%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0. % 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 07:00:59 EDT 2022 % Result : Theorem 0.21s 0.57s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0. % 0.08/0.14 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n016.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 600 % 0.13/0.36 % DateTime : Sat Jun 18 04:44:51 EDT 2022 % 0.13/0.36 % CPUTime : % 0.21/0.57 (* PROOF-FOUND *) % 0.21/0.57 % SZS status Theorem % 0.21/0.57 (* BEGIN-PROOF *) % 0.21/0.57 % SZS output start Proof % 0.21/0.57 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, (((parallel_lines L M)/\(orthogonal_lines L N))->(orthogonal_lines M N))))). % 0.21/0.57 Proof. % 0.21/0.57 assert (zenon_L1_ : forall (zenon_TN_bp : zenon_U) (zenon_TM_bq : zenon_U) (zenon_TL_br : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TL_br Y)->((convergent_lines zenon_TL_br Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TM_bq zenon_TN_bp)) -> (~(convergent_lines zenon_TN_bp zenon_TN_bp)) -> (~(convergent_lines zenon_TL_br zenon_TM_bq)) -> (convergent_lines zenon_TL_br zenon_TN_bp) -> False). % 0.21/0.57 do 3 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27 zenon_H28. % 0.21/0.57 generalize (zenon_H24 zenon_TN_bp). zenon_intro zenon_H2c. % 0.21/0.57 generalize (zenon_H2c zenon_TM_bq). zenon_intro zenon_H2d. % 0.21/0.57 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.21/0.57 exact (zenon_H2f zenon_H28). % 0.21/0.57 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.21/0.57 exact (zenon_H27 zenon_H31). % 0.21/0.57 generalize (ax6 zenon_TN_bp). zenon_intro zenon_H32. % 0.21/0.57 generalize (zenon_H32 zenon_TM_bq). zenon_intro zenon_H33. % 0.21/0.57 generalize (zenon_H33 zenon_TN_bp). zenon_intro zenon_H34. % 0.21/0.57 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.21/0.57 exact (zenon_H36 zenon_H30). % 0.21/0.57 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.21/0.57 exact (zenon_H26 zenon_H38). % 0.21/0.57 exact (zenon_H25 zenon_H37). % 0.21/0.57 (* end of lemma zenon_L1_ *) % 0.21/0.57 assert (zenon_L2_ : forall (zenon_TL_br : zenon_U) (zenon_TN_bp : zenon_U) (zenon_TM_bq : zenon_U), (~(convergent_lines zenon_TM_bq zenon_TN_bp)) -> (~(convergent_lines zenon_TL_br zenon_TM_bq)) -> (convergent_lines zenon_TL_br zenon_TN_bp) -> False). % 0.21/0.57 do 3 intro. intros zenon_H25 zenon_H27 zenon_H28. % 0.21/0.57 generalize (apart3 zenon_TN_bp). zenon_intro zenon_H26. % 0.21/0.57 generalize (ax6 zenon_TL_br). zenon_intro zenon_H24. % 0.21/0.57 apply (zenon_L1_ zenon_TN_bp zenon_TM_bq zenon_TL_br); trivial. % 0.21/0.57 (* end of lemma zenon_L2_ *) % 0.21/0.57 assert (zenon_L3_ : forall (zenon_TN_bp : zenon_U) (zenon_TL_br : zenon_U), (~(~(unorthogonal_lines zenon_TL_br zenon_TN_bp))) -> (~(unorthogonal_lines zenon_TL_br zenon_TN_bp)) -> False). % 0.21/0.57 do 2 intro. intros zenon_H39 zenon_H3a. % 0.21/0.57 exact (zenon_H39 zenon_H3a). % 0.21/0.57 (* end of lemma zenon_L3_ *) % 0.21/0.57 apply NNPP. intro zenon_G. % 0.21/0.57 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, (((parallel_lines L M)/\(orthogonal_lines L N))->(orthogonal_lines M N))))) zenon_G); [ zenon_intro zenon_H3b; idtac ]. % 0.21/0.57 elim zenon_H3b. zenon_intro zenon_TL_br. zenon_intro zenon_H3c. % 0.21/0.57 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, (((parallel_lines zenon_TL_br M)/\(orthogonal_lines zenon_TL_br N))->(orthogonal_lines M N)))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ]. % 0.21/0.57 elim zenon_H3d. zenon_intro zenon_TM_bq. zenon_intro zenon_H3e. % 