%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 01:32:