%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU250+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n029.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 16:00:36 EDT 2022 % Result : Theorem 0.36s 0.53s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU250+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n029.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 : Mon Jun 20 11:57:00 EDT 2022 % 0.13/0.34 % CPUTime : % 0.36/0.53 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 0.36/0.53 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 0.36/0.53 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.36/0.53 (* PROOF-FOUND *) % 0.36/0.53 % SZS status Theorem % 0.36/0.53 (* BEGIN-PROOF *) % 0.36/0.53 % SZS output start Proof % 0.36/0.53 Theorem t20_wellord1 : (forall A : zenon_U, (forall B : zenon_U, ((relation B)->((subset (relation_field (relation_restriction B A)) (relation_field B))/\(subset (relation_field (relation_restriction B A)) A))))). % 0.36/0.53 Proof. % 0.36/0.53 apply NNPP. intro zenon_G. % 0.36/0.53 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((relation B)->((subset (relation_field (relation_restriction B A)) (relation_field B))/\(subset (relation_field (relation_restriction B A)) A))))) zenon_G); [ zenon_intro zenon_H22; idtac ]. % 0.36/0.53 elim zenon_H22. zenon_intro zenon_TA_bj. zenon_intro zenon_H24. % 0.36/0.53 apply (zenon_notallex_s (fun B : zenon_U => ((relation B)->((subset (relation_field (relation_restriction B zenon_TA_bj)) (relation_field B))/\(subset (relation_field (relation_restriction B zenon_TA_bj)) zenon_TA_bj)))) zenon_H24); [ zenon_intro zenon_H25; idtac ]. % 0.36/0.53 elim zenon_H25. zenon_intro zenon_TB_bm. zenon_intro zenon_H27. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.36/0.53 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.36/0.53 generalize (d3_tarski (relation_field (relation_restriction zenon_TB_bm zenon_TA_bj))). zenon_intro zenon_H2c. % 0.36/0.53 generalize (zenon_H2c (relation_field zenon_TB_bm)). zenon_intro zenon_H2d. % 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ]. % 0.36/0.53 apply (zenon_notallex_s (fun C : zenon_U => ((in C (relation_field (relation_restriction zenon_TB_bm zenon_TA_bj)))->(in C (relation_field zenon_TB_bm)))) zenon_H30); [ zenon_intro zenon_H31; idtac ]. % 0.36/0.53 elim zenon_H31. zenon_intro zenon_TC_by. zenon_intro zenon_H33. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.36/0.53 generalize (t19_wellord1 zenon_TC_by). zenon_intro zenon_H36. % 0.36/0.53 generalize (zenon_H36 zenon_TA_bj). zenon_intro zenon_H37. % 0.36/0.53 generalize (zenon_H37 zenon_TB_bm). zenon_intro zenon_H38. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.36/0.53 exact (zenon_H3a zenon_H29). % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.36/0.53 exact (zenon_H3c zenon_H35). % 0.36/0.53 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.36/0.53 exact (zenon_H34 zenon_H3e). % 0.36/0.53 exact (zenon_H2b zenon_H2f). % 0.36/0.53 generalize (d3_tarski (relation_field (relation_restriction zenon_TB_bm zenon_TA_bj))). zenon_intro zenon_H2c. % 0.36/0.53 generalize (zenon_H2c zenon_TA_bj). zenon_intro zenon_H3f. % 0.36/0.53 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H2a; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 0.36/0.53 apply (zenon_notallex_s (fun C : zenon_U => ((in C (relation_field (relation_restriction zenon_TB_bm zenon_TA_bj)))->(in C zenon_TA_bj))) zenon_H42); [ zenon_intro zenon_H43; idtac ]. % 0.36/0.53 elim zenon_H43. zenon_intro zenon_TC_cq. zenon_intro zenon_H45. % 0.36/0.53 apply (zenon_notimply_s _ _ zenon_H45). zenon_intro zenon_H47. zenon_intro zenon_H46. % 0.36/0.53 generalize (t19_wellord1 zenon_TC_cq). zenon_intro zenon_H48. % 0.36/0.53 generalize (zenon_H48 zenon_TA_bj). zenon_intro zenon_H49. % 0.36/0.53 generalize (zenon_H49 zenon_TB_bm). zenon_intro zenon_H4a. % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H3a | zenon_intro zenon_H4b ]. % 0.36/0.53 exact (zenon_H3a zenon_H29). % 0.36/0.53 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 0.36/0.53 exact (zenon_H4d zenon_H47). % 0.36/0.53 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4f. zenon_intro zenon_H4e. % 0.36/0.53 exact (zenon_H46 zenon_H4e). % 0.36/0.53 exact (zenon_H2a zenon_H41). % 0.36/0.53 Qed. % 0.36/0.53 % SZS output end Proof % 0.36/0.53 (* END-PROOF *) % 0.36/0.53 nodes searched: 669 % 0.36/0.53 max branch formulas: 348 % 0.36/0.53 proof nodes created: 80 % 0.36/0.53 formulas created: 4009 % 0.36/0.53 %------------------------------------------------------------------------------