3.08 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_H51; idtac ]. % 2.88/3.08 elim zenon_H51. zenon_intro zenon_TX_v. zenon_intro zenon_H52. % 2.88/3.08 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines zenon_TX_v Y)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point zenon_TX_v Y) U))/\(~(apart_point_and_line (intersection_point zenon_TX_v Y) V)))))->((~(apart_point_and_line (intersection_point U V) zenon_TX_v))/\(~(apart_point_and_line (intersection_point U V) Y))))))) zenon_H52); [ zenon_intro zenon_H53; idtac ]. % 2.88/3.08 elim zenon_H53. zenon_intro zenon_TY_u. zenon_intro zenon_H54. % 2.88/3.08 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((convergent_lines zenon_TX_v zenon_TY_u)/\((convergent_lines U V)/\((~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) U))/\(~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) V)))))->((~(apart_point_and_line (intersection_point U V) zenon_TX_v))/\(~(apart_point_and_line (intersection_point U V) zenon_TY_u)))))) zenon_H54); [ zenon_intro zenon_H55; idtac ]. % 2.88/3.08 elim zenon_H55. zenon_intro zenon_TU_x. zenon_intro zenon_H56. % 2.88/3.08 apply (zenon_notallex_s (fun V : zenon_U => (((convergent_lines zenon_TX_v zenon_TY_u)/\((convergent_lines zenon_TU_x V)/\((~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) zenon_TU_x))/\(~(apart_point_and_line (intersection_point zenon_TX_v zenon_TY_u) V)))))->((~(apart_point_and_line (intersection_point zenon_TU_x V) zenon_TX_v))/\(~(apart_point_and_line (intersection_point zenon_TU_x V) zenon_TY_u))))) zenon_H56); [ zenon_intro zenon_H57; idtac ]. % 2.88/3.08 elim zenon_H57. zenon_intro zenon_TV_w. zenon_intro zenon_H58. % 2.88/3.08 apply (zenon_notimply_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 2.88/3.08 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_H2f. zenon_intro zenon_H5b. % 2.88/3.08 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H25. zenon_intro zenon_H5c. % 2.88/3.08 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H12. zenon_intro zenon_H13. % 2.88/3.08 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ]. % 2.88/3.08 apply zenon_H5e. zenon_intro zenon_H5f. % 2.88/3.08 generalize (apart2 zenon_TV_w). zenon_intro zenon_H48. % 2.88/3.08 generalize (ceq2 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H49. % 2.88/3.08 generalize (ceq1 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H47. % 2.88/3.08 generalize (zenon_H47 zenon_TX_v). zenon_intro zenon_H60. % 2.88/3.08 generalize (apart5 zenon_TU_x). zenon_intro zenon_H61. % 2.88/3.08 generalize (zenon_H61 zenon_TV_w). zenon_intro zenon_H62. % 2.88/3.08 generalize (zenon_H62 zenon_TV_w). zenon_intro zenon_H63. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H1d | zenon_intro zenon_H64 ]. % 2.88/3.08 generalize (ceq3 zenon_TU_x). zenon_intro zenon_H4e. % 2.88/3.08 generalize (zenon_H4e zenon_TV_w). zenon_intro zenon_H4f. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H2b | zenon_intro zenon_Hf ]. % 2.88/3.08 exact (zenon_H2b zenon_H25). % 2.88/3.08 exact (zenon_H1d zenon_Hf). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H64); [ zenon_intro zenon_Hf | zenon_intro zenon_H50 ]. % 2.88/3.08 generalize (zenon_H49 zenon_TV_w). zenon_intro zenon_H4a. % 2.88/3.08 generalize (zenon_H4a zenon_TV_w). zenon_intro zenon_H4c. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H11 | zenon_intro zenon_H4d ]. % 2.88/3.08 generalize (con2 zenon_TX_v). zenon_intro zenon_H39. % 2.88/3.08 generalize (zenon_H39 zenon_TY_u). zenon_intro zenon_H30. % 2.88/3.08 generalize (apart1 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H31. % 2.88/3.08 generalize (zenon_H30 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H32. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 2.88/3.08 exact (zenon_H34 zenon_H2f). % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 2.88/3.08 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37. % 2.88/3.08 generalize (zenon_H60 (intersection_point zenon_TX_v zenon_TY_u)). zenon_intro zenon_H65. % 2.88/3.08 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H67 | zenon_intro zenon_H66 ]. % 2.88/3.08 exact (zenon_H67 zenon_H5f). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_He | zenon_intro zenon_H68 ]. % 2.88/3.08 apply (zenon_L2_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 exact (zenon_H38 zenon_H68). % 2.88/3.08 exact (zenon_H31 zenon_H35). % 2.88/3.08 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H50 | zenon_intro zenon_H22 ]. % 2.88/3.08 exact (zenon_H48 zenon_H50). % 2.88/3.08 apply (zenon_L3_ zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 exact (zenon_H48 zenon_H50). % 2.88/3.08 apply zenon_H5d. zenon_intro zenon_H3c. % 2.88/3.08 generalize (apart2 zenon_TY_u). zenon_intro zenon_H3b. % 2.88/3.08 generalize (apart2 zenon_TV_w). zenon_intro zenon_H48. % 2.88/3.08 generalize (ceq2 (intersection_point zenon_TU_x zenon_TV_w)). zenon_intro zenon_H49. % 2.88/3.08 apply (zenon_L8_ zenon_TY_u zenon_TX_v zenon_TV_w zenon_TU_x); trivial. % 2.88/3.08 Qed. % 2.88/3.08 % SZS output end Proof % 2.88/3.08 (* END-PROOF *) % 2.88/3.08 nodes searched: 409118 % 2.88/3.08 max branch formulas: 7190 % 2.88/3.08 proof nodes created: 6210 % 2.88/3.08 formulas created: 465272 % 2.88/3.08 %------------------------------------------------------------------------------