%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO213+1 : 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 07:00:54 EDT 2022 % Result : Theorem 0.37s 0.55s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO213+1 : TPTP v8.1.0. Released v3.3.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n018.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 00:21:17 EDT 2022 % 0.12/0.33 % CPUTime : % 0.37/0.55 (* PROOF-FOUND *) % 0.37/0.55 % SZS status Theorem % 0.37/0.55 (* BEGIN-PROOF *) % 0.37/0.55 % SZS output start Proof % 0.37/0.55 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)))))). % 0.37/0.55 Proof. % 0.37/0.55 assert (zenon_L1_ : forall (zenon_TL_ba : zenon_U) (zenon_TN_bb : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines zenon_TN_bb Y)->((distinct_lines zenon_TN_bb Z)\/(distinct_lines Y Z))))) -> (~(distinct_lines zenon_TL_ba zenon_TN_bb)) -> (distinct_lines zenon_TN_bb zenon_TL_ba) -> False). % 0.37/0.55 do 2 intro. intros zenon_H17 zenon_H18 zenon_H19. % 0.37/0.55 generalize (zenon_H17 zenon_TL_ba). zenon_intro zenon_H1c. % 0.37/0.55 generalize (zenon_H1c zenon_TN_bb). zenon_intro zenon_H1d. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.37/0.55 exact (zenon_H1f zenon_H19). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.37/0.55 generalize (apart2 zenon_TN_bb). zenon_intro zenon_H22. % 0.37/0.55 exact (zenon_H22 zenon_H21). % 0.37/0.55 exact (zenon_H18 zenon_H20). % 0.37/0.55 (* end of lemma zenon_L1_ *) % 0.37/0.55 assert (zenon_L2_ : forall (zenon_TL_ba : zenon_U) (zenon_TN_bb : zenon_U) (zenon_TM_bm : zenon_U), (~(unorthogonal_lines zenon_TM_bm zenon_TN_bb)) -> (~(convergent_lines zenon_TL_ba zenon_TM_bm)) -> (~(distinct_lines zenon_TL_ba zenon_TN_bb)) -> (forall M : zenon_U, ((convergent_lines zenon_TM_bm M)\/(unorthogonal_lines zenon_TM_bm M))) -> False). % 0.37/0.55 do 3 intro. intros zenon_H23 zenon_H24 zenon_H18 zenon_H25. % 0.37/0.55 generalize (apart3 zenon_TM_bm). zenon_intro zenon_H27. % 0.37/0.55 generalize (zenon_H25 zenon_TN_bb). zenon_intro zenon_H28. % 0.37/0.55 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.37/0.55 generalize (ceq3 zenon_TM_bm). zenon_intro zenon_H2b. % 0.37/0.55 generalize (zenon_H2b zenon_TN_bb). zenon_intro zenon_H2c. % 0.37/0.55 generalize (ax6 zenon_TM_bm). zenon_intro zenon_H2d. % 0.37/0.55 generalize (apart5 zenon_TN_bb). zenon_intro zenon_H17. % 0.37/0.55 generalize (zenon_H2c zenon_TL_ba). zenon_intro zenon_H2e. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.37/0.55 exact (zenon_H30 zenon_H2a). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H19 | zenon_intro zenon_H31 ]. % 0.37/0.55 apply (zenon_L1_ zenon_TL_ba zenon_TN_bb); trivial. % 0.37/0.55 generalize (zenon_H2d zenon_TL_ba). zenon_intro zenon_H32. % 0.37/0.55 generalize (zenon_H32 zenon_TM_bm). zenon_intro zenon_H33. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.37/0.55 exact (zenon_H35 zenon_H31). