%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU424+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 16:02:08 EDT 2022 % Result : Theorem 0.18s 0.50s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU424+1 : TPTP v8.1.0. Released v3.4.0. % 0.04/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n004.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 : Mon Jun 20 13:30:08 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.50 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.18/0.50 (* PROOF-FOUND *) % 0.18/0.50 % SZS status Theorem % 0.18/0.50 (* BEGIN-PROOF *) % 0.18/0.50 % SZS output start Proof % 0.18/0.50 Theorem t18_relset_2 : (forall A : zenon_U, ((~(v1_xboole_0 A))->(forall B : zenon_U, (forall C : zenon_U, ((m1_subset_1 C (k1_zfmisc_1 A))->(forall D : zenon_U, ((m2_relset_1 D A B)->(m1_subset_1 (a_4_0_relset_2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))))))))). % 0.18/0.50 Proof. % 0.18/0.50 apply NNPP. intro zenon_G. % 0.18/0.50 apply (zenon_notallex_s (fun A : zenon_U => ((~(v1_xboole_0 A))->(forall B : zenon_U, (forall C : zenon_U, ((m1_subset_1 C (k1_zfmisc_1 A))->(forall D : zenon_U, ((m2_relset_1 D A B)->(m1_subset_1 (a_4_0_relset_2 A B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))))))))) zenon_G); [ zenon_intro zenon_H25; idtac ]. % 0.18/0.50 elim zenon_H25. zenon_intro zenon_TA_bm. zenon_intro zenon_H27. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.18/0.50 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, ((m1_subset_1 C (k1_zfmisc_1 zenon_TA_bm))->(forall D : zenon_U, ((m2_relset_1 D zenon_TA_bm B)->(m1_subset_1 (a_4_0_relset_2 zenon_TA_bm B C D) (k1_zfmisc_1 (k1_zfmisc_1 B)))))))) zenon_H28); [ zenon_intro zenon_H2a; idtac ]. % 0.18/0.50 elim zenon_H2a. zenon_intro zenon_TB_br. zenon_intro zenon_H2c. % 0.18/0.50 apply (zenon_notallex_s (fun C : zenon_U => ((m1_subset_1 C (k1_zfmisc_1 zenon_TA_bm))->(forall D : zenon_U, ((m2_relset_1 D zenon_TA_bm zenon_TB_br)->(m1_subset_1 (a_4_0_relset_2 zenon_TA_bm zenon_TB_br C D) (k1_zfmisc_1 (k1_zfmisc_1 zenon_TB_br))))))) zenon_H2c); [ zenon_intro zenon_H2d; idtac ]. % 0.18/0.50 elim zenon_H2d. zenon_intro zenon_TC_bu. zenon_intro zenon_H2f. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30. % 0.18/0.50 apply (zenon_notallex_s (fun D : zenon_U => ((m2_relset_1 D zenon_TA_bm zenon_TB_br)->(m1_subset_1 (a_4_0_relset_2 zenon_TA_bm zenon_TB_br zenon_TC_bu D) (k1_zfmisc_1 (k1_zfmisc_1 zenon_TB_br))))) zenon_H30); [ zenon_intro zenon_H32; idtac ]. % 0.18/0.50 elim zenon_H32. zenon_intro zenon_TD_bz. zenon_intro zenon_H34. % 0.18/0.50 apply (zenon_notimply_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.18/0.50 generalize (redefinition_m2_relset_1 zenon_TA_bm). zenon_intro zenon_H37. % 0.18/0.50 generalize (zenon_H37 zenon_TB_br). zenon_intro zenon_H38. % 0.18/0.50 generalize (zenon_H38 zenon_TD_bz). zenon_intro zenon_H39. % 0.18/0.50 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3c; zenon_intro zenon_H3b | zenon_intro zenon_H36; zenon_intro zenon_H3a ]. % 0.18/0.50 exact (zenon_H3c zenon_H36). % 0.18/0.50 generalize (s8_domain_1__e1_22__relset_2 zenon_TA_bm). zenon_intro zenon_H3d. % 0.18/0.50 generalize (zenon_H3d zenon_TB_br). zenon_intro zenon_H3e. % 0.18/0.50 generalize (zenon_H3e zenon_TC_bu). zenon_intro zenon_H3f. % 0.18/0.50 generalize (zenon_H3f zenon_TD_bz). zenon_intro zenon_H40. % 0.18/0.50 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ]. % 0.18/0.50 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.18/0.50 exact (zenon_H44 zenon_H29). % 0.18/0.50 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H3c ]. % 0.18/0.50 exact (zenon_H45 zenon_H31). % 0.18/0.50 generalize (redefinition_m2_relset_1 zenon_TA_bm). zenon_intro zenon_H37. % 0.18/0.50 generalize (zenon_H37 zenon_TB_br). zenon_intro zenon_H38. % 0.18/0.50 generalize (zenon_H38 zenon_TD_bz). zenon_intro zenon_H39. % 0.18/0.50 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3c; zenon_intro zenon_H3b | zenon_intro zenon_H36; zenon_intro zenon_H3a ]. % 0.18/0.50 exact (zenon_H3b zenon_H3a). % 0.18/0.50 exact (zenon_H3c zenon_H36). % 0.18/0.50 exact (zenon_H35 zenon_H41). % 0.18/0.50 Qed. % 0.18/0.50 % SZS output end Proof % 0.18/0.50 (* END-PROOF *) % 0.18/0.50 nodes searched: 218 % 0.18/0.50 max branch formulas: 248 % 0.18/0.50 proof nodes created: 28 % 0.18/0.50 formulas created: 1990 % 0.18/0.50 %------------------------------------------------------------------------------