%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 06:33:21 EDT 2022 % Result : Theorem 0.78s 1.01s % Output : Proof 0.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n016.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jul 9 19:51:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.78/1.01 (* PROOF-FOUND *) % 0.78/1.01 % SZS status Theorem % 0.78/1.01 (* BEGIN-PROOF *) % 0.78/1.01 % SZS output start Proof % 0.78/1.01 Theorem corollary_of_null_class_is_subclass : (forall X : zenon_U, ((subclass X (null_class))->(X = (null_class)))). % 0.78/1.01 Proof. % 0.78/1.01 assert (zenon_L1_ : forall (zenon_TX_bt : zenon_U), (~(subclass (null_class) zenon_TX_bt)) -> False). % 0.78/1.01 do 1 intro. intros zenon_H2c. % 0.78/1.01 generalize (subclass_defn (null_class)). zenon_intro zenon_H2e. % 0.78/1.01 generalize (zenon_H2e zenon_TX_bt). zenon_intro zenon_H2f. % 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H2c; zenon_intro zenon_H32 | zenon_intro zenon_H31; zenon_intro zenon_H30 ]. % 0.78/1.01 apply (zenon_notallex_s (fun U : zenon_U => ((member U (null_class))->(member U zenon_TX_bt))) zenon_H32); [ zenon_intro zenon_H33; idtac ]. % 0.78/1.01 elim zenon_H33. zenon_intro zenon_TU_ca. zenon_intro zenon_H35. % 0.78/1.01 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.78/1.01 generalize (null_class_defn zenon_TU_ca). zenon_intro zenon_H38. % 0.78/1.01 exact (zenon_H38 zenon_H37). % 0.78/1.01 exact (zenon_H2c zenon_H31). % 0.78/1.01 (* end of lemma zenon_L1_ *) % 0.78/1.01 assert (zenon_L2_ : forall (zenon_TX_bt : zenon_U), (forall U : zenon_U, ((member U zenon_TX_bt)->(member U (null_class)))) -> (~(subclass zenon_TX_bt (null_class))) -> False). % 0.78/1.01 do 1 intro. intros zenon_H39 zenon_H3a. % 0.78/1.01 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H3b. % 0.78/1.01 generalize (zenon_H3b (null_class)). zenon_intro zenon_H3c. % 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3a; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H39 ]. % 0.78/1.01 exact (zenon_H3e zenon_H39). % 0.78/1.01 exact (zenon_H3a zenon_H3d). % 0.78/1.01 (* end of lemma zenon_L2_ *) % 0.78/1.01 apply NNPP. intro zenon_G. % 0.78/1.01 apply (zenon_notallex_s (fun X : zenon_U => ((subclass X (null_class))->(X = (null_class)))) zenon_G); [ zenon_intro zenon_H3f; idtac ]. % 0.78/1.01 elim zenon_H3f. zenon_intro zenon_TX_bt. zenon_intro zenon_H40. % 0.78/1.01 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H3d. zenon_intro zenon_H41. % 0.78/1.01 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H3b. % 0.78/1.01 generalize (zenon_H3b (null_class)). zenon_intro zenon_H3c. % 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3a; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H39 ]. % 0.78/1.01 exact (zenon_H3a zenon_H3d). % 0.78/1.01 generalize (extensionality (null_class)). zenon_intro zenon_H42. % 0.78/1.01 generalize (zenon_H42 zenon_TX_bt). zenon_intro zenon_H43. % 0.78/1.01 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H47; zenon_intro zenon_H46 | zenon_intro zenon_H45; zenon_intro zenon_H44 ]. % 0.78/1.01 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H2c | zenon_intro zenon_H3a ]. % 0.78/1.01 apply (zenon_L1_ zenon_TX_bt); trivial. % 0.78/1.01 apply (zenon_L2_ zenon_TX_bt); trivial. % 0.78/1.01 apply zenon_H41. apply sym_equal. exact zenon_H45. % 0.78/1.01 Qed. % 0.78/1.01 % SZS output end Proof % 0.78/1.01 (* END-PROOF *) % 0.78/1.01 nodes searched: 25708 % 0.78/1.01 max branch formulas: 2260 % 0.78/1.01 proof nodes created: 1190 % 0.78/1.01 formulas created: 101486 % 0.78/1.01 %------------------------------------------------------------------------------