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.37/0.55 exact (zenon_H27 zenon_H37). % 0.37/0.55 exact (zenon_H24 zenon_H36). % 0.37/0.55 exact (zenon_H23 zenon_H29). % 0.37/0.55 (* end of lemma zenon_L2_ *) % 0.37/0.55 assert (zenon_L3_ : forall (zenon_TM_bm : zenon_U) (zenon_TN_bb : zenon_U) (zenon_TL_ba : zenon_U), (~(distinct_lines zenon_TL_ba zenon_TN_bb)) -> (~(convergent_lines zenon_TL_ba zenon_TM_bm)) -> (~(unorthogonal_lines zenon_TM_bm zenon_TN_bb)) -> False). % 0.37/0.55 do 3 intro. intros zenon_H18 zenon_H24 zenon_H23. % 0.37/0.55 generalize (occu1 zenon_TM_bm). zenon_intro zenon_H25. % 0.37/0.55 apply (zenon_L2_ zenon_TL_ba zenon_TN_bb zenon_TM_bm); trivial. % 0.37/0.55 (* end of lemma zenon_L3_ *) % 0.37/0.55 apply NNPP. intro zenon_G. % 0.37/0.55 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_H38; idtac ]. % 0.37/0.55 elim zenon_H38. zenon_intro zenon_TL_ba. zenon_intro zenon_H39. % 0.37/0.55 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unorthogonal_lines zenon_TL_ba M)->((distinct_lines zenon_TL_ba N)\/(unorthogonal_lines M N))))) zenon_H39); [ zenon_intro zenon_H3a; idtac ]. % 0.37/0.55 elim zenon_H3a. zenon_intro zenon_TM_bm. zenon_intro zenon_H3b. % 0.37/0.55 apply (zenon_notallex_s (fun N : zenon_U => ((unorthogonal_lines zenon_TL_ba zenon_TM_bm)->((distinct_lines zenon_TL_ba N)\/(unorthogonal_lines zenon_TM_bm N)))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ]. % 0.37/0.55 elim zenon_H3c. zenon_intro zenon_TN_bb. zenon_intro zenon_H3d. % 0.37/0.55 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.37/0.55 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H18. zenon_intro zenon_H23. % 0.37/0.55 generalize (oac1 zenon_TL_ba). zenon_intro zenon_H40. % 0.37/0.55 generalize (zenon_H40 zenon_TM_bm). zenon_intro zenon_H41. % 0.37/0.55 generalize (zenon_H41 zenon_TN_bb). zenon_intro zenon_H42. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.37/0.55 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H24 | zenon_intro zenon_H45 ]. % 0.37/0.55 apply (zenon_L3_ zenon_TM_bm zenon_TN_bb zenon_TL_ba); trivial. % 0.37/0.55 exact (zenon_H45 zenon_H3f). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.37/0.55 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.37/0.55 generalize (ceq3 zenon_TL_ba). zenon_intro zenon_H4a. % 0.37/0.55 generalize (zenon_H4a zenon_TN_bb). zenon_intro zenon_H4b. % 0.37/0.55 generalize (apart5 zenon_TN_bb). zenon_intro zenon_H17. % 0.37/0.55 generalize (zenon_H4b zenon_TL_ba). zenon_intro zenon_H4c. % 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.37/0.55 exact (zenon_H4e zenon_H49). % 0.37/0.55 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ]. % 0.37/0.55 apply (zenon_L1_ zenon_TL_ba zenon_TN_bb); trivial. % 0.37/0.55 generalize (apart3 zenon_TL_ba). zenon_intro zenon_H50. % 0.37/0.55 exact (zenon_H50 zenon_H4f). % 0.37/0.55 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.37/0.55 exact (zenon_H23 zenon_H29). % 0.37/0.55 Qed. % 0.37/0.55 % SZS output end Proof % 0.37/0.55 (* END-PROOF *) % 0.37/0.55 nodes searched: 2630 % 0.37/0.55 max branch formulas: 856 % 0.37/0.55 proof nodes created: 247 % 0.37/0.55 formulas created: 10724 % 0.37/0.55 %------------------------------------------------------------------------------