%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET603+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 06:37:14 EDT 2022 % Result : Theorem 0.40s 0.57s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET603+4 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n009.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 20:28:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.40/0.57 (* PROOF-FOUND *) % 0.40/0.57 % SZS status Theorem % 0.40/0.57 (* BEGIN-PROOF *) % 0.40/0.57 % SZS output start Proof % 0.40/0.57 Theorem thI30 : (forall E : zenon_U, (equal_set (difference E (empty_set)) E)). % 0.40/0.57 Proof. % 0.40/0.57 assert (zenon_L1_ : forall (zenon_TX_n : zenon_U), (member zenon_TX_n (empty_set)) -> False). % 0.40/0.57 do 1 intro. intros zenon_Hc. % 0.40/0.57 generalize (empty_set zenon_TX_n). zenon_intro zenon_He. % 0.40/0.57 exact (zenon_He zenon_Hc). % 0.40/0.57 (* end of lemma zenon_L1_ *) % 0.40/0.57 assert (zenon_L2_ : forall (zenon_TX_n : zenon_U), (~(~(member zenon_TX_n (empty_set)))) -> False). % 0.40/0.57 do 1 intro. intros zenon_Hf. % 0.40/0.57 apply zenon_Hf. zenon_intro zenon_Hc. % 0.40/0.57 apply (zenon_L1_ zenon_TX_n); trivial. % 0.40/0.57 (* end of lemma zenon_L2_ *) % 0.40/0.57 apply NNPP. intro zenon_G. % 0.40/0.57 apply (zenon_notallex_s (fun E : zenon_U => (equal_set (difference E (empty_set)) E)) zenon_G); [ zenon_intro zenon_H10; idtac ]. % 0.40/0.57 elim zenon_H10. zenon_intro zenon_TE_r. zenon_intro zenon_H12. % 0.40/0.57 generalize (equal_set (difference zenon_TE_r (empty_set))). zenon_intro zenon_H13. % 0.40/0.57 generalize (zenon_H13 zenon_TE_r). zenon_intro zenon_H14. % 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H12; zenon_intro zenon_H17 | zenon_intro zenon_H16; zenon_intro zenon_H15 ]. % 0.40/0.57 apply (zenon_notand_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 0.40/0.57 generalize (subset (difference zenon_TE_r (empty_set))). zenon_intro zenon_H1a. % 0.40/0.57 generalize (zenon_H1a zenon_TE_r). zenon_intro zenon_H1b. % 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H19; zenon_intro zenon_H1e | zenon_intro zenon_H1d; zenon_intro zenon_H1c ]. % 0.40/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X (difference zenon_TE_r (empty_set)))->(member X zenon_TE_r))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ]. % 0.40/0.57 elim zenon_H1f. zenon_intro zenon_TX_bg. zenon_intro zenon_H21. % 0.40/0.57 apply (zenon_notimply_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.40/0.57 generalize (difference zenon_TX_bg). zenon_intro zenon_H24. % 0.40/0.57 generalize (zenon_H24 (empty_set)). zenon_intro zenon_H25. % 0.40/0.57 generalize (zenon_H25 zenon_TE_r). zenon_intro zenon_H26. % 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H29; zenon_intro zenon_H28 | zenon_intro zenon_H23; zenon_intro zenon_H27 ]. % 0.40/0.57 exact (zenon_H29 zenon_H23). % 0.40/0.57 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.40/0.57 exact (zenon_H22 zenon_H2b). % 0.40/0.57 exact (zenon_H19 zenon_H1d). % 0.40/0.57 generalize (subset zenon_TE_r). zenon_intro zenon_H2c. % 0.40/0.57 generalize (zenon_H2c (difference zenon_TE_r (empty_set))). zenon_intro zenon_H2d. % 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H18; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 0.40/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TE_r)->(member X (difference zenon_TE_r (empty_set))))) zenon_H30); [ zenon_intro zenon_H31; idtac ]. % 0.40/0.57 elim zenon_H31. zenon_intro zenon_TX_n. zenon_intro zenon_H32. % 0.40/0.57 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.40/0.57 generalize (difference zenon_TX_n). zenon_intro zenon_H35. % 0.40/0.57 generalize (zenon_H35 (empty_set)). zenon_intro zenon_H36. % 0.40/0.57 generalize (zenon_H36 zenon_TE_r). zenon_intro zenon_H37. % 0.40/0.57 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H33; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ]. % 0.40/0.57 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3b | zenon_intro zenon_Hf ]. % 0.40/0.57 exact (zenon_H3b zenon_H34). % 0.40/0.57 apply (zenon_L2_ zenon_TX_n); trivial. % 0.40/0.57 exact (zenon_H33 zenon_H39). % 0.40/0.57 exact (zenon_H18 zenon_H2f). % 0.40/0.57 exact (zenon_H12 zenon_H16). % 0.40/0.57 Qed. % 0.40/0.57 % SZS output end Proof % 0.40/0.57 (* END-PROOF *) % 0.40/0.57 nodes searched: 2166 % 0.40/0.57 max branch formulas: 698 % 0.40/0.57 proof nodes created: 118 % 0.40/0.57 formulas created: 12436 % 0.40/0.57 %------------------------------------------------------------------------------