%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n009.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 06:38:01 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 % 0.03/0.12 % Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n009.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 08:54:22 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 thI19 : (forall A : zenon_U, (forall B : zenon_U, ((equal_set A (intersection A B))<->(subset A B)))). % 0.91/1.10 Proof. % 0.91/1.10 assert (zenon_L1_ : forall (zenon_TA_q : zenon_U) (zenon_TB_r : zenon_U) (zenon_TX_s : zenon_U), (~(~(member zenon_TX_s zenon_TB_r))) -> (member zenon_TX_s zenon_TA_q) -> (~(member zenon_TX_s (intersection zenon_TA_q zenon_TB_r))) -> (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_s (intersection A B))<->((member zenon_TX_s A)/\(member zenon_TX_s B))))) -> False). % 0.91/1.10 do 3 intro. intros zenon_Hc zenon_Hd zenon_He zenon_Hf. % 0.91/1.10 apply zenon_Hc. zenon_intro zenon_H13. % 0.91/1.10 generalize (zenon_Hf zenon_TA_q). zenon_intro zenon_H14. % 0.91/1.10 generalize (zenon_H14 zenon_TB_r). zenon_intro zenon_H15. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_He; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 0.91/1.10 exact (zenon_H1a zenon_Hd). % 0.91/1.10 exact (zenon_H19 zenon_H13). % 0.91/1.10 exact (zenon_He zenon_H17). % 0.91/1.10 (* end of lemma zenon_L1_ *) % 0.91/1.10 assert (zenon_L2_ : forall (zenon_TX_s : zenon_U) (zenon_TB_r : zenon_U) (zenon_TA_q : zenon_U), (forall X : zenon_U, ((member X zenon_TA_q)->(member X zenon_TB_r))) -> (member zenon_TX_s zenon_TA_q) -> (~(member zenon_TX_s zenon_TB_r)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H1b zenon_Hd zenon_H19. % 0.91/1.10 generalize (zenon_H1b zenon_TX_s). zenon_intro zenon_H1c. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1a | zenon_intro zenon_H13 ]. % 0.91/1.10 exact (zenon_H1a zenon_Hd). % 0.91/1.10 exact (zenon_H19 zenon_H13). % 0.91/1.10 (* end of lemma zenon_L2_ *) % 0.91/1.10 assert (zenon_L3_ : forall (zenon_TB_r : zenon_U) (zenon_TA_q : zenon_U) (zenon_TX_bf : zenon_U), ((member zenon_TX_bf zenon_TA_q)/\(member zenon_TX_bf zenon_TB_r)) -> (~(member zenon_TX_bf zenon_TB_r)) -> False). % 0.91/1.10 do 3 intro. intros zenon_H1d zenon_H1e. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.91/1.10 exact (zenon_H1e zenon_H20). % 0.91/1.10 (* end of lemma zenon_L3_ *) % 0.91/1.10 apply NNPP. intro zenon_G. % 0.91/1.10 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((equal_set A (intersection A B))<->(subset A B)))) zenon_G); [ zenon_intro zenon_H22; idtac ]. % 0.91/1.10 elim zenon_H22. zenon_intro zenon_TA_q. zenon_intro zenon_H23. % 0.91/1.10 apply (zenon_notallex_s (fun B : zenon_U => ((equal_set zenon_TA_q (intersection zenon_TA_q B))<->(subset zenon_TA_q B))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 0.91/1.10 elim zenon_H24. zenon_intro zenon_TB_r. zenon_intro zenon_H25. % 0.91/1.10 apply (zenon_notequiv_s _ _ zenon_H25); [ zenon_intro zenon_H29; zenon_intro zenon_H28 | zenon_intro zenon_H27; zenon_intro zenon_H26 ]. % 0.91/1.10 generalize (equal_set zenon_TA_q). zenon_intro zenon_H2a. % 0.91/1.10 generalize (zenon_H2a (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H2b. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H27; zenon_intro zenon_H2c ]. % 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e. % 0.91/1.10 generalize (zenon_H2e zenon_TB_r). zenon_intro zenon_H2f. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H26; zenon_intro zenon_H30 | zenon_intro zenon_H28; zenon_intro zenon_H1b ]. % 0.91/1.10 exact (zenon_H26 zenon_H28). % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e. % 0.91/1.10 generalize (zenon_H2e (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H33. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H32; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_q)->(member X (intersection zenon_TA_q zenon_TB_r)))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 0.91/1.10 elim zenon_H37. zenon_intro zenon_TX_s. zenon_intro zenon_H38. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_Hd. zenon_intro zenon_He. % 0.91/1.10 generalize (difference zenon_TX_s). zenon_intro zenon_H39. % 0.91/1.10 generalize (intersection zenon_TX_s). zenon_intro zenon_Hf. % 0.91/1.10 generalize (zenon_H39 zenon_TB_r). zenon_intro zenon_H3a. % 0.91/1.10 generalize (zenon_H3a zenon_TA_q). zenon_intro zenon_H3b. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H3c ]. % 0.91/1.10 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H1a | zenon_intro zenon_Hc ]. % 0.91/1.10 exact (zenon_H1a zenon_Hd). % 0.91/1.10 apply (zenon_L1_ zenon_TA_q zenon_TB_r zenon_TX_s); trivial. % 0.91/1.10 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_Hd. zenon_intro zenon_H19. % 0.91/1.10 apply (zenon_L2_ zenon_TX_s zenon_TB_r zenon_TA_q); trivial. % 0.91/1.10 exact (zenon_H32 zenon_H35). % 0.91/1.10 generalize (subset (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H40. % 0.91/1.10 generalize (zenon_H40 zenon_TA_q). zenon_intro zenon_H41. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H31; zenon_intro zenon_H44 | zenon_intro zenon_H43; zenon_intro zenon_H42 ]. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X (intersection zenon_TA_q zenon_TB_r))->(member X zenon_TA_q))) zenon_H44); [ zenon_intro zenon_H45; idtac ]. % 0.91/1.10 elim zenon_H45. zenon_intro zenon_TX_cs. zenon_intro zenon_H47. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.91/1.10 generalize (intersection zenon_TX_cs). zenon_intro zenon_H4a. % 0.91/1.10 generalize (zenon_H4a zenon_TA_q). zenon_intro zenon_H4b. % 0.91/1.10 generalize (zenon_H4b zenon_TB_r). zenon_intro zenon_H4c. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 0.91/1.10 exact (zenon_H4f zenon_H49). % 0.91/1.10 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.91/1.10 exact (zenon_H48 zenon_H51). % 0.91/1.10 exact (zenon_H31 zenon_H43). % 0.91/1.10 exact (zenon_H29 zenon_H27). % 0.91/1.10 generalize (equal_set zenon_TA_q). zenon_intro zenon_H2a. % 0.91/1.10 generalize (zenon_H2a (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H2b. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H27; zenon_intro zenon_H2c ]. % 0.91/1.10 exact (zenon_H29 zenon_H27). % 0.91/1.10 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H35. zenon_intro zenon_H43. % 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e. % 0.91/1.10 generalize (zenon_H2e (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H33. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H32; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ]. % 0.91/1.10 exact (zenon_H32 zenon_H35). % 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e. % 0.91/1.10 generalize (zenon_H2e zenon_TB_r). zenon_intro zenon_H2f. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H26; zenon_intro zenon_H30 | zenon_intro zenon_H28; zenon_intro zenon_H1b ]. % 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_q)->(member X zenon_TB_r))) zenon_H30); [ zenon_intro zenon_H52; idtac ]. % 0.91/1.10 elim zenon_H52. zenon_intro zenon_TX_bf. zenon_intro zenon_H53. % 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H53). zenon_intro zenon_H21. zenon_intro zenon_H1e. % 0.91/1.10 generalize (intersection zenon_TX_bf). zenon_intro zenon_H54. % 0.91/1.10 generalize (zenon_H54 zenon_TA_q). zenon_intro zenon_H55. % 0.91/1.10 generalize (zenon_H55 zenon_TB_r). zenon_intro zenon_H56. % 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H59; zenon_intro zenon_H58 | zenon_intro zenon_H57; zenon_intro zenon_H1d ]. % 0.91/1.10 generalize (zenon_H34 zenon_TX_bf). zenon_intro zenon_H5a. % 0.91/1.10 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H57 ]. % 0.91/1.10 exact (zenon_H5b zenon_H21). % 0.91/1.10 exact (zenon_H59 zenon_H57). % 0.91/1.10 apply (zenon_L3_ zenon_TB_r zenon_TA_q zenon_TX_bf); trivial. % 0.91/1.10 exact (zenon_H26 zenon_H28). % 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: 26774 % 0.91/1.10 max branch formulas: 5616 % 0.91/1.10 proof nodes created: 881 % 0.91/1.10 formulas created: 163249 % 0.91/1.10 %------------------------------------------------------------------------------