%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL674+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 01:32:44 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 : LCL674+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 02:09:28 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_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_H6. zenon_intro zenon_H8. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H8). zenon_intro zenon_Ha. zenon_intro zenon_H9. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 0.12/0.43 apply zenon_H7. zenon_intro zenon_Hd. % 0.12/0.43 generalize (zenon_Ha zenon_TX_e). zenon_intro zenon_He. % 0.12/0.43 apply (zenon_or_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ]. % 0.12/0.43 generalize (reflexivity zenon_TX_e). zenon_intro zenon_H11. % 0.12/0.43 exact (zenon_H10 zenon_H11). % 0.12/0.43 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H13. zenon_intro zenon_H12. % 0.12/0.43 apply (zenon_or_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.12/0.43 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_e X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))) zenon_H17); [ zenon_intro zenon_H18; idtac ]. % 0.12/0.43 elim zenon_H18. zenon_intro zenon_TX_z. zenon_intro zenon_H1a. % 0.12/0.43 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.12/0.43 apply zenon_H1b. zenon_intro zenon_H1d. % 0.12/0.43 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 0.12/0.43 apply zenon_H1c. zenon_intro zenon_H20. % 0.12/0.43 generalize (zenon_Hd zenon_TX_z). zenon_intro zenon_H21. % 0.12/0.43 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ]. % 0.12/0.43 exact (zenon_H23 zenon_H20). % 0.12/0.43 exact (zenon_H1f zenon_H22). % 0.12/0.43 apply (zenon_notand_s _ _ zenon_H14); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.12/0.43 exact (zenon_H25 zenon_Hc). % 0.12/0.43 exact (zenon_H24 zenon_Hb). % 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: 464 % 0.12/0.43 %------------------------------------------------------------------------------