%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO209+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n014.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 07:00:51 EDT 2022 % Result : Theorem 0.20s 0.54s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : GEO209+2 : TPTP v8.1.0. Released v3.3.0. % 0.14/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n014.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Fri Jun 17 17:34:19 EDT 2022 % 0.14/0.35 % CPUTime : % 0.20/0.54 (* PROOF-FOUND *) % 0.20/0.54 % SZS status Theorem % 0.20/0.54 (* BEGIN-PROOF *) % 0.20/0.54 % SZS output start Proof % 0.20/0.54 Theorem con : (forall A : zenon_U, (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, (((apart_point_and_line A L)/\((~(apart_point_and_line A M))/\((~(apart_point_and_line A N))/\((~(convergent_lines M L))/\(~(convergent_lines N L))))))->(~(distinct_lines M N))))))). % 0.20/0.54 Proof. % 0.20/0.54 apply NNPP. intro zenon_G. % 0.20/0.54 apply (zenon_notallex_s (fun A : zenon_U => (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, (((apart_point_and_line A L)/\((~(apart_point_and_line A M))/\((~(apart_point_and_line A N))/\((~(convergent_lines M L))/\(~(convergent_lines N L))))))->(~(distinct_lines M N))))))) zenon_G); [ zenon_intro zenon_H10; idtac ]. % 0.20/0.54 elim zenon_H10. zenon_intro zenon_TA_r. zenon_intro zenon_H12. % 0.20/0.54 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, (((apart_point_and_line zenon_TA_r L)/\((~(apart_point_and_line zenon_TA_r M))/\((~(apart_point_and_line zenon_TA_r N))/\((~(convergent_lines M L))/\(~(convergent_lines N L))))))->(~(distinct_lines M N)))))) zenon_H12); [ zenon_intro zenon_H13; idtac ]. % 0.20/0.54 elim zenon_H13. zenon_intro zenon_TL_u. zenon_intro zenon_H15. % 0.20/0.54 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, (((apart_point_and_line zenon_TA_r zenon_TL_u)/\((~(apart_point_and_line zenon_TA_r M))/\((~(apart_point_and_line zenon_TA_r N))/\((~(convergent_lines M zenon_TL_u))/\(~(convergent_lines N zenon_TL_u))))))->(~(distinct_lines M N))))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 0.20/0.54 elim zenon_H16. zenon_intro zenon_TM_x. zenon_intro zenon_H18. % 0.20/0.54 apply (zenon_notallex_s (fun N : zenon_U => (((apart_point_and_line zenon_TA_r zenon_TL_u)/\((~(apart_point_and_line zenon_TA_r zenon_TM_x))/\((~(apart_point_and_line zenon_TA_r N))/\((~(convergent_lines zenon_TM_x zenon_TL_u))/\(~(convergent_lines N zenon_TL_u))))))->(~(distinct_lines zenon_TM_x N)))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.20/0.54 elim zenon_H19. zenon_intro zenon_TN_ba. zenon_intro zenon_H1b. % 0.20/0.54 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.20/0.54 apply zenon_H1c. zenon_intro zenon_H1e. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.20/0.54 generalize (cup1 zenon_TA_r). zenon_intro zenon_H27. % 0.20/0.54 generalize (zenon_H27 zenon_TM_x). zenon_intro zenon_H28. % 0.20/0.54 generalize (zenon_H28 zenon_TN_ba). zenon_intro zenon_H29. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.20/0.54 exact (zenon_H2b zenon_H1e). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.20/0.54 exact (zenon_H22 zenon_H2d). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.20/0.54 exact (zenon_H24 zenon_H2f). % 0.20/0.54 generalize (apart6 zenon_TM_x). zenon_intro zenon_H30. % 0.20/0.54 generalize (zenon_H30 zenon_TN_ba). zenon_intro zenon_H31. % 0.20/0.54 generalize (zenon_H31 zenon_TL_u). zenon_intro zenon_H32. % 0.20/0.54 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.20/0.54 exact (zenon_H34 zenon_H2e). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.20/0.54 exact (zenon_H26 zenon_H36). % 0.20/0.54 exact (zenon_H25 zenon_H35). % 0.20/0.54 Qed. % 0.20/0.54 % SZS output end Proof % 0.20/0.54 (* END-PROOF *) % 0.20/0.54 nodes searched: 681 % 0.20/0.54 max branch formulas: 429 % 0.20/0.54 proof nodes created: 68 % 0.20/0.54 formulas created: 3235 % 0.20/0.54 %------------------------------------------------------------------------------