%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET805+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 06:38:41 EDT 2022 % Result : Theorem 0.91s 1.10s % Output : Proof 0.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET805+4 : TPTP v8.1.0. Released v3.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n029.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 23:51:31 EDT 2022 % 0.12/0.33 % CPUTime : % 0.91/1.10 (* PROOF-FOUND *) % 0.91/1.10 % SZS status Theorem % 0.91/1.10 (* BEGIN-PROOF *) % 0.91/1.10 % SZS output start Proof % 0.91/1.10 Theorem thIV17 : (forall R : zenon_U, (forall E : zenon_U, ((order R E)->(forall X : zenon_U, ((subset X E)->(order R X)))))). % 0.91/1.10 Proof. % 0.91/1.10 assert (zenon_L1_ : forall (zenon_TY_z : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U), (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TY_z zenon_TX_bb) -> (~(member zenon_TY_z zenon_TE_ba)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H16 zenon_H17 zenon_H18. % 0.91/1.10 generalize (zenon_H16 zenon_TY_z). zenon_intro zenon_H1c. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.91/1.10 exact (zenon_H1e zenon_H17). % 0.91/1.10 exact (zenon_H18 zenon_H1d). % 0.91/1.10 (* end of lemma zenon_L1_ *) % 0.91/1.10 assert (zenon_L2_ : forall (zenon_TX_bb : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TY_z : zenon_U), (~((member zenon_TY_z zenon_TE_ba)/\(member zenon_TY_z zenon_TE_ba))) -> (member zenon_TY_z zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> False). % 0.91/1.10 do 3 intro. intros zenon_H1f zenon_H17 zenon_H16. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H18 | zenon_intro zenon_H18 ]. % 0.91/1.10 apply (zenon_L1_ zenon_TY_z zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 apply (zenon_L1_ zenon_TY_z zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 (* end of lemma zenon_L2_ *) % 0.91/1.10 assert (zenon_L3_ : forall (zenon_TY_z : zenon_U) (zenon_TX_bl : zenon_U) (zenon_TR_bm : zenon_U) (zenon_TE_ba : zenon_U), (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TE_ba)/\(member Y zenon_TE_ba))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y X))->(X = Y))))) -> (~(zenon_TX_bl = zenon_TY_z)) -> (apply zenon_TR_bm zenon_TX_bl zenon_TY_z) -> (apply zenon_TR_bm zenon_TY_z zenon_TX_bl) -> (member zenon_TX_bl zenon_TE_ba) -> (member zenon_TY_z zenon_TE_ba) -> False). % 0.91/1.10 do 4 intro. intros zenon_H20 zenon_H21 zenon_H22 zenon_H23 zenon_H24 zenon_H1d. % 0.91/1.10 generalize (zenon_H20 zenon_TY_z). zenon_intro zenon_H27. % 0.91/1.10 generalize (zenon_H27 zenon_TX_bl). zenon_intro zenon_H28. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H18 | zenon_intro zenon_H2b ]. % 0.91/1.10 exact (zenon_H18 zenon_H1d). % 0.91/1.10 exact (zenon_H2b zenon_H24). % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.91/1.10 exact (zenon_H2f zenon_H23). % 0.91/1.10 exact (zenon_H2e zenon_H22). % 0.91/1.10 apply zenon_H21. apply sym_equal. exact zenon_H2c. % 0.91/1.10 (* end of lemma zenon_L3_ *) % 0.91/1.10 assert (zenon_L4_ : forall (zenon_TX_bb : zenon_U) (zenon_TY_z : zenon_U) (zenon_TR_bm : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bl : zenon_U), (~(~(member zenon_TX_bl zenon_TE_ba))) -> (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TE_ba)/\(member Y zenon_TE_ba))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y X))->(X = Y))))) -> (~(zenon_TX_bl = zenon_TY_z)) -> (apply zenon_TR_bm zenon_TX_bl zenon_TY_z) -> (apply zenon_TR_bm zenon_TY_z zenon_TX_bl) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TY_z zenon_TX_bb) -> False). % 0.91/1.10 do 5 intro. intros zenon_H30 zenon_H20 zenon_H21 zenon_H22 zenon_H23 zenon_H16 zenon_H17. % 0.91/1.10 apply zenon_H30. zenon_intro zenon_H24. % 0.91/1.10 generalize (intersection zenon_TY_z). zenon_intro zenon_H31. % 0.91/1.10 generalize (zenon_H31 zenon_TE_ba). zenon_intro zenon_H32. % 0.91/1.10 generalize (zenon_H32 zenon_TE_ba). zenon_intro zenon_H33. