%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET604+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 06:37:15 EDT 2022 % Result : Theorem 0.19s 0.51s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET604+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n004.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jul 10 14:05:52 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.51 (* PROOF-FOUND *) % 0.19/0.51 % SZS status Theorem % 0.19/0.51 (* BEGIN-PROOF *) % 0.19/0.51 % SZS output start Proof % 0.19/0.51 Theorem prove_no_difference_with_empty_set : (forall B : zenon_U, ((difference (empty_set) B) = (empty_set))). % 0.19/0.51 Proof. % 0.19/0.51 apply NNPP. intro zenon_G. % 0.19/0.51 apply (zenon_notallex_s (fun B : zenon_U => ((difference (empty_set) B) = (empty_set))) zenon_G); [ zenon_intro zenon_H9; idtac ]. % 0.19/0.51 elim zenon_H9. zenon_intro zenon_TB_k. zenon_intro zenon_Hb. % 0.19/0.51 generalize (difference_empty_set (empty_set)). zenon_intro zenon_Hc. % 0.19/0.51 generalize (zenon_Hc zenon_TB_k). zenon_intro zenon_Hd. % 0.19/0.51 apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_Hb; zenon_intro zenon_H10 | zenon_intro zenon_Hf; zenon_intro zenon_He ]. % 0.19/0.51 generalize (empty_set_subset zenon_TB_k). zenon_intro zenon_He. % 0.19/0.51 exact (zenon_H10 zenon_He). % 0.19/0.51 exact (zenon_Hb zenon_Hf). % 0.19/0.51 Qed. % 0.19/0.51 % SZS output end Proof % 0.19/0.51 (* END-PROOF *) % 0.19/0.51 nodes searched: 138 % 0.19/0.51 max branch formulas: 97 % 0.19/0.51 proof nodes created: 13 % 0.19/0.51 formulas created: 857 % 0.19/0.51 %------------------------------------------------------------------------------