%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : MGT048+1 : TPTP v9.3.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 06:24:23 AM UTC 2026 % Result : Theorem 1.34s 1.63s % Output : Proof 1.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT048+1 : TPTP v9.3.0. Released v2.4.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.10/0.36 % Computer : n027.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Mon Sep 7 13:16:30 UTC 2026 % 0.10/0.37 % CPUTime : % 1.34/1.63 (* PROOF-FOUND *) % 1.34/1.63 % SZS status Theorem % 1.34/1.63 (* BEGIN-PROOF *) % 1.34/1.63 % SZS output start Proof % 1.34/1.63 Theorem lemma_5 : (forall X : zenon_U, (forall T0 : zenon_U, (forall T : zenon_U, (((organization X)/\(greater (age X T) (age X T0)))->(smaller (capability X T) (capability X T0)))))). % 1.34/1.63 Proof. % 1.34/1.63 assert (zenon_L1_ : forall (zenon_TT0_p : zenon_U) (zenon_TT_q : zenon_U) (zenon_TX_r : zenon_U), (forall Y : zenon_U, ((smaller (stock_of_knowledge zenon_TX_r zenon_TT_q) Y)\/(((stock_of_knowledge zenon_TX_r zenon_TT_q) = Y)\/(greater (stock_of_knowledge zenon_TX_r zenon_TT_q) Y)))) -> (~(greater (stock_of_knowledge zenon_TX_r zenon_TT0_p) (stock_of_knowledge zenon_TX_r zenon_TT_q))) -> (~((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))) -> (~(greater (stock_of_knowledge zenon_TX_r zenon_TT_q) (stock_of_knowledge zenon_TX_r zenon_TT0_p))) -> False). % 1.34/1.63 do 3 intro. intros zenon_Hb zenon_Hc zenon_Hd zenon_He. % 1.34/1.63 generalize (zenon_Hb (stock_of_knowledge zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H12. % 1.34/1.63 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 1.34/1.63 generalize (definition_smaller (stock_of_knowledge zenon_TX_r zenon_TT_q)). zenon_intro zenon_H15. % 1.34/1.63 generalize (zenon_H15 (stock_of_knowledge zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H16. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H18; zenon_intro zenon_Hc | zenon_intro zenon_H14; zenon_intro zenon_H17 ]. % 1.34/1.63 exact (zenon_H18 zenon_H14). % 1.34/1.63 exact (zenon_Hc zenon_H17). % 1.34/1.63 apply (zenon_or_s _ _ zenon_H13); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 1.34/1.63 exact (zenon_Hd zenon_H1a). % 1.34/1.63 exact (zenon_He zenon_H19). % 1.34/1.63 (* end of lemma zenon_L1_ *) % 1.34/1.63 assert (zenon_L2_ : forall (zenon_TT0_p : zenon_U) (zenon_TT_q : zenon_U) (zenon_TX_r : zenon_U), (smaller (capability zenon_TX_r zenon_TT_q) (capability zenon_TX_r zenon_TT0_p)) -> (~(greater (capability zenon_TX_r zenon_TT0_p) (capability zenon_TX_r zenon_TT_q))) -> False). % 1.34/1.63 do 3 intro. intros zenon_H1b zenon_H1c. % 1.34/1.63 generalize (definition_smaller (capability zenon_TX_r zenon_TT_q)). zenon_intro zenon_H1d. % 1.34/1.63 generalize (zenon_H1d (capability zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H1e. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H20; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1f ]. % 1.34/1.63 exact (zenon_H20 zenon_H1b). % 1.34/1.63 exact (zenon_H1c zenon_H1f). % 1.34/1.63 (* end of lemma zenon_L2_ *) % 1.34/1.63 assert (zenon_L3_ : forall (zenon_TT0_p : zenon_U) (zenon_TT_q : zenon_U) (zenon_TX_r : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_r)/\(greater (age zenon_TX_r T) (age zenon_TX_r T0)))->(greater (internal_friction zenon_TX_r T) (internal_friction zenon_TX_r T0))))) -> (organization zenon_TX_r) -> (greater (age zenon_TX_r zenon_TT_q) (age zenon_TX_r zenon_TT0_p)) -> (forall T : zenon_U, ((organization zenon_TX_r)->((((greater (stock_of_knowledge zenon_TX_r T) (stock_of_knowledge zenon_TX_r zenon_TT0_p))/\(smaller_or_equal (internal_friction zenon_TX_r T) (internal_friction zenon_TX_r zenon_TT0_p)))->(greater (capability zenon_TX_r T) (capability zenon_TX_r zenon_TT0_p)))/\((((smaller_or_equal (stock_of_knowledge zenon_TX_r T) (stock_of_knowledge zenon_TX_r zenon_TT0_p))/\(greater (internal_friction zenon_TX_r T) (internal_friction zenon_TX_r zenon_TT0_p)))->(smaller (capability zenon_TX_r T) (capability zenon_TX_r zenon_TT0_p)))/\((((stock_of_knowledge zenon_TX_r T) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))/\((internal_friction zenon_TX_r T) = (internal_friction zenon_TX_r zenon_TT0_p)))->((capability zenon_TX_r T) = (capability zenon_TX_r zenon_TT0_p))))))) -> (~(greater (stock_of_knowledge zenon_TX_r zenon_TT0_p) (stock_of_knowledge zenon_TX_r zenon_TT_q))) -> (~(greater (stock_of_knowledge zenon_TX_r zenon_TT_q) (stock_of_knowledge zenon_TX_r zenon_TT0_p))) -> (~(greater (capability zenon_TX_r zenon_TT0_p) (capability zenon_TX_r zenon_TT_q))) -> False). % 1.34/1.63 do 3 intro. intros zenon_H21 zenon_H22 zenon_H23 zenon_H24 zenon_Hc zenon_He zenon_H1c. % 1.34/1.63 generalize (zenon_H21 zenon_TT0_p). zenon_intro zenon_H25. % 1.34/1.63 generalize (meaning_postulate_greater_comparable (stock_of_knowledge zenon_TX_r zenon_TT_q)). zenon_intro zenon_Hb. % 1.34/1.63 generalize (zenon_H25 zenon_TT_q). zenon_intro zenon_H26. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 1.34/1.63 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 exact (zenon_H29 zenon_H23). % 1.34/1.63 generalize (zenon_H24 zenon_TT_q). zenon_intro zenon_H2b. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2a | zenon_intro zenon_H2c ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 1.34/1.63 apply (zenon_and_s _ _ zenon_H2d). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H31 | zenon_intro zenon_H1b ]. % 1.34/1.63 apply (zenon_notand_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ]. % 1.34/1.63 generalize (definition_smaller_or_equal (stock_of_knowledge zenon_TX_r zenon_TT_q)). zenon_intro zenon_H34. % 1.34/1.63 generalize (zenon_H34 (stock_of_knowledge zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H35. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H35); [ zenon_intro zenon_H33; zenon_intro zenon_H38 | zenon_intro zenon_H37; zenon_intro zenon_H36 ]. % 1.34/1.63 apply (zenon_notor_s _ _ zenon_H38). zenon_intro zenon_H18. zenon_intro zenon_Hd. % 1.34/1.63 apply (zenon_L1_ zenon_TT0_p zenon_TT_q zenon_TX_r); trivial. % 1.34/1.63 exact (zenon_H33 zenon_H37). % 1.34/1.63 exact (zenon_H32 zenon_H27). % 1.34/1.63 apply (zenon_L2_ zenon_TT0_p zenon_TT_q zenon_TX_r); trivial. % 1.34/1.63 (* end of lemma zenon_L3_ *) % 1.34/1.63 assert (zenon_L4_ : forall (zenon_TT0_p : zenon_U) (zenon_TX_r : zenon_U), (forall T : zenon_U, ((organization zenon_TX_r)->((stock_of_knowledge zenon_TX_r T) = (stock_of_knowledge zenon_TX_r zenon_E)))) -> (organization zenon_TX_r) -> (~((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_E))) -> False). % 1.34/1.63 do 2 intro. intros zenon_H39 zenon_H22 zenon_H3a. % 1.34/1.63 generalize (zenon_H39 zenon_TT0_p). zenon_intro zenon_H3b. