%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 15:59:26 EDT 2022 % Result : Theorem 0.19s 0.49s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n010.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 : Sun Jun 19 08:51:07 EDT 2022 % 0.12/0.33 % CPUTime : % 0.19/0.49 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.19/0.49 (* PROOF-FOUND *) % 0.19/0.49 % SZS status Theorem % 0.19/0.49 (* BEGIN-PROOF *) % 0.19/0.49 % SZS output start Proof % 0.19/0.49 Theorem t28_finsub_1 : ((finite_subsets (empty_set)) = (singleton (empty_set))). % 0.19/0.49 Proof. % 0.19/0.49 apply NNPP. intro zenon_G. % 0.19/0.49 cut (((powerset (empty_set)) = (singleton (empty_set))) = ((finite_subsets (empty_set)) = (singleton (empty_set)))). % 0.19/0.49 intro zenon_D_pnotp. % 0.19/0.49 apply zenon_G. % 0.19/0.49 rewrite <- zenon_D_pnotp. % 0.19/0.49 exact t1_zfmisc_1. % 0.19/0.49 cut (((singleton (empty_set)) = (singleton (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 0.19/0.49 cut (((powerset (empty_set)) = (finite_subsets (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 0.19/0.49 congruence. % 0.19/0.49 elim (classic ((finite_subsets (empty_set)) = (finite_subsets (empty_set)))); [ zenon_intro zenon_H24 | zenon_intro zenon_H25 ]. % 0.19/0.49 cut (((finite_subsets (empty_set)) = (finite_subsets (empty_set))) = ((powerset (empty_set)) = (finite_subsets (empty_set)))). % 0.19/0.49 intro zenon_D_pnotp. % 0.19/0.49 apply zenon_H23. % 0.19/0.49 rewrite <- zenon_D_pnotp. % 0.19/0.49 exact zenon_H24. % 0.19/0.49 cut (((finite_subsets (empty_set)) = (finite_subsets (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.19/0.49 cut (((finite_subsets (empty_set)) = (powerset (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 0.19/0.49 congruence. % 0.19/0.49 generalize (t27_finsub_1 (empty_set)). zenon_intro zenon_H27. % 0.19/0.49 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.19/0.49 generalize (cc1_finset_1 (empty_set)). zenon_intro zenon_H2a. % 0.19/0.49 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.19/0.49 exact (zenon_H2c fc1_xboole_0). % 0.19/0.49 exact (zenon_H29 zenon_H2b). % 0.19/0.49 exact (zenon_H26 zenon_H28). % 0.19/0.49 apply zenon_H25. apply refl_equal. % 0.19/0.49 apply zenon_H25. apply refl_equal. % 0.19/0.49 apply zenon_H22. apply refl_equal. % 0.19/0.49 Qed. % 0.19/0.49 % SZS output end Proof % 0.19/0.49 (* END-PROOF *) % 0.19/0.49 nodes searched: 183 % 0.19/0.49 max branch formulas: 195 % 0.19/0.49 proof nodes created: 20 % 0.19/0.49 formulas created: 1303 % 0.19/0.49 %------------------------------------------------------------------------------