%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL658+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 01:32:38 PM UTC 2026 % Result : Theorem 0.39s 0.63s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL658+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.10/0.36 % Computer : n004.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 09:05:29 UTC 2026 % 0.13/0.36 % CPUTime : % 0.39/0.63 (* PROOF-FOUND *) % 0.39/0.63 % SZS status Theorem % 0.39/0.63 (* BEGIN-PROOF *) % 0.39/0.63 % SZS output start Proof % 0.39/0.63 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)))))))))))))))))))). % 0.39/0.63 Proof. % 0.39/0.63 assert (zenon_L1_ : forall (zenon_TY_g : zenon_U), ((p1 zenon_TY_g)\/((forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_g X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))) -> (~(p1 zenon_TY_g)) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False). % 0.39/0.63 do 1 intro. intros zenon_H2 zenon_H3 zenon_H4 zenon_H5. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H2); [ zenon_intro zenon_H8 | zenon_intro zenon_H7 ]. % 0.39/0.63 exact (zenon_H3 zenon_H8). % 0.39/0.63 apply (zenon_or_s _ _ zenon_H7); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ]. % 0.39/0.63 exact (zenon_H4 zenon_Ha). % 0.39/0.63 exact (zenon_H9 zenon_H5). % 0.39/0.63 (* end of lemma zenon_L1_ *) % 0.39/0.63 assert (zenon_L2_ : forall (zenon_TX_o : zenon_U) (zenon_TY_g : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))) -> (r1 zenon_TY_g zenon_TX_o) -> (forall Y : zenon_U, ((~(r1 zenon_TX_o Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))) -> False). % 0.39/0.63 do 2 intro. intros zenon_Hb zenon_Hc zenon_Hd. % 0.39/0.63 generalize (zenon_Hb zenon_TX_o). zenon_intro zenon_Hf. % 0.39/0.63 apply (zenon_or_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 0.39/0.63 exact (zenon_H11 zenon_Hc). % 0.39/0.63 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_o X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))) zenon_H10); [ zenon_intro zenon_H12; idtac ]. % 0.39/0.63 elim zenon_H12. zenon_intro zenon_TX_t. zenon_intro zenon_H14. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.39/0.63 apply zenon_H16. zenon_intro zenon_H19. % 0.39/0.63 generalize (zenon_Hd zenon_TX_t). zenon_intro zenon_H1a. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.39/0.63 exact (zenon_H1c zenon_H19). % 0.39/0.63 exact (zenon_H18 zenon_H1b). % 0.39/0.63 (* end of lemma zenon_L2_ *) % 0.39/0.63 assert (zenon_L3_ : forall (zenon_TY_bf : zenon_U), (~((forall X : zenon_U, ((~(r1 zenon_TY_bf X))\/(p1 X)))\/(~(p1 zenon_TY_bf)))) -> (~(p1 zenon_TY_bf)) -> False). % 0.39/0.63 do 1 intro. intros zenon_H1d zenon_H1e. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.39/0.63 exact (zenon_H20 zenon_H1e). % 0.39/0.63 (* end of lemma zenon_L3_ *) % 0.39/0.63 assert (zenon_L4_ : forall (zenon_TY_g : zenon_U), (~(forall X : zenon_U, ((~(r1 zenon_TY_g 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))))))))))))) -> ((forall X : zenon_U, ((~(r1 zenon_TY_g 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 zenon_TY_g 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 zenon_TY_g X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False). % 0.39/0.63 do 1 intro. intros zenon_H22 zenon_H23 zenon_H5. % 0.39/0.63 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_g 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_H22); [ zenon_intro zenon_H24; idtac ]. % 0.39/0.63 elim zenon_H24. zenon_intro zenon_TX_bl. zenon_intro zenon_H26. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H27). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H29). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.39/0.63 apply zenon_H2b. zenon_intro zenon_H2d. % 0.39/0.63 apply zenon_H28. zenon_intro zenon_H2e. % 0.39/0.63 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bl Y))\/(p1 Y))) zenon_H2a); [ zenon_intro zenon_H2f; idtac ]. % 0.39/0.63 elim zenon_H2f. zenon_intro zenon_TY_bf. zenon_intro zenon_H30. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H1e. % 0.39/0.63 apply zenon_H31. zenon_intro zenon_H32. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H33 | zenon_intro zenon_H9 ]. % 0.39/0.63 generalize (zenon_H2d zenon_TY_bf). zenon_intro zenon_H34. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.39/0.63 exact (zenon_H36 zenon_H32). % 0.39/0.63 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H1d ]. % 0.39/0.63 generalize (zenon_H33 zenon_TX_bl). zenon_intro zenon_H38. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.39/0.63 exact (zenon_H3a zenon_H2e). % 0.39/0.63 generalize (zenon_H39 zenon_TY_bf). zenon_intro zenon_H3b. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H36 | zenon_intro zenon_H3c ]. % 0.39/0.63 exact (zenon_H36 zenon_H32). % 0.39/0.63 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 0.39/0.63 exact (zenon_H1e zenon_H3e). % 0.39/0.63 exact (zenon_H3d zenon_H37). % 0.39/0.63 apply (zenon_L3_ zenon_TY_bf); trivial. % 0.39/0.63 exact (zenon_H9 zenon_H5). % 0.39/0.63 (* end of lemma zenon_L4_ *) % 0.39/0.63 apply NNPP. intro zenon_G. % 0.39/0.63 apply zenon_G. zenon_intro zenon_H3f. % 0.39/0.63 elim zenon_H3f. zenon_intro zenon_TX_cm. zenon_intro zenon_H41. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.39/0.63 apply zenon_H43. zenon_intro zenon_H44. % 0.39/0.63 apply zenon_H42. zenon_intro zenon_H45. % 0.39/0.63 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cm 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_H45); [ zenon_intro zenon_H46; idtac ]. % 0.39/0.63 elim zenon_H46. zenon_intro zenon_TY_g. zenon_intro zenon_H47. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H48). zenon_intro zenon_H4b. zenon_intro zenon_H4a. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H4a). zenon_intro zenon_H4. zenon_intro zenon_H4c. % 0.39/0.63 apply zenon_H4c. zenon_intro zenon_H5. % 0.39/0.63 apply zenon_H49. zenon_intro zenon_H4d. % 0.39/0.63 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H4); [ zenon_intro zenon_H4e; idtac ]. % 0.39/0.63 elim zenon_H4e. zenon_intro zenon_TX_o. zenon_intro zenon_H4f. % 0.39/0.63 apply (zenon_notor_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.39/0.63 apply zenon_H51. zenon_intro zenon_Hc. % 0.39/0.63 apply zenon_H50. zenon_intro zenon_H52. % 0.39/0.63 generalize (zenon_H44 zenon_TY_g). zenon_intro zenon_H53. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.39/0.63 exact (zenon_H55 zenon_H4d). % 0.39/0.63 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H57. zenon_intro zenon_H56. % 0.39/0.63 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H2. zenon_intro zenon_H58. % 0.39/0.63 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H59. zenon_intro zenon_H23. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.39/0.63 exact (zenon_H4b zenon_H5b). % 0.39/0.63 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H3 | zenon_intro zenon_H5c ]. % 0.39/0.63 apply (zenon_L1_ zenon_TY_g); trivial. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_Hb | zenon_intro zenon_H22 ]. % 0.39/0.63 generalize (zenon_H59 zenon_TX_o). zenon_intro zenon_H5d. % 0.39/0.63 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H11 | zenon_intro zenon_H5e ]. % 0.39/0.63 exact (zenon_H11 zenon_Hc). % 0.39/0.63 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_Hd | zenon_intro zenon_H5f ]. % 0.39/0.63 apply (zenon_L2_ zenon_TX_o zenon_TY_g); trivial. % 0.39/0.63 exact (zenon_H5f zenon_H52). % 0.39/0.63 apply (zenon_L4_ zenon_TY_g); trivial. % 0.39/0.63 Qed. % 0.39/0.63 % SZS output end Proof % 0.39/0.63 (* END-PROOF *) % 0.39/0.63 nodes searched: 4652 % 0.39/0.63 max branch formulas: 1331 % 0.39/0.63 proof nodes created: 530 % 0.39/0.63 formulas created: 22670 % 0.39/0.63 %------------------------------------------------------------------------------