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H2a | zenon_intro zenon_H3c ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 exact (zenon_H3a zenon_H3c). % 1.34/1.63 (* end of lemma zenon_L4_ *) % 1.34/1.63 assert (zenon_L5_ : forall (zenon_TT0_p : zenon_U) (zenon_TX_r : zenon_U), (~(smaller_or_equal (internal_friction zenon_TX_r zenon_TT0_p) (internal_friction zenon_TX_r zenon_TT0_p))) -> False). % 1.34/1.63 do 2 intro. intros zenon_H3d. % 1.34/1.63 generalize (definition_smaller_or_equal (internal_friction zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H3e. % 1.34/1.63 generalize (zenon_H3e (internal_friction zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H3f. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H3d; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 1.34/1.63 apply (zenon_notor_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 1.34/1.63 apply zenon_H43. apply refl_equal. % 1.34/1.63 exact (zenon_H3d zenon_H41). % 1.34/1.63 (* end of lemma zenon_L5_ *) % 1.34/1.63 assert (zenon_L6_ : forall (zenon_TT0_p : zenon_U) (zenon_TX_r : zenon_U), (forall Y : zenon_U, (~((greater (capability zenon_TX_r zenon_TT0_p) Y)/\(greater Y (capability zenon_TX_r zenon_TT0_p))))) -> (greater (capability zenon_TX_r zenon_TT0_p) (capability zenon_TX_r zenon_TT0_p)) -> False). % 1.34/1.63 do 2 intro. intros zenon_H45 zenon_H46. % 1.34/1.63 generalize (zenon_H45 (capability zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H47. % 1.34/1.63 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H48 ]. % 1.34/1.63 exact (zenon_H48 zenon_H46). % 1.34/1.63 exact (zenon_H48 zenon_H46). % 1.34/1.63 (* end of lemma zenon_L6_ *) % 1.34/1.63 assert (zenon_L7_ : forall (zenon_TT_q : zenon_U) (zenon_TT0_p : 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_p)))->(greater (internal_friction zenon_TX_r T) (internal_friction zenon_TX_r zenon_TT0_p)))) -> (organization zenon_TX_r) -> (greater (age zenon_TX_r zenon_TT_q) (age zenon_TX_r zenon_TT0_p)) -> (~(greater (internal_friction zenon_TX_r zenon_TT_q) (internal_friction zenon_TX_r zenon_TT0_p))) -> False). % 1.34/1.63 do 3 intro. intros zenon_H25 zenon_H22 zenon_H23 zenon_H32. % 1.34/1.63 generalize (zenon_H25 zenon_TT_q). zenon_intro zenon_H26. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 1.34/1.63 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 exact (zenon_H29 zenon_H23). % 1.34/1.63 exact (zenon_H32 zenon_H27). % 1.34/1.63 (* end of lemma zenon_L7_ *) % 1.34/1.63 assert (zenon_L8_ : forall (zenon_TT0_p : zenon_U) (zenon_TT_q : zenon_U) (zenon_TX_r : zenon_U), (forall T0 : zenon_U, (forall T : zenon_U, (((organization zenon_TX_r)/\(greater (age zenon_TX_r T) (age zenon_TX_r T0)))->(greater (internal_friction zenon_TX_r T) (internal_friction zenon_TX_r T0))))) -> (~(greater (internal_friction zenon_TX_r zenon_TT_q) (internal_friction zenon_TX_r zenon_TT0_p))) -> (greater (age zenon_TX_r zenon_TT_q) (age zenon_TX_r