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H36; zenon_intro zenon_H1f | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.91/1.10 apply (zenon_L2_ zenon_TX_bb zenon_TE_ba zenon_TY_z); trivial. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H1d. zenon_intro zenon_H1d. % 0.91/1.10 apply (zenon_L3_ zenon_TY_z zenon_TX_bl zenon_TR_bm zenon_TE_ba); trivial. % 0.91/1.10 (* end of lemma zenon_L4_ *) % 0.91/1.10 assert (zenon_L5_ : forall (zenon_TX_bl : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U), (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TX_bl zenon_TX_bb) -> (~(member zenon_TX_bl zenon_TE_ba)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H16 zenon_H37 zenon_H2b. % 0.91/1.10 generalize (zenon_H16 zenon_TX_bl). zenon_intro zenon_H38. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H39 | zenon_intro zenon_H24 ]. % 0.91/1.10 exact (zenon_H39 zenon_H37). % 0.91/1.10 exact (zenon_H2b zenon_H24). % 0.91/1.10 (* end of lemma zenon_L5_ *) % 0.91/1.10 assert (zenon_L6_ : forall (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U) (zenon_TX_bl : zenon_U), ((member zenon_TX_bl zenon_TX_bb)/\(~(member zenon_TX_bl zenon_TE_ba))) -> (member zenon_TX_bl zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> False). % 0.91/1.10 do 3 intro. intros zenon_H3a zenon_H37 zenon_H16. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H37. zenon_intro zenon_H2b. % 0.91/1.10 apply (zenon_L5_ zenon_TX_bl zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 (* end of lemma zenon_L6_ *) % 0.91/1.10 assert (zenon_L7_ : forall (zenon_TY_cj : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U), (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TY_cj zenon_TX_bb) -> (~(member zenon_TY_cj zenon_TE_ba)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H16 zenon_H3b zenon_H3c. % 0.91/1.10 generalize (zenon_H16 zenon_TY_cj). zenon_intro zenon_H3e. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.91/1.10 exact (zenon_H40 zenon_H3b). % 0.91/1.10 exact (zenon_H3c zenon_H3f). % 0.91/1.10 (* end of lemma zenon_L7_ *) % 0.91/1.10 assert (zenon_L8_ : forall (zenon_TZ_cp : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U), (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TZ_cp zenon_TX_bb) -> (~(member zenon_TZ_cp zenon_TE_ba)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H16 zenon_H41 zenon_H42. % 0.91/1.10 generalize (zenon_H16 zenon_TZ_cp). zenon_intro zenon_H44. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.91/1.10 exact (zenon_H46 zenon_H41). % 0.91/1.10 exact (zenon_H42 zenon_H45). % 0.91/1.10 (* end of lemma zenon_L8_ *) % 0.91/1.10 assert (zenon_L9_ : forall (zenon_TZ_cp : zenon_U), (member zenon_TZ_cp (empty_set)) -> False). % 0.91/1.10 do 1 intro. intros zenon_H47. % 0.91/1.10 generalize (empty_set zenon_TZ_cp). zenon_intro zenon_H48. % 0.91/1.10 exact (zenon_H48 zenon_H47). % 0.91/1.10 (* end of lemma zenon_L9_ *) % 0.91/1.10 assert (zenon_L10_ : forall (zenon_TZ_cp : zenon_U), (~(~(member zenon_TZ_cp (empty_set)))) -> False). % 0.91/1.10 do 1 intro. intros zenon_H49. % 0.91/1.10 apply zenon_H49. zenon_intro zenon_H47. % 0.91/1.10 apply (zenon_L9_ zenon_TZ_cp); trivial. % 0.91/1.10 (* end of lemma zenon_L10_ *) % 0.91/1.10 assert (zenon_L11_ : forall (zenon_TX_bb : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TZ_cp : zenon_U), (~((member zenon_TZ_cp zenon_TE_ba)/\(~(member zenon_TZ_cp (empty_set))))) -> (member zenon_TZ_cp zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> False). % 0.91/1.10 do 3 intro. intros zenon_H4a zenon_H41 zenon_H16. