%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n007.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 06:39:18 EDT 2022 % Result : Theorem 0.88s 1.06s % Output : Proof 0.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET867+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n007.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jul 11 02:06:32 EDT 2022 % 0.13/0.34 % CPUTime : % 0.88/1.06 (* PROOF-FOUND *) % 0.88/1.06 % SZS status Theorem % 0.88/1.06 (* BEGIN-PROOF *) % 0.88/1.06 % SZS output start Proof % 0.88/1.06 Theorem t2_zfmisc_1 : ((union (empty_set)) = (empty_set)). % 0.88/1.06 Proof. % 0.88/1.06 assert (zenon_L1_ : (~((empty_set) = (empty_set))) -> False). % 0.88/1.06 do 0 intro. intros zenon_H7. % 0.88/1.06 apply zenon_H7. apply refl_equal. % 0.88/1.06 (* end of lemma zenon_L1_ *) % 0.88/1.06 apply NNPP. intro zenon_G. % 0.88/1.06 generalize (d4_tarski (empty_set)). zenon_intro zenon_H8. % 0.88/1.06 generalize (zenon_H8 (empty_set)). zenon_intro zenon_H9. % 0.88/1.06 apply (zenon_equiv_s _ _ zenon_H9); [ zenon_intro zenon_Hd; zenon_intro zenon_Hc | zenon_intro zenon_Hb; zenon_intro zenon_Ha ]. % 0.88/1.06 apply (zenon_notallex_s (fun C : zenon_U => ((in C (empty_set))<->(exists D : zenon_U, ((in C D)/\(in D (empty_set)))))) zenon_Hc); [ zenon_intro zenon_He; idtac ]. % 0.88/1.06 elim zenon_He. zenon_intro zenon_TC_p. zenon_intro zenon_H10. % 0.88/1.06 apply (zenon_notequiv_s _ _ zenon_H10); [ zenon_intro zenon_H14; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.88/1.06 elim zenon_H13. zenon_intro zenon_TD_v. zenon_intro zenon_H16. % 0.88/1.06 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.88/1.06 generalize (d1_xboole_0 (empty_set)). zenon_intro zenon_H19. % 0.88/1.06 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H7; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ]. % 0.88/1.06 apply zenon_H7. apply refl_equal. % 0.88/1.06 generalize (zenon_H1a zenon_TD_v). zenon_intro zenon_H1d. % 0.88/1.06 exact (zenon_H1d zenon_H17). % 0.88/1.06 generalize (d1_xboole_0 (empty_set)). zenon_intro zenon_H19. % 0.88/1.06 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H7; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ]. % 0.88/1.06 apply zenon_H7. apply refl_equal. % 0.88/1.06 generalize (zenon_H1a zenon_TC_p). zenon_intro zenon_H14. % 0.88/1.06 exact (zenon_H14 zenon_H12). % 0.88/1.06 apply zenon_G. apply sym_equal. exact zenon_Hb. % 0.88/1.06 Qed. % 0.88/1.06 % SZS output end Proof % 0.88/1.06 (* END-PROOF *) % 0.88/1.06 nodes searched: 26059 % 0.88/1.06 max branch formulas: 1667 % 0.88/1.06 proof nodes created: 2493 % 0.88/1.06 formulas created: 95856 % 0.88/1.06 %------------------------------------------------------------------------------