%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 06:38:43 EDT 2022 % Result : Theorem 2.66s 2.90s % Output : Proof 2.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET810+4 : TPTP v8.1.0. Released v3.2.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n012.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 : Sun Jul 10 07:12:43 EDT 2022 % 0.12/0.33 % CPUTime : % 2.66/2.90 (* PROOF-FOUND *) % 2.66/2.90 % SZS status Theorem % 2.66/2.90 (* BEGIN-PROOF *) % 2.66/2.90 % SZS output start Proof % 2.66/2.90 Theorem thV3 : (forall A : zenon_U, (forall B : zenon_U, (((member A (on))/\(member B (on)))->(~((member A B)/\(member B A)))))). % 2.66/2.90 Proof. % 2.66/2.90 assert (zenon_L1_ : forall (zenon_TA_y : zenon_U) (zenon_TB_z : zenon_U), (~(~(member zenon_TB_z zenon_TB_z))) -> (member zenon_TB_z zenon_TA_y) -> (member zenon_TA_y zenon_TB_z) -> (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TB_z)/\(member Y zenon_TB_z))->(~((apply (member_predicate) X Y)/\(apply (member_predicate) Y X)))))) -> False). % 2.66/2.90 do 2 intro. intros zenon_H14 zenon_H15 zenon_H16 zenon_H17. % 2.66/2.90 apply zenon_H14. zenon_intro zenon_H1a. % 2.66/2.90 generalize (zenon_H17 zenon_TA_y). zenon_intro zenon_H1b. % 2.66/2.90 generalize (rel_member zenon_TB_z). zenon_intro zenon_H1c. % 2.66/2.90 generalize (rel_member zenon_TA_y). zenon_intro zenon_H1d. % 2.66/2.90 generalize (zenon_H1c zenon_TA_y). zenon_intro zenon_H1e. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H15 ]. % 2.66/2.90 exact (zenon_H20 zenon_H15). % 2.66/2.90 generalize (zenon_H1d zenon_TB_z). zenon_intro zenon_H22. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H22); [ zenon_intro zenon_H25; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H16 ]. % 2.66/2.90 exact (zenon_H24 zenon_H16). % 2.66/2.90 generalize (zenon_H1b zenon_TB_z). zenon_intro zenon_H26. % 2.66/2.90 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 2.66/2.90 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H24 | zenon_intro zenon_H29 ]. % 2.66/2.90 exact (zenon_H24 zenon_H16). % 2.66/2.90 exact (zenon_H29 zenon_H1a). % 2.66/2.90 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H25 | zenon_intro zenon_H21 ]. % 2.66/2.90 exact (zenon_H25 zenon_H23). % 2.66/2.90 exact (zenon_H21 zenon_H1f). % 2.66/2.90 (* end of lemma zenon_L1_ *) % 2.66/2.90 assert (zenon_L2_ : forall (zenon_TA_y : zenon_U) (zenon_TB_z : zenon_U), (~((member zenon_TB_z (on))/\(~(member zenon_TB_z zenon_TB_z)))) -> (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TB_z)/\(member Y zenon_TB_z))->(~((apply (member_predicate) X Y)/\(apply (member_predicate) Y X)))))) -> (member zenon_TA_y zenon_TB_z) -> (member zenon_TB_z zenon_TA_y) -> (member zenon_TB_z (on)) -> False). % 2.66/2.90 do 2 intro. intros zenon_H2a zenon_H17 zenon_H16 zenon_H15 zenon_H2b. % 2.66/2.90 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H14 ]. % 2.66/2.90 exact (zenon_H2c zenon_H2b). % 2.66/2.90 apply (zenon_L1_ zenon_TA_y zenon_TB_z); trivial. % 2.66/2.90 (* end of lemma zenon_L2_ *) % 2.66/2.90 assert (zenon_L3_ : forall (zenon_TB_z : zenon_U) (zenon_TA_y : zenon_U), (forall X : zenon_U, ((member X zenon_TA_y)->(member X zenon_TB_z))) -> (member zenon_TB_z zenon_TA_y) -> (~(member zenon_TB_z zenon_TB_z)) -> False). % 2.66/2.90 do 2 intro. intros zenon_H2d zenon_H15 zenon_H29. % 2.66/2.90 generalize (zenon_H2d zenon_TB_z). zenon_intro zenon_H2e. % 2.66/2.90 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1a ]. % 2.66/2.90 exact (zenon_H20 zenon_H15). % 2.66/2.90 exact (zenon_H29 zenon_H1a). % 2.66/2.90 (* end of lemma zenon_L3_ *) % 2.66/2.90 assert (zenon_L4_ : forall (zenon_TB_z : zenon_U) (zenon_TA_y : zenon_U), (subset zenon_TA_y zenon_TB_z) -> (member zenon_TB_z zenon_TA_y) -> (~(member zenon_TB_z zenon_TB_z)) -> False). % 2.66/2.90 do 2 intro. intros zenon_H2f zenon_H15 zenon_H29. % 2.66/2.90 generalize (subset zenon_TA_y). zenon_intro zenon_H30. % 2.66/2.90 generalize (zenon_H30 zenon_TB_z). zenon_intro zenon_H31. