%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 01:32:37 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 % 0.00/0.03 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n016.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 02:20:14 UTC 2026 % 0.09/0.35 % 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))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p2 X)/\((~(p102 X))/\(p101 X))))))))\/(~((~(p101 Y))/\(p100 Y))))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p2 X))\/(~(p101 X)))))\/(p2 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(p101 X)))))\/(~(p2 Y))))\/(~(p101 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p1 X))\/(~(p100 X)))))\/(p1 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(p100 X)))))\/(~(p1 Y))))\/(~(p100 Y)))/\(((p101 Y)\/(~(p102 Y)))/\((p100 Y)\/(~(p101 Y)))))))))/\((~(p101 X))/\(p100 X)))))))). % 0.12/0.43 Proof. % 0.12/0.43 apply NNPP. intro zenon_G. % 0.12/0.43 apply zenon_G. zenon_intro zenon_H2. % 0.12/0.43 elim zenon_H2. zenon_intro zenon_TX_d. zenon_intro zenon_H4. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H4). zenon_intro zenon_H6. zenon_intro zenon_H5. % 0.12/0.43 apply zenon_H5. zenon_intro zenon_H7. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H8). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.12/0.43 apply zenon_H6. zenon_intro zenon_Hc. % 0.12/0.43 generalize (zenon_H9 zenon_TX_d). zenon_intro zenon_Hd. % 0.12/0.43 apply (zenon_or_s _ _ zenon_Hd); [ zenon_intro zenon_Hf | zenon_intro zenon_He ]. % 0.12/0.43 generalize (reflexivity zenon_TX_d). zenon_intro zenon_H10. % 0.12/0.43 exact (zenon_Hf zenon_H10). % 0.12/0.43 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.12/0.43 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H14 | zenon_intro zenon_H13 ]. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.12/0.43 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_d X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))) zenon_H16); [ zenon_intro zenon_H17; idtac ]. % 0.12/0.43 elim zenon_H17. zenon_intro zenon_TX_y. zenon_intro zenon_H19. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.12/0.43 apply zenon_H1a. zenon_intro zenon_H1c. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.12/0.43 apply zenon_H1b. zenon_intro zenon_H1f. % 0.12/0.43 generalize (zenon_Hc zenon_TX_y). zenon_intro zenon_H20. % 0.12/0.43 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ]. % 0.12/0.43 exact (zenon_H22 zenon_H1f). % 0.12/0.43 exact (zenon_H1e zenon_H21). % 0.12/0.43 apply (zenon_notand_s _ _ zenon_H13); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.12/0.43 exact (zenon_H24 zenon_Hb). % 0.12/0.43 exact (zenon_H23 zenon_Ha). % 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: 49 % 0.12/0.43 max branch formulas: 57 % 0.12/0.43 proof nodes created: 19 % 0.12/0.43 formulas created: 450 % 0.12/0.43 %------------------------------------------------------------------------------