%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET002+3 : TPTP v8.1.0. Released v2.2.0. % 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 06:32:10 EDT 2022 % Result : Theorem 0.18s 0.53s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET002+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % 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 : Sat Jul 9 19:29:00 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.53 (* PROOF-FOUND *) % 0.18/0.53 % SZS status Theorem % 0.18/0.53 (* BEGIN-PROOF *) % 0.18/0.53 % SZS output start Proof % 0.18/0.53 Theorem prove_idempotency_of_union : (forall B : zenon_U, ((union B B) = B)). % 0.18/0.53 Proof. % 0.18/0.53 apply NNPP. intro zenon_G. % 0.18/0.53 apply (zenon_notallex_s (fun B : zenon_U => ((union B B) = B)) zenon_G); [ zenon_intro zenon_H8; idtac ]. % 0.18/0.53 elim zenon_H8. zenon_intro zenon_TB_j. zenon_intro zenon_Ha. % 0.18/0.53 generalize (equal_member_defn zenon_TB_j). zenon_intro zenon_Hb. % 0.18/0.53 generalize (zenon_Hb (union zenon_TB_j zenon_TB_j)). zenon_intro zenon_Hc. % 0.18/0.53 apply (zenon_equiv_s _ _ zenon_Hc); [ zenon_intro zenon_H10; zenon_intro zenon_Hf | zenon_intro zenon_He; zenon_intro zenon_Hd ]. % 0.18/0.53 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_j)<->(member D (union zenon_TB_j zenon_TB_j)))) zenon_Hf); [ zenon_intro zenon_H11; idtac ]. % 0.18/0.53 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13. % 0.18/0.53 apply (zenon_notequiv_s _ _ zenon_H13); [ zenon_intro zenon_H17; zenon_intro zenon_H16 | zenon_intro zenon_H15; zenon_intro zenon_H14 ]. % 0.18/0.53 generalize (union_defn zenon_TB_j). zenon_intro zenon_H18. % 0.18/0.54 generalize (zenon_H18 zenon_TB_j). zenon_intro zenon_H19. % 0.18/0.54 generalize (zenon_H19 zenon_TD_s). zenon_intro zenon_H1a. % 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H14; zenon_intro zenon_H1c | zenon_intro zenon_H16; zenon_intro zenon_H1b ]. % 0.18/0.54 exact (zenon_H14 zenon_H16). % 0.18/0.54 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H15 | zenon_intro zenon_H15 ]. % 0.18/0.54 exact (zenon_H17 zenon_H15). % 0.18/0.54 exact (zenon_H17 zenon_H15). % 0.18/0.54 generalize (union_defn zenon_TB_j). zenon_intro zenon_H18. % 0.18/0.54 generalize (zenon_H18 zenon_TB_j). zenon_intro zenon_H19. % 0.18/0.54 generalize (zenon_H19 zenon_TD_s). zenon_intro zenon_H1a. % 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H14; zenon_intro zenon_H1c | zenon_intro zenon_H16; zenon_intro zenon_H1b ]. % 0.18/0.54 apply (zenon_notor_s _ _ zenon_H1c). zenon_intro zenon_H17. zenon_intro zenon_H17. % 0.18/0.54 exact (zenon_H17 zenon_H15). % 0.18/0.54 exact (zenon_H14 zenon_H16). % 0.18/0.54 apply zenon_Ha. apply sym_equal. exact zenon_He. % 0.18/0.54 Qed. % 0.18/0.54 % SZS output end Proof % 0.18/0.54 (* END-PROOF *) % 0.18/0.54 nodes searched: 886 % 0.18/0.54 max branch formulas: 324 % 0.18/0.54 proof nodes created: 105 % 0.18/0.54 formulas created: 3479 % 0.18/0.54 %------------------------------------------------------------------------------