%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET199+4 : TPTP v8.1.0. Released v2.2.0. % 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 06:34:51 EDT 2022 % Result : Theorem 0.71s 0.88s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET199+4 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.12 % 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 01:55:43 EDT 2022 % 0.12/0.33 % CPUTime : % 0.71/0.88 (* PROOF-FOUND *) % 0.71/0.88 % SZS status Theorem % 0.71/0.88 (* BEGIN-PROOF *) % 0.71/0.88 % SZS output start Proof % 0.71/0.88 Theorem thI46 : (forall A : zenon_U, (forall X : zenon_U, (forall Y : zenon_U, (((subset A X)/\(subset A Y))<->(subset A (intersection X Y)))))). % 0.71/0.88 Proof. % 0.71/0.88 assert (zenon_L1_ : forall (zenon_TX_p : zenon_U) (zenon_TY_q : zenon_U) (zenon_TA_r : zenon_U), (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TY_q))) -> (member zenon_TX_p zenon_TA_r) -> (~(member zenon_TX_p zenon_TY_q)) -> False). % 0.71/0.88 do 3 intro. intros zenon_Hc zenon_Hd zenon_He. % 0.71/0.88 generalize (zenon_Hc zenon_TX_p). zenon_intro zenon_H12. % 0.71/0.88 apply (zenon_imply_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 0.71/0.88 exact (zenon_H14 zenon_Hd). % 0.71/0.88 exact (zenon_He zenon_H13). % 0.71/0.88 (* end of lemma zenon_L1_ *) % 0.71/0.88 assert (zenon_L2_ : forall (zenon_TY_q : zenon_U) (zenon_TX_y : zenon_U) (zenon_TX_p : zenon_U), (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_p (intersection A B))<->((member zenon_TX_p A)/\(member zenon_TX_p B))))) -> (~(member zenon_TX_p (intersection zenon_TX_y zenon_TY_q))) -> (member zenon_TX_p zenon_TX_y) -> (member zenon_TX_p zenon_TY_q) -> False). % 0.71/0.88 do 3 intro. intros zenon_H15 zenon_H16 zenon_H17 zenon_H13. % 0.71/0.88 generalize (zenon_H15 zenon_TX_y). zenon_intro zenon_H19. % 0.71/0.88 generalize (zenon_H19 zenon_TY_q). zenon_intro zenon_H1a. % 0.71/0.88 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H16; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ]. % 0.71/0.88 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H1e | zenon_intro zenon_He ]. % 0.71/0.88 exact (zenon_H1e zenon_H17). % 0.71/0.88 exact (zenon_He zenon_H13). % 0.71/0.88 exact (zenon_H16 zenon_H1c). % 0.71/0.88 (* end of lemma zenon_L2_ *) % 0.71/0.88 assert (zenon_L3_ : forall (zenon_TA_r : zenon_U) (zenon_TY_q : zenon_U) (zenon_TX_y : zenon_U) (zenon_TX_p : zenon_U), (~(~(member zenon_TX_p zenon_TX_y))) -> (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_p (intersection A B))<->((member zenon_TX_p A)/\(member zenon_TX_p B))))) -> (~(member zenon_TX_p (intersection zenon_TX_y zenon_TY_q))) -> (member zenon_TX_p zenon_TA_r) -> (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TY_q))) -> (forall B : zenon_U, ((member zenon_TX_p (intersection zenon_TA_r B))<->((member zenon_TX_p zenon_TA_r)/\(member zenon_TX_p B)))) -> False). % 0.71/0.88 do 4 intro. intros zenon_H1f zenon_H15 zenon_H16 zenon_Hd zenon_Hc zenon_H20. % 0.71/0.88 apply zenon_H1f. zenon_intro zenon_H17. % 0.71/0.88 generalize (zenon_H20 zenon_TY_q). zenon_intro zenon_H21. % 0.71/0.88 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H25; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ]. % 0.71/0.88 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H14 | zenon_intro zenon_He ]. % 0.71/0.88 exact (zenon_H14 zenon_Hd). % 0.71/0.88 apply (zenon_L1_ zenon_TX_p zenon_TY_q zenon_TA_r); trivial. % 0.71/0.88 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_Hd. zenon_intro zenon_H13. % 0.71/0.88 apply (zenon_L2_ zenon_TY_q zenon_TX_y zenon_TX_p); trivial. % 0.71/0.88 (* end of lemma zenon_L3_ *) % 0.71/0.88 assert (zenon_L4_ : forall (zenon_TX_p : zenon_U) (zenon_TX_y : zenon_U) (zenon_TA_r : zenon_U), (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TX_y))) -> (member