%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 : Tue Jul 19 06:38:39 EDT 2022 % Result : Theorem 0.45s 0.63s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET800+4 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.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 Jul 9 23:18:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.45/0.63 (* PROOF-FOUND *) % 0.45/0.63 % SZS status Theorem % 0.45/0.63 (* BEGIN-PROOF *) % 0.45/0.63 % SZS output start Proof % 0.45/0.63 Theorem thIV12 : (forall R : zenon_U, (forall E : zenon_U, ((order R E)->(forall X1 : zenon_U, (forall X2 : zenon_U, (((subset X1 E)/\((subset X2 E)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((greatest_lower_bound M1 X1 R E)/\(greatest_lower_bound M2 X2 R E))->(apply R M2 M1)))))))))). % 0.45/0.63 Proof. % 0.45/0.63 assert (zenon_L1_ : forall (zenon_TM2_z : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX2_bb : zenon_U), (forall X : zenon_U, ((member X zenon_TX2_bb)->(member X zenon_TE_ba))) -> (member zenon_TM2_z zenon_TX2_bb) -> (~(member zenon_TM2_z zenon_TE_ba)) -> False). % 0.45/0.63 do 3 intro. intros zenon_H16 zenon_H17 zenon_H18. % 0.45/0.63 generalize (zenon_H16 zenon_TM2_z). zenon_intro zenon_H1c. % 0.45/0.63 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.45/0.63 exact (zenon_H1e zenon_H17). % 0.45/0.63 exact (zenon_H18 zenon_H1d). % 0.45/0.63 (* end of lemma zenon_L1_ *) % 0.45/0.63 apply NNPP. intro zenon_G. % 0.45/0.63 apply (zenon_notallex_s (fun R : zenon_U => (forall E : zenon_U, ((order R E)->(forall X1 : zenon_U, (forall X2 : zenon_U, (((subset X1 E)/\((subset X2 E)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((greatest_lower_bound M1 X1 R E)/\(greatest_lower_bound M2 X2 R E))->(apply R M2 M1)))))))))) zenon_G); [ zenon_intro zenon_H1f; idtac ]. % 0.45/0.63 elim zenon_H1f. zenon_intro zenon_TR_bg. zenon_intro zenon_H21. % 0.45/0.63 apply (zenon_notallex_s (fun E : zenon_U => ((order zenon_TR_bg E)->(forall X1 : zenon_U, (forall X2 : zenon_U, (((subset X1 E)/\((subset X2 E)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((greatest_lower_bound M1 X1 zenon_TR_bg E)/\(greatest_lower_bound M2 X2 zenon_TR_bg E))->(apply zenon_TR_bg M2 M1))))))))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.45/0.63 elim zenon_H22. zenon_intro zenon_TE_ba. zenon_intro zenon_H23. % 0.45/0.63 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.45/0.63 apply (zenon_notallex_s (fun X1 : zenon_U => (forall X2 : zenon_U, (((subset X1 zenon_TE_ba)/\((subset X2 zenon_TE_ba)/\(subset X1 X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((greatest_lower_bound M1 X1 zenon_TR_bg zenon_TE_ba)/\(greatest_lower_bound M2 X2 zenon_TR_bg zenon_TE_ba))->(apply zenon_TR_bg M2 M1))))))) zenon_H24); [ zenon_intro zenon_H26; idtac ]. % 0.45/0.63 elim zenon_H26. zenon_intro zenon_TX1_bn. zenon_intro zenon_H28. % 0.45/0.63 apply (zenon_notallex_s (fun X2 : zenon_U => (((subset zenon_TX1_bn zenon_TE_ba)/\((subset X2 zenon_TE_ba)/\(subset zenon_TX1_bn X2)))->(forall M1 : zenon_U, (forall M2 : zenon_U, (((greatest_lower_bound M1 zenon_TX1_bn zenon_TR_bg zenon_TE_ba)/\(greatest_lower_bound M2 X2 zenon_TR_bg zenon_TE_ba))->(apply zenon_TR_bg M2 M1)))))) zenon_H28); [ zenon_intro zenon_H29; idtac ]. % 0.45/0.63 elim zenon_H29. zenon_intro zenon_TX2_bb. zenon_intro zenon_H2a. % 0.45/0.63 apply (zenon_notimply_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.45/0.63 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.45/0.63 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.45/0.63 generalize (subset zenon_TX2_bb). zenon_intro zenon_H31. % 0.45/0.63 generalize (zenon_H31 zenon_TE_ba). zenon_intro zenon_H32. % 0.45/0.63 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H34; zenon_intro zenon_H33 | zenon_intro zenon_H30; zenon_intro zenon_H16 ]. % 0.45/0.63 exact (zenon_H34 zenon_H30). % 0.45/0.63 generalize (subset zenon_TX1_bn). zenon_intro zenon_H35. % 0.45/0.63 generalize (zenon_H35 zenon_TX2_bb). zenon_intro zenon_H36. % 0.45/0.63 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H39; zenon_intro zenon_H38 | zenon_intro zenon_H2f; zenon_intro zenon_H37 ]. % 0.45/0.63 exact (zenon_H39 zenon_H2f). % 0.45/0.63 apply (zenon_notallex_s (fun M1 : zenon_U => (forall M2 : zenon_U, (((greatest_lower_bound M1 zenon_TX1_bn zenon_TR_bg zenon_TE_ba)/\(greatest_lower_bound M2 zenon_TX2_bb zenon_TR_bg zenon_TE_ba))->(apply zenon_TR_bg M2 M1)))) zenon_H2b); [ zenon_intro zenon_H3a; idtac ]. % 0.45/0.63 elim zenon_H3a. zenon_intro zenon_TM1_ch. zenon_intro zenon_H3c. % 0.45/0.63 apply (zenon_notallex_s (fun M2 : zenon_U => (((greatest_lower_bound zenon_TM1_ch zenon_TX1_bn zenon_TR_bg zenon_TE_ba)/\(greatest_lower_bound M2 zenon_TX2_bb zenon_TR_bg zenon_TE_ba))->(apply zenon_TR_bg M2 zenon_TM1_ch))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ]. % 0.45/0.63 elim zenon_H3d. zenon_intro zenon_TM2_z. zenon_intro zenon_H3e. % 0.45/0.63 apply (zenon_notimply_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.45/0.63 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41. % 0.45/0.63 generalize (greatest_lower_bound zenon_TM1_ch). zenon_intro zenon_H43. % 0.45/0.63 generalize (zenon_H43 zenon_TX1_bn). zenon_intro zenon_H44. % 0.45/0.63 generalize (zenon_H44 zenon_TR_bg). zenon_intro zenon_H45. % 0.45/0.63 generalize (zenon_H45 zenon_TE_ba). zenon_intro zenon_H46. % 0.45/0.63 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H49; zenon_intro zenon_H48 | zenon_intro zenon_H42; zenon_intro zenon_H47 ]. % 0.45/0.63 exact (zenon_H49 zenon_H42). % 0.45/0.63 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 0.45/0.63 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 0.45/0.63 generalize (greatest_lower_bound zenon_TM2_z). zenon_intro zenon_H4e. % 0.45/0.63 generalize (zenon_H4e zenon_TX2_bb). zenon_intro zenon_H4f. % 0.45/0.63 generalize (zenon_H4f zenon_TR_bg). zenon_intro zenon_H50. % 0.45/0.63 generalize (zenon_H50 zenon_TE_ba). zenon_intro zenon_H51. % 0.45/0.63 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H54; zenon_intro zenon_H53 | zenon_intro zenon_H41; zenon_intro zenon_H52 ]. % 0.45/0.63 exact (zenon_H54 zenon_H41). % 0.45/0.63 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H17. zenon_intro zenon_H55. % 0.45/0.63 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H56. % 0.45/0.63 generalize (lower_bound zenon_TR_bg). zenon_intro zenon_H58. % 0.45/0.63 generalize (zenon_H58 zenon_TX2_bb). zenon_intro zenon_H59. % 0.45/0.63 generalize (zenon_H59 zenon_TM2_z). zenon_intro zenon_H5a. % 0.45/0.63 apply (zenon_equiv_s _ _ zenon_H5a); [ zenon_intro zenon_H5d; zenon_intro zenon_H5c | zenon_intro zenon_H57; zenon_intro zenon_H5b ]. % 0.45/0.63 exact (zenon_H5d zenon_H57). % 0.45/0.63 generalize (zenon_H4c zenon_TM2_z). zenon_intro zenon_H5e. % 0.45/0.63 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ]. % 0.45/0.63 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H18 | zenon_intro zenon_H61 ]. % 0.45/0.64 apply (zenon_L1_ zenon_TM2_z zenon_TE_ba zenon_TX2_bb); trivial. % 0.45/0.64 generalize (lower_bound zenon_TR_bg). zenon_intro zenon_H58. % 0.45/0.64 generalize (zenon_H58 zenon_TX1_bn). zenon_intro zenon_H62. % 0.45/0.64 generalize (zenon_H62 zenon_TM2_z). zenon_intro zenon_H63. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H61; zenon_intro zenon_H66 | zenon_intro zenon_H65; zenon_intro zenon_H64 ]. % 0.45/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TX1_bn)->(apply zenon_TR_bg zenon_TM2_z X))) zenon_H66); [ zenon_intro zenon_H67; idtac ]. % 0.45/0.64 elim zenon_H67. zenon_intro zenon_TX_ea. zenon_intro zenon_H69. % 0.45/0.64 apply (zenon_notimply_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H6a. % 0.45/0.64 generalize (zenon_H5b zenon_TX_ea). zenon_intro zenon_H6c. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 0.45/0.64 generalize (zenon_H37 zenon_TX_ea). zenon_intro zenon_H6f. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ]. % 0.45/0.64 exact (zenon_H71 zenon_H6b). % 0.45/0.64 exact (zenon_H6e zenon_H70). % 0.45/0.64 exact (zenon_H6a zenon_H6d). % 0.45/0.64 exact (zenon_H61 zenon_H65). % 0.45/0.64 exact (zenon_H3f zenon_H5f). % 0.45/0.64 Qed. % 0.45/0.64 % SZS output end Proof % 0.45/0.64 (* END-PROOF *) % 0.45/0.64 nodes searched: 5994 % 0.45/0.64 max branch formulas: 1489 % 0.45/0.64 proof nodes created: 299 % 0.45/0.64 formulas created: 36190 % 0.45/0.64 %------------------------------------------------------------------------------