%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU147+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 15:59:41 EDT 2022 % Result : Theorem 83.79s 84.04s % Output : Proof 83.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU147+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n012.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 02:14:22 EDT 2022 % 0.12/0.34 % CPUTime : % 83.79/84.04 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 83.79/84.04 (* PROOF-FOUND *) % 83.79/84.04 % SZS status Theorem % 83.79/84.04 (* BEGIN-PROOF *) % 83.79/84.04 % SZS output start Proof % 83.79/84.04 Theorem t1_zfmisc_1 : ((powerset (empty_set)) = (singleton (empty_set))). % 83.79/84.04 Proof. % 83.79/84.04 assert (zenon_L1_ : forall (zenon_TC_q : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset zenon_TC_q (empty_set))) -> (forall C : zenon_U, ((in C (singleton (empty_set)))<->(C = (empty_set)))) -> (in zenon_TC_q (singleton (empty_set))) -> False). % 83.79/84.04 do 1 intro. intros zenon_Hc zenon_Hd zenon_He zenon_Hf. % 83.79/84.04 generalize (zenon_Hc zenon_TC_q). zenon_intro zenon_H11. % 83.79/84.04 cut ((subset zenon_TC_q zenon_TC_q) = (subset zenon_TC_q (empty_set))). % 83.79/84.04 intro zenon_D_pnotp. % 83.79/84.04 apply zenon_Hd. % 83.79/84.04 rewrite <- zenon_D_pnotp. % 83.79/84.04 exact zenon_H11. % 83.79/84.04 cut ((zenon_TC_q = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 83.79/84.04 cut ((zenon_TC_q = zenon_TC_q)); [idtac | apply NNPP; zenon_intro zenon_H13]. % 83.79/84.04 congruence. % 83.79/84.04 apply zenon_H13. apply refl_equal. % 83.79/84.04 generalize (zenon_He zenon_TC_q). zenon_intro zenon_H14. % 83.79/84.04 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H16; zenon_intro zenon_H12 | zenon_intro zenon_Hf; zenon_intro zenon_H15 ]. % 83.79/84.04 exact (zenon_H16 zenon_Hf). % 83.79/84.04 exact (zenon_H12 zenon_H15). % 83.79/84.04 (* end of lemma zenon_L1_ *) % 83.79/84.04 apply NNPP. intro zenon_G. % 83.79/84.04 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_Hc | zenon_intro zenon_H17 ]. % 83.79/84.04 generalize (d1_tarski (empty_set)). zenon_intro zenon_H18. % 83.79/84.04 generalize (d1_zfmisc_1 (empty_set)). zenon_intro zenon_H19. % 83.79/84.04 generalize (zenon_H18 (singleton (empty_set))). zenon_intro zenon_H1a. % 83.79/84.04 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H1d; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_He ]. % 83.79/84.04 apply zenon_H1d. apply refl_equal. % 83.79/84.04 generalize (zenon_H19 (singleton (empty_set))). zenon_intro zenon_H1e. % 83.79/84.04 apply (zenon_equiv_s _ _ zenon_H1e); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H20; zenon_intro zenon_H1f ]. % 83.79/84.04 apply (zenon_notallex_s (fun C : zenon_U => ((in C (singleton (empty_set)))<->(subset C (empty_set)))) zenon_H21); [ zenon_intro zenon_H23; idtac ]. % 83.79/84.04 elim zenon_H23. zenon_intro zenon_TC_q. zenon_intro zenon_H24. % 83.79/84.04 apply (zenon_notequiv_s _ _ zenon_H24); [ zenon_intro zenon_H16; zenon_intro zenon_H25 | zenon_intro zenon_Hf; zenon_intro zenon_Hd ]. % 83.79/84.04 generalize (t3_xboole_1 zenon_TC_q). zenon_intro zenon_H26. % 83.79/84.04 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_Hd | zenon_intro zenon_H15 ]. % 83.79/84.04 exact (zenon_Hd zenon_H25). % 83.79/84.04 generalize (zenon_He zenon_TC_q). zenon_intro zenon_H14. % 83.79/84.04 apply (zenon_equiv_s _ _ zenon_H14); [ zenon_intro zenon_H16; zenon_intro zenon_H12 | zenon_intro zenon_Hf; zenon_intro zenon_H15 ]. % 83.79/84.04 exact (zenon_H12 zenon_H15). % 83.79/84.04 exact (zenon_H16 zenon_Hf). % 83.79/84.04 apply (zenon_L1_ zenon_TC_q); trivial. % 83.79/84.04 apply zenon_G. apply sym_equal. exact zenon_H20. % 83.79/84.04 apply zenon_H17. zenon_intro zenon_Tx_bn. apply NNPP. zenon_intro zenon_H28. % 83.79/84.04 generalize (reflexivity_r1_tarski zenon_Tx_bn). zenon_intro zenon_H0. % 83.79/84.04 generalize (zenon_H0 zenon_E). zenon_intro zenon_H29. % 83.79/84.04 exact (zenon_H28 zenon_H29). % 83.79/84.04 Qed. % 83.79/84.04 % SZS output end Proof % 83.79/84.04 (* END-PROOF *) % 83.79/84.04 nodes searched: 1321505 % 83.79/84.04 max branch formulas: 13028 % 83.79/84.04 proof nodes created: 73236 % 83.79/84.04 formulas created: 5945424 % 83.79/84.04 %------------------------------------------------------------------------------