zenon_TX_p zenon_TA_r) -> (~(member zenon_TX_p zenon_TX_y)) -> False). % 0.71/0.88 do 3 intro. intros zenon_H26 zenon_Hd zenon_H1e. % 0.71/0.88 generalize (zenon_H26 zenon_TX_p). zenon_intro zenon_H27. % 0.71/0.88 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H14 | zenon_intro zenon_H17 ]. % 0.71/0.88 exact (zenon_H14 zenon_Hd). % 0.71/0.88 exact (zenon_H1e zenon_H17). % 0.71/0.88 (* end of lemma zenon_L4_ *) % 0.71/0.88 assert (zenon_L5_ : forall (zenon_TX_y : zenon_U) (zenon_TA_r : zenon_U) (zenon_TX_p : zenon_U), ((member zenon_TX_p zenon_TA_r)/\(~(member zenon_TX_p zenon_TX_y))) -> (member zenon_TX_p zenon_TA_r) -> (forall X : zenon_U, ((member X zenon_TA_r)->(member X zenon_TX_y))) -> False). % 0.71/0.88 do 3 intro. intros zenon_H28 zenon_Hd zenon_H26. % 0.71/0.88 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_Hd. zenon_intro zenon_H1e. % 0.71/0.88 apply (zenon_L4_ zenon_TX_p zenon_TX_y zenon_TA_r); trivial. % 0.71/0.88 (* end of lemma zenon_L5_ *) % 0.71/0.88 apply NNPP. intro zenon_G. % 0.71/0.88 apply (zenon_notallex_s (fun A : zenon_U => (forall X : zenon_U, (forall Y : zenon_U, (((subset A X)/\(subset A Y))<->(subset A (intersection X Y)))))) zenon_G); [ zenon_intro zenon_H29; idtac ]. % 0.71/0.88 elim zenon_H29. zenon_intro zenon_TA_r. zenon_intro zenon_H2a. % 0.71/0.88 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((subset zenon_TA_r X)/\(subset zenon_TA_r Y))<->(subset zenon_TA_r (intersection X Y))))) zenon_H2a); [ zenon_intro zenon_H2b; idtac ]. % 0.71/0.88 elim zenon_H2b. zenon_intro zenon_TX_y. zenon_intro zenon_H2c. % 0.71/0.88 apply (zenon_notallex_s (fun Y : zenon_U => (((subset zenon_TA_r zenon_TX_y)/\(subset zenon_TA_r Y))<->(subset zenon_TA_r (intersection zenon_TX_y Y)))) zenon_H2c); [ zenon_intro zenon_H2d; idtac ]. % 0.71/0.88 elim zenon_H2d. zenon_intro zenon_TY_q. zenon_intro zenon_H2e. % 0.71/0.88 apply (zenon_notequiv_s _ _ zenon_H2e); [ zenon_intro zenon_H32; zenon_intro zenon_H31 | zenon_intro zenon_H30; zenon_intro zenon_H2f ]. % 0.71/0.88 generalize (subset zenon_TA_r). zenon_intro zenon_H33. % 0.71/0.88 generalize (zenon_H33 (intersection zenon_TX_y zenon_TY_q)). zenon_intro zenon_H34. % 0.71/0.88 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H2f; zenon_intro zenon_H36 | zenon_intro zenon_H31; zenon_intro zenon_H35 ]. % 0.71/0.88 exact (zenon_H2f zenon_H31). % 0.71/0.88 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.71/0.88 generalize (subset zenon_TA_r). zenon_intro zenon_H33. % 0.71/0.88 generalize (zenon_H33 zenon_TX_y). zenon_intro zenon_H39. % 0.71/0.88 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H38; zenon_intro zenon_H3b | zenon_intro zenon_H3a; zenon_intro zenon_H26 ]. % 0.71/0.88 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_r)->(member X zenon_TX_y))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ]. % 0.71/0.88 elim zenon_H3c. zenon_intro zenon_TX_cj. zenon_intro zenon_H3e. % 0.71/0.88 apply (zenon_notimply_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.71/0.88 generalize (intersection zenon_TX_cj). zenon_intro zenon_H41. % 0.71/0.88 generalize (zenon_H41 zenon_TX_y). zenon_intro zenon_H42. % 0.71/0.88 generalize (zenon_H42 zenon_TY_q). zenon_intro zenon_H43. % 0.71/0.88 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H47; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 0.71/0.88 generalize (zenon_H35 zenon_TX_cj). zenon_intro zenon_H48. % 0.71/0.89 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H49 | zenon_intro zenon_H45 ]. % 0.71/0.89 exact (zenon_H49 zenon_H40). % 0.71/0.89 exact (zenon_H47 zenon_H45). % 0.71/0.89 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 0.71/0.89 exact (zenon_H3f zenon_H4b). % 0.71/0.89 exact (zenon_H38 zenon_H3a). % 0.71/0.89 generalize (subset