%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 15:59:28 EDT 2022 % Result : Theorem 6.33s 6.50s % Output : Proof 6.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU120+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.11/0.32 % Computer : n004.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sun Jun 19 13:23:53 EDT 2022 % 0.11/0.33 % CPUTime : % 6.33/6.50 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 6.33/6.50 (* PROOF-FOUND *) % 6.33/6.50 % SZS status Theorem % 6.33/6.50 (* BEGIN-PROOF *) % 6.33/6.50 % SZS output start Proof % 6.33/6.50 Theorem t4_xboole_0 : (forall A : zenon_U, (forall B : zenon_U, ((~((~(disjoint A B))/\(forall C : zenon_U, (~(in C (set_intersection2 A B))))))/\(~((exists C : zenon_U, (in C (set_intersection2 A B)))/\(disjoint A B)))))). % 6.33/6.50 Proof. % 6.33/6.50 apply NNPP. intro zenon_G. % 6.33/6.50 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((~((~(disjoint A B))/\(forall C : zenon_U, (~(in C (set_intersection2 A B))))))/\(~((exists C : zenon_U, (in C (set_intersection2 A B)))/\(disjoint A B)))))) zenon_G); [ zenon_intro zenon_Hd; idtac ]. % 6.33/6.50 elim zenon_Hd. zenon_intro zenon_TA_o. zenon_intro zenon_Hf. % 6.33/6.50 apply (zenon_notallex_s (fun B : zenon_U => ((~((~(disjoint zenon_TA_o B))/\(forall C : zenon_U, (~(in C (set_intersection2 zenon_TA_o B))))))/\(~((exists C : zenon_U, (in C (set_intersection2 zenon_TA_o B)))/\(disjoint zenon_TA_o B))))) zenon_Hf); [ zenon_intro zenon_H10; idtac ]. % 6.33/6.50 elim zenon_H10. zenon_intro zenon_TB_r. zenon_intro zenon_H12. % 6.33/6.50 apply (zenon_notand_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 6.33/6.50 apply zenon_H14. zenon_intro zenon_H15. % 6.33/6.50 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 6.33/6.50 generalize (d7_xboole_0 zenon_TA_o). zenon_intro zenon_H18. % 6.33/6.50 generalize (zenon_H18 zenon_TB_r). zenon_intro zenon_H19. % 6.33/6.50 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H17; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ]. % 6.33/6.50 generalize (d1_xboole_0 (set_intersection2 zenon_TA_o zenon_TB_r)). zenon_intro zenon_H1d. % 6.33/6.50 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H1c; zenon_intro zenon_H1e | zenon_intro zenon_H1a; zenon_intro zenon_H16 ]. % 6.33/6.50 exact (zenon_H1e zenon_H16). % 6.33/6.50 exact (zenon_H1c zenon_H1a). % 6.33/6.50 exact (zenon_H17 zenon_H1b). % 6.33/6.50 apply zenon_H13. zenon_intro zenon_H1f. % 6.33/6.50 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H20. zenon_intro zenon_H1b. % 6.33/6.50 elim zenon_H20. zenon_intro zenon_TC_bh. zenon_intro zenon_H22. % 6.33/6.50 generalize (d7_xboole_0 zenon_TA_o). zenon_intro zenon_H18. % 6.33/6.50 generalize (zenon_H18 zenon_TB_r). zenon_intro zenon_H19. % 6.33/6.50 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H17; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ]. % 6.33/6.50 exact (zenon_H17 zenon_H1b). % 6.33/6.50 generalize (d1_xboole_0 (set_intersection2 zenon_TA_o zenon_TB_r)). zenon_intro zenon_H1d. % 6.33/6.50 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H1c; zenon_intro zenon_H1e | zenon_intro zenon_H1a; zenon_intro zenon_H16 ]. % 6.33/6.50 exact (zenon_H1c zenon_H1a). % 6.33/6.50 generalize (zenon_H16 zenon_TC_bh). zenon_intro zenon_H23. % 6.33/6.50 exact (zenon_H23 zenon_H22). % 6.33/6.50 Qed. % 6.33/6.50 % SZS output end Proof % 6.33/6.50 (* END-PROOF *) % 6.33/6.50 nodes searched: 201461 % 6.33/6.50 max branch formulas: 3828 % 6.33/6.50 proof nodes created: 11899 % 6.33/6.50 formulas created: 421339 % 6.33/6.50 %------------------------------------------------------------------------------