%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 15:59:27 EDT 2022 % Result : Theorem 0.19s 0.52s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU120+1 : TPTP v8.1.0. Released v3.3.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n018.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 Jun 19 23:41:34 EDT 2022 % 0.19/0.34 % CPUTime : % 0.19/0.52 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 0.19/0.52 (* PROOF-FOUND *) % 0.19/0.52 % SZS status Theorem % 0.19/0.52 (* BEGIN-PROOF *) % 0.19/0.52 % SZS output start Proof % 0.19/0.52 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)))))). % 0.19/0.52 Proof. % 0.19/0.52 apply NNPP. intro zenon_G. % 0.19/0.52 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_Hb; idtac ]. % 0.19/0.52 elim zenon_Hb. zenon_intro zenon_TA_m. zenon_intro zenon_Hd. % 0.19/0.52 apply (zenon_notallex_s (fun B : zenon_U => ((~((~(disjoint zenon_TA_m B))/\(forall C : zenon_U, (~(in C (set_intersection2 zenon_TA_m B))))))/\(~((exists C : zenon_U, (in C (set_intersection2 zenon_TA_m B)))/\(disjoint zenon_TA_m B))))) zenon_Hd); [ zenon_intro zenon_He; idtac ]. % 0.19/0.52 elim zenon_He. zenon_intro zenon_TB_p. zenon_intro zenon_H10. % 0.19/0.52 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.19/0.52 apply zenon_H12. zenon_intro zenon_H13. % 0.19/0.52 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.19/0.52 generalize (d7_xboole_0 zenon_TA_m). zenon_intro zenon_H16. % 0.19/0.52 generalize (zenon_H16 zenon_TB_p). zenon_intro zenon_H17. % 0.19/0.52 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 0.19/0.52 generalize (d1_xboole_0 (set_intersection2 zenon_TA_m zenon_TB_p)). zenon_intro zenon_H1b. % 0.19/0.52 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1a; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H14 ]. % 0.19/0.52 exact (zenon_H1c zenon_H14). % 0.19/0.52 exact (zenon_H1a zenon_H18). % 0.19/0.52 exact (zenon_H15 zenon_H19). % 0.19/0.52 apply zenon_H11. zenon_intro zenon_H1d. % 0.19/0.52 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1e. zenon_intro zenon_H19. % 0.19/0.52 elim zenon_H1e. zenon_intro zenon_TC_bf. zenon_intro zenon_H20. % 0.19/0.52 generalize (d7_xboole_0 zenon_TA_m). zenon_intro zenon_H16. % 0.19/0.52 generalize (zenon_H16 zenon_TB_p). zenon_intro zenon_H17. % 0.19/0.52 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H1a | zenon_intro zenon_H19; zenon_intro zenon_H18 ]. % 0.19/0.52 exact (zenon_H15 zenon_H19). % 0.19/0.52 generalize (d1_xboole_0 (set_intersection2 zenon_TA_m zenon_TB_p)). zenon_intro zenon_H1b. % 0.19/0.52 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H1a; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H14 ]. % 0.19/0.52 exact (zenon_H1a zenon_H18). % 0.19/0.52 generalize (zenon_H14 zenon_TC_bf). zenon_intro zenon_H21. % 0.19/0.52 exact (zenon_H21 zenon_H20). % 0.19/0.52 Qed. % 0.19/0.52 % SZS output end Proof % 0.19/0.52 (* END-PROOF *) % 0.19/0.52 nodes searched: 346 % 0.19/0.52 max branch formulas: 103 % 0.19/0.52 proof nodes created: 48 % 0.19/0.52 formulas created: 948 % 0.19/0.52 %------------------------------------------------------------------------------