%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO226+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 07:01:06 EDT 2022 % Result : Theorem 0.63s 0.84s % Output : Proof 0.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO226+3 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n022.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 : Sat Jun 18 02:42:32 EDT 2022 % 0.13/0.34 % CPUTime : % 0.63/0.84 (* PROOF-FOUND *) % 0.63/0.84 % SZS status Theorem % 0.63/0.84 (* BEGIN-PROOF *) % 0.63/0.84 % SZS output start Proof % 0.63/0.84 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (((line L)/\((line M)/\(convergent_lines L M)))->(exists X : zenon_U, ((point X)->((incident_point_and_line X L)/\(incident_point_and_line X M))))))). % 0.63/0.84 Proof. % 0.63/0.84 apply NNPP. intro zenon_G. % 0.63/0.84 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (((line L)/\((line M)/\(convergent_lines L M)))->(exists X : zenon_U, ((point X)->((incident_point_and_line X L)/\(incident_point_and_line X M))))))) zenon_G); [ zenon_intro zenon_H24; idtac ]. % 0.63/0.84 elim zenon_H24. zenon_intro zenon_TL_bl. zenon_intro zenon_H26. % 0.63/0.84 apply (zenon_notallex_s (fun M : zenon_U => (((line zenon_TL_bl)/\((line M)/\(convergent_lines zenon_TL_bl M)))->(exists X : zenon_U, ((point X)->((incident_point_and_line X zenon_TL_bl)/\(incident_point_and_line X M)))))) zenon_H26); [ zenon_intro zenon_H27; idtac ]. % 0.63/0.84 elim zenon_H27. zenon_intro zenon_TM_bo. zenon_intro zenon_H29. % 0.63/0.84 apply (zenon_notimply_s _ _ zenon_H29). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.63/0.84 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 0.63/0.84 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 0.63/0.84 generalize (ci3 zenon_TM_bo). zenon_intro zenon_H30. % 0.63/0.84 generalize (ax6 zenon_TL_bl). zenon_intro zenon_H31. % 0.63/0.84 generalize (zenon_H31 zenon_TM_bo). zenon_intro zenon_H32. % 0.63/0.84 generalize (apart3 zenon_TL_bl). zenon_intro zenon_H33. % 0.63/0.84 generalize (zenon_H32 zenon_TL_bl). zenon_intro zenon_H34. % 0.63/0.84 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.63/0.84 exact (zenon_H36 zenon_H2e). % 0.63/0.84 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.63/0.84 exact (zenon_H33 zenon_H38). % 0.63/0.84 generalize (zenon_H30 zenon_TL_bl). zenon_intro zenon_H39. % 0.63/0.84 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.63/0.84 exact (zenon_H3b zenon_H37). % 0.63/0.84 apply zenon_H2a. exists (intersection_point zenon_TM_bo zenon_TL_bl). apply NNPP. zenon_intro zenon_H3c. % 0.63/0.84 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.63/0.84 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.63/0.84 generalize (a4 (intersection_point zenon_TM_bo zenon_TL_bl)). zenon_intro zenon_H41. % 0.63/0.84 generalize (zenon_H41 zenon_TL_bl). zenon_intro zenon_H42. % 0.63/0.84 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H40; zenon_intro zenon_H45 | zenon_intro zenon_H44; zenon_intro zenon_H43 ]. % 0.63/0.84 apply zenon_H45. zenon_intro zenon_H46. % 0.63/0.84 generalize (ci4 zenon_TM_bo). zenon_intro zenon_H47. % 0.63/0.84 generalize (zenon_H47 zenon_TL_bl). zenon_intro zenon_H48. % 0.63/0.84 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H3b | zenon_intro zenon_H43 ]. % 0.63/0.84 exact (zenon_H3b zenon_H37). % 0.63/0.84 exact (zenon_H43 zenon_H46). % 0.63/0.84 exact (zenon_H40 zenon_H44). % 0.63/0.84 generalize (a4 (intersection_point zenon_TM_bo zenon_TL_bl)). zenon_intro zenon_H41. % 0.63/0.84 generalize (zenon_H41 zenon_TM_bo). zenon_intro zenon_H49. % 0.63/0.84 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H3f; zenon_intro zenon_H4b | zenon_intro zenon_H4a; zenon_intro zenon_H3a ]. % 0.63/0.84 exact (zenon_H4b zenon_H3a). % 0.63/0.84 exact (zenon_H3f zenon_H4a). % 0.63/0.84 Qed. % 0.63/0.84 % SZS output end Proof % 0.63/0.84 (* END-PROOF *) % 0.63/0.84 nodes searched: 22860 % 0.63/0.84 max branch formulas: 3044 % 0.63/0.84 proof nodes created: 928 % 0.63/0.84 formulas created: 63703 % 0.63/0.84 %------------------------------------------------------------------------------