%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO193+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 07:00:38 EDT 2022 % Result : Theorem 0.12s 0.40s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : GEO193+3 : TPTP v8.1.0. Released v4.0.0. % 0.00/0.08 % Command : run_zenon %s %d % 0.07/0.26 % Computer : n032.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 600 % 0.07/0.26 % DateTime : Fri Jun 17 21:52:01 EDT 2022 % 0.07/0.26 % CPUTime : % 0.12/0.40 (* PROOF-FOUND *) % 0.12/0.40 % SZS status Theorem % 0.12/0.40 (* BEGIN-PROOF *) % 0.12/0.40 % SZS output start Proof % 0.12/0.40 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Z Y) X)))))). % 0.12/0.40 Proof. % 0.12/0.40 assert (zenon_L1_ : forall (zenon_TY_bm : zenon_U) (zenon_TZ_bn : zenon_U), (apart_point_and_line (intersection_point zenon_TZ_bn zenon_TY_bm) zenon_TY_bm) -> (convergent_lines zenon_TZ_bn zenon_TY_bm) -> False). % 0.12/0.40 do 2 intro. intros zenon_H24 zenon_H25. % 0.12/0.40 generalize (ci4 zenon_TZ_bn). zenon_intro zenon_H28. % 0.12/0.40 generalize (zenon_H28 zenon_TY_bm). zenon_intro zenon_H29. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.12/0.40 exact (zenon_H2b zenon_H25). % 0.12/0.40 exact (zenon_H2a zenon_H24). % 0.12/0.40 (* end of lemma zenon_L1_ *) % 0.12/0.40 apply NNPP. intro zenon_G. % 0.12/0.40 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Z Y) X)))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 0.12/0.40 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e. % 0.12/0.40 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_bt Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_bt Z)))->((apart_point_and_line (intersection_point zenon_TX_bt Y) Z)->(apart_point_and_line (intersection_point Z Y) zenon_TX_bt))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ]. % 0.12/0.40 elim zenon_H2f. zenon_intro zenon_TY_bm. zenon_intro zenon_H30. % 0.12/0.40 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_bt zenon_TY_bm)/\((convergent_lines Z zenon_TY_bm)/\(convergent_lines zenon_TX_bt Z)))->((apart_point_and_line (intersection_point zenon_TX_bt zenon_TY_bm) Z)->(apart_point_and_line (intersection_point Z zenon_TY_bm) zenon_TX_bt)))) zenon_H30); [ zenon_intro zenon_H31; idtac ]. % 0.12/0.40 elim zenon_H31. zenon_intro zenon_TZ_bn. zenon_intro zenon_H32. % 0.12/0.40 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.12/0.40 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.12/0.40 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H38. zenon_intro zenon_H37. % 0.12/0.40 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H25. zenon_intro zenon_H39. % 0.12/0.40 generalize (ci3 zenon_TZ_bn). zenon_intro zenon_H3a. % 0.12/0.40 generalize (zenon_H3a zenon_TY_bm). zenon_intro zenon_H3b. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H2b | zenon_intro zenon_H3c ]. % 0.12/0.40 exact (zenon_H2b zenon_H25). % 0.12/0.40 generalize (ceq3 zenon_TX_bt). zenon_intro zenon_H3d. % 0.12/0.40 generalize (zenon_H3d zenon_TY_bm). zenon_intro zenon_H3e. % 0.12/0.40 generalize (ceq2 (intersection_point zenon_TX_bt zenon_TY_bm)). zenon_intro zenon_H3f. % 0.12/0.40 generalize (zenon_H3f zenon_TY_bm). zenon_intro zenon_H40. % 0.12/0.40 generalize (ceq1 (intersection_point zenon_TX_bt zenon_TY_bm)). zenon_intro zenon_H41. % 0.12/0.40 generalize (zenon_H41 zenon_TZ_bn). zenon_intro zenon_H42. % 0.12/0.40 generalize (zenon_H42 (intersection_point zenon_TZ_bn zenon_TY_bm)). zenon_intro zenon_H43. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.12/0.40 exact (zenon_H45 zenon_H36). % 0.12/0.40 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.12/0.40 generalize (cu1 (intersection_point zenon_TX_bt zenon_TY_bm)). zenon_intro zenon_H48. % 0.12/0.40 generalize (zenon_H48 (intersection_point zenon_TZ_bn zenon_TY_bm)). zenon_intro zenon_H49. % 0.12/0.40 generalize (zenon_H40 zenon_TY_bm). zenon_intro zenon_H4a. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.12/0.40 generalize (apart3 zenon_TX_bt). zenon_intro zenon_H4d. % 0.12/0.40 generalize (zenon_H3e zenon_TX_bt). zenon_intro zenon_H4e. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ]. % 0.12/0.40 exact (zenon_H50 zenon_H38). % 0.12/0.40 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 0.12/0.40 generalize (ci3 zenon_TX_bt). zenon_intro zenon_H53. % 0.12/0.40 generalize (zenon_H49 zenon_TY_bm). zenon_intro zenon_H54. % 0.12/0.40 generalize (zenon_H54 zenon_TX_bt). zenon_intro zenon_H55. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.12/0.40 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.12/0.40 exact (zenon_H59 zenon_H47). % 0.12/0.40 exact (zenon_H58 zenon_H52). % 0.12/0.40 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.12/0.40 exact (zenon_H4c zenon_H5b). % 0.12/0.40 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ]. % 0.12/0.40 generalize (zenon_H53 zenon_TY_bm). zenon_intro zenon_H5e. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H50 | zenon_intro zenon_H5f ]. % 0.12/0.40 exact (zenon_H50 zenon_H38). % 0.12/0.40 exact (zenon_H5f zenon_H5d). % 0.12/0.40 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H24 | zenon_intro zenon_H60 ]. % 0.12/0.40 apply (zenon_L1_ zenon_TY_bm zenon_TZ_bn); trivial. % 0.12/0.40 exact (zenon_H35 zenon_H60). % 0.12/0.40 exact (zenon_H4d zenon_H51). % 0.12/0.40 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H61 | zenon_intro zenon_H5b ]. % 0.12/0.40 generalize (apart2 zenon_TY_bm). zenon_intro zenon_H62. % 0.12/0.40 exact (zenon_H62 zenon_H61). % 0.12/0.40 generalize (ci4 zenon_TX_bt). zenon_intro zenon_H63. % 0.12/0.40 generalize (zenon_H63 zenon_TY_bm). zenon_intro zenon_H64. % 0.12/0.40 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H50 | zenon_intro zenon_H4c ]. % 0.12/0.40 exact (zenon_H50 zenon_H38). % 0.12/0.40 exact (zenon_H4c zenon_H5b). % 0.12/0.40 exact (zenon_H3c zenon_H46). % 0.12/0.40 Qed. % 0.12/0.40 % SZS output end Proof % 0.12/0.40 (* END-PROOF *) % 0.12/0.40 nodes searched: 1728 % 0.12/0.40 max branch formulas: 905 % 0.12/0.40 proof nodes created: 182 % 0.12/0.40 formulas created: 7763 % 0.12/0.40 %------------------------------------------------------------------------------