%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO225+2 : TPTP v8.1.0. Released v3.3.0. % 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 07:01:05 EDT 2022 % Result : Theorem 0.21s 0.52s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO225+2 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.13 % 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 : Fri Jun 17 21:10:17 EDT 2022 % 0.21/0.34 % CPUTime : % 0.21/0.52 (* PROOF-FOUND *) % 0.21/0.52 % SZS status Theorem % 0.21/0.52 (* BEGIN-PROOF *) % 0.21/0.52 % SZS output start Proof % 0.21/0.52 Theorem con : (forall A : zenon_U, (forall B : zenon_U, (((point A)/\((point B)/\(distinct_points A B)))->(exists X : zenon_U, ((line X)->((~(apart_point_and_line A X))/\(~(apart_point_and_line B X)))))))). % 0.21/0.52 Proof. % 0.21/0.52 apply NNPP. intro zenon_G. % 0.21/0.52 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((point A)/\((point B)/\(distinct_points A B)))->(exists X : zenon_U, ((line X)->((~(apart_point_and_line A X))/\(~(apart_point_and_line B X)))))))) zenon_G); [ zenon_intro zenon_H11; idtac ]. % 0.21/0.52 elim zenon_H11. zenon_intro zenon_TA_s. zenon_intro zenon_H13. % 0.21/0.52 apply (zenon_notallex_s (fun B : zenon_U => (((point zenon_TA_s)/\((point B)/\(distinct_points zenon_TA_s B)))->(exists X : zenon_U, ((line X)->((~(apart_point_and_line zenon_TA_s X))/\(~(apart_point_and_line B X))))))) zenon_H13); [ zenon_intro zenon_H14; idtac ]. % 0.21/0.52 elim zenon_H14. zenon_intro zenon_TB_v. zenon_intro zenon_H16. % 0.21/0.52 apply (zenon_notimply_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.21/0.52 apply (zenon_and_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.21/0.52 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.21/0.52 generalize (apart1 zenon_TB_v). zenon_intro zenon_H1d. % 0.21/0.52 generalize (con1 zenon_TA_s). zenon_intro zenon_H1e. % 0.21/0.52 generalize (apart1 zenon_TA_s). zenon_intro zenon_H1f. % 0.21/0.52 generalize (zenon_H1e zenon_TB_v). zenon_intro zenon_H20. % 0.21/0.52 generalize (zenon_H20 zenon_TA_s). zenon_intro zenon_H21. % 0.21/0.52 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.21/0.52 exact (zenon_H23 zenon_H1b). % 0.21/0.52 apply (zenon_imply_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.21/0.52 generalize (zenon_H20 zenon_TB_v). zenon_intro zenon_H26. % 0.21/0.52 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H23 | zenon_intro zenon_H27 ]. % 0.21/0.52 exact (zenon_H23 zenon_H1b). % 0.21/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.21/0.52 apply zenon_H17. exists (line_connecting zenon_TA_s zenon_TB_v). apply NNPP. zenon_intro zenon_H2a. % 0.21/0.52 apply (zenon_notimply_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.21/0.52 apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.21/0.52 exact (zenon_H2e zenon_H25). % 0.21/0.52 exact (zenon_H2d zenon_H29). % 0.21/0.52 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.21/0.52 exact (zenon_H1d zenon_H2f). % 0.21/0.52 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H31. zenon_intro zenon_H1b. % 0.21/0.52 exact (zenon_H1f zenon_H31). % 0.21/0.52 Qed. % 0.21/0.52 % SZS output end Proof % 0.21/0.52 (* END-PROOF *) % 0.21/0.52 nodes searched: 611 % 0.21/0.52 max branch formulas: 366 % 0.21/0.52 proof nodes created: 82 % 0.21/0.52 formulas created: 2977 % 0.21/0.52 %------------------------------------------------------------------------------