%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU121+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 0.35s 0.54s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU121+2 : TPTP v8.1.0. Released v3.3.0. % 0.08/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n022.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 Jun 19 11:46:46 EDT 2022 % 0.13/0.35 % CPUTime : % 0.35/0.54 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 0.35/0.54 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.35/0.54 (* PROOF-FOUND *) % 0.35/0.54 % SZS status Theorem % 0.35/0.54 (* BEGIN-PROOF *) % 0.35/0.54 % SZS output start Proof % 0.35/0.54 Theorem t1_xboole_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((subset A B)/\(subset B C))->(subset A C))))). % 0.35/0.54 Proof. % 0.35/0.54 apply NNPP. intro zenon_G. % 0.35/0.54 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((subset A B)/\(subset B C))->(subset A C))))) zenon_G); [ zenon_intro zenon_H13; idtac ]. % 0.35/0.54 elim zenon_H13. zenon_intro zenon_TA_u. zenon_intro zenon_H15. % 0.35/0.54 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((subset zenon_TA_u B)/\(subset B C))->(subset zenon_TA_u C)))) zenon_H15); [ zenon_intro zenon_H16; idtac ]. % 0.35/0.54 elim zenon_H16. zenon_intro zenon_TB_x. zenon_intro zenon_H18. % 0.35/0.54 apply (zenon_notallex_s (fun C : zenon_U => (((subset zenon_TA_u zenon_TB_x)/\(subset zenon_TB_x C))->(subset zenon_TA_u C))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.35/0.54 elim zenon_H19. zenon_intro zenon_TC_ba. zenon_intro zenon_H1b. % 0.35/0.54 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.35/0.54 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.35/0.54 generalize (d3_tarski zenon_TA_u). zenon_intro zenon_H20. % 0.35/0.54 generalize (zenon_H20 zenon_TB_x). zenon_intro zenon_H21. % 0.35/0.54 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H24; zenon_intro zenon_H23 | zenon_intro zenon_H1f; zenon_intro zenon_H22 ]. % 0.35/0.54 exact (zenon_H24 zenon_H1f). % 0.35/0.54 generalize (d3_tarski zenon_TB_x). zenon_intro zenon_H25. % 0.35/0.54 generalize (zenon_H25 zenon_TC_ba). zenon_intro zenon_H26. % 0.35/0.54 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H29; zenon_intro zenon_H28 | zenon_intro zenon_H1e; zenon_intro zenon_H27 ]. % 0.35/0.54 exact (zenon_H29 zenon_H1e). % 0.35/0.54 generalize (d3_tarski zenon_TA_u). zenon_intro zenon_H20. % 0.35/0.54 generalize (zenon_H20 zenon_TC_ba). zenon_intro zenon_H2a. % 0.35/0.54 apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H1c; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H2b ]. % 0.35/0.54 apply (zenon_notallex_s (fun C : zenon_U => ((in C zenon_TA_u)->(in C zenon_TC_ba))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 0.35/0.54 elim zenon_H2e. zenon_intro zenon_TC_bv. zenon_intro zenon_H30. % 0.35/0.54 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.35/0.54 generalize (zenon_H27 zenon_TC_bv). zenon_intro zenon_H33. % 0.35/0.54 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.35/0.54 generalize (zenon_H22 zenon_TC_bv). zenon_intro zenon_H36. % 0.35/0.54 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.35/0.54 exact (zenon_H38 zenon_H32). % 0.35/0.54 exact (zenon_H35 zenon_H37). % 0.35/0.54 exact (zenon_H31 zenon_H34). % 0.35/0.54 exact (zenon_H1c zenon_H2c). % 0.35/0.54 Qed. % 0.35/0.54 % SZS output end Proof % 0.35/0.54 (* END-PROOF *) % 0.35/0.54 nodes searched: 770 % 0.35/0.54 max branch formulas: 447 % 0.35/0.54 proof nodes created: 61 % 0.35/0.54 formulas created: 4837 % 0.35/0.54 %------------------------------------------------------------------------------