%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 07:01:03 EDT 2022 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO222+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n022.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 : Sat Jun 18 10:57:47 EDT 2022 % 0.12/0.34 % CPUTime : % 0.38/0.61 (* PROOF-FOUND *) % 0.38/0.61 % SZS status Theorem % 0.38/0.61 (* BEGIN-PROOF *) % 0.38/0.61 % SZS output start Proof % 0.38/0.61 Theorem con : (forall A : zenon_U, (forall L : zenon_U, (parallel_lines L (orthogonal_through_point (orthogonal_through_point L A) A)))). % 0.38/0.61 Proof. % 0.38/0.61 assert (zenon_L1_ : forall (zenon_TA_bn : zenon_U) (zenon_TL_bo : zenon_U), (~(convergent_lines zenon_TL_bo (orthogonal_through_point zenon_TL_bo zenon_TA_bn))) -> (convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TL_bo) -> (forall Z : zenon_U, ((convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TL_bo)->((convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) Z)\/(convergent_lines zenon_TL_bo Z)))) -> False). % 0.38/0.61 do 2 intro. intros zenon_H24 zenon_H25 zenon_H26. % 0.38/0.61 generalize (apart3 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H29. % 0.38/0.61 generalize (zenon_H26 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H2a. % 0.38/0.61 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.38/0.61 exact (zenon_H2c zenon_H25). % 0.38/0.61 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.38/0.61 exact (zenon_H29 zenon_H2e). % 0.38/0.61 exact (zenon_H24 zenon_H2d). % 0.38/0.61 (* end of lemma zenon_L1_ *) % 0.38/0.61 assert (zenon_L2_ : forall (zenon_TA_bn : zenon_U) (zenon_TL_bo : zenon_U), (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn) zenon_TL_bo) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn) zenon_TL_bo) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn) (orthogonal_through_point zenon_TL_bo zenon_TA_bn))) -> (~(unorthogonal_lines zenon_TL_bo (orthogonal_through_point zenon_TL_bo zenon_TA_bn))) -> False). % 0.38/0.61 do 2 intro. intros zenon_H2f zenon_H30 zenon_H31 zenon_H32. % 0.38/0.61 generalize (oac1 (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn)). zenon_intro zenon_H33. % 0.38/0.61 generalize (zenon_H33 zenon_TL_bo). zenon_intro zenon_H34. % 0.38/0.61 generalize (zenon_H34 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H35. % 0.38/0.61 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.38/0.61 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.38/0.61 exact (zenon_H39 zenon_H2f). % 0.38/0.61 exact (zenon_H38 zenon_H30). % 0.38/0.61 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.38/0.61 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.38/0.61 exact (zenon_H31 zenon_H3c). % 0.38/0.61 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H2d. zenon_intro zenon_H3e. % 0.38/0.61 exact (zenon_H32 zenon_H3e). % 0.38/0.61 (* end of lemma zenon_L2_ *) % 0.38/0.61 assert (zenon_L3_ : forall (zenon_TL_bo : zenon_U), ((convergent_lines zenon_TL_bo zenon_TL_bo)/\(unorthogonal_lines zenon_TL_bo zenon_TL_bo)) -> (~(convergent_lines zenon_TL_bo zenon_TL_bo)) -> False). % 0.38/0.61 do 1 intro. intros zenon_H3f zenon_H40. % 0.38/0.61 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.38/0.61 exact (zenon_H40 zenon_H42). % 0.38/0.61 (* end of lemma zenon_L3_ *) % 0.38/0.61 assert (zenon_L4_ : forall (zenon_TA_bn : zenon_U) (zenon_TL_bo : zenon_U), (forall N : zenon_U, (((convergent_lines zenon_TL_bo (orthogonal_through_point zenon_TL_bo zenon_TA_bn))/\(unorthogonal_lines zenon_TL_bo (orthogonal_through_point zenon_TL_bo zenon_TA_bn)))->(((convergent_lines zenon_TL_bo N)/\(unorthogonal_lines zenon_TL_bo N))\/((convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) N)/\(unorthogonal_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) N))))) -> (convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TL_bo) -> (forall Z : zenon_U, ((convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TL_bo)->((convergent_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) Z)\/(convergent_lines zenon_TL_bo Z)))) -> (convergent_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn) zenon_TL_bo) -> (unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn) zenon_TL_bo) -> (~(unorthogonal_lines (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn) (orthogonal_through_point zenon_TL_bo zenon_TA_bn))) -> (~(convergent_lines