%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 : Mon Jul 18 15:55:26 EDT 2022 % Result : Theorem 0.21s 0.55s % Output : Proof 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : NUM414+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.15 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n020.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Tue Jul 5 18:44:44 EDT 2022 % 0.14/0.36 % CPUTime : % 0.21/0.55 Zenon warning: unused variable (B : zenon_U) in irreflexivity_r2_xboole_0 % 0.21/0.55 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.21/0.55 (* PROOF-FOUND *) % 0.21/0.55 % SZS status Theorem % 0.21/0.55 (* BEGIN-PROOF *) % 0.21/0.55 % SZS output start Proof % 0.21/0.55 Theorem t50_ordinal1 : (forall A : zenon_U, ((ordinal A)->(forall B : zenon_U, ((ordinal B)->(~((~(proper_subset A B))/\((~(A = B))/\(~(proper_subset B A))))))))). % 0.21/0.55 Proof. % 0.21/0.55 apply NNPP. intro zenon_G. % 0.21/0.55 apply (zenon_notallex_s (fun A : zenon_U => ((ordinal A)->(forall B : zenon_U, ((ordinal B)->(~((~(proper_subset A B))/\((~(A = B))/\(~(proper_subset B A))))))))) zenon_G); [ zenon_intro zenon_H2a; idtac ]. % 0.21/0.55 elim zenon_H2a. zenon_intro zenon_TA_br. zenon_intro zenon_H2c. % 0.21/0.55 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 0.21/0.55 apply (zenon_notallex_s (fun B : zenon_U => ((ordinal B)->(~((~(proper_subset zenon_TA_br B))/\((~(zenon_TA_br = B))/\(~(proper_subset B zenon_TA_br))))))) zenon_H2d); [ zenon_intro zenon_H2f; idtac ]. % 0.21/0.55 elim zenon_H2f. zenon_intro zenon_TB_bw. zenon_intro zenon_H31. % 0.21/0.55 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.21/0.55 apply zenon_H32. zenon_intro zenon_H34. % 0.21/0.55 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 0.21/0.55 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H38. zenon_intro zenon_H37. % 0.21/0.55 generalize (d8_xboole_0 zenon_TA_br). zenon_intro zenon_H39. % 0.21/0.55 generalize (zenon_H39 zenon_TB_bw). zenon_intro zenon_H3a. % 0.21/0.55 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H36; zenon_intro zenon_H3d | zenon_intro zenon_H3c; zenon_intro zenon_H3b ]. % 0.21/0.55 generalize (d8_xboole_0 zenon_TB_bw). zenon_intro zenon_H3e. % 0.21/0.55 generalize (zenon_H3e zenon_TA_br). zenon_intro zenon_H3f. % 0.21/0.55 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H37; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.21/0.55 generalize (connectedness_r1_ordinal1 zenon_TB_bw). zenon_intro zenon_H47. % 0.21/0.55 generalize (redefinition_r1_ordinal1 zenon_TA_br). zenon_intro zenon_H48. % 0.21/0.55 generalize (zenon_H48 zenon_TB_bw). zenon_intro zenon_H49. % 0.21/0.55 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 0.21/0.55 exact (zenon_H4d zenon_H2e). % 0.21/0.55 exact (zenon_H4c zenon_H33). % 0.21/0.55 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H50; zenon_intro zenon_H46 | zenon_intro zenon_H4f; zenon_intro zenon_H4e ]. % 0.21/0.55 generalize (redefinition_r1_ordinal1 zenon_TB_bw). zenon_intro zenon_H51. % 0.21/0.55 generalize (zenon_H51 zenon_TA_br). zenon_intro zenon_H52. % 0.21/0.55 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 0.21/0.55 exact (zenon_H4c zenon_H33). % 0.21/0.55 exact (zenon_H4d zenon_H2e). % 0.21/0.55 apply (zenon_equiv_s _ _ zenon_H53); [ zenon_intro zenon_H57; zenon_intro zenon_H44 | zenon_intro zenon_H56; zenon_intro zenon_H55 ]. % 0.21/0.55 generalize (zenon_H47 zenon_TA_br). zenon_intro zenon_H58. % 0.21/0.55 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H54 | zenon_intro zenon_H59 ]. % 0.21/0.55 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H4c | zenon_intro zenon_H4d ]. % 0.21/0.55 exact (zenon_H4c zenon_H33). % 0.21/0.55 exact (zenon_H4d zenon_H2e). % 0.21/0.55 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H56 | zenon_intro zenon_H4f ]. % 0.21/0.55 exact (zenon_H57 zenon_H56). % 0.21/0.55 exact (zenon_H50 zenon_H4f). % 0.21/0.55 exact (zenon_H44 zenon_H55). % 0.21/0.55 exact (zenon_H46 zenon_H4e). % 0.21/0.55 exact (zenon_H45 zenon_H38). % 0.21/0.55 apply zenon_H43. zenon_intro zenon_H5a. % 0.21/0.55 apply zenon_H38. apply sym_equal. exact zenon_H5a. % 0.21/0.55 exact (zenon_H37 zenon_H41). % 0.21/0.55 exact (zenon_H36 zenon_H3c). % 0.21/0.55 Qed. % 0.21/0.55 % SZS output end Proof % 0.21/0.55 (* END-PROOF *) % 0.21/0.55 nodes searched: 338 % 0.21/0.55 max branch formulas: 331 % 0.21/0.55 proof nodes created: 59 % 0.21/0.55 formulas created: 1907 % 0.21/0.55 %------------------------------------------------------------------------------