%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL640+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:31 PM UTC 2026 % Result : Theorem 0.38s 0.65s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL640+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.10/0.37 % Computer : n017.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 13:30:36 UTC 2026 % 0.10/0.37 % CPUTime : % 0.38/0.65 (* PROOF-FOUND *) % 0.38/0.65 % SZS status Theorem % 0.38/0.65 (* BEGIN-PROOF *) % 0.38/0.65 % SZS output start Proof % 0.38/0.65 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))/\((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))))\/(~(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))))))). % 0.38/0.65 Proof. % 0.38/0.65 assert (zenon_L1_ : forall (zenon_TY_d : zenon_U), (~((forall X : zenon_U, ((~(r1 zenon_TY_d X))\/(p1 X)))\/(~(p1 zenon_TY_d)))) -> (~(p1 zenon_TY_d)) -> False). % 0.38/0.65 do 1 intro. intros zenon_H1 zenon_H2. % 0.38/0.65 apply (zenon_notor_s _ _ zenon_H1). zenon_intro zenon_H5. zenon_intro zenon_H4. % 0.38/0.65 exact (zenon_H4 zenon_H2). % 0.38/0.65 (* end of lemma zenon_L1_ *) % 0.38/0.65 apply NNPP. intro zenon_G. % 0.38/0.65 apply zenon_G. zenon_intro zenon_H6. % 0.38/0.65 elim zenon_H6. zenon_intro zenon_TX_h. zenon_intro zenon_H8. % 0.38/0.65 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Ha. zenon_intro zenon_H9. % 0.38/0.65 apply zenon_Ha. zenon_intro zenon_Hb. % 0.38/0.65 apply zenon_H9. zenon_intro zenon_Hc. % 0.38/0.65 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_h Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ]. % 0.38/0.65 elim zenon_Hd. zenon_intro zenon_TY_o. zenon_intro zenon_Hf. % 0.38/0.65 apply (zenon_notor_s _ _ zenon_Hf). zenon_intro zenon_H11. zenon_intro zenon_H10. % 0.38/0.65 apply (zenon_notor_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12. % 0.38/0.65 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.38/0.65 apply zenon_H14. zenon_intro zenon_H16. % 0.38/0.65 apply zenon_H11. zenon_intro zenon_H17. % 0.38/0.65 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_o X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H15); [ zenon_intro zenon_H18; idtac ]. % 0.38/0.65 elim zenon_H18. zenon_intro zenon_TX_z. zenon_intro zenon_H1a. % 0.38/0.65 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.38/0.65 apply zenon_H1c. zenon_intro zenon_H1d. % 0.38/0.65 apply zenon_H1b. zenon_intro zenon_H1e. % 0.38/0.65 generalize (zenon_Hb zenon_TY_o). zenon_intro zenon_H1f. % 0.38/0.65 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.38/0.65 exact (zenon_H21 zenon_H17). % 0.38/0.65 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.38/0.65 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.38/0.65 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.38/0.65 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.38/0.65 exact (zenon_H13 zenon_H29). % 0.38/0.65 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 0.38/0.66 exact (zenon_H2b zenon_H2d). % 0.38/0.66 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.38/0.66 exact (zenon_H15 zenon_H2f). % 0.38/0.66 exact (zenon_H2e zenon_H16). % 0.38/0.66 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.38/0.66 generalize (zenon_H27 zenon_TX_z). zenon_intro zenon_H32. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.38/0.66 exact (zenon_H34 zenon_H1d). % 0.38/0.66 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.38/0.66 generalize (zenon_H31 zenon_TX_z). zenon_intro zenon_H37. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H34 | zenon_intro zenon_H38 ]. % 0.38/0.66 exact (zenon_H34 zenon_H1d). % 0.38/0.66 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_z X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))) zenon_H38); [ zenon_intro zenon_H39; idtac ]. % 0.38/0.66 elim zenon_H39. zenon_intro zenon_TX_cg. zenon_intro zenon_H3b. % 0.38/0.66 apply (zenon_notor_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.38/0.66 apply (zenon_notor_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.38/0.66 apply zenon_H3d. zenon_intro zenon_H40. % 0.38/0.66 generalize (zenon_H36 zenon_TX_cg). zenon_intro zenon_H41. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.38/0.66 exact (zenon_H43 zenon_H40). % 0.38/0.66 exact (zenon_H3f zenon_H42). % 0.38/0.66 exact (zenon_H35 zenon_H1e). % 0.38/0.66 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_o X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))) zenon_H30); [ zenon_intro zenon_H44; idtac ]. % 0.38/0.66 elim zenon_H44. zenon_intro zenon_TX_cr. zenon_intro zenon_H46. % 0.38/0.66 apply (zenon_notor_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.38/0.66 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.38/0.66 apply (zenon_notor_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.38/0.66 apply zenon_H4b. zenon_intro zenon_H4d. % 0.38/0.66 apply zenon_H48. zenon_intro zenon_H4e. % 0.38/0.66 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cr Y))\/(p1 Y))) zenon_H4a); [ zenon_intro zenon_H4f; idtac ]. % 0.38/0.66 elim zenon_H4f. zenon_intro zenon_TY_d. zenon_intro zenon_H50. % 0.38/0.66 apply (zenon_notor_s _ _ zenon_H50). zenon_intro zenon_H51. zenon_intro zenon_H2. % 0.38/0.66 apply zenon_H51. zenon_intro zenon_H52. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H53 | zenon_intro zenon_H2e ]. % 0.38/0.66 generalize (zenon_H4d zenon_TY_d). zenon_intro zenon_H54. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.38/0.66 exact (zenon_H56 zenon_H52). % 0.38/0.66 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H1 ]. % 0.38/0.66 generalize (zenon_H53 zenon_TX_cr). zenon_intro zenon_H58. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 0.38/0.66 exact (zenon_H5a zenon_H4e). % 0.38/0.66 generalize (zenon_H59 zenon_TY_d). zenon_intro zenon_H5b. % 0.38/0.66 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H56 | zenon_intro zenon_H5c ]. % 0.38/0.66 exact (zenon_H56 zenon_H52). % 0.38/0.66 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ]. % 0.38/0.66 exact (zenon_H2 zenon_H5e). % 0.38/0.66 exact (zenon_H5d zenon_H57). % 0.38/0.66 apply (zenon_L1_ zenon_TY_d); trivial. % 0.38/0.66 exact (zenon_H2e zenon_H16). % 0.38/0.66 Qed. % 0.38/0.66 % SZS output end Proof % 0.38/0.66 (* END-PROOF *) % 0.38/0.66 nodes searched: 4323 % 0.38/0.66 max branch formulas: 1618 % 0.38/0.66 proof nodes created: 463 % 0.38/0.66 formulas created: 24144 % 0.38/0.66 %------------------------------------------------------------------------------