zenon_TL_bo zenon_TL_bo)) -> (~(unorthogonal_lines (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TL_bo)) -> False). % 0.38/0.61 do 2 intro. intros zenon_H43 zenon_H25 zenon_H26 zenon_H2f zenon_H30 zenon_H31 zenon_H40 zenon_H44. % 0.38/0.61 generalize (zenon_H43 zenon_TL_bo). zenon_intro zenon_H45. % 0.38/0.61 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.38/0.61 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H24 | zenon_intro zenon_H32 ]. % 0.38/0.61 apply (zenon_L1_ zenon_TA_bn zenon_TL_bo); trivial. % 0.38/0.61 apply (zenon_L2_ zenon_TA_bn zenon_TL_bo); trivial. % 0.38/0.61 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H3f | zenon_intro zenon_H48 ]. % 0.38/0.61 apply (zenon_L3_ zenon_TL_bo); trivial. % 0.38/0.61 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H25. zenon_intro zenon_H49. % 0.38/0.61 exact (zenon_H44 zenon_H49). % 0.38/0.61 (* end of lemma zenon_L4_ *) % 0.38/0.61 apply NNPP. intro zenon_G. % 0.38/0.61 apply (zenon_notallex_s (fun A : zenon_U => (forall L : zenon_U, (parallel_lines L (orthogonal_through_point (orthogonal_through_point L A) A)))) zenon_G); [ zenon_intro zenon_H4a; idtac ]. % 0.38/0.61 elim zenon_H4a. zenon_intro zenon_TA_bn. zenon_intro zenon_H4b. % 0.38/0.61 apply (zenon_notallex_s (fun L : zenon_U => (parallel_lines L (orthogonal_through_point (orthogonal_through_point L zenon_TA_bn) zenon_TA_bn))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ]. % 0.38/0.61 elim zenon_H4c. zenon_intro zenon_TL_bo. zenon_intro zenon_H4d. % 0.38/0.61 generalize (a3 zenon_TL_bo). zenon_intro zenon_H4e. % 0.38/0.61 generalize (zenon_H4e (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn)). zenon_intro zenon_H4f. % 0.38/0.61 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H4d; zenon_intro zenon_H52 | zenon_intro zenon_H51; zenon_intro zenon_H50 ]. % 0.38/0.61 apply zenon_H52. zenon_intro zenon_H53. % 0.38/0.61 generalize (ax6 zenon_TL_bo). zenon_intro zenon_H54. % 0.38/0.61 generalize (zenon_H54 (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn)). zenon_intro zenon_H55. % 0.38/0.61 generalize (apart3 zenon_TL_bo). zenon_intro zenon_H40. % 0.38/0.61 generalize (zenon_H55 zenon_TL_bo). zenon_intro zenon_H56. % 0.38/0.61 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H50 | zenon_intro zenon_H57 ]. % 0.38/0.61 exact (zenon_H50 zenon_H53). % 0.38/0.61 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H42 | zenon_intro zenon_H2f ]. % 0.38/0.61 exact (zenon_H40 zenon_H42). % 0.38/0.61 generalize (oac1 zenon_TL_bo). zenon_intro zenon_H58. % 0.38/0.61 generalize (ooc1 zenon_TA_bn). zenon_intro zenon_H59. % 0.38/0.61 generalize (zenon_H59 zenon_TL_bo). zenon_intro zenon_H44. % 0.38/0.61 generalize (occu1 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H5a. % 0.38/0.61 generalize (zenon_H5a zenon_TL_bo). zenon_intro zenon_H5b. % 0.38/0.61 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H25 | zenon_intro zenon_H49 ]. % 0.38/0.61 generalize (ax6 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H5c. % 0.38/0.61 generalize (zenon_H5c zenon_TL_bo). zenon_intro zenon_H26. % 0.38/0.61 generalize (zenon_H59 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H31. % 0.38/0.61 generalize (zenon_H58 (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H43. % 0.38/0.61 generalize (couo1 (orthogonal_through_point (orthogonal_through_point zenon_TL_bo zenon_TA_bn) zenon_TA_bn)). zenon_intro zenon_H5d. % 0.38/0.61 generalize (zenon_H5d (orthogonal_through_point zenon_TL_bo zenon_TA_bn)). zenon_intro zenon_H5e. % 0.38/0.61 generalize (zenon_H5e zenon_TL_bo). zenon_intro zenon_H5f. % 0.38/0.61 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H60 | zenon_intro zenon_H2c ]. % 0.38/0.61 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H62 | zenon_intro zenon_H61 ]. % 0.38/0.61 exact (zenon_H62 zenon_H31). % 0.38/0.61 apply zenon_H61. zenon_intro zenon_H30. % 0.38/0.61 apply (zenon_L4_ zenon_TA_bn zenon_TL_bo); trivial. % 0.38/0.61 exact (zenon_H2c zenon_H25). % 0.38/0.61 exact (zenon_H44 zenon_H49). % 0.38/0.61 exact (zenon_H4d zenon_H51). % 0.38/0.61 Qed. % 0.38/0.61 % SZS output end Proof % 0.38/0.61 (* END-PROOF *) % 0.38/0.61 nodes searched: 6459 % 0.38/0.61 max branch formulas: 1388 % 0.38/0.61 proof nodes created: 407 % 0.38/0.61 formulas created: 16981 % 0.38/0.61 %------------------------------------------------------------------------------