%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 06:39:26 EDT 2022 % Result : Theorem 1.20s 1.42s % Output : Proof 1.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET891+1 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n018.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 15:58:28 EDT 2022 % 0.12/0.34 % CPUTime : % 1.20/1.42 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 1.20/1.42 (* PROOF-FOUND *) % 1.20/1.42 % SZS status Theorem % 1.20/1.42 (* BEGIN-PROOF *) % 1.20/1.42 % SZS output start Proof % 1.20/1.42 Theorem t32_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((union (unordered_pair (singleton A) (singleton B))) = (unordered_pair A B)))). % 1.20/1.42 Proof. % 1.20/1.42 apply NNPP. intro zenon_G. % 1.20/1.42 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((union (unordered_pair (singleton A) (singleton B))) = (unordered_pair A B)))) zenon_G); [ zenon_intro zenon_Ha; idtac ]. % 1.20/1.42 elim zenon_Ha. zenon_intro zenon_TA_l. zenon_intro zenon_Hc. % 1.20/1.42 apply (zenon_notallex_s (fun B : zenon_U => ((union (unordered_pair (singleton zenon_TA_l) (singleton B))) = (unordered_pair zenon_TA_l B))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ]. % 1.20/1.42 elim zenon_Hd. zenon_intro zenon_TB_o. zenon_intro zenon_Hf. % 1.20/1.42 generalize (t41_enumset1 zenon_TA_l). zenon_intro zenon_H10. % 1.20/1.42 generalize (zenon_H10 zenon_TB_o). zenon_intro zenon_H11. % 1.20/1.42 apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (~((union (unordered_pair (singleton zenon_TA_l) (singleton zenon_TB_o))) = zenon_Vg))) _ _ zenon_Hf zenon_H11). zenon_intro zenon_H12. % 1.20/1.42 generalize (l52_zfmisc_1 (singleton zenon_TA_l)). zenon_intro zenon_H13. % 1.20/1.42 generalize (zenon_H13 (singleton zenon_TB_o)). zenon_intro zenon_H14. % 1.20/1.42 exact (zenon_H12 zenon_H14). % 1.20/1.42 Qed. % 1.20/1.42 % SZS output end Proof % 1.20/1.42 (* END-PROOF *) % 1.20/1.42 nodes searched: 6161 % 1.20/1.42 max branch formulas: 791 % 1.20/1.42 proof nodes created: 217 % 1.20/1.42 formulas created: 29184 % 1.20/1.42 %------------------------------------------------------------------------------