%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET797+4 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 06:38:38 EDT 2022 % Result : Theorem 0.18s 0.54s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET797+4 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n021.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 : Sat Jul 9 23:00:36 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.54 (* PROOF-FOUND *) % 0.18/0.54 % SZS status Theorem % 0.18/0.54 (* BEGIN-PROOF *) % 0.18/0.54 % SZS output start Proof % 0.18/0.54 Theorem thIV9 : (forall R : zenon_U, (forall E : zenon_U, ((order R E)->(forall X : zenon_U, (forall Y : zenon_U, (((subset X E)/\((subset Y E)/\(subset X Y)))->(forall M : zenon_U, ((upper_bound M R Y)->(upper_bound M R X))))))))). % 0.18/0.54 Proof. % 0.18/0.54 apply NNPP. intro zenon_G. % 0.18/0.54 apply (zenon_notallex_s (fun R : zenon_U => (forall E : zenon_U, ((order R E)->(forall X : zenon_U, (forall Y : zenon_U, (((subset X E)/\((subset Y E)/\(subset X Y)))->(forall M : zenon_U, ((upper_bound M R Y)->(upper_bound M R X))))))))) zenon_G); [ zenon_intro zenon_H16; idtac ]. % 0.18/0.54 elim zenon_H16. zenon_intro zenon_TR_x. zenon_intro zenon_H18. % 0.18/0.54 apply (zenon_notallex_s (fun E : zenon_U => ((order zenon_TR_x E)->(forall X : zenon_U, (forall Y : zenon_U, (((subset X E)/\((subset Y E)/\(subset X Y)))->(forall M : zenon_U, ((upper_bound M zenon_TR_x Y)->(upper_bound M zenon_TR_x X)))))))) zenon_H18); [ zenon_intro zenon_H19; idtac ]. % 0.18/0.54 elim zenon_H19. zenon_intro zenon_TE_ba. zenon_intro zenon_H1b. % 0.18/0.54 apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.18/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((subset X zenon_TE_ba)/\((subset Y zenon_TE_ba)/\(subset X Y)))->(forall M : zenon_U, ((upper_bound M zenon_TR_x Y)->(upper_bound M zenon_TR_x X)))))) zenon_H1c); [ zenon_intro zenon_H1e; idtac ]. % 0.18/0.54 elim zenon_H1e. zenon_intro zenon_TX_bf. zenon_intro zenon_H20. % 0.18/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (((subset zenon_TX_bf zenon_TE_ba)/\((subset Y zenon_TE_ba)/\(subset zenon_TX_bf Y)))->(forall M : zenon_U, ((upper_bound M zenon_TR_x Y)->(upper_bound M zenon_TR_x zenon_TX_bf))))) zenon_H20); [ zenon_intro zenon_H21; idtac ]. % 0.18/0.54 elim zenon_H21. zenon_intro zenon_TY_bi. zenon_intro zenon_H23. % 0.18/0.54 apply (zenon_notimply_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.18/0.54 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.18/0.54 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.18/0.54 generalize (subset zenon_TX_bf). zenon_intro zenon_H2a. % 0.18/0.54 generalize (zenon_H2a zenon_TY_bi). zenon_intro zenon_H2b. % 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H28; zenon_intro zenon_H2c ]. % 0.18/0.54 exact (zenon_H2e zenon_H28). % 0.18/0.54 apply (zenon_notallex_s (fun M : zenon_U => ((upper_bound M zenon_TR_x zenon_TY_bi)->(upper_bound M zenon_TR_x zenon_TX_bf))) zenon_H24); [ zenon_intro zenon_H2f; idtac ]. % 0.18/0.54 elim zenon_H2f. zenon_intro zenon_TM_bw. zenon_intro zenon_H31. % 0.18/0.54 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.18/0.54 generalize (upper_bound zenon_TR_x). zenon_intro zenon_H34. % 0.18/0.54 generalize (zenon_H34 zenon_TY_bi). zenon_intro zenon_H35. % 0.18/0.54 generalize (zenon_H35 zenon_TM_bw). zenon_intro zenon_H36. % 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H36); [ zenon_intro zenon_H39; zenon_intro zenon_H38 | zenon_intro zenon_H33; zenon_intro zenon_H37 ]. % 0.18/0.54 exact (zenon_H39 zenon_H33). % 0.18/0.54 generalize (upper_bound zenon_TR_x). zenon_intro zenon_H34. % 0.18/0.54 generalize (zenon_H34 zenon_TX_bf). zenon_intro zenon_H3a. % 0.18/0.54 generalize (zenon_H3a zenon_TM_bw). zenon_intro zenon_H3b. % 0.18/0.54 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H32; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H3c ]. % 0.18/0.54 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TX_bf)->(apply zenon_TR_x X zenon_TM_bw))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ]. % 0.18/0.54 elim zenon_H3f. zenon_intro zenon_TX_cm. zenon_intro zenon_H41. % 0.18/0.54 apply (zenon_notimply_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.18/0.54 generalize (zenon_H37 zenon_TX_cm). zenon_intro zenon_H44. % 0.18/0.54 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.18/0.54 generalize (zenon_H2c zenon_TX_cm). zenon_intro zenon_H47. % 0.18/0.54 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.18/0.54 exact (zenon_H49 zenon_H43). % 0.18/0.54 exact (zenon_H46 zenon_H48). % 0.18/0.54 exact (zenon_H42 zenon_H45). % 0.18/0.54 exact (zenon_H32 zenon_H3d). % 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: 1078 % 0.18/0.54 max branch formulas: 742 % 0.18/0.54 proof nodes created: 72 % 0.18/0.54 formulas created: 7886 % 0.18/0.54 %------------------------------------------------------------------------------