zenon_TT0_p)) -> (organization zenon_TX_r) -> False). % 1.34/1.63 do 3 intro. intros zenon_H21 zenon_H32 zenon_H23 zenon_H22. % 1.34/1.63 generalize (zenon_H21 zenon_TT0_p). zenon_intro zenon_H25. % 1.34/1.63 apply (zenon_L7_ zenon_TT_q zenon_TT0_p zenon_TX_r); trivial. % 1.34/1.63 (* end of lemma zenon_L8_ *) % 1.34/1.63 assert (zenon_L9_ : forall (zenon_TT0_p : zenon_U) (zenon_TT_q : zenon_U) (zenon_TX_r : zenon_U), (organization zenon_TX_r) -> (greater (age zenon_TX_r zenon_TT_q) (age zenon_TX_r zenon_TT0_p)) -> (~(greater (internal_friction zenon_TX_r zenon_TT_q) (internal_friction zenon_TX_r zenon_TT0_p))) -> False). % 1.34/1.63 do 3 intro. intros zenon_H22 zenon_H23 zenon_H32. % 1.34/1.63 generalize (assumption_12 zenon_TX_r). zenon_intro zenon_H21. % 1.34/1.63 apply (zenon_L8_ zenon_TT0_p zenon_TT_q zenon_TX_r); trivial. % 1.34/1.63 (* end of lemma zenon_L9_ *) % 1.34/1.63 assert (zenon_L10_ : forall (zenon_TT0_p : zenon_U) (zenon_TT_q : zenon_U) (zenon_TX_r : zenon_U), (greater (age zenon_TX_r zenon_TT_q) (age zenon_TX_r zenon_TT0_p)) -> (organization zenon_TX_r) -> (~(smaller_or_equal (internal_friction zenon_TX_r zenon_TT0_p) (internal_friction zenon_TX_r zenon_TT_q))) -> False). % 1.34/1.63 do 3 intro. intros zenon_H23 zenon_H22 zenon_H49. % 1.34/1.63 generalize (definition_smaller_or_equal (internal_friction zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H3e. % 1.34/1.63 generalize (zenon_H3e (internal_friction zenon_TX_r zenon_TT_q)). zenon_intro zenon_H4a. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H49; zenon_intro zenon_H4d | zenon_intro zenon_H4c; zenon_intro zenon_H4b ]. % 1.34/1.63 apply (zenon_notor_s _ _ zenon_H4d). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 1.34/1.63 generalize (definition_smaller (internal_friction zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H50. % 1.34/1.63 generalize (zenon_H50 (internal_friction zenon_TX_r zenon_TT_q)). zenon_intro zenon_H51. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H4f; zenon_intro zenon_H32 | zenon_intro zenon_H52; zenon_intro zenon_H27 ]. % 1.34/1.63 apply (zenon_L9_ zenon_TT0_p zenon_TT_q zenon_TX_r); trivial. % 1.34/1.63 exact (zenon_H4f zenon_H52). % 1.34/1.63 exact (zenon_H49 zenon_H4c). % 1.34/1.63 (* end of lemma zenon_L10_ *) % 1.34/1.63 apply NNPP. intro zenon_G. % 1.34/1.63 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)))->(smaller (capability X T) (capability X T0)))))) zenon_G); [ zenon_intro zenon_H53; idtac ]. % 1.34/1.63 elim zenon_H53. zenon_intro zenon_TX_r. zenon_intro zenon_H54. % 1.34/1.63 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)))->(smaller (capability zenon_TX_r T) (capability zenon_TX_r T0))))) zenon_H54); [ zenon_intro zenon_H55; idtac ]. % 1.34/1.63 elim zenon_H55. zenon_intro zenon_TT0_p. zenon_intro zenon_H56. % 1.34/1.63 apply (zenon_notallex_s (fun T : zenon_U => (((organization zenon_TX_r)/\(greater (age zenon_TX_r T) (age zenon_TX_r zenon_TT0_p)))->(smaller (capability zenon_TX_r T) (capability zenon_TX_r zenon_TT0_p)))) zenon_H56); [ zenon_intro zenon_H57; idtac ]. % 1.34/1.63 elim zenon_H57. zenon_intro zenon_TT_q. zenon_intro zenon_H58. % 1.34/1.63 apply (zenon_notimply_s _ _ zenon_H58). zenon_intro