%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 06:32:45 EDT 2022 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET027+3 : TPTP v8.1.0. Released v2.2.0. % 0.10/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n027.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 04:58:02 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.50 (* PROOF-FOUND *) % 0.19/0.50 % SZS status Theorem % 0.19/0.50 (* BEGIN-PROOF *) % 0.19/0.50 % SZS output start Proof % 0.19/0.50 Theorem prove_transitivity_of_subset : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset C D))->(subset B D))))). % 0.19/0.50 Proof. % 0.19/0.50 apply NNPP. intro zenon_G. % 0.19/0.50 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, (((subset B C)/\(subset C D))->(subset B D))))) zenon_G); [ zenon_intro zenon_H3; idtac ]. % 0.19/0.50 elim zenon_H3. zenon_intro zenon_TB_e. zenon_intro zenon_H5. % 0.19/0.50 apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, (((subset zenon_TB_e C)/\(subset C D))->(subset zenon_TB_e D)))) zenon_H5); [ zenon_intro zenon_H6; idtac ]. % 0.19/0.50 elim zenon_H6. zenon_intro zenon_TC_h. zenon_intro zenon_H8. % 0.19/0.50 apply (zenon_notallex_s (fun D : zenon_U => (((subset zenon_TB_e zenon_TC_h)/\(subset zenon_TC_h D))->(subset zenon_TB_e D))) zenon_H8); [ zenon_intro zenon_H9; idtac ]. % 0.19/0.50 elim zenon_H9. zenon_intro zenon_TD_k. zenon_intro zenon_Hb. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.19/0.50 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_Hf. zenon_intro zenon_He. % 0.19/0.50 generalize (subset_defn zenon_TB_e). zenon_intro zenon_H10. % 0.19/0.50 generalize (zenon_H10 zenon_TC_h). zenon_intro zenon_H11. % 0.19/0.50 apply (zenon_equiv_s _ _ zenon_H11); [ zenon_intro zenon_H14; zenon_intro zenon_H13 | zenon_intro zenon_Hf; zenon_intro zenon_H12 ]. % 0.19/0.50 exact (zenon_H14 zenon_Hf). % 0.19/0.50 generalize (subset_defn zenon_TC_h). zenon_intro zenon_H15. % 0.19/0.50 generalize (zenon_H15 zenon_TD_k). zenon_intro zenon_H16. % 0.19/0.50 apply (zenon_equiv_s _ _ zenon_H16); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_He; zenon_intro zenon_H17 ]. % 0.19/0.50 exact (zenon_H19 zenon_He). % 0.19/0.50 generalize (subset_defn zenon_TB_e). zenon_intro zenon_H10. % 0.19/0.50 generalize (zenon_H10 zenon_TD_k). zenon_intro zenon_H1a. % 0.19/0.50 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_Hc; zenon_intro zenon_H1d | zenon_intro zenon_H1c; zenon_intro zenon_H1b ]. % 0.19/0.50 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_e)->(member D zenon_TD_k))) zenon_H1d); [ zenon_intro zenon_H1e; idtac ]. % 0.19/0.50 elim zenon_H1e. zenon_intro zenon_TD_bf. zenon_intro zenon_H20. % 0.19/0.50 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.19/0.50 generalize (zenon_H17 zenon_TD_bf). zenon_intro zenon_H23. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.19/0.50 generalize (zenon_H12 zenon_TD_bf). zenon_intro zenon_H26. % 0.19/0.50 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 0.19/0.50 exact (zenon_H28 zenon_H22). % 0.19/0.50 exact (zenon_H25 zenon_H27). % 0.19/0.50 exact (zenon_H21 zenon_H24). % 0.19/0.50 exact (zenon_Hc zenon_H1c). % 0.19/0.50 Qed. % 0.19/0.50 % SZS output end Proof % 0.19/0.50 (* END-PROOF *) % 0.19/0.50 nodes searched: 28 % 0.19/0.50 max branch formulas: 27 % 0.19/0.50 proof nodes created: 18 % 0.19/0.50 formulas created: 208 % 0.19/0.50 %------------------------------------------------------------------------------