%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT044+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:24:22 AM UTC 2026 % Result : Theorem 0.95s 1.20s % Output : Proof 0.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT044+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n010.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Mon Sep 7 13:07:26 UTC 2026 % 0.09/0.36 % CPUTime : % 0.95/1.20 (* PROOF-FOUND *) % 0.95/1.20 % SZS status Theorem % 0.95/1.20 (* BEGIN-PROOF *) % 0.95/1.20 % SZS output start Proof % 0.95/1.20 Theorem lemma_3 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\(greater (age X T) (age X T0)))->(greater (capability X T) (capability X T0)))))). % 0.95/1.20 Proof. % 0.95/1.20 assert (zenon_L1_ : forall (zenon_TT_p : zenon_U) (zenon_TT0_q : zenon_U) (zenon_TX_r : zenon_U), (forall T : zenon_U, (((organization zenon_TX_r)/\(greater (age zenon_TX_r T) (age zenon_TX_r zenon_TT0_q)))->(greater (stock_of_knowledge zenon_TX_r T) (stock_of_knowledge zenon_TX_r zenon_TT0_q)))) -> (organization zenon_TX_r) -> (greater (age zenon_TX_r zenon_TT_p) (age zenon_TX_r zenon_TT0_q)) -> (~(greater (stock_of_knowledge zenon_TX_r zenon_TT_p) (stock_of_knowledge zenon_TX_r zenon_TT0_q))) -> False). % 0.95/1.20 do 3 intro. intros zenon_Hb zenon_Hc zenon_Hd zenon_He. % 0.95/1.20 generalize (zenon_Hb zenon_TT_p). zenon_intro zenon_H12. % 0.95/1.20 apply (zenon_imply_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 0.95/1.20 apply (zenon_notand_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.95/1.20 exact (zenon_H16 zenon_Hc). % 0.95/1.20 exact (zenon_H15 zenon_Hd). % 0.95/1.20 exact (zenon_He zenon_H13). % 0.95/1.20 (* end of lemma zenon_L1_ *) % 0.95/1.20 assert (zenon_L2_ : forall (zenon_TT_p : zenon_U) (zenon_TT0_q : zenon_U) (zenon_TX_r : zenon_U), (~(greater (internal_friction zenon_TX_r zenon_TT0_q) (internal_friction zenon_TX_r zenon_TT_p))) -> (~((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_TT0_q))) -> (~(greater (internal_friction zenon_TX_r zenon_TT_p) (internal_friction zenon_TX_r zenon_TT0_q))) -> False). % 0.95/1.20 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19. % 0.95/1.20 generalize (meaning_postulate_greater_comparable (internal_friction zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H1a. % 0.95/1.20 generalize (zenon_H1a (internal_friction zenon_TX_r zenon_TT_p)). zenon_intro zenon_H1b. % 0.95/1.20 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.95/1.20 generalize (definition_smaller (internal_friction zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H1e. % 0.95/1.20 generalize (zenon_H1e (internal_friction zenon_TX_r zenon_TT_p)). zenon_intro zenon_H1f. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H21; zenon_intro zenon_H19 | zenon_intro zenon_H1d; zenon_intro zenon_H20 ]. % 0.95/1.21 exact (zenon_H21 zenon_H1d). % 0.95/1.21 exact (zenon_H19 zenon_H20). % 0.95/1.21 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.95/1.21 apply zenon_H18. apply sym_equal. exact zenon_H23. % 0.95/1.21 exact (zenon_H17 zenon_H22). % 0.95/1.21 (* end of lemma zenon_L2_ *) % 0.95/1.21 assert (zenon_L3_ : forall (zenon_TT0_q : zenon_U) (zenon_TX_r : zenon_U), (forall T : zenon_U, ((organization zenon_TX_r)->((internal_friction zenon_TX_r T) = (internal_friction zenon_TX_r zenon_E)))) -> (organization zenon_TX_r) -> (~((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_E))) -> False). % 0.95/1.21 do 2 intro. intros zenon_H24 zenon_Hc zenon_H25. % 0.95/1.21 generalize (zenon_H24 zenon_TT0_q). zenon_intro zenon_H26. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H16 | zenon_intro zenon_H27 ]. % 0.95/1.21 exact (zenon_H16 zenon_Hc). % 0.95/1.21 exact (zenon_H25 zenon_H27). % 0.95/1.21 (* end of lemma zenon_L3_ *) % 0.95/1.21 assert (zenon_L4_ : forall (zenon_TT0_q : zenon_U) (zenon_TX_r : zenon_U), (greater (capability zenon_TX_r zenon_TT0_q) (capability zenon_TX_r zenon_TT0_q)) -> False). % 0.95/1.21 do 2 intro. intros zenon_H28. % 0.95/1.21 generalize (meaning_postulate_greater_strict (capability zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H29. % 0.95/1.21 generalize (zenon_H29 (capability zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H2a. