%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO170+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 07:00:21 EDT 2022 % Result : Theorem 0.21s 0.51s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO170+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sat Jun 18 15:08:57 EDT 2022 % 0.14/0.34 % CPUTime : % 0.21/0.51 (* PROOF-FOUND *) % 0.21/0.51 % SZS status Theorem % 0.21/0.51 (* BEGIN-PROOF *) % 0.21/0.51 % SZS output start Proof % 0.21/0.51 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((incident_point_and_line X Z)/\(incident_point_and_line Y Z)))->(equal_lines Z (line_connecting X Y)))))). % 0.21/0.51 Proof. % 0.21/0.51 apply NNPP. intro zenon_G. % 0.21/0.51 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((incident_point_and_line X Z)/\(incident_point_and_line Y Z)))->(equal_lines Z (line_connecting X Y)))))) zenon_G); [ zenon_intro zenon_H24; idtac ]. % 0.21/0.51 elim zenon_H24. zenon_intro zenon_TX_bl. zenon_intro zenon_H26. % 0.21/0.51 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_bl Y)/\((incident_point_and_line zenon_TX_bl Z)/\(incident_point_and_line Y Z)))->(equal_lines Z (line_connecting zenon_TX_bl Y))))) zenon_H26); [ zenon_intro zenon_H27; idtac ]. % 0.21/0.51 elim zenon_H27. zenon_intro zenon_TY_bo. zenon_intro zenon_H29. % 0.21/0.51 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_bl zenon_TY_bo)/\((incident_point_and_line zenon_TX_bl Z)/\(incident_point_and_line zenon_TY_bo Z)))->(equal_lines Z (line_connecting zenon_TX_bl zenon_TY_bo)))) zenon_H29); [ zenon_intro zenon_H2a; idtac ]. % 0.21/0.51 elim zenon_H2a. zenon_intro zenon_TZ_br. zenon_intro zenon_H2c. % 0.21/0.51 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.21/0.51 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.21/0.51 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.21/0.51 generalize (a4 zenon_TX_bl). zenon_intro zenon_H33. % 0.21/0.51 generalize (zenon_H33 zenon_TZ_br). zenon_intro zenon_H34. % 0.21/0.51 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H32; zenon_intro zenon_H35 ]. % 0.21/0.51 exact (zenon_H37 zenon_H32). % 0.21/0.51 generalize (a4 zenon_TY_bo). zenon_intro zenon_H38. % 0.21/0.51 generalize (zenon_H38 zenon_TZ_br). zenon_intro zenon_H39. % 0.21/0.51 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3c; zenon_intro zenon_H3b | zenon_intro zenon_H31; zenon_intro zenon_H3a ]. % 0.21/0.51 exact (zenon_H3c zenon_H31). % 0.21/0.51 generalize (ax2 zenon_TZ_br). zenon_intro zenon_H3d. % 0.21/0.51 generalize (zenon_H3d (line_connecting zenon_TX_bl zenon_TY_bo)). zenon_intro zenon_H3e. % 0.21/0.51 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H2d; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ]. % 0.21/0.51 apply zenon_H41. zenon_intro zenon_H42. % 0.21/0.51 generalize (cu1 zenon_TX_bl). zenon_intro zenon_H43. % 0.21/0.51 generalize (zenon_H43 zenon_TY_bo). zenon_intro zenon_H44. % 0.21/0.51 generalize (ci1 zenon_TX_bl). zenon_intro zenon_H45. % 0.21/0.51 generalize (ci2 zenon_TX_bl). zenon_intro zenon_H46. % 0.21/0.51 generalize (zenon_H45 zenon_TY_bo). zenon_intro zenon_H47. % 0.21/0.51 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.21/0.51 exact (zenon_H49 zenon_H30). % 0.21/0.51 generalize (zenon_H46 zenon_TY_bo). zenon_intro zenon_H4a. % 0.21/0.51 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H49 | zenon_intro zenon_H4b ]. % 0.21/0.51 exact (zenon_H49 zenon_H30). % 0.21/0.51 generalize (zenon_H44 zenon_TZ_br). zenon_intro zenon_H4c. % 0.21/0.51 generalize (zenon_H4c (line_connecting zenon_TX_bl zenon_TY_bo)). zenon_intro zenon_H4d. % 0.21/0.51 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 0.21/0.51 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H49 | zenon_intro zenon_H3f ]. % 0.21/0.51 exact (zenon_H49 zenon_H30). % 0.21/0.51 exact (zenon_H3f zenon_H42). % 0.21/0.51 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.21/0.51 exact (zenon_H35 zenon_H51). % 0.21/0.51 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.21/0.51 exact (zenon_H48 zenon_H53). % 0.21/0.51 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.21/0.51 exact (zenon_H3a zenon_H55). % 0.21/0.51 exact (zenon_H4b zenon_H54). % 0.21/0.51 exact (zenon_H2d zenon_H40). % 0.21/0.51 Qed. % 0.21/0.51 % SZS output end Proof % 0.21/0.51 (* END-PROOF *) % 0.21/0.51 nodes searched: 486 % 0.21/0.51 max branch formulas: 400 % 0.21/0.51 proof nodes created: 62 % 0.21/0.51 formulas created: 3182 % 0.21/0.51 %------------------------------------------------------------------------------