%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 07:00:29 EDT 2022 % Result : Theorem 0.37s 0.54s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.14 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n015.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sat Jun 18 01:14:28 EDT 2022 % 0.13/0.35 % CPUTime : % 0.37/0.54 (* PROOF-FOUND *) % 0.37/0.54 % SZS status Theorem % 0.37/0.54 (* BEGIN-PROOF *) % 0.37/0.54 % SZS output start Proof % 0.37/0.54 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Z (line_connecting Y X))))))). % 0.37/0.54 Proof. % 0.37/0.54 apply NNPP. intro zenon_G. % 0.37/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Z (line_connecting Y X))))))) zenon_G); [ zenon_intro zenon_Hd; idtac ]. % 0.37/0.54 elim zenon_Hd. zenon_intro zenon_TX_o. zenon_intro zenon_Hf. % 0.37/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((distinct_points zenon_TX_o Y)->((apart_point_and_line Z (line_connecting zenon_TX_o Y))->(apart_point_and_line Z (line_connecting Y zenon_TX_o)))))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 0.37/0.54 elim zenon_H10. zenon_intro zenon_TY_r. zenon_intro zenon_H12. % 0.37/0.54 apply (zenon_notallex_s (fun Z : zenon_U => ((distinct_points zenon_TX_o zenon_TY_r)->((apart_point_and_line Z (line_connecting zenon_TX_o zenon_TY_r))->(apart_point_and_line Z (line_connecting zenon_TY_r zenon_TX_o))))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 0.37/0.54 elim zenon_H13. zenon_intro zenon_TZ_u. zenon_intro zenon_H15. % 0.37/0.54 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.37/0.54 apply (zenon_notimply_s _ _ zenon_H16). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.37/0.54 generalize (apart1 zenon_TY_r). zenon_intro zenon_H1a. % 0.37/0.54 generalize (con1 zenon_TY_r). zenon_intro zenon_H1b. % 0.37/0.54 generalize (cu1 zenon_TX_o). zenon_intro zenon_H1c. % 0.37/0.54 generalize (apart4 zenon_TX_o). zenon_intro zenon_H1d. % 0.37/0.54 generalize (zenon_H1c zenon_TY_r). zenon_intro zenon_H1e. % 0.37/0.54 generalize (zenon_H1d zenon_TY_r). zenon_intro zenon_H1f. % 0.37/0.54 generalize (con1 zenon_TX_o). zenon_intro zenon_H20. % 0.37/0.54 generalize (apart1 zenon_TX_o). zenon_intro zenon_H21. % 0.37/0.54 generalize (zenon_H20 zenon_TY_r). zenon_intro zenon_H22. % 0.37/0.54 generalize (zenon_H1b zenon_TX_o). zenon_intro zenon_H23. % 0.37/0.54 generalize (ceq2 zenon_TZ_u). zenon_intro zenon_H24. % 0.37/0.54 generalize (zenon_H22 zenon_TY_r). zenon_intro zenon_H25. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.37/0.54 exact (zenon_H27 zenon_H17). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.37/0.54 generalize (zenon_H22 zenon_TX_o). zenon_intro zenon_H2a. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H27 | zenon_intro zenon_H2b ]. % 0.37/0.54 exact (zenon_H27 zenon_H17). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.37/0.54 generalize (zenon_H1f zenon_TX_o). zenon_intro zenon_H2e. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H27 | zenon_intro zenon_H2f ]. % 0.37/0.54 exact (zenon_H27 zenon_H17). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.37/0.54 exact (zenon_H21 zenon_H31). % 0.37/0.54 generalize (zenon_H23 zenon_TY_r). zenon_intro zenon_H32. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.37/0.54 exact (zenon_H34 zenon_H30). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.37/0.54 generalize (zenon_H23 zenon_TX_o). zenon_intro zenon_H37. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H34 | zenon_intro zenon_H38 ]. % 0.37/0.54 exact (zenon_H34 zenon_H30). % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.37/0.54 generalize (zenon_H24 (line_connecting zenon_TX_o zenon_TY_r)). zenon_intro zenon_H3b. % 0.37/0.54 generalize (zenon_H3b (line_connecting zenon_TY_r zenon_TX_o)). zenon_intro zenon_H3c. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.37/0.54 exact (zenon_H3e zenon_H19). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.37/0.54 generalize (zenon_H1e (line_connecting zenon_TX_o zenon_TY_r)). zenon_intro zenon_H41. % 0.37/0.54 generalize (zenon_H41 (line_connecting zenon_TY_r zenon_TX_o)). zenon_intro zenon_H42. % 0.37/0.54 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.37/0.54 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H27 | zenon_intro zenon_H45 ]. % 0.37/0.54 exact (zenon_H27 zenon_H17). % 0.37/0.54 exact (zenon_H45 zenon_H40). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.37/0.54 exact (zenon_H2d zenon_H47). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.37/0.54 exact (zenon_H3a zenon_H49). % 0.37/0.54 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 0.37/0.54 exact (zenon_H29 zenon_H4b). % 0.37/0.54 exact (zenon_H36 zenon_H4a). % 0.37/0.54 exact (zenon_H18 zenon_H3f). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H17. zenon_intro zenon_H31. % 0.37/0.54 exact (zenon_H21 zenon_H31). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H4c. zenon_intro zenon_H30. % 0.37/0.54 exact (zenon_H1a zenon_H4c). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H31. zenon_intro zenon_H17. % 0.37/0.54 exact (zenon_H21 zenon_H31). % 0.37/0.54 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H30. zenon_intro zenon_H4c. % 0.37/0.54 exact (zenon_H1a zenon_H4c). % 0.37/0.54 Qed. % 0.37/0.54 % SZS output end Proof % 0.37/0.54 (* END-PROOF *) % 0.37/0.54 nodes searched: 615 % 0.37/0.54 max branch formulas: 350 % 0.37/0.54 proof nodes created: 111 % 0.37/0.54 formulas created: 2936 % 0.37/0.54 %------------------------------------------------------------------------------