%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 16:00:32 EDT 2022 % Result : Theorem 0.39s 0.58s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SEU242+1 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n017.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 21:09:28 EDT 2022 % 0.12/0.33 % CPUTime : % 0.39/0.58 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 0.39/0.58 (* PROOF-FOUND *) % 0.39/0.58 % SZS status Theorem % 0.39/0.58 (* BEGIN-PROOF *) % 0.39/0.58 % SZS output start Proof % 0.39/0.58 Theorem l4_wellord1 : (forall A : zenon_U, ((relation A)->((connected A)<->(forall B : zenon_U, (forall C : zenon_U, (~((in B (relation_field A))/\((in C (relation_field A))/\((~(B = C))/\((~(in (ordered_pair B C) A))/\(~(in (ordered_pair C B) A)))))))))))). % 0.39/0.58 Proof. % 0.39/0.58 apply NNPP. intro zenon_G. % 0.39/0.58 apply (zenon_notallex_s (fun A : zenon_U => ((relation A)->((connected A)<->(forall B : zenon_U, (forall C : zenon_U, (~((in B (relation_field A))/\((in C (relation_field A))/\((~(B = C))/\((~(in (ordered_pair B C) A))/\(~(in (ordered_pair C B) A)))))))))))) zenon_G); [ zenon_intro zenon_H1c; idtac ]. % 0.39/0.58 elim zenon_H1c. zenon_intro zenon_TA_bd. zenon_intro zenon_H1e. % 0.39/0.58 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.39/0.58 apply (zenon_notequiv_s _ _ zenon_H1f); [ zenon_intro zenon_H24; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ]. % 0.39/0.58 generalize (d14_relat_2 zenon_TA_bd). zenon_intro zenon_H25. % 0.39/0.58 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.39/0.58 exact (zenon_H27 zenon_H20). % 0.39/0.58 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H24; zenon_intro zenon_H29 | zenon_intro zenon_H22; zenon_intro zenon_H28 ]. % 0.39/0.58 generalize (d6_relat_2 zenon_TA_bd). zenon_intro zenon_H2a. % 0.39/0.58 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H27 | zenon_intro zenon_H2b ]. % 0.39/0.58 exact (zenon_H27 zenon_H20). % 0.39/0.58 generalize (zenon_H2b (relation_field zenon_TA_bd)). zenon_intro zenon_H2c. % 0.39/0.58 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H29; zenon_intro zenon_H21 | zenon_intro zenon_H28; zenon_intro zenon_H23 ]. % 0.39/0.58 exact (zenon_H21 zenon_H23). % 0.39/0.58 exact (zenon_H29 zenon_H28). % 0.39/0.58 exact (zenon_H24 zenon_H22). % 0.39/0.58 generalize (d6_relat_2 zenon_TA_bd). zenon_intro zenon_H2a. % 0.39/0.58 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H27 | zenon_intro zenon_H2b ]. % 0.39/0.58 exact (zenon_H27 zenon_H20). % 0.39/0.58 generalize (zenon_H2b (relation_field zenon_TA_bd)). zenon_intro zenon_H2c. % 0.39/0.58 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H29; zenon_intro zenon_H21 | zenon_intro zenon_H28; zenon_intro zenon_H23 ]. % 0.39/0.58 generalize (d14_relat_2 zenon_TA_bd). zenon_intro zenon_H25. % 0.39/0.58 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.39/0.58 exact (zenon_H27 zenon_H20). % 0.39/0.58 apply (zenon_equiv_s _ _ zenon_H26); [ zenon_intro zenon_H24; zenon_intro zenon_H29 | zenon_intro zenon_H22; zenon_intro zenon_H28 ]. % 0.39/0.58 exact (zenon_H24 zenon_H22). % 0.39/0.58 exact (zenon_H29 zenon_H28). % 0.39/0.58 exact (zenon_H21 zenon_H23). % 0.39/0.58 Qed. % 0.39/0.58 % SZS output end Proof % 0.39/0.58 (* END-PROOF *) % 0.39/0.58 nodes searched: 3461 % 0.39/0.58 max branch formulas: 870 % 0.39/0.58 proof nodes created: 324 % 0.39/0.58 formulas created: 15122 % 0.39/0.58 %------------------------------------------------------------------------------