%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 18:21:53 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 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))))))). % 0.19/0.50 Proof. % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 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_H12; idtac ]. % 0.19/0.50 elim zenon_H12. zenon_intro zenon_TA_t. zenon_intro zenon_H14. % 0.19/0.50 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, (((apart_point_and_line zenon_TA_t L)/\((~(apart_point_and_line zenon_TA_t M))/\((~(apart_point_and_line zenon_TA_t N))/\((~(convergent_lines M L))/\(~(convergent_lines N L))))))->(~(distinct_lines M N)))))) zenon_H14); [ zenon_intro zenon_H15; idtac ]. % 0.19/0.50 elim zenon_H15. zenon_intro zenon_TL_w. zenon_intro zenon_H17. % 0.19/0.50 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, (((apart_point_and_line zenon_TA_t zenon_TL_w)/\((~(apart_point_and_line zenon_TA_t M))/\((~(apart_point_and_line zenon_TA_t N))/\((~(convergent_lines M zenon_TL_w))/\(~(convergent_lines N zenon_TL_w))))))->(~(distinct_lines M N))))) zenon_H17); [ zenon_intro zenon_H18; idtac ]. % 0.19/0.50 elim zenon_H18. zenon_intro zenon_TM_z. zenon_intro zenon_H1a. % 0.19/0.50 apply (zenon_notallex_s (fun N : zenon_U => (((apart_point_and_line zenon_TA_t zenon_TL_w)/\((~(apart_point_and_line zenon_TA_t zenon_TM_z))/\((~(apart_point_and_line zenon_TA_t N))/\((~(convergent_lines zenon_TM_z zenon_TL_w))/\(~(convergent_lines N zenon_TL_w))))))->(~(distinct_lines zenon_TM_z N)))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ]. % 0.19/0.50 elim zenon_H1b. zenon_intro zenon_TN_bc. zenon_intro zenon_H1d. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.19/0.50 apply zenon_H1e. zenon_intro zenon_H20. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H24. zenon_intro zenon_H23. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.19/0.50 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.19/0.50 generalize (cup1 zenon_TA_t). zenon_intro zenon_H29. % 0.19/0.50 generalize (zenon_H29 zenon_TM_z). zenon_intro zenon_H2a. % 0.19/0.50 generalize (zenon_H2a zenon_TN_bc). zenon_intro zenon_H2b. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.19/0.50 exact (zenon_H2d zenon_H20). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.19/0.50 exact (zenon_H24 zenon_H2f). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.19/0.50 exact (zenon_H26 zenon_H31). % 0.19/0.50 generalize (ax6 zenon_TM_z). zenon_intro zenon_H32. % 0.19/0.50 generalize (zenon_H32 zenon_TN_bc). zenon_intro zenon_H33. % 0.19/0.50 generalize (zenon_H33 zenon_TL_w). zenon_intro zenon_H34. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.19/0.50 exact (zenon_H36 zenon_H30). % 0.19/0.50 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.19/0.50 exact (zenon_H28 zenon_H38). % 0.19/0.50 exact (zenon_H27 zenon_H37). % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 480 % 0.19/0.50 max branch formulas: 356 % 0.19/0.50 proof nodes created: 64 % 0.19/0.50 formulas created: 2663 % 0.19/0.50 %------------------------------------------------------------------------------