%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU123+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 15:59:30 EDT 2022 % Result : Theorem 0.20s 0.59s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU123+2 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n015.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 17:08:14 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.59 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 0.20/0.59 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.20/0.59 (* PROOF-FOUND *) % 0.20/0.59 % SZS status Theorem % 0.20/0.59 (* BEGIN-PROOF *) % 0.20/0.59 % SZS output start Proof % 0.20/0.59 Theorem t3_xboole_1 : (forall A : zenon_U, ((subset A (empty_set))->(A = (empty_set)))). % 0.20/0.59 Proof. % 0.20/0.59 apply NNPP. intro zenon_G. % 0.20/0.59 apply (zenon_notallex_s (fun A : zenon_U => ((subset A (empty_set))->(A = (empty_set)))) zenon_G); [ zenon_intro zenon_H16; idtac ]. % 0.20/0.59 elim zenon_H16. zenon_intro zenon_TA_x. zenon_intro zenon_H18. % 0.20/0.59 apply (zenon_notimply_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.20/0.59 generalize (d3_tarski zenon_TA_x). zenon_intro zenon_H1b. % 0.20/0.59 generalize (zenon_H1b (empty_set)). zenon_intro zenon_H1c. % 0.20/0.59 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H1a; zenon_intro zenon_H1d ]. % 0.20/0.59 exact (zenon_H1f zenon_H1a). % 0.20/0.59 generalize (d10_xboole_0 (empty_set)). zenon_intro zenon_H20. % 0.20/0.59 generalize (t2_xboole_1 zenon_TA_x). zenon_intro zenon_H21. % 0.20/0.59 generalize (d3_tarski (empty_set)). zenon_intro zenon_H22. % 0.20/0.59 generalize (zenon_H22 zenon_TA_x). zenon_intro zenon_H23. % 0.20/0.59 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H21; zenon_intro zenon_H24 ]. % 0.20/0.59 exact (zenon_H26 zenon_H21). % 0.20/0.59 generalize (zenon_H20 zenon_TA_x). zenon_intro zenon_H27. % 0.20/0.59 apply (zenon_equiv_s _ _ zenon_H27); [ zenon_intro zenon_H2b; zenon_intro zenon_H2a | zenon_intro zenon_H29; zenon_intro zenon_H28 ]. % 0.20/0.59 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H26 | zenon_intro zenon_H1f ]. % 0.20/0.59 generalize (d3_tarski (empty_set)). zenon_intro zenon_H22. % 0.20/0.59 generalize (zenon_H22 zenon_TA_x). zenon_intro zenon_H23. % 0.20/0.59 apply (zenon_equiv_s _ _ zenon_H23); [ zenon_intro zenon_H26; zenon_intro zenon_H25 | zenon_intro zenon_H21; zenon_intro zenon_H24 ]. % 0.20/0.59 exact (zenon_H25 zenon_H24). % 0.20/0.59 exact (zenon_H26 zenon_H21). % 0.20/0.59 generalize (d3_tarski zenon_TA_x). zenon_intro zenon_H1b. % 0.20/0.59 generalize (zenon_H1b (empty_set)). zenon_intro zenon_H1c. % 0.20/0.59 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1f; zenon_intro zenon_H1e | zenon_intro zenon_H1a; zenon_intro zenon_H1d ]. % 0.20/0.59 exact (zenon_H1e zenon_H1d). % 0.20/0.59 exact (zenon_H1f zenon_H1a). % 0.20/0.59 apply zenon_H19. apply sym_equal. exact zenon_H29. % 0.20/0.59 Qed. % 0.20/0.59 % SZS output end Proof % 0.20/0.59 (* END-PROOF *) % 0.20/0.59 nodes searched: 2313 % 0.20/0.59 max branch formulas: 544 % 0.20/0.59 proof nodes created: 158 % 0.20/0.59 formulas created: 10969 % 0.20/0.59 %------------------------------------------------------------------------------