zenon_H59. zenon_intro zenon_H20. % 1.34/1.63 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H22. zenon_intro zenon_H23. % 1.34/1.63 generalize (definition_smaller (capability zenon_TX_r zenon_TT_q)). zenon_intro zenon_H1d. % 1.34/1.63 generalize (zenon_H1d (capability zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H1e. % 1.34/1.63 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H20; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1f ]. % 1.34/1.63 generalize (assumption_5 zenon_TX_r). zenon_intro zenon_H5a. % 1.34/1.63 generalize (zenon_H5a zenon_TT_q). zenon_intro zenon_H5b. % 1.34/1.63 generalize (zenon_H5b zenon_TT0_p). zenon_intro zenon_H5c. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H2a | zenon_intro zenon_H5d ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H60 | zenon_intro zenon_H1f ]. % 1.34/1.63 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_Hc | zenon_intro zenon_H49 ]. % 1.34/1.63 generalize (assumption_12 zenon_TX_r). zenon_intro zenon_H21. % 1.34/1.63 generalize (assumption_10 zenon_TX_r). zenon_intro zenon_H0. % 1.34/1.63 generalize (zenon_H0 zenon_E). zenon_intro zenon_H39. % 1.34/1.63 generalize (zenon_H39 zenon_TT_q). zenon_intro zenon_H61. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H2a | zenon_intro zenon_H62 ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 generalize (meaning_postulate_greater_strict (capability zenon_TX_r zenon_TT0_p)). zenon_intro zenon_H45. % 1.34/1.63 generalize (zenon_H5a zenon_TT0_p). zenon_intro zenon_H24. % 1.34/1.63 generalize (zenon_H24 zenon_TT0_p). zenon_intro zenon_H63. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H2a | zenon_intro zenon_H64 ]. % 1.34/1.63 exact (zenon_H2a zenon_H22). % 1.34/1.63 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H65. % 1.34/1.63 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H46 ]. % 1.34/1.63 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H68 | zenon_intro zenon_H3d ]. % 1.34/1.63 elim (classic ((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_TT_q))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 1.34/1.63 elim (classic (greater (stock_of_knowledge zenon_TX_r zenon_TT_q) (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [ zenon_intro zenon_H19 | zenon_intro zenon_He ]. % 1.34/1.63 elim (classic (greater (stock_of_knowledge zenon_TX_r zenon_E) (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 1.34/1.63 cut ((greater (stock_of_knowledge zenon_TX_r zenon_E) (stock_of_knowledge zenon_TX_r zenon_TT0_p)) = (greater (stock_of_knowledge zenon_TX_r zenon_TT0_p) (stock_of_knowledge zenon_TX_r zenon_TT0_p))). % 1.34/1.63 intro zenon_D_pnotp. % 1.34/1.63 apply zenon_H68. % 1.34/1.63 rewrite <- zenon_D_pnotp. % 1.34/1.63 exact zenon_H6b. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 1.34/1.63 congruence. % 1.34/1.63 elim (classic ((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [ zenon_intro zenon_H6f | zenon_intro zenon_H6d ]. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_TT0_p)) = ((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))). % 1.34/1.63 intro zenon_D_pnotp. % 1.34/1.63 apply zenon_H6e. % 1.34/1.63 rewrite <- zenon_D_pnotp. % 1.34/1.63 exact zenon_H6f. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 1.34/1.63 congruence. % 1.34/1.63 apply (zenon_L4_ zenon_TT0_p zenon_TX_r); trivial. % 1.34/1.63 apply zenon_H6d. apply refl_equal. % 1.34/1.63 apply zenon_H6d. apply refl_equal. % 1.34/1.63 apply zenon_H6d. apply refl_equal. % 1.34/1.63 cut ((greater (stock_of_knowledge zenon_TX_r zenon_TT_q) (stock_of_knowledge zenon_TX_r zenon_TT0_p)) = (greater (stock_of_knowledge zenon_TX_r zenon_E) (stock_of_knowledge zenon_TX_r zenon_TT0_p))). % 1.34/1.63 intro zenon_D_pnotp. % 1.34/1.63 apply zenon_H6c. % 1.34/1.63 rewrite <- zenon_D_pnotp. % 1.34/1.63 exact zenon_H19. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_TT0_p) = (stock_of_knowledge zenon_TX_r zenon_TT0_p))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 1.34/1.63 cut (((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 1.34/1.63 congruence. % 1.34/1.63 elim (classic ((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_E))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 1.34/1.64 cut (((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_E)) = ((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_E))). % 1.34/1.64 intro zenon_D_pnotp. % 1.34/1.64 apply zenon_H70. % 1.34/1.64 rewrite <- zenon_D_pnotp. % 1.34/1.64 exact zenon_H71. % 1.34/1.64 cut (((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 1.34/1.64 cut (((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_TT_q))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 1.34/1.64 congruence. % 1.34/1.64 exact (zenon_H6a zenon_H69). % 1.34/1.64 apply zenon_H72. apply refl_equal. % 1.34/1.64 apply zenon_H72. apply refl_equal. % 1.34/1.64 apply zenon_H6d. apply refl_equal. % 1.34/1.64 apply (zenon_L3_ zenon_TT0_p zenon_TT_q zenon_TX_r); trivial. % 1.34/1.64 elim (classic ((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_TT_q))); [ zenon_intro zenon_H73 | zenon_intro zenon_H74 ]. % 1.34/1.64 cut (((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_TT_q)) = ((stock_of_knowledge zenon_TX_r zenon_E) = (stock_of_knowledge zenon_TX_r zenon_TT_q))). % 1.34/1.64 intro zenon_D_pnotp. % 1.34/1.64 apply zenon_H6a. % 1.34/1.64 rewrite <- zenon_D_pnotp. % 1.34/1.64 exact zenon_H73. % 1.34/1.64 cut (((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_TT_q))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 1.34/1.64 cut (((stock_of_knowledge zenon_TX_r zenon_TT_q) = (stock_of_knowledge zenon_TX_r zenon_E))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 1.34/1.64 congruence. % 1.34/1.64 exact (zenon_H70 zenon_H62). % 1.34/1.64 apply zenon_H74. apply refl_equal. % 1.34/1.64 apply zenon_H74. apply refl_equal. % 1.34/1.64 apply (zenon_L5_ zenon_TT0_p zenon_TX_r); trivial. % 1.34/1.64 apply (zenon_L6_ zenon_TT0_p zenon_TX_r); trivial. % 1.34/1.64 apply (zenon_L10_ zenon_TT0_p zenon_TT_q zenon_TX_r); trivial. % 1.34/1.64 exact (zenon_H1c zenon_H1f). % 1.34/1.64 exact (zenon_H20 zenon_H1b). % 1.34/1.64 Qed. % 1.34/1.64 % SZS output end Proof % 1.34/1.64 (* END-PROOF *) % 1.34/1.64 nodes searched: 46851 % 1.34/1.64 max branch formulas: 1083 % 1.34/1.64 proof nodes created: 1020 % 1.34/1.64 formulas created: 21302 % 1.34/1.64 %------------------------------------------------------------------------------