%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 16:00:33 EDT 2022 % Result : Theorem 2.94s 3.15s % Output : Proof 2.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SEU243+1 : TPTP v8.1.0. Released v3.3.0. % 0.13/0.14 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n010.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sun Jun 19 20:11:07 EDT 2022 % 0.13/0.35 % CPUTime : % 2.94/3.15 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 2.94/3.15 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 2.94/3.15 (* PROOF-FOUND *) % 2.94/3.15 % SZS status Theorem % 2.94/3.15 (* BEGIN-PROOF *) % 2.94/3.15 % SZS output start Proof % 2.94/3.15 Theorem t5_wellord1 : (forall A : zenon_U, ((relation A)->((well_founded_relation A)<->(is_well_founded_in A (relation_field A))))). % 2.94/3.15 Proof. % 2.94/3.15 apply NNPP. intro zenon_G. % 2.94/3.15 apply (zenon_notallex_s (fun A : zenon_U => ((relation A)->((well_founded_relation A)<->(is_well_founded_in A (relation_field A))))) zenon_G); [ zenon_intro zenon_H1e; idtac ]. % 2.94/3.15 elim zenon_H1e. zenon_intro zenon_TA_bf. zenon_intro zenon_H20. % 2.94/3.15 apply (zenon_notimply_s _ _ zenon_H20). zenon_intro zenon_H22. zenon_intro zenon_H21. % 2.94/3.15 apply (zenon_notequiv_s _ _ zenon_H21); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H24; zenon_intro zenon_H23 ]. % 2.94/3.15 generalize (d2_wellord1 zenon_TA_bf). zenon_intro zenon_H27. % 2.94/3.15 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 2.94/3.15 exact (zenon_H29 zenon_H22). % 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H26; zenon_intro zenon_H2b | zenon_intro zenon_H24; zenon_intro zenon_H2a ]. % 2.94/3.15 generalize (d3_wellord1 zenon_TA_bf). zenon_intro zenon_H2c. % 2.94/3.15 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H29 | zenon_intro zenon_H2d ]. % 2.94/3.15 exact (zenon_H29 zenon_H22). % 2.94/3.15 generalize (zenon_H2d (relation_field zenon_TA_bf)). zenon_intro zenon_H2e. % 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H23; zenon_intro zenon_H2b | zenon_intro zenon_H25; zenon_intro zenon_H2a ]. % 2.94/3.15 exact (zenon_H23 zenon_H25). % 2.94/3.15 exact (zenon_H2b zenon_H2a). % 2.94/3.15 exact (zenon_H26 zenon_H24). % 2.94/3.15 generalize (d3_wellord1 zenon_TA_bf). zenon_intro zenon_H2c. % 2.94/3.15 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H29 | zenon_intro zenon_H2d ]. % 2.94/3.15 exact (zenon_H29 zenon_H22). % 2.94/3.15 generalize (zenon_H2d (relation_field zenon_TA_bf)). zenon_intro zenon_H2e. % 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H23; zenon_intro zenon_H2b | zenon_intro zenon_H25; zenon_intro zenon_H2a ]. % 2.94/3.15 generalize (d2_wellord1 zenon_TA_bf). zenon_intro zenon_H27. % 2.94/3.15 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 2.94/3.15 exact (zenon_H29 zenon_H22). % 2.94/3.15 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H26; zenon_intro zenon_H2b | zenon_intro zenon_H24; zenon_intro zenon_H2a ]. % 2.94/3.15 exact (zenon_H26 zenon_H24). % 2.94/3.15 exact (zenon_H2b zenon_H2a). % 2.94/3.15 exact (zenon_H23 zenon_H25). % 2.94/3.15 Qed. % 2.94/3.15 % SZS output end Proof % 2.94/3.15 (* END-PROOF *) % 2.94/3.15 nodes searched: 69222 % 2.94/3.15 max branch formulas: 6525 % 2.94/3.15 proof nodes created: 2284 % 2.94/3.15 formulas created: 219411 % 2.94/3.15 %------------------------------------------------------------------------------