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H31); [ zenon_intro zenon_H33; zenon_intro zenon_H32 | zenon_intro zenon_H2f; zenon_intro zenon_H2d ]. % 2.66/2.90 exact (zenon_H33 zenon_H2f). % 2.66/2.90 apply (zenon_L3_ zenon_TB_z zenon_TA_y); trivial. % 2.66/2.90 (* end of lemma zenon_L4_ *) % 2.66/2.90 assert (zenon_L5_ : forall (zenon_TA_y : zenon_U) (zenon_TB_z : zenon_U), (forall X : zenon_U, ((member X zenon_TB_z)->(subset X zenon_TB_z))) -> (member zenon_TA_y zenon_TB_z) -> (~(member zenon_TB_z zenon_TB_z)) -> (member zenon_TB_z zenon_TA_y) -> False). % 2.66/2.90 do 2 intro. intros zenon_H34 zenon_H16 zenon_H29 zenon_H15. % 2.66/2.90 generalize (zenon_H34 zenon_TA_y). zenon_intro zenon_H35. % 2.66/2.90 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H24 | zenon_intro zenon_H2f ]. % 2.66/2.90 exact (zenon_H24 zenon_H16). % 2.66/2.90 apply (zenon_L4_ zenon_TB_z zenon_TA_y); trivial. % 2.66/2.90 (* end of lemma zenon_L5_ *) % 2.66/2.90 apply NNPP. intro zenon_G. % 2.66/2.90 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((member A (on))/\(member B (on)))->(~((member A B)/\(member B A)))))) zenon_G); [ zenon_intro zenon_H36; idtac ]. % 2.66/2.90 elim zenon_H36. zenon_intro zenon_TA_y. zenon_intro zenon_H37. % 2.66/2.90 apply (zenon_notallex_s (fun B : zenon_U => (((member zenon_TA_y (on))/\(member B (on)))->(~((member zenon_TA_y B)/\(member B zenon_TA_y))))) zenon_H37); [ zenon_intro zenon_H38; idtac ]. % 2.66/2.90 elim zenon_H38. zenon_intro zenon_TB_z. zenon_intro zenon_H39. % 2.66/2.90 apply (zenon_notimply_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 2.66/2.90 apply zenon_H3a. zenon_intro zenon_H3c. % 2.66/2.90 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H16. zenon_intro zenon_H15. % 2.66/2.90 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H2b. % 2.66/2.90 generalize (ordinal_number zenon_TB_z). zenon_intro zenon_H3e. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H2c; zenon_intro zenon_H40 | zenon_intro zenon_H2b; zenon_intro zenon_H3f ]. % 2.66/2.90 exact (zenon_H2c zenon_H2b). % 2.66/2.90 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 2.66/2.90 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H34. % 2.66/2.90 generalize (strict_well_order (member_predicate)). zenon_intro zenon_H44. % 2.66/2.90 generalize (zenon_H44 zenon_TB_z). zenon_intro zenon_H45. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H43; zenon_intro zenon_H46 ]. % 2.66/2.90 exact (zenon_H48 zenon_H43). % 2.66/2.90 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 2.66/2.90 generalize (strict_order (member_predicate)). zenon_intro zenon_H4b. % 2.66/2.90 generalize (zenon_H4b zenon_TB_z). zenon_intro zenon_H4c. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H4a; zenon_intro zenon_H4d ]. % 2.66/2.90 exact (zenon_H4f zenon_H4a). % 2.66/2.90 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H17. zenon_intro zenon_H50. % 2.66/2.90 generalize (difference zenon_TB_z). zenon_intro zenon_H51. % 2.66/2.90 generalize (zenon_H51 zenon_TB_z). zenon_intro zenon_H52. % 2.66/2.90 generalize (zenon_H52 (on)). zenon_intro zenon_H53. % 2.66/2.90 apply (zenon_equiv_s _ _ zenon_H53); [ zenon_intro zenon_H56; zenon_intro zenon_H2a | zenon_intro zenon_H55; zenon_intro zenon_H54 ]. % 2.66/2.90 apply (zenon_L2_ zenon_TA_y zenon_TB_z); trivial. % 2.66/2.90 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H2b. zenon_intro zenon_H29. % 2.66/2.90 apply (zenon_L5_ zenon_TA_y zenon_TB_z); trivial. % 2.66/2.90 Qed. % 2.66/2.90 % SZS output end Proof % 2.66/2.90 (* END-PROOF *) % 2.66/2.90 nodes searched: 128172 % 2.66/2.90 max branch formulas: 8317 % 2.66/2.90 proof nodes created: 3642 % 2.66/2.90 formulas created: 527410 % 2.66/2.90 %------------------------------------------------------------------------------