%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 01:32:44 PM UTC 2026 % Result : Theorem 0.12s 0.43s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL672+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.08/0.34 % Computer : n013.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Sat Sep 5 14:33:49 UTC 2026 % 0.08/0.34 % CPUTime : % 0.12/0.43 (* PROOF-FOUND *) % 0.12/0.43 % SZS status Theorem % 0.12/0.43 (* BEGIN-PROOF *) % 0.12/0.43 % SZS output start Proof % 0.12/0.43 Theorem main : (~(exists X : zenon_U, (~(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(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))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 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))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 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))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((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))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))). % 0.12/0.43 Proof. % 0.12/0.43 apply NNPP. intro zenon_G. % 0.12/0.43 apply zenon_G. zenon_intro zenon_H3. % 0.12/0.43 elim zenon_H3. zenon_intro zenon_TX_e. zenon_intro zenon_H5. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H5). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H6). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_Hc). zenon_intro zenon_Hf. zenon_intro zenon_He. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10. % 0.12/0.43 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_e 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_H11); [ zenon_intro zenon_H12; idtac ]. % 0.12/0.43 elim zenon_H12. zenon_intro zenon_TY_t. zenon_intro zenon_H14. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.12/0.43 apply zenon_H16. zenon_intro zenon_H19. % 0.12/0.43 apply (zenon_notand_s _ _ zenon_H9); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ]. % 0.12/0.43 exact (zenon_H1b zenon_Hf). % 0.12/0.43 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ]. % 0.12/0.43 apply zenon_H1d. zenon_intro zenon_H1e. % 0.12/0.43 generalize (zenon_H1e zenon_TX_e). zenon_intro zenon_H1f. % 0.12/0.43 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 0.12/0.43 generalize (reflexivity zenon_TX_e). zenon_intro zenon_H22. % 0.12/0.43 exact (zenon_H21 zenon_H22). % 0.12/0.43 generalize (zenon_H20 zenon_TY_t). zenon_intro zenon_H23. % 0.12/0.43 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.12/0.43 exact (zenon_H25 zenon_H19). % 0.12/0.43 apply (zenon_notand_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.12/0.43 exact (zenon_H27 zenon_H18). % 0.12/0.43 exact (zenon_H26 zenon_H17). % 0.12/0.43 exact (zenon_H1c zenon_H10). % 0.12/0.43 Qed. % 0.12/0.43 % SZS output end Proof % 0.12/0.43 (* END-PROOF *) % 0.12/0.43 nodes searched: 235 % 0.12/0.43 max branch formulas: 167 % 0.12/0.43 proof nodes created: 54 % 0.12/0.43 formulas created: 1159 % 0.12/0.43 %------------------------------------------------------------------------------