zenon_TA_r). zenon_intro zenon_H33. % 0.71/0.89 generalize (zenon_H33 zenon_TY_q). zenon_intro zenon_H4c. % 0.71/0.89 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H37; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_Hc ]. % 0.71/0.89 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_r)->(member X zenon_TY_q))) zenon_H4e); [ zenon_intro zenon_H4f; idtac ]. % 0.71/0.89 elim zenon_H4f. zenon_intro zenon_TX_dc. zenon_intro zenon_H51. % 0.71/0.89 apply (zenon_notimply_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 0.71/0.89 generalize (intersection zenon_TX_dc). zenon_intro zenon_H54. % 0.71/0.89 generalize (zenon_H54 zenon_TX_y). zenon_intro zenon_H55. % 0.71/0.89 generalize (zenon_H55 zenon_TY_q). zenon_intro zenon_H56. % 0.71/0.89 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H5a; zenon_intro zenon_H59 | zenon_intro zenon_H58; zenon_intro zenon_H57 ]. % 0.71/0.89 generalize (zenon_H35 zenon_TX_dc). zenon_intro zenon_H5b. % 0.71/0.89 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5c | zenon_intro zenon_H58 ]. % 0.71/0.89 exact (zenon_H5c zenon_H53). % 0.71/0.89 exact (zenon_H5a zenon_H58). % 0.71/0.89 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 0.71/0.89 exact (zenon_H52 zenon_H5d). % 0.71/0.89 exact (zenon_H37 zenon_H4d). % 0.71/0.89 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H3a. zenon_intro zenon_H4d. % 0.71/0.89 generalize (subset zenon_TA_r). zenon_intro zenon_H33. % 0.71/0.89 generalize (zenon_H33 zenon_TX_y). zenon_intro zenon_H39. % 0.71/0.89 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H38; zenon_intro zenon_H3b | zenon_intro zenon_H3a; zenon_intro zenon_H26 ]. % 0.71/0.89 exact (zenon_H38 zenon_H3a). % 0.71/0.89 generalize (subset zenon_TA_r). zenon_intro zenon_H33. % 0.71/0.89 generalize (zenon_H33 zenon_TY_q). zenon_intro zenon_H4c. % 0.71/0.89 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H37; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_Hc ]. % 0.71/0.89 exact (zenon_H37 zenon_H4d). % 0.71/0.89 generalize (subset zenon_TA_r). zenon_intro zenon_H33. % 0.71/0.89 generalize (zenon_H33 (intersection zenon_TX_y zenon_TY_q)). zenon_intro zenon_H34. % 0.71/0.89 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H2f; zenon_intro zenon_H36 | zenon_intro zenon_H31; zenon_intro zenon_H35 ]. % 0.71/0.89 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_r)->(member X (intersection zenon_TX_y zenon_TY_q)))) zenon_H36); [ zenon_intro zenon_H5f; idtac ]. % 0.71/0.89 elim zenon_H5f. zenon_intro zenon_TX_p. zenon_intro zenon_H60. % 0.71/0.89 apply (zenon_notimply_s _ _ zenon_H60). zenon_intro zenon_Hd. zenon_intro zenon_H16. % 0.71/0.89 generalize (difference zenon_TX_p). zenon_intro zenon_H61. % 0.71/0.89 generalize (intersection zenon_TX_p). zenon_intro zenon_H15. % 0.71/0.89 generalize (zenon_H15 zenon_TA_r). zenon_intro zenon_H20. % 0.71/0.89 generalize (zenon_H61 zenon_TX_y). zenon_intro zenon_H62. % 0.71/0.89 generalize (zenon_H62 zenon_TA_r). zenon_intro zenon_H63. % 0.71/0.89 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H66; zenon_intro zenon_H65 | zenon_intro zenon_H64; zenon_intro zenon_H28 ]. % 0.71/0.89 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H14 | zenon_intro zenon_H1f ]. % 0.71/0.89 exact (zenon_H14 zenon_Hd). % 0.71/0.89 apply (zenon_L3_ zenon_TA_r zenon_TY_q zenon_TX_y zenon_TX_p); trivial. % 0.71/0.89 apply (zenon_L5_ zenon_TX_y zenon_TA_r zenon_TX_p); trivial. % 0.71/0.89 exact (zenon_H2f zenon_H31). % 0.71/0.89 Qed. % 0.71/0.89 % SZS output end Proof % 0.71/0.89 (* END-PROOF *) % 0.71/0.89 nodes searched: 17767 % 0.71/0.89 max branch formulas: 2385 % 0.71/0.89 proof nodes created: 709 % 0.71/0.89 formulas created: 104643 % 0.71/0.89 %------------------------------------------------------------------------------