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H42 | zenon_intro zenon_H49 ]. % 0.91/1.10 apply (zenon_L8_ zenon_TZ_cp zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 apply (zenon_L10_ zenon_TZ_cp); trivial. % 0.91/1.10 (* end of lemma zenon_L11_ *) % 0.91/1.10 assert (zenon_L12_ : forall (zenon_TX_bb : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TZ_cp : zenon_U), (~((member zenon_TZ_cp zenon_TE_ba)/\(~(member zenon_TZ_cp (empty_set))))) -> (~(member zenon_TZ_cp (empty_set))) -> (member zenon_TZ_cp zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> False). % 0.91/1.10 do 3 intro. intros zenon_H4a zenon_H48 zenon_H41 zenon_H16. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H42 | zenon_intro zenon_H49 ]. % 0.91/1.10 apply (zenon_L8_ zenon_TZ_cp zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 exact (zenon_H49 zenon_H48). % 0.91/1.10 (* end of lemma zenon_L12_ *) % 0.91/1.10 assert (zenon_L13_ : forall (zenon_TY_cj : zenon_U) (zenon_TZ_cp : zenon_U) (zenon_TR_bm : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_dc : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, (((member zenon_TX_dc zenon_TE_ba)/\((member Y zenon_TE_ba)/\(member Z zenon_TE_ba)))->(((apply zenon_TR_bm zenon_TX_dc Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm zenon_TX_dc Z))))) -> (~(apply zenon_TR_bm zenon_TX_dc zenon_TZ_cp)) -> (apply zenon_TR_bm zenon_TY_cj zenon_TZ_cp) -> (apply zenon_TR_bm zenon_TX_dc zenon_TY_cj) -> (member zenon_TZ_cp zenon_TE_ba) -> (member zenon_TY_cj zenon_TE_ba) -> (member zenon_TX_dc zenon_TE_ba) -> False). % 0.91/1.10 do 5 intro. intros zenon_H4b zenon_H4c zenon_H4d zenon_H4e zenon_H45 zenon_H3f zenon_H4f. % 0.91/1.10 generalize (zenon_H4b zenon_TY_cj). zenon_intro zenon_H51. % 0.91/1.10 generalize (zenon_H51 zenon_TZ_cp). zenon_intro zenon_H52. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.91/1.10 exact (zenon_H56 zenon_H4f). % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H3c | zenon_intro zenon_H42 ]. % 0.91/1.10 exact (zenon_H3c zenon_H3f). % 0.91/1.10 exact (zenon_H42 zenon_H45). % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 0.91/1.10 exact (zenon_H5a zenon_H4e). % 0.91/1.10 exact (zenon_H59 zenon_H4d). % 0.91/1.10 exact (zenon_H4c zenon_H57). % 0.91/1.10 (* end of lemma zenon_L13_ *) % 0.91/1.10 assert (zenon_L14_ : forall (zenon_TR_bm : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_dc : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U) (zenon_TZ_cp : zenon_U), (forall E : zenon_U, ((member zenon_TZ_cp (difference E (empty_set)))<->((member zenon_TZ_cp E)/\(~(member zenon_TZ_cp (empty_set)))))) -> (~(member zenon_TZ_cp (empty_set))) -> (member zenon_TZ_cp zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TX_dc zenon_TE_ba) -> (member zenon_TY_cj zenon_TE_ba) -> (apply zenon_TR_bm zenon_TX_dc zenon_TY_cj) -> (apply zenon_TR_bm zenon_TY_cj zenon_TZ_cp) -> (~(apply zenon_TR_bm zenon_TX_dc zenon_TZ_cp)) -> (forall Y : zenon_U, (forall Z : zenon_U, (((member zenon_TX_dc zenon_TE_ba)/\((member Y zenon_TE_ba)/\(member Z zenon_TE_ba)))->(((apply zenon_TR_bm zenon_TX_dc Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm zenon_TX_dc Z))))) -> False). % 0.91/1.10 do 6 intro. intros zenon_H5b zenon_H48 zenon_H41 zenon_H16 zenon_H4f zenon_H3f zenon_H4e zenon_H4d zenon_H4c zenon_H4b. % 0.91/1.10 generalize (zenon_H5b zenon_TE_ba). zenon_intro zenon_H5c. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H5c); [ zenon_intro zenon_H5f; zenon_intro zenon_H4a | zenon_intro zenon_H5e; zenon_intro zenon_H5d ]. % 0.91/1.10 apply (zenon_L12_ zenon_TX_bb zenon_TE_ba zenon_TZ_cp); trivial. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H45. zenon_intro zenon_H48. % 0.91/1.10 apply (zenon_L13_ zenon_TY_cj zenon_TZ_cp zenon_TR_bm zenon_TE_ba zenon_TX_dc); trivial. % 0.91/1.10 (* end of lemma zenon_L14_ *) % 0.91/1.10 assert (zenon_L15_ : forall (zenon_TR_bm : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bb : zenon_U) (zenon_TZ_cp : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_dc : zenon_U), (~(~(member zenon_TX_dc zenon_TE_ba))) -> (forall E : zenon_U, ((member zenon_TZ_cp (difference E (empty_set)))<->((member zenon_TZ_cp E)/\(~(member zenon_TZ_cp (empty_set)))))) -> (~(member zenon_TZ_cp (empty_set))) -> (member zenon_TZ_cp zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TY_cj zenon_TE_ba) -> (apply zenon_TR_bm zenon_TX_dc zenon_TY_cj) -> (apply zenon_TR_bm zenon_TY_cj zenon_TZ_cp) -> (~(apply zenon_TR_bm zenon_TX_dc zenon_TZ_cp)) -> (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((member X zenon_TE_ba)/\((member Y zenon_TE_ba)/\(member Z zenon_TE_ba)))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm X Z)))))) -> False). % 0.91/1.10 do 6 intro. intros zenon_H60 zenon_H5b zenon_H48 zenon_H41 zenon_H16 zenon_H3f zenon_H4e zenon_H4d zenon_H4c zenon_H61. % 0.91/1.10 apply zenon_H60. zenon_intro zenon_H4f. % 0.91/1.10 generalize (zenon_H61 zenon_TX_dc). zenon_intro zenon_H4b. % 0.91/1.10 apply (zenon_L14_ zenon_TR_bm zenon_TY_cj zenon_TX_dc zenon_TE_ba zenon_TX_bb zenon_TZ_cp); trivial. % 0.91/1.10 (* end of lemma zenon_L15_ *) % 0.91/1.10 assert (zenon_L16_ : forall (zenon_TX_dc : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U), (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TX_dc zenon_TX_bb) -> (~(member zenon_TX_dc zenon_TE_ba)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H16 zenon_H62 zenon_H56. % 0.91/1.10 generalize (zenon_H16 zenon_TX_dc). zenon_intro zenon_H63. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H64 | zenon_intro zenon_H4f ]. % 0.91/1.10 exact (zenon_H64 zenon_H62). % 0.91/1.10 exact (zenon_H56 zenon_H4f). % 0.91/1.10 (* end of lemma zenon_L16_ *) % 0.91/1.10 assert (zenon_L17_ : forall (zenon_TE_ba : zenon_U) (zenon_TX_bb : zenon_U) (zenon_TX_dc : zenon_U), ((member zenon_TX_dc zenon_TX_bb)/\(~(member zenon_TX_dc zenon_TE_ba))) -> (member zenon_TX_dc zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> False). % 0.91/1.10 do 3 intro. intros zenon_H65 zenon_H62 zenon_H16. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H62. zenon_intro zenon_H56. % 0.91/1.10 apply (zenon_L16_ zenon_TX_dc zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 (* end of lemma zenon_L17_ *) % 0.91/1.10 assert (zenon_L18_ : forall (zenon_TX_bb : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TZ_cp : zenon_U) (zenon_TR_bm : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TX_dc : zenon_U), (forall E : zenon_U, ((member zenon_TX_dc (difference E zenon_TE_ba))<->((member zenon_TX_dc E)/\(~(member zenon_TX_dc zenon_TE_ba))))) -> (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((member