0.21/0.57 apply (zenon_notallex_s (fun N : zenon_U => (((parallel_lines zenon_TL_br zenon_TM_bq)/\(orthogonal_lines zenon_TL_br N))->(orthogonal_lines zenon_TM_bq N))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.21/0.57 elim zenon_H3f. zenon_intro zenon_TN_bp. zenon_intro zenon_H40. % 0.21/0.57 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.21/0.57 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.21/0.57 generalize (a3 zenon_TL_br). zenon_intro zenon_H45. % 0.21/0.57 generalize (zenon_H45 zenon_TM_bq). zenon_intro zenon_H46. % 0.21/0.57 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H44; zenon_intro zenon_H27 ]. % 0.21/0.57 exact (zenon_H48 zenon_H44). % 0.21/0.57 generalize (a5 zenon_TL_br). zenon_intro zenon_H49. % 0.21/0.57 generalize (zenon_H49 zenon_TN_bp). zenon_intro zenon_H4a. % 0.21/0.57 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4b; zenon_intro zenon_H39 | zenon_intro zenon_H43; zenon_intro zenon_H3a ]. % 0.21/0.57 exact (zenon_H4b zenon_H43). % 0.21/0.57 generalize (a5 zenon_TM_bq). zenon_intro zenon_H4c. % 0.21/0.57 generalize (zenon_H4c zenon_TN_bp). zenon_intro zenon_H4d. % 0.21/0.57 apply (zenon_equiv_s _ _ zenon_H4d); [ zenon_intro zenon_H41; zenon_intro zenon_H50 | zenon_intro zenon_H4f; zenon_intro zenon_H4e ]. % 0.21/0.58 apply zenon_H50. zenon_intro zenon_H51. % 0.21/0.58 generalize (coipo1 zenon_TL_br). zenon_intro zenon_H52. % 0.21/0.58 generalize (oac1 zenon_TM_bq). zenon_intro zenon_H53. % 0.21/0.58 generalize (apart3 zenon_TM_bq). zenon_intro zenon_H54. % 0.21/0.58 generalize (zenon_H52 zenon_TN_bp). zenon_intro zenon_H55. % 0.21/0.58 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H39 ]. % 0.21/0.58 apply zenon_H56. zenon_intro zenon_H28. % 0.21/0.58 generalize (zenon_H53 zenon_TN_bp). zenon_intro zenon_H57. % 0.21/0.58 generalize (zenon_H57 zenon_TM_bq). zenon_intro zenon_H58. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 0.21/0.58 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H25 | zenon_intro zenon_H4e ]. % 0.21/0.58 apply (zenon_L2_ zenon_TL_br zenon_TN_bp zenon_TM_bq); trivial. % 0.21/0.58 exact (zenon_H4e zenon_H51). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ]. % 0.21/0.58 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 0.21/0.58 exact (zenon_H54 zenon_H5e). % 0.21/0.58 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H30. zenon_intro zenon_H5f. % 0.21/0.58 generalize (cotno1 zenon_TL_br). zenon_intro zenon_H60. % 0.21/0.58 generalize (zenon_H60 zenon_TN_bp). zenon_intro zenon_H61. % 0.21/0.58 generalize (zenon_H61 zenon_TM_bq). zenon_intro zenon_H62. % 0.21/0.58 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.21/0.58 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 0.21/0.58 apply (zenon_notor_s _ _ zenon_H66). zenon_intro zenon_H56. zenon_intro zenon_H39. % 0.21/0.58 exact (zenon_H39 zenon_H3a). % 0.21/0.58 apply (zenon_notor_s _ _ zenon_H65). zenon_intro zenon_H47. zenon_intro zenon_H67. % 0.21/0.58 exact (zenon_H47 zenon_H27). % 0.21/0.58 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H36 | zenon_intro zenon_H68 ]. % 0.21/0.58 exact (zenon_H36 zenon_H30). % 0.21/0.58 exact (zenon_H68 zenon_H5f). % 0.21/0.58 exact (zenon_H39 zenon_H3a). % 0.21/0.58 exact (zenon_H41 zenon_H4f). % 0.21/0.58 Qed. % 0.21/0.58 % SZS output end Proof % 0.21/0.58 (* END-PROOF *) % 0.21/0.58 nodes searched: 1693 % 0.21/0.58 max branch formulas: 724 % 0.21/0.58 proof nodes created: 183 % 0.21/0.58 formulas created: 7682 % 0.21/0.58 %------------------------------------------------------------------------------