%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n023.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 07:00:55 EDT 2022 % Result : Theorem 0.18s 0.56s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n023.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 14:14:19 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.56 (* PROOF-FOUND *) % 0.18/0.56 % SZS status Theorem % 0.18/0.56 (* BEGIN-PROOF *) % 0.18/0.56 % SZS output start Proof % 0.18/0.56 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((distinct_lines L N)\/(unorthogonal_lines M N)))))). % 0.18/0.56 Proof. % 0.18/0.56 assert (zenon_L1_ : forall (zenon_TL_z : zenon_U) (zenon_TN_ba : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines zenon_TN_ba Y)->((distinct_lines zenon_TN_ba Z)\/(distinct_lines Y Z))))) -> (~(distinct_lines zenon_TL_z zenon_TN_ba)) -> (~(distinct_lines zenon_TN_ba zenon_TN_ba)) -> (distinct_lines zenon_TN_ba zenon_TL_z) -> False). % 0.18/0.56 do 2 intro. intros zenon_H15 zenon_H16 zenon_H17 zenon_H18. % 0.18/0.56 generalize (zenon_H15 zenon_TL_z). zenon_intro zenon_H1b. % 0.18/0.56 generalize (zenon_H1b zenon_TN_ba). zenon_intro zenon_H1c. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.18/0.56 exact (zenon_H1e zenon_H18). % 0.18/0.56 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 0.18/0.56 exact (zenon_H17 zenon_H20). % 0.18/0.56 exact (zenon_H16 zenon_H1f). % 0.18/0.56 (* end of lemma zenon_L1_ *) % 0.18/0.56 assert (zenon_L2_ : forall (zenon_TN_ba : zenon_U) (zenon_TL_z : zenon_U) (zenon_TM_bk : zenon_U), (forall M : zenon_U, ((convergent_lines zenon_TM_bk M)\/(unorthogonal_lines zenon_TM_bk M))) -> (~(convergent_lines zenon_TL_z zenon_TM_bk)) -> (~(distinct_lines zenon_TL_z zenon_TN_ba)) -> (~(unorthogonal_lines zenon_TM_bk zenon_TN_ba)) -> False). % 0.18/0.56 do 3 intro. intros zenon_H21 zenon_H22 zenon_H16 zenon_H23. % 0.18/0.56 generalize (zenon_H21 zenon_TN_ba). zenon_intro zenon_H25. % 0.18/0.56 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.18/0.56 generalize (apart3 zenon_TM_bk). zenon_intro zenon_H28. % 0.18/0.56 generalize (apart2 zenon_TN_ba). zenon_intro zenon_H17. % 0.18/0.56 generalize (ceq3 zenon_TN_ba). zenon_intro zenon_H29. % 0.18/0.56 generalize (apart5 zenon_TN_ba). zenon_intro zenon_H15. % 0.18/0.56 generalize (apart6 zenon_TM_bk). zenon_intro zenon_H2a. % 0.18/0.56 generalize (zenon_H2a zenon_TN_ba). zenon_intro zenon_H2b. % 0.18/0.56 generalize (zenon_H2b zenon_TL_z). zenon_intro zenon_H2c. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 0.18/0.56 exact (zenon_H2e zenon_H27). % 0.18/0.56 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.18/0.56 generalize (zenon_H2a zenon_TL_z). zenon_intro zenon_H31. % 0.18/0.56 generalize (zenon_H31 zenon_TM_bk). zenon_intro zenon_H32. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.18/0.56 exact (zenon_H34 zenon_H30). % 0.18/0.56 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.18/0.56 exact (zenon_H28 zenon_H36). % 0.18/0.56 exact (zenon_H22 zenon_H35). % 0.18/0.56 generalize (zenon_H29 zenon_TL_z). zenon_intro zenon_H37. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H18 ]. % 0.18/0.56 exact (zenon_H38 zenon_H2f). % 0.18/0.56 apply (zenon_L1_ zenon_TL_z zenon_TN_ba); trivial. % 0.18/0.56 exact (zenon_H23 zenon_H26). % 0.18/0.56 (* end of lemma zenon_L2_ *) % 0.18/0.56 assert (zenon_L3_ : forall (zenon_TN_ba : zenon_U) (zenon_TL_z : zenon_U), (~(distinct_lines zenon_TL_z zenon_TN_ba)) -> (convergent_lines zenon_TL_z zenon_TN_ba) -> False). % 0.18/0.56 do 2 intro. intros zenon_H16 zenon_H39. % 0.18/0.56 generalize (ceq3 zenon_TL_z). zenon_intro zenon_H3a. % 0.18/0.56 generalize (zenon_H3a zenon_TN_ba). zenon_intro zenon_H3b. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H1f ]. % 0.18/0.56 exact (zenon_H3c zenon_H39). % 0.18/0.56 exact (zenon_H16 zenon_H1f). % 0.18/0.56 (* end of lemma zenon_L3_ *) % 0.18/0.56 apply NNPP. intro zenon_G. % 0.18/0.56 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((distinct_lines L N)\/(unorthogonal_lines M N)))))) zenon_G); [ zenon_intro zenon_H3d; idtac ]. % 0.18/0.56 elim zenon_H3d. zenon_intro zenon_TL_z. zenon_intro zenon_H3e. % 0.18/0.56 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unorthogonal_lines zenon_TL_z M)->((distinct_lines zenon_TL_z N)\/(unorthogonal_lines M N))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.18/0.56 elim zenon_H3f. zenon_intro zenon_TM_bk. zenon_intro zenon_H40. % 0.18/0.56 apply (zenon_notallex_s (fun N : zenon_U => ((unorthogonal_lines zenon_TL_z zenon_TM_bk)->((distinct_lines zenon_TL_z N)\/(unorthogonal_lines zenon_TM_bk N)))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 0.18/0.56 elim zenon_H41. zenon_intro zenon_TN_ba. zenon_intro zenon_H42. % 0.18/0.56 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 0.18/0.56 apply (zenon_notor_s _ _ zenon_H43). zenon_intro zenon_H16. zenon_intro zenon_H23. % 0.18/0.56 generalize (oac1 zenon_TL_z). zenon_intro zenon_H45. % 0.18/0.56 generalize (zenon_H45 zenon_TM_bk). zenon_intro zenon_H46. % 0.18/0.56 generalize (occu1 zenon_TM_bk). zenon_intro zenon_H21. % 0.18/0.56 generalize (zenon_H46 zenon_TN_ba). zenon_intro zenon_H47. % 0.18/0.56 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.18/0.56 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H22 | zenon_intro zenon_H4a ]. % 0.18/0.56 apply (zenon_L2_ zenon_TN_ba zenon_TL_z zenon_TM_bk); trivial. % 0.18/0.56 exact (zenon_H4a zenon_H44). % 0.18/0.56 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 0.18/0.56 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H39. zenon_intro zenon_H4d. % 0.18/0.56 apply (zenon_L3_ zenon_TN_ba zenon_TL_z); trivial. % 0.18/0.56 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.18/0.56 exact (zenon_H23 zenon_H26). % 0.18/0.56 Qed. % 0.18/0.56 % SZS output end Proof % 0.18/0.56 (* END-PROOF *) % 0.18/0.56 nodes searched: 2810 % 0.18/0.56 max branch formulas: 709 % 0.18/0.56 proof nodes created: 295 % 0.18/0.56 formulas created: 8914 % 0.18/0.56 %------------------------------------------------------------------------------