%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 06:37:07 EDT 2022 % Result : Theorem 2.15s 2.31s % Output : Proof 2.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET593+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n011.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jul 10 11:36:11 EDT 2022 % 0.13/0.34 % CPUTime : % 2.15/2.31 (* PROOF-FOUND *) % 2.15/2.31 % SZS status Theorem % 2.15/2.31 (* BEGIN-PROOF *) % 2.15/2.31 % SZS output start Proof % 2.15/2.31 Theorem prove_th52 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((subset B (union C D))->((subset (difference B C) D)/\(subset (difference B D) C)))))). % 2.15/2.31 Proof. % 2.15/2.31 assert (zenon_L1_ : forall (zenon_TC_k : zenon_U) (zenon_TD_l : zenon_U) (zenon_TD_m : zenon_U), (~(member zenon_TD_m (union zenon_TD_l zenon_TC_k))) -> (member zenon_TD_m (union zenon_TC_k zenon_TD_l)) -> ((union zenon_TD_l zenon_TC_k) = (union zenon_TC_k zenon_TD_l)) -> False). % 2.15/2.31 do 3 intro. intros zenon_H7 zenon_H8 zenon_H9. % 2.15/2.31 cut ((member zenon_TD_m (union zenon_TC_k zenon_TD_l)) = (member zenon_TD_m (union zenon_TD_l zenon_TC_k))). % 2.15/2.31 intro zenon_D_pnotp. % 2.15/2.31 apply zenon_H7. % 2.15/2.31 rewrite <- zenon_D_pnotp. % 2.15/2.31 exact zenon_H8. % 2.15/2.31 cut (((union zenon_TC_k zenon_TD_l) = (union zenon_TD_l zenon_TC_k))); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 2.15/2.31 cut ((zenon_TD_m = zenon_TD_m)); [idtac | apply NNPP; zenon_intro zenon_He]. % 2.15/2.31 congruence. % 2.15/2.31 apply zenon_He. apply refl_equal. % 2.15/2.31 apply zenon_Hd. apply sym_equal. exact zenon_H9. % 2.15/2.31 (* end of lemma zenon_L1_ *) % 2.15/2.31 apply NNPP. intro zenon_G. % 2.15/2.31 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((subset B (union C D))->((subset (difference B C) D)/\(subset (difference B D) C)))))) zenon_G); [ zenon_intro zenon_Hf; idtac ]. % 2.15/2.31 elim zenon_Hf. zenon_intro zenon_TB_q. zenon_intro zenon_H11. % 2.15/2.31 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((subset zenon_TB_q (union C D))->((subset (difference zenon_TB_q C) D)/\(subset (difference zenon_TB_q D) C))))) zenon_H11); [ zenon_intro zenon_H12; idtac ]. % 2.15/2.31 elim zenon_H12. zenon_intro zenon_TC_k. zenon_intro zenon_H13. % 2.15/2.31 apply (zenon_notallex_s (fun D : zenon_U => ((subset zenon_TB_q (union zenon_TC_k D))->((subset (difference zenon_TB_q zenon_TC_k) D)/\(subset (difference zenon_TB_q D) zenon_TC_k)))) zenon_H13); [ zenon_intro zenon_H14; idtac ]. % 2.15/2.31 elim zenon_H14. zenon_intro zenon_TD_l. zenon_intro zenon_H15. % 2.15/2.31 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 2.15/2.31 generalize (subset_defn zenon_TB_q). zenon_intro zenon_H18. % 2.15/2.31 generalize (zenon_H18 (union zenon_TC_k zenon_TD_l)). zenon_intro zenon_H19. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H17; zenon_intro zenon_H1a ]. % 2.15/2.31 exact (zenon_H1c zenon_H17). % 2.15/2.31 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 2.15/2.31 generalize (subset_defn (difference zenon_TB_q zenon_TC_k)). zenon_intro zenon_H1f. % 2.15/2.31 generalize (zenon_H1f zenon_TD_l). zenon_intro zenon_H20. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1e; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ]. % 2.15/2.31 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_q zenon_TC_k))->(member D zenon_TD_l))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 2.15/2.31 elim zenon_H24. zenon_intro zenon_TD_bl. zenon_intro zenon_H26. % 2.15/2.31 apply (zenon_notimply_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H27. % 2.15/2.31 generalize (union_defn zenon_TC_k). zenon_intro zenon_H29. % 2.15/2.31 generalize (zenon_H29 zenon_TD_l). zenon_intro zenon_H2a. % 2.15/2.31 generalize (zenon_H2a zenon_TD_bl). zenon_intro zenon_H2b. