%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET056+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n015.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 06:33:11 EDT 2022 % Result : Theorem 0.46s 0.70s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET056+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n015.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jul 10 22:41:08 EDT 2022 % 0.13/0.33 % CPUTime : % 0.46/0.70 (* PROOF-FOUND *) % 0.46/0.70 % SZS status Theorem % 0.46/0.70 (* BEGIN-PROOF *) % 0.46/0.70 % SZS output start Proof % 0.46/0.70 Theorem equality1 : (forall X : zenon_U, (forall Y : zenon_U, ((X = Y)\/((exists U : zenon_U, ((member U X)/\(~(member U Y))))\/(exists W : zenon_U, ((member W Y)/\(~(member W X)))))))). % 0.46/0.70 Proof. % 0.46/0.70 apply NNPP. intro zenon_G. % 0.46/0.70 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, ((X = Y)\/((exists U : zenon_U, ((member U X)/\(~(member U Y))))\/(exists W : zenon_U, ((member W Y)/\(~(member W X)))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 0.46/0.70 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e. % 0.46/0.70 apply (zenon_notallex_s (fun Y : zenon_U => ((zenon_TX_bt = Y)\/((exists U : zenon_U, ((member U zenon_TX_bt)/\(~(member U Y))))\/(exists W : zenon_U, ((member W Y)/\(~(member W zenon_TX_bt))))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ]. % 0.46/0.70 elim zenon_H2f. zenon_intro zenon_TY_bw. zenon_intro zenon_H31. % 0.46/0.70 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.46/0.70 apply (zenon_notor_s _ _ zenon_H32). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.46/0.70 generalize (extensionality zenon_TY_bw). zenon_intro zenon_H36. % 0.46/0.70 generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37. % 0.46/0.70 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3b; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ]. % 0.46/0.70 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.46/0.70 generalize (subclass_defn zenon_TY_bw). zenon_intro zenon_H3e. % 0.46/0.70 generalize (zenon_H3e zenon_TX_bt). zenon_intro zenon_H3f. % 0.46/0.70 apply (zenon_equiv_s _ _ zenon_H3f); [ zenon_intro zenon_H3d; zenon_intro zenon_H42 | zenon_intro zenon_H41; zenon_intro zenon_H40 ]. % 0.46/0.70 apply (zenon_notallex_s (fun U : zenon_U => ((member U zenon_TY_bw)->(member U zenon_TX_bt))) zenon_H42); [ zenon_intro zenon_H43; idtac ]. % 0.46/0.70 elim zenon_H43. zenon_intro zenon_TU_cq. zenon_intro zenon_H45. % 0.46/0.70 apply (zenon_notimply_s _ _ zenon_H45). zenon_intro zenon_H47. zenon_intro zenon_H46. % 0.46/0.70 apply zenon_H34. exists zenon_TU_cq. apply NNPP. zenon_intro zenon_H48. % 0.46/0.70 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.46/0.70 exact (zenon_H4a zenon_H47). % 0.46/0.70 exact (zenon_H49 zenon_H46). % 0.46/0.70 exact (zenon_H3d zenon_H41). % 0.46/0.70 generalize (subclass_defn zenon_TX_bt). zenon_intro zenon_H4b. % 0.46/0.70 generalize (zenon_H4b zenon_TY_bw). zenon_intro zenon_H4c. % 0.46/0.70 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H3c; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ]. % 0.46/0.70 apply (zenon_notallex_s (fun U : zenon_U => ((member U zenon_TX_bt)->(member U zenon_TY_bw))) zenon_H4f); [ zenon_intro zenon_H50; idtac ]. % 0.46/0.70 elim zenon_H50. zenon_intro zenon_TU_dd. zenon_intro zenon_H52. % 0.46/0.70 apply (zenon_notimply_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53. % 0.46/0.70 apply zenon_H35. exists zenon_TU_dd. apply NNPP. zenon_intro zenon_H55. % 0.46/0.70 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.46/0.70 exact (zenon_H57 zenon_H54). % 0.46/0.70 exact (zenon_H56 zenon_H53). % 0.46/0.70 exact (zenon_H3c zenon_H4e). % 0.46/0.70 apply zenon_H33. apply sym_equal. exact zenon_H39. % 0.46/0.70 Qed. % 0.46/0.70 % SZS output end Proof % 0.46/0.70 (* END-PROOF *) % 0.46/0.70 nodes searched: 6097 % 0.46/0.70 max branch formulas: 1977 % 0.46/0.70 proof nodes created: 729 % 0.46/0.70 formulas created: 34690 % 0.46/0.70 %------------------------------------------------------------------------------