X zenon_TE_ba)/\((member Y zenon_TE_ba)/\(member Z zenon_TE_ba)))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm X Z)))))) -> (~(apply zenon_TR_bm zenon_TX_dc zenon_TZ_cp)) -> (apply zenon_TR_bm zenon_TY_cj zenon_TZ_cp) -> (apply zenon_TR_bm zenon_TX_dc zenon_TY_cj) -> (member zenon_TY_cj zenon_TE_ba) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TZ_cp zenon_TX_bb) -> (~(member zenon_TZ_cp (empty_set))) -> (forall E : zenon_U, ((member zenon_TZ_cp (difference E (empty_set)))<->((member zenon_TZ_cp E)/\(~(member zenon_TZ_cp (empty_set)))))) -> (member zenon_TX_dc zenon_TX_bb) -> False). % 0.91/1.10 do 6 intro. intros zenon_H66 zenon_H61 zenon_H4c zenon_H4d zenon_H4e zenon_H3f zenon_H16 zenon_H41 zenon_H48 zenon_H5b zenon_H62. % 0.91/1.10 generalize (zenon_H66 zenon_TX_bb). zenon_intro zenon_H67. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H6a; zenon_intro zenon_H69 | zenon_intro zenon_H68; zenon_intro zenon_H65 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H64 | zenon_intro zenon_H60 ]. % 0.91/1.10 exact (zenon_H64 zenon_H62). % 0.91/1.10 apply (zenon_L15_ zenon_TR_bm zenon_TY_cj zenon_TX_bb zenon_TZ_cp zenon_TE_ba zenon_TX_dc); trivial. % 0.91/1.10 apply (zenon_L17_ zenon_TE_ba zenon_TX_bb zenon_TX_dc); trivial. % 0.91/1.10 (* end of lemma zenon_L18_ *) % 0.91/1.10 assert (zenon_L19_ : forall (zenon_TR_bm : zenon_U) (zenon_TX_dc : zenon_U) (zenon_TX_bb : zenon_U) (zenon_TZ_cp : zenon_U) (zenon_TE_ba : zenon_U) (zenon_TY_cj : zenon_U), (~(~(member zenon_TY_cj zenon_TE_ba))) -> (member zenon_TZ_cp zenon_TX_bb) -> (forall X : zenon_U, ((member X zenon_TX_bb)->(member X zenon_TE_ba))) -> (member zenon_TX_dc zenon_TX_bb) -> (forall E : zenon_U, ((member zenon_TZ_cp (difference E (empty_set)))<->((member zenon_TZ_cp E)/\(~(member zenon_TZ_cp (empty_set)))))) -> (apply zenon_TR_bm zenon_TX_dc zenon_TY_cj) -> (apply zenon_TR_bm zenon_TY_cj zenon_TZ_cp) -> (~(apply zenon_TR_bm zenon_TX_dc zenon_TZ_cp)) -> (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((member X zenon_TE_ba)/\((member Y zenon_TE_ba)/\(member Z zenon_TE_ba)))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm X Z)))))) -> (forall A : zenon_U, (forall E : zenon_U, ((member zenon_TX_dc (difference E A))<->((member zenon_TX_dc E)/\(~(member zenon_TX_dc A)))))) -> False). % 0.91/1.10 do 6 intro. intros zenon_H6b zenon_H41 zenon_H16 zenon_H62 zenon_H5b zenon_H4e zenon_H4d zenon_H4c zenon_H61 zenon_H6c. % 0.91/1.10 apply zenon_H6b. zenon_intro zenon_H3f. % 0.91/1.10 generalize (zenon_H6c zenon_TE_ba). zenon_intro zenon_H66. % 0.91/1.10 generalize (zenon_H5b zenon_TE_ba). zenon_intro zenon_H5c. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H5c); [ zenon_intro zenon_H5f; zenon_intro zenon_H4a | zenon_intro zenon_H5e; zenon_intro zenon_H5d ]. % 0.91/1.10 apply (zenon_L11_ zenon_TX_bb zenon_TE_ba zenon_TZ_cp); trivial. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H45. zenon_intro zenon_H48. % 0.91/1.10 apply (zenon_L18_ zenon_TX_bb zenon_TY_cj zenon_TZ_cp zenon_TR_bm zenon_TE_ba zenon_TX_dc); trivial. % 0.91/1.10 (* end of lemma zenon_L19_ *) % 0.91/1.10 apply NNPP. intro zenon_G. % 0.91/1.10 apply (zenon_notallex_s (fun R : zenon_U => (forall E : zenon_U, ((order R E)->(forall X : zenon_U, ((subset X E)->(order R X)))))) zenon_G); [ zenon_intro zenon_H6d; idtac ]. % 0.91/1.10 elim zenon_H6d. zenon_intro zenon_TR_bm. zenon_intro zenon_H6e. % 0.91/1.10 apply (zenon_notallex_s (fun E : zenon_U => ((order zenon_TR_bm E)->(forall X : zenon_U, ((subset X E)->(order zenon_TR_bm X))))) zenon_H6e); [ zenon_intro zenon_H6f; idtac ]. % 0.91/1.10 elim zenon_H6f. zenon_intro zenon_TE_ba. zenon_intro zenon_H70. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H70). zenon_intro zenon_H72. zenon_intro zenon_H71. % 0.91/1.10 generalize (order zenon_TR_bm). zenon_intro zenon_H73. % 0.91/1.10 generalize (zenon_H73 zenon_TE_ba). zenon_intro zenon_H74. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H77; zenon_intro zenon_H76 | zenon_intro zenon_H72; zenon_intro zenon_H75 ]. % 0.91/1.10 exact (zenon_H77 zenon_H72). % 0.91/1.10 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H79. zenon_intro zenon_H78. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H20. zenon_intro zenon_H61. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((subset X zenon_TE_ba)->(order zenon_TR_bm X))) zenon_H71); [ zenon_intro zenon_H7a; idtac ]. % 0.91/1.10 elim zenon_H7a. zenon_intro zenon_TX_bb. zenon_intro zenon_H7b. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H7b). zenon_intro zenon_H7d. zenon_intro zenon_H7c. % 0.91/1.10 generalize (subset zenon_TX_bb). zenon_intro zenon_H7e. % 0.91/1.10 generalize (zenon_H7e zenon_TE_ba). zenon_intro zenon_H7f. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H7f); [ zenon_intro zenon_H81; zenon_intro zenon_H80 | zenon_intro zenon_H7d; zenon_intro zenon_H16 ]. % 0.91/1.10 exact (zenon_H81 zenon_H7d). % 0.91/1.10 generalize (order zenon_TR_bm). zenon_intro zenon_H73. % 0.91/1.10 generalize (zenon_H73 zenon_TX_bb). zenon_intro zenon_H82. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H82); [ zenon_intro zenon_H7c; zenon_intro zenon_H85 | zenon_intro zenon_H84; zenon_intro zenon_H83 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ]. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TX_bb)->(apply zenon_TR_bm X X))) zenon_H87); [ zenon_intro zenon_H88; idtac ]. % 0.91/1.10 elim zenon_H88. zenon_intro zenon_TX_fh. zenon_intro zenon_H8a. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 0.91/1.10 generalize (zenon_H79 zenon_TX_fh). zenon_intro zenon_H8d. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H8d); [ zenon_intro zenon_H8f | zenon_intro zenon_H8e ]. % 0.91/1.10 generalize (zenon_H16 zenon_TX_fh). zenon_intro zenon_H90. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 0.91/1.10 exact (zenon_H92 zenon_H8c). % 0.91/1.10 exact (zenon_H8f zenon_H91). % 0.91/1.10 exact (zenon_H8b zenon_H8e). % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H86); [ zenon_intro zenon_H94 | zenon_intro zenon_H93 ]. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((member X zenon_TX_bb)/\(member Y zenon_TX_bb))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y X))->(X = Y))))) zenon_H94); [ zenon_intro zenon_H95; idtac ]. % 0.91/1.10 elim zenon_H95. zenon_intro zenon_TX_bl. zenon_intro zenon_H96. % 0.91/1.10 apply (zenon_notallex_s (fun Y : zenon_U => (((member zenon_TX_bl zenon_TX_bb)/\(member Y zenon_TX_bb))->(((apply zenon_TR_bm zenon_TX_bl Y)/\(apply zenon_TR_bm Y zenon_TX_bl))->(zenon_TX_bl = Y)))) zenon_H96); [ zenon_intro zenon_H97; idtac ]. % 0.91/1.10 elim zenon_H97. zenon_intro zenon_TY_z. zenon_intro zenon_H98. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H98). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H99). zenon_intro zenon_H9b. zenon_intro zenon_H21. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H22. zenon_intro zenon_H23. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H9a). zenon_intro zenon_H37. zenon_intro zenon_H17. % 0.91/1.10 generalize (difference zenon_TX_bl). zenon_intro zenon_H9c. % 0.91/1.10 generalize (zenon_H9c zenon_TE_ba). zenon_intro zenon_H9d. % 0.91/1.10 generalize (zenon_H9d zenon_TX_bb). zenon_intro zenon_H9e. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H9e); [ zenon_intro zenon_Ha1; zenon_intro zenon_Ha0 | zenon_intro zenon_H9f; zenon_intro zenon_H3a ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_Ha0); [ zenon_intro zenon_H39 | zenon_intro zenon_H30 ]. % 0.91/1.10 exact (zenon_H39 zenon_H37). % 0.91/1.10 apply (zenon_L4_ zenon_TX_bb zenon_TY_z zenon_TR_bm zenon_TE_ba zenon_TX_bl); trivial. % 0.91/1.10 apply (zenon_L6_ zenon_TE_ba zenon_TX_bb zenon_TX_bl); trivial. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((member X zenon_TX_bb)/\((member Y zenon_TX_bb)/\(member Z zenon_TX_bb)))->(((apply zenon_TR_bm X Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm X Z)))))) zenon_H93); [ zenon_intro zenon_Ha2; idtac ]. % 0.91/1.10 elim zenon_Ha2. zenon_intro zenon_TX_dc. zenon_intro zenon_Ha3. % 0.91/1.10 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((member zenon_TX_dc zenon_TX_bb)/\((member Y zenon_TX_bb)/\(member Z zenon_TX_bb)))->(((apply zenon_TR_bm zenon_TX_dc Y)/\(apply zenon_TR_bm Y Z))->(apply zenon_TR_bm zenon_TX_dc Z))))) zenon_Ha3); [ zenon_intro zenon_Ha4; idtac ]. % 0.91/1.10 elim zenon_Ha4. zenon_intro zenon_TY_cj. zenon_intro zenon_Ha5. % 0.91/1.10 apply (zenon_notallex_s (fun Z : zenon_U => (((member zenon_TX_dc zenon_TX_bb)/\((member zenon_TY_cj zenon_TX_bb)/\(member Z zenon_TX_bb)))->(((apply zenon_TR_bm zenon_TX_dc zenon_TY_cj)/\(apply zenon_TR_bm zenon_TY_cj Z))->(apply zenon_TR_bm zenon_TX_dc Z)))) zenon_Ha5); [ zenon_intro zenon_Ha6; idtac ]. % 0.91/1.10 elim zenon_Ha6. zenon_intro zenon_TZ_cp. zenon_intro zenon_Ha7. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_Ha7). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_Ha8). zenon_intro zenon_Haa. zenon_intro zenon_H4c. % 0.91/1.10 apply (zenon_and_s _ _ zenon_Haa). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.91/1.10 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_H62. zenon_intro zenon_Hab. % 0.91/1.10 apply (zenon_and_s _ _ zenon_Hab). zenon_intro zenon_H3b. zenon_intro zenon_H41. % 0.91/1.10 generalize (difference zenon_TZ_cp). zenon_intro zenon_Hac. % 0.91/1.10 generalize (difference zenon_TX_dc). zenon_intro zenon_H6c. % 0.91/1.10 generalize (difference zenon_TY_cj). zenon_intro zenon_Had. % 0.91/1.10 generalize (zenon_Hac (empty_set)). zenon_intro zenon_H5b. % 0.91/1.10 generalize (zenon_Had zenon_TE_ba). zenon_intro zenon_Hae. % 0.91/1.10 generalize (zenon_Hae zenon_TE_ba). zenon_intro zenon_Haf. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_Haf); [ zenon_intro zenon_Hb3; zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1; zenon_intro zenon_Hb0 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H3c | zenon_intro zenon_H6b ]. % 0.91/1.10 apply (zenon_L7_ zenon_TY_cj zenon_TE_ba zenon_TX_bb); trivial. % 0.91/1.10 apply (zenon_L19_ zenon_TR_bm zenon_TX_dc zenon_TX_bb zenon_TZ_cp zenon_TE_ba zenon_TY_cj); trivial. % 0.91/1.10 apply (zenon_and_s _ _ zenon_Hb0). zenon_intro zenon_H3f. zenon_intro zenon_H3c. % 0.91/1.10 exact (zenon_H3c zenon_H3f). % 0.91/1.10 exact (zenon_H7c zenon_H84). % 0.91/1.10 Qed. % 0.91/1.10 % SZS output end Proof % 0.91/1.10 (* END-PROOF *) % 0.91/1.10 nodes searched: 33454 % 0.91/1.10 max branch formulas: 1627 % 0.91/1.10 proof nodes created: 1438 % 0.91/1.10 formulas created: 123439 % 0.91/1.10 %------------------------------------------------------------------------------