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2b | zenon_intro zenon_H2b ]. % 0.95/1.21 exact (zenon_H2b zenon_H28). % 0.95/1.21 exact (zenon_H2b zenon_H28). % 0.95/1.21 (* end of lemma zenon_L4_ *) % 0.95/1.21 assert (zenon_L5_ : forall (zenon_TT0_q : zenon_U) (zenon_TX_r : zenon_U), (smaller (capability zenon_TX_r zenon_TT0_q) (capability zenon_TX_r zenon_TT0_q)) -> False). % 0.95/1.21 do 2 intro. intros zenon_H2c. % 0.95/1.21 generalize (definition_smaller (capability zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H2d. % 0.95/1.21 generalize (zenon_H2d (capability zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H2e. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H2f; zenon_intro zenon_H2b | zenon_intro zenon_H2c; zenon_intro zenon_H28 ]. % 0.95/1.21 exact (zenon_H2f zenon_H2c). % 0.95/1.21 apply (zenon_L4_ zenon_TT0_q zenon_TX_r); trivial. % 0.95/1.21 (* end of lemma zenon_L5_ *) % 0.95/1.21 apply NNPP. intro zenon_G. % 0.95/1.21 apply (zenon_notallex_s (fun X : zenon_U => (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\(greater (age X T) (age X T0)))->(greater (capability X T) (capability X T0)))))) zenon_G); [ zenon_intro zenon_H30; idtac ]. % 0.95/1.21 elim zenon_H30. zenon_intro zenon_TX_r. zenon_intro zenon_H31. % 0.95/1.21 apply (zenon_notallex_s (fun T0 : zenon_U => (forall T : zenon_U, (((organization zenon_TX_r)/\(greater (age zenon_TX_r T) (age zenon_TX_r T0)))->(greater (capability zenon_TX_r T) (capability zenon_TX_r T0))))) zenon_H31); [ zenon_intro zenon_H32; idtac ]. % 0.95/1.21 elim zenon_H32. zenon_intro zenon_TT0_q. zenon_intro zenon_H33. % 0.95/1.21 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_r)/\(greater (age zenon_TX_r T) (age zenon_TX_r zenon_TT0_q)))->(greater (capability zenon_TX_r T) (capability zenon_TX_r zenon_TT0_q)))) zenon_H33); [ zenon_intro zenon_H34; idtac ]. % 0.95/1.21 elim zenon_H34. zenon_intro zenon_TT_p. zenon_intro zenon_H35. % 0.95/1.21 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.95/1.21 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hc. zenon_intro zenon_Hd. % 0.95/1.21 generalize (assumption_5 zenon_TX_r). zenon_intro zenon_H38. % 0.95/1.21 generalize (zenon_H38 zenon_TT0_q). zenon_intro zenon_H39. % 0.95/1.21 generalize (zenon_H39 zenon_TT0_q). zenon_intro zenon_H3a. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H16 | zenon_intro zenon_H3b ]. % 0.95/1.21 exact (zenon_H16 zenon_Hc). % 0.95/1.21 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.95/1.21 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H40 | zenon_intro zenon_H2c ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.95/1.21 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H43. % 0.95/1.21 generalize (zenon_H43 (stock_of_knowledge zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H44. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H42; zenon_intro zenon_H47 | zenon_intro zenon_H46; zenon_intro zenon_H45 ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.95/1.21 apply zenon_H48. apply refl_equal. % 0.95/1.21 exact (zenon_H42 zenon_H46). % 0.95/1.21 generalize (zenon_H39 zenon_TT_p). zenon_intro zenon_H4a. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H16 | zenon_intro zenon_H4b ]. % 0.95/1.21 exact (zenon_H16 zenon_Hc). % 0.95/1.21 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 0.95/1.21 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_He | zenon_intro zenon_H50 ]. % 0.95/1.21 generalize (assumption_7 zenon_TX_r). zenon_intro zenon_H51. % 0.95/1.21 generalize (zenon_H51 zenon_TT0_q). zenon_intro zenon_Hb. % 0.95/1.21 apply (zenon_L1_ zenon_TT_p zenon_TT0_q zenon_TX_r); trivial. % 0.95/1.21 generalize (definition_smaller_or_equal (internal_friction zenon_TX_r zenon_TT_p)). zenon_intro zenon_H52. % 0.95/1.21 generalize (zenon_H52 (internal_friction zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H53. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H53); [ zenon_intro zenon_H50; zenon_intro zenon_H56 | zenon_intro zenon_H55; zenon_intro zenon_H54 ]. % 0.95/1.21 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H57. zenon_intro zenon_H18. % 0.95/1.21 generalize (definition_smaller (internal_friction zenon_TX_r zenon_TT_p)). zenon_intro zenon_H58. % 0.95/1.21 generalize (zenon_H58 (internal_friction zenon_TX_r zenon_TT0_q)). zenon_intro zenon_H59. % 0.95/1.21 apply (zenon_equiv_s _ _ zenon_H59); [ zenon_intro zenon_H57; zenon_intro zenon_H17 | zenon_intro zenon_H5a; zenon_intro zenon_H22 ]. % 0.95/1.21 generalize (assumption_9 zenon_TX_r). zenon_intro zenon_H0. % 0.95/1.21 generalize (zenon_H0 zenon_E). zenon_intro zenon_H24. % 0.95/1.21 generalize (zenon_H24 zenon_TT_p). zenon_intro zenon_H5b. % 