%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n003.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 01:32:30 PM UTC 2026 % Result : Theorem 0.12s 0.44s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.07/0.34 % Computer : n003.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.34 % CPULimit : 300 % 0.07/0.34 % WCLimit : 300 % 0.07/0.34 % DateTime : Fri Sep 4 19:39:19 UTC 2026 % 0.07/0.35 % CPUTime : % 0.12/0.44 (* PROOF-FOUND *) % 0.12/0.44 % SZS status Theorem % 0.12/0.44 (* BEGIN-PROOF *) % 0.12/0.44 % SZS output start Proof % 0.12/0.44 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))\/(~(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 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))\/(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))\/False))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))))))). % 0.12/0.44 Proof. % 0.12/0.44 apply NNPP. intro zenon_G. % 0.12/0.44 apply zenon_G. zenon_intro zenon_H1. % 0.12/0.44 elim zenon_H1. zenon_intro zenon_TX_c. zenon_intro zenon_H3. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H3). zenon_intro zenon_H5. zenon_intro zenon_H4. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H4). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H6). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.12/0.44 apply zenon_Hd. zenon_intro zenon_He. % 0.12/0.44 apply zenon_Hb. zenon_intro zenon_Hf. % 0.12/0.44 apply zenon_H5. zenon_intro zenon_H10. % 0.12/0.44 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_c Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_Hc); [ zenon_intro zenon_H11; idtac ]. % 0.12/0.44 elim zenon_H11. zenon_intro zenon_TY_s. zenon_intro zenon_H13. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H14). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.12/0.44 apply zenon_H16. zenon_intro zenon_H18. % 0.12/0.44 apply zenon_H15. zenon_intro zenon_H19. % 0.12/0.44 generalize (zenon_H10 zenon_TY_s). zenon_intro zenon_H1a. % 0.12/0.44 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 0.12/0.44 exact (zenon_H1c zenon_H19). % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.12/0.44 apply zenon_H1e. zenon_intro zenon_H1f. % 0.12/0.44 generalize (zenon_Hf zenon_TY_s). zenon_intro zenon_H20. % 0.12/0.44 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H1c | zenon_intro zenon_H21 ]. % 0.12/0.44 exact (zenon_H1c zenon_H19). % 0.12/0.44 apply (zenon_notand_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.12/0.44 apply zenon_H23. zenon_intro zenon_H24. % 0.12/0.44 generalize (zenon_He zenon_TY_s). zenon_intro zenon_H25. % 0.12/0.44 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H1c | zenon_intro zenon_H26 ]. % 0.12/0.44 exact (zenon_H1c zenon_H19). % 0.12/0.44 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_s X))\/False)) zenon_H26); [ zenon_intro zenon_H27; idtac ]. % 0.12/0.44 elim zenon_H27. zenon_intro zenon_TX_bo. zenon_intro zenon_H29. % 0.12/0.44 apply (zenon_notor_s _ _ zenon_H29). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.12/0.44 apply zenon_H2b. zenon_intro zenon_H2c. % 0.12/0.44 generalize (zenon_H24 zenon_TX_bo). zenon_intro zenon_H2d. % 0.12/0.44 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.12/0.44 exact (zenon_H2f zenon_H2c). % 0.12/0.44 generalize (zenon_H1f zenon_TX_bo). zenon_intro zenon_H30. % 0.12/0.44 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H2f | zenon_intro zenon_H31 ]. % 0.12/0.44 exact (zenon_H2f zenon_H2c). % 0.12/0.44 exact (zenon_H31 zenon_H2e). % 0.12/0.44 exact (zenon_H22 zenon_H18). % 0.12/0.44 exact (zenon_H1d zenon_H17). % 0.12/0.44 Qed. % 0.12/0.44 % SZS output end Proof % 0.12/0.44 (* END-PROOF *) % 0.12/0.44 nodes searched: 572 % 0.12/0.44 max branch formulas: 372 % 0.12/0.44 proof nodes created: 91 % 0.12/0.44 formulas created: 2605 % 0.12/0.44 %------------------------------------------------------------------------------