%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO192+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 07:00:37 EDT 2022 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO192+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n018.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 18:21:03 EDT 2022 % 0.12/0.34 % CPUTime : % 0.38/0.57 (* PROOF-FOUND *) % 0.38/0.57 % SZS status Theorem % 0.38/0.57 (* BEGIN-PROOF *) % 0.38/0.57 % SZS output start Proof % 0.38/0.57 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))). % 0.38/0.57 Proof. % 0.38/0.57 assert (zenon_L1_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bo Y)->(~(apart_point_and_line (intersection_point zenon_TX_bo Y) zenon_TX_bo)))) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TX_bo) -> False). % 0.38/0.57 do 2 intro. intros zenon_H24 zenon_H25 zenon_H26. % 0.38/0.57 generalize (zenon_H24 zenon_TY_bn). zenon_intro zenon_H29. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.38/0.57 exact (zenon_H2b zenon_H25). % 0.38/0.57 exact (zenon_H2a zenon_H26). % 0.38/0.57 (* end of lemma zenon_L1_ *) % 0.38/0.57 apply NNPP. intro zenon_G. % 0.38/0.57 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 0.38/0.57 elim zenon_H2c. zenon_intro zenon_TX_bo. zenon_intro zenon_H2d. % 0.38/0.57 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((convergent_lines zenon_TX_bo Y)->((apart_point_and_line (intersection_point zenon_TX_bo Y) Z)->((distinct_lines zenon_TX_bo Z)/\(distinct_lines Y Z)))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 0.38/0.57 elim zenon_H2e. zenon_intro zenon_TY_bn. zenon_intro zenon_H2f. % 0.38/0.57 apply (zenon_notallex_s (fun Z : zenon_U => ((convergent_lines zenon_TX_bo zenon_TY_bn)->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z)->((distinct_lines zenon_TX_bo Z)/\(distinct_lines zenon_TY_bn Z))))) zenon_H2f); [ zenon_intro zenon_H30; idtac ]. % 0.38/0.57 elim zenon_H30. zenon_intro zenon_TZ_bx. zenon_intro zenon_H32. % 0.38/0.57 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H25. zenon_intro zenon_H33. % 0.38/0.57 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.38/0.57 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.38/0.57 generalize (ceq2 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H38. % 0.38/0.57 generalize (zenon_H38 zenon_TZ_bx). zenon_intro zenon_H39. % 0.38/0.57 generalize (ci3 zenon_TX_bo). zenon_intro zenon_H24. % 0.38/0.57 generalize (zenon_H39 zenon_TX_bo). zenon_intro zenon_H3a. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.38/0.57 exact (zenon_H3c zenon_H35). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H26 ]. % 0.38/0.57 generalize (apart2 zenon_TZ_bx). zenon_intro zenon_H3e. % 0.38/0.57 generalize (apart5 zenon_TZ_bx). zenon_intro zenon_H3f. % 0.38/0.57 generalize (zenon_H3f zenon_TX_bo). zenon_intro zenon_H40. % 0.38/0.57 generalize (zenon_H40 zenon_TZ_bx). zenon_intro zenon_H41. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.38/0.57 exact (zenon_H43 zenon_H3d). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.38/0.57 exact (zenon_H3e zenon_H45). % 0.38/0.57 exact (zenon_H37 zenon_H44). % 0.38/0.57 apply (zenon_L1_ zenon_TY_bn zenon_TX_bo); trivial. % 0.38/0.57 generalize (ceq2 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H38. % 0.38/0.57 generalize (zenon_H38 zenon_TZ_bx). zenon_intro zenon_H39. % 0.38/0.57 generalize (zenon_H38 zenon_TY_bn). zenon_intro zenon_H46. % 0.38/0.57 generalize (apart2 zenon_TY_bn). zenon_intro zenon_H47. % 0.38/0.57 generalize (zenon_H46 zenon_TY_bn). zenon_intro zenon_H48. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.38/0.57 generalize (zenon_H39 zenon_TY_bn). zenon_intro zenon_H4b. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H3c | zenon_intro zenon_H4c ]. % 0.38/0.57 exact (zenon_H3c zenon_H35). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.38/0.57 generalize (apart5 zenon_TZ_bx). zenon_intro zenon_H3f. % 0.38/0.57 generalize (zenon_H3f zenon_TY_bn). zenon_intro zenon_H4f. % 0.38/0.57 generalize (zenon_H4f zenon_TZ_bx). zenon_intro zenon_H50. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 0.38/0.57 exact (zenon_H52 zenon_H4e). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H45 | zenon_intro zenon_H53 ]. % 0.38/0.57 generalize (apart2 zenon_TZ_bx). zenon_intro zenon_H3e. % 0.38/0.57 exact (zenon_H3e zenon_H45). % 0.38/0.57 exact (zenon_H36 zenon_H53). % 0.38/0.57 exact (zenon_H4a zenon_H4d). % 0.38/0.57 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H54 | zenon_intro zenon_H4d ]. % 0.38/0.57 exact (zenon_H47 zenon_H54). % 0.38/0.57 generalize (ci4 zenon_TX_bo). zenon_intro zenon_H55. % 0.38/0.57 generalize (zenon_H55 zenon_TY_bn). zenon_intro zenon_H56. % 0.38/0.57 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H2b | zenon_intro zenon_H4a ]. % 0.38/0.57 exact (zenon_H2b zenon_H25). % 0.38/0.57 exact (zenon_H4a zenon_H4d). % 0.38/0.57 Qed. % 0.38/0.57 % SZS output end Proof % 0.38/0.57 (* END-PROOF *) % 0.38/0.57 nodes searched: 3646 % 0.38/0.57 max branch formulas: 974 % 0.38/0.57 proof nodes created: 390 % 0.38/0.57 formulas created: 12544 % 0.38/0.57 %------------------------------------------------------------------------------