%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 06:34:48 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 % 0.06/0.12 % Problem : SET194+3 : TPTP v8.1.0. Released v2.2.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n005.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 13:22:22 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_subset_of_union : (forall B : zenon_U, (forall C : zenon_U, (subset B (union B C)))). % 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 => (forall C : zenon_U, (subset B (union B C)))) zenon_G); [ zenon_intro zenon_H6; idtac ]. % 0.19/0.51 elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8. % 0.19/0.51 apply (zenon_notallex_s (fun C : zenon_U => (subset zenon_TB_h (union zenon_TB_h C))) zenon_H8); [ zenon_intro zenon_H9; idtac ]. % 0.19/0.51 elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb. % 0.19/0.51 generalize (subset_defn zenon_TB_h). zenon_intro zenon_Hc. % 0.19/0.51 generalize (zenon_Hc (union zenon_TB_h zenon_TC_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 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_h)->(member D (union zenon_TB_h zenon_TC_k)))) zenon_H10); [ zenon_intro zenon_H11; idtac ]. % 0.19/0.51 elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13. % 0.19/0.51 apply (zenon_notimply_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.19/0.51 generalize (union_defn zenon_TB_h). zenon_intro zenon_H16. % 0.19/0.51 generalize (zenon_H16 zenon_TC_k). zenon_intro zenon_H17. % 0.19/0.51 generalize (zenon_H17 zenon_TD_s). zenon_intro zenon_H18. % 0.19/0.51 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H14; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_H19 ]. % 0.19/0.51 apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.19/0.51 exact (zenon_H1d zenon_H15). % 0.19/0.51 exact (zenon_H14 zenon_H1a). % 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: 360 % 0.19/0.51 max branch formulas: 196 % 0.19/0.51 proof nodes created: 40 % 0.19/0.51 formulas created: 1755 % 0.19/0.51 %------------------------------------------------------------------------------