0.95/1.21 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H16 | zenon_intro zenon_H5c ]. % 0.95/1.21 exact (zenon_H16 zenon_Hc). % 0.95/1.21 elim (classic ((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_TT_p))); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ]. % 0.95/1.21 elim (classic (greater (internal_friction zenon_TX_r zenon_TT_p) (internal_friction zenon_TX_r zenon_TT0_q))); [ zenon_intro zenon_H20 | zenon_intro zenon_H19 ]. % 0.95/1.21 elim (classic (greater (internal_friction zenon_TX_r zenon_E) (internal_friction zenon_TX_r zenon_TT0_q))); [ zenon_intro zenon_H5f | zenon_intro zenon_H60 ]. % 0.95/1.21 cut ((greater (internal_friction zenon_TX_r zenon_E) (internal_friction zenon_TX_r zenon_TT0_q)) = (greater (internal_friction zenon_TX_r zenon_TT0_q) (internal_friction zenon_TX_r zenon_TT0_q))). % 0.95/1.21 intro zenon_D_pnotp. % 0.95/1.21 apply zenon_H41. % 0.95/1.21 rewrite <- zenon_D_pnotp. % 0.95/1.21 exact zenon_H5f. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_TT0_q))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_TT0_q))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 0.95/1.21 congruence. % 0.95/1.21 elim (classic ((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_TT0_q))); [ zenon_intro zenon_H63 | zenon_intro zenon_H61 ]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_TT0_q)) = ((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_TT0_q))). % 0.95/1.21 intro zenon_D_pnotp. % 0.95/1.21 apply zenon_H62. % 0.95/1.21 rewrite <- zenon_D_pnotp. % 0.95/1.21 exact zenon_H63. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_TT0_q))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.95/1.21 congruence. % 0.95/1.21 apply (zenon_L3_ zenon_TT0_q zenon_TX_r); trivial. % 0.95/1.21 apply zenon_H61. apply refl_equal. % 0.95/1.21 apply zenon_H61. apply refl_equal. % 0.95/1.21 apply zenon_H61. apply refl_equal. % 0.95/1.21 cut ((greater (internal_friction zenon_TX_r zenon_TT_p) (internal_friction zenon_TX_r zenon_TT0_q)) = (greater (internal_friction zenon_TX_r zenon_E) (internal_friction zenon_TX_r zenon_TT0_q))). % 0.95/1.21 intro zenon_D_pnotp. % 0.95/1.21 apply zenon_H60. % 0.95/1.21 rewrite <- zenon_D_pnotp. % 0.95/1.21 exact zenon_H20. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT0_q) = (internal_friction zenon_TX_r zenon_TT0_q))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 0.95/1.21 congruence. % 0.95/1.21 elim (classic ((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_E))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_E)) = ((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_E))). % 0.95/1.21 intro zenon_D_pnotp. % 0.95/1.21 apply zenon_H64. % 0.95/1.21 rewrite <- zenon_D_pnotp. % 0.95/1.21 exact zenon_H65. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_TT_p))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 0.95/1.21 congruence. % 0.95/1.21 exact (zenon_H5e zenon_H5d). % 0.95/1.21 apply zenon_H66. apply refl_equal. % 0.95/1.21 apply zenon_H66. apply refl_equal. % 0.95/1.21 apply zenon_H61. apply refl_equal. % 0.95/1.21 apply (zenon_L2_ zenon_TT_p zenon_TT0_q zenon_TX_r); trivial. % 0.95/1.21 elim (classic ((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_TT_p))); [ zenon_intro zenon_H67 | zenon_intro zenon_H68 ]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_TT_p)) = ((internal_friction zenon_TX_r zenon_E) = (internal_friction zenon_TX_r zenon_TT_p))). % 0.95/1.21 intro zenon_D_pnotp. % 0.95/1.21 apply zenon_H5e. % 0.95/1.21 rewrite <- zenon_D_pnotp. % 0.95/1.21 exact zenon_H67. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_TT_p))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 0.95/1.21 cut (((internal_friction zenon_TX_r zenon_TT_p) = (internal_friction zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 0.95/1.21 congruence. % 0.95/1.21 exact (zenon_H64 zenon_H5c). % 0.95/1.21 apply zenon_H68. apply refl_equal. % 0.95/1.21 apply zenon_H68. apply refl_equal. % 0.95/1.21 exact (zenon_H57 zenon_H5a). % 0.95/1.21 exact (zenon_H50 zenon_H55). % 0.95/1.21 exact (zenon_H36 zenon_H4e). % 0.95/1.21 apply (zenon_L5_ zenon_TT0_q zenon_TX_r); trivial. % 0.95/1.21 Qed. % 0.95/1.21 % SZS output end Proof % 0.95/1.21 (* END-PROOF *) % 0.95/1.21 nodes searched: 34588 % 0.95/1.21 max branch formulas: 974 % 0.95/1.21 proof nodes created: 660 % 0.95/1.21 formulas created: 16889 % 0.95/1.21 %------------------------------------------------------------------------------