%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 15:59:42 EDT 2022 % Result : Theorem 72.62s 72.81s % Output : Proof 72.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.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 : Sat Jun 18 22:34:08 EDT 2022 % 0.13/0.34 % CPUTime : % 72.62/72.81 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 72.62/72.81 (* PROOF-FOUND *) % 72.62/72.81 % SZS status Theorem % 72.62/72.81 (* BEGIN-PROOF *) % 72.62/72.81 % SZS output start Proof % 72.62/72.81 Theorem t1_zfmisc_1 : ((powerset (empty_set)) = (singleton (empty_set))). % 72.62/72.81 Proof. % 72.62/72.81 assert (zenon_L1_ : forall (zenon_TC_p : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset zenon_TC_p (empty_set))) -> (forall C : zenon_U, ((in C (singleton (empty_set)))<->(C = (empty_set)))) -> (in zenon_TC_p (singleton (empty_set))) -> False). % 72.62/72.81 do 1 intro. intros zenon_Hb zenon_Hc zenon_Hd zenon_He. % 72.62/72.81 generalize (zenon_Hb zenon_TC_p). zenon_intro zenon_H10. % 72.62/72.81 cut ((subset zenon_TC_p zenon_TC_p) = (subset zenon_TC_p (empty_set))). % 72.62/72.81 intro zenon_D_pnotp. % 72.62/72.81 apply zenon_Hc. % 72.62/72.81 rewrite <- zenon_D_pnotp. % 72.62/72.81 exact zenon_H10. % 72.62/72.81 cut ((zenon_TC_p = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H11]. % 72.62/72.81 cut ((zenon_TC_p = zenon_TC_p)); [idtac | apply NNPP; zenon_intro zenon_H12]. % 72.62/72.81 congruence. % 72.62/72.81 apply zenon_H12. apply refl_equal. % 72.62/72.81 generalize (zenon_Hd zenon_TC_p). zenon_intro zenon_H13. % 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H15; zenon_intro zenon_H11 | zenon_intro zenon_He; zenon_intro zenon_H14 ]. % 72.62/72.81 exact (zenon_H15 zenon_He). % 72.62/72.81 exact (zenon_H11 zenon_H14). % 72.62/72.81 (* end of lemma zenon_L1_ *) % 72.62/72.81 apply NNPP. intro zenon_G. % 72.62/72.81 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_Hb | zenon_intro zenon_H16 ]. % 72.62/72.81 generalize (d1_tarski (empty_set)). zenon_intro zenon_H17. % 72.62/72.81 generalize (d1_zfmisc_1 (empty_set)). zenon_intro zenon_H18. % 72.62/72.81 generalize (zenon_H17 (singleton (empty_set))). zenon_intro zenon_H19. % 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_Hd ]. % 72.62/72.81 apply zenon_H1c. apply refl_equal. % 72.62/72.81 generalize (zenon_H18 (singleton (empty_set))). zenon_intro zenon_H1d. % 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H1d); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ]. % 72.62/72.81 apply (zenon_notallex_s (fun C : zenon_U => ((in C (singleton (empty_set)))<->(subset C (empty_set)))) zenon_H20); [ zenon_intro zenon_H22; idtac ]. % 72.62/72.81 elim zenon_H22. zenon_intro zenon_TC_p. zenon_intro zenon_H23. % 72.62/72.81 apply (zenon_notequiv_s _ _ zenon_H23); [ zenon_intro zenon_H15; zenon_intro zenon_H24 | zenon_intro zenon_He; zenon_intro zenon_Hc ]. % 72.62/72.81 generalize (t3_xboole_1 zenon_TC_p). zenon_intro zenon_H25. % 72.62/72.81 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_Hc | zenon_intro zenon_H14 ]. % 72.62/72.81 exact (zenon_Hc zenon_H24). % 72.62/72.81 generalize (zenon_Hd zenon_TC_p). zenon_intro zenon_H13. % 72.62/72.81 apply (zenon_equiv_s _ _ zenon_H13); [ zenon_intro zenon_H15; zenon_intro zenon_H11 | zenon_intro zenon_He; zenon_intro zenon_H14 ]. % 72.62/72.81 exact (zenon_H11 zenon_H14). % 72.62/72.81 exact (zenon_H15 zenon_He). % 72.62/72.81 apply (zenon_L1_ zenon_TC_p); trivial. % 72.62/72.81 apply zenon_G. apply sym_equal. exact zenon_H1f. % 72.62/72.81 apply zenon_H16. zenon_intro zenon_Tx_bm. apply NNPP. zenon_intro zenon_H27. % 72.62/72.81 generalize (reflexivity_r1_tarski zenon_Tx_bm). zenon_intro zenon_H0. % 72.62/72.81 generalize (zenon_H0 zenon_E). zenon_intro zenon_H28. % 72.62/72.81 exact (zenon_H27 zenon_H28). % 72.62/72.81 Qed. % 72.62/72.81 % SZS output end Proof % 72.62/72.81 (* END-PROOF *) % 72.62/72.81 nodes searched: 1321505 % 72.62/72.81 max branch formulas: 13028 % 72.62/72.81 proof nodes created: 73236 % 72.62/72.81 formulas created: 6062416 % 72.62/72.81 %------------------------------------------------------------------------------