%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n014.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 06:34:24 EDT 2022 % Result : Theorem 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n014.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 Jul 10 00:48:05 EDT 2022 % 0.12/0.33 % CPUTime : % 0.46/0.64 (* PROOF-FOUND *) % 0.46/0.64 % SZS status Theorem % 0.46/0.64 (* BEGIN-PROOF *) % 0.46/0.64 % SZS output start Proof % 0.46/0.64 Theorem prove_th61 : (forall B : zenon_U, ((intersection B (empty_set)) = (empty_set))). % 0.46/0.64 Proof. % 0.46/0.64 assert (zenon_L1_ : forall (zenon_TD_k : zenon_U), (member zenon_TD_k (empty_set)) -> False). % 0.46/0.64 do 1 intro. intros zenon_H9. % 0.46/0.64 generalize (empty_set_defn zenon_TD_k). zenon_intro zenon_Hb. % 0.46/0.64 exact (zenon_Hb zenon_H9). % 0.46/0.64 (* end of lemma zenon_L1_ *) % 0.46/0.64 apply NNPP. intro zenon_G. % 0.46/0.64 apply (zenon_notallex_s (fun B : zenon_U => ((intersection B (empty_set)) = (empty_set))) zenon_G); [ zenon_intro zenon_Hc; idtac ]. % 0.46/0.64 elim zenon_Hc. zenon_intro zenon_TB_n. zenon_intro zenon_He. % 0.46/0.64 generalize (equal_member_defn (empty_set)). zenon_intro zenon_Hf. % 0.46/0.64 generalize (zenon_Hf (intersection zenon_TB_n (empty_set))). zenon_intro zenon_H10. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H14; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ]. % 0.46/0.64 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))<->(member D (intersection zenon_TB_n (empty_set))))) zenon_H13); [ zenon_intro zenon_H15; idtac ]. % 0.46/0.64 elim zenon_H15. zenon_intro zenon_TD_k. zenon_intro zenon_H16. % 0.46/0.64 apply (zenon_notequiv_s _ _ zenon_H16); [ zenon_intro zenon_Hb; zenon_intro zenon_H18 | zenon_intro zenon_H9; zenon_intro zenon_H17 ]. % 0.46/0.64 generalize (intersection_defn zenon_TB_n). zenon_intro zenon_H19. % 0.46/0.64 generalize (zenon_H19 (empty_set)). zenon_intro zenon_H1a. % 0.46/0.64 generalize (zenon_H1a zenon_TD_k). zenon_intro zenon_H1b. % 0.46/0.64 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H17; zenon_intro zenon_H1d | zenon_intro zenon_H18; zenon_intro zenon_H1c ]. % 0.46/0.64 exact (zenon_H17 zenon_H18). % 0.46/0.64 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H9. % 0.46/0.64 exact (zenon_Hb zenon_H9). % 0.46/0.64 apply (zenon_L1_ zenon_TD_k); trivial. % 0.46/0.64 apply zenon_He. apply sym_equal. exact zenon_H12. % 0.46/0.64 Qed. % 0.46/0.64 % SZS output end Proof % 0.46/0.64 (* END-PROOF *) % 0.46/0.64 nodes searched: 6410 % 0.46/0.64 max branch formulas: 798 % 0.46/0.64 proof nodes created: 411 % 0.46/0.64 formulas created: 15401 % 0.46/0.64 %------------------------------------------------------------------------------