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H2c ]. % 2.15/2.31 generalize (zenon_H1a zenon_TD_bl). zenon_intro zenon_H30. % 2.15/2.31 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H31 | zenon_intro zenon_H2d ]. % 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32. % 2.15/2.31 generalize (zenon_H32 zenon_TC_k). zenon_intro zenon_H33. % 2.15/2.31 generalize (zenon_H33 zenon_TD_bl). zenon_intro zenon_H34. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H28; zenon_intro zenon_H35 ]. % 2.15/2.31 exact (zenon_H37 zenon_H28). % 2.15/2.31 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H39. zenon_intro zenon_H38. % 2.15/2.31 exact (zenon_H31 zenon_H39). % 2.15/2.31 exact (zenon_H2f zenon_H2d). % 2.15/2.31 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32. % 2.15/2.31 generalize (zenon_H32 zenon_TC_k). zenon_intro zenon_H33. % 2.15/2.31 generalize (zenon_H33 zenon_TD_bl). zenon_intro zenon_H34. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H28; zenon_intro zenon_H35 ]. % 2.15/2.31 exact (zenon_H37 zenon_H28). % 2.15/2.31 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H39. zenon_intro zenon_H38. % 2.15/2.31 exact (zenon_H38 zenon_H3b). % 2.15/2.31 exact (zenon_H27 zenon_H3a). % 2.15/2.31 exact (zenon_H1e zenon_H22). % 2.15/2.31 generalize (subset_defn (difference zenon_TB_q zenon_TD_l)). zenon_intro zenon_H3c. % 2.15/2.31 generalize (zenon_H3c zenon_TC_k). zenon_intro zenon_H3d. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H1d; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3e ]. % 2.15/2.31 apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_q zenon_TD_l))->(member D zenon_TC_k))) zenon_H40); [ zenon_intro zenon_H41; idtac ]. % 2.15/2.31 elim zenon_H41. zenon_intro zenon_TD_m. zenon_intro zenon_H42. % 2.15/2.31 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43. % 2.15/2.31 generalize (commutativity_of_union zenon_TD_l). zenon_intro zenon_H45. % 2.15/2.31 generalize (zenon_H45 zenon_TC_k). zenon_intro zenon_H9. % 2.15/2.31 generalize (union_defn zenon_TD_l). zenon_intro zenon_H46. % 2.15/2.31 generalize (zenon_H46 zenon_TC_k). zenon_intro zenon_H47. % 2.15/2.31 generalize (zenon_H47 zenon_TD_m). zenon_intro zenon_H48. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H7; zenon_intro zenon_H4b | zenon_intro zenon_H4a; zenon_intro zenon_H49 ]. % 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32. % 2.15/2.31 generalize (zenon_H1a zenon_TD_m). zenon_intro zenon_H4c. % 2.15/2.31 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4d | zenon_intro zenon_H8 ]. % 2.15/2.31 generalize (zenon_H32 zenon_TD_l). zenon_intro zenon_H4e. % 2.15/2.31 generalize (zenon_H4e zenon_TD_m). zenon_intro zenon_H4f. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H44; zenon_intro zenon_H50 ]. % 2.15/2.31 exact (zenon_H52 zenon_H44). % 2.15/2.31 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H54. zenon_intro zenon_H53. % 2.15/2.31 exact (zenon_H4d zenon_H54). % 2.15/2.31 apply (zenon_L1_ zenon_TC_k zenon_TD_l zenon_TD_m); trivial. % 2.15/2.31 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 2.15/2.31 generalize (difference_defn zenon_TB_q). zenon_intro zenon_H32. % 2.15/2.31 generalize (zenon_H32 zenon_TD_l). zenon_intro zenon_H4e. % 2.15/2.31 generalize (zenon_H4e zenon_TD_m). zenon_intro zenon_H4f. % 2.15/2.31 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H44; zenon_intro zenon_H50 ]. % 2.15/2.31 exact (zenon_H52 zenon_H44). % 2.15/2.31 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H54. zenon_intro zenon_H53. % 2.15/2.31 exact (zenon_H53 zenon_H56). % 2.15/2.31 exact (zenon_H43 zenon_H55). % 2.15/2.31 exact (zenon_H1d zenon_H3f). % 2.15/2.31 Qed. % 2.15/2.31 % SZS output end Proof % 2.15/2.31 (* END-PROOF *) % 2.15/2.31 nodes searched: 79628 % 2.15/2.31 max branch formulas: 3580 % 2.15/2.31 proof nodes created: 3881 % 2.15/2.31 formulas created: 142906 % 2.15/2.31 %------------------------------------------------------------------------------