%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0. % 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:36 PM UTC 2026 % Result : Theorem 0.19s 0.47s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL654+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n020.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 00:39:12 UTC 2026 % 0.09/0.37 % CPUTime : % 0.19/0.47 (* PROOF-FOUND *) % 0.19/0.47 % SZS status Theorem % 0.19/0.47 (* BEGIN-PROOF *) % 0.19/0.47 % SZS output start Proof % 0.19/0.47 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))\/((~(forall Y : zenon_U, ((~(r1 X 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 Y : zenon_U, ((~(r1 X 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 X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))\/(forall Y : zenon_U, ((~(r1 X 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)))))))))))))). % 0.19/0.47 Proof. % 0.19/0.47 assert (zenon_L1_ : forall (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_j 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 X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_i X))\/(p1 X))) -> False). % 0.19/0.47 do 3 intro. intros zenon_H2 zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 0.19/0.47 generalize (zenon_H2 zenon_TY_i). zenon_intro zenon_Ha. % 0.19/0.47 apply (zenon_or_s _ _ zenon_Ha); [ zenon_intro zenon_Hc | zenon_intro zenon_Hb ]. % 0.19/0.47 exact (zenon_Hc zenon_H3). % 0.19/0.47 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 0.19/0.47 apply zenon_He. zenon_intro zenon_Hf. % 0.19/0.47 generalize (zenon_Hf zenon_TX_h). zenon_intro zenon_H10. % 0.19/0.47 apply (zenon_or_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.19/0.47 exact (zenon_H12 zenon_H4). % 0.19/0.47 exact (zenon_H11 zenon_H5). % 0.19/0.47 apply zenon_Hd. zenon_intro zenon_H13. % 0.19/0.47 generalize (zenon_H13 zenon_TY_i). zenon_intro zenon_H14. % 0.19/0.47 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ]. % 0.19/0.47 generalize (reflexivity zenon_TY_i). zenon_intro zenon_H17. % 0.19/0.47 exact (zenon_H16 zenon_H17). % 0.19/0.47 exact (zenon_H15 zenon_H6). % 0.19/0.47 (* end of lemma zenon_L1_ *) % 0.19/0.47 apply NNPP. intro zenon_G. % 0.19/0.47 apply zenon_G. zenon_intro zenon_H18. % 0.19/0.47 elim zenon_H18. zenon_intro zenon_TX_j. zenon_intro zenon_H19. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H1c). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.19/0.47 apply zenon_H1f. zenon_intro zenon_H2. % 0.19/0.47 apply zenon_H1d. zenon_intro zenon_H22. % 0.19/0.47 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_j 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))))))) zenon_H20); [ zenon_intro zenon_H23; idtac ]. % 0.19/0.47 elim zenon_H23. zenon_intro zenon_TY_i. zenon_intro zenon_H24. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H25). zenon_intro zenon_H28. zenon_intro zenon_H27. % 0.19/0.47 apply zenon_H27. zenon_intro zenon_H6. % 0.19/0.47 apply zenon_H26. zenon_intro zenon_H3. % 0.19/0.47 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_i X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))) zenon_H28); [ zenon_intro zenon_H29; idtac ]. % 0.19/0.47 elim zenon_H29. zenon_intro zenon_TX_h. zenon_intro zenon_H2a. % 0.19/0.47 apply (zenon_notor_s _ _ zenon_H2a). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.19/0.47 apply zenon_H2c. zenon_intro zenon_H4. % 0.19/0.47 generalize (zenon_H22 zenon_TY_i). zenon_intro zenon_H2d. % 0.19/0.47 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_Hc | zenon_intro zenon_H2e ]. % 0.19/0.47 exact (zenon_Hc zenon_H3). % 0.19/0.47 generalize (zenon_H2e zenon_TX_h). zenon_intro zenon_H2f. % 0.19/0.47 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H12 | zenon_intro zenon_H30 ]. % 0.19/0.47 exact (zenon_H12 zenon_H4). % 0.19/0.47 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.19/0.47 apply zenon_H32. zenon_intro zenon_H5. % 0.19/0.47 apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 0.19/0.47 exact (zenon_H31 zenon_H2b). % 0.19/0.47 Qed. % 0.19/0.47 % SZS output end Proof % 0.19/0.47 (* END-PROOF *) % 0.19/0.47 nodes searched: 2536 % 0.19/0.47 max branch formulas: 1252 % 0.19/0.47 proof nodes created: 321 % 0.19/0.47 formulas created: 11829 % 0.19/0.47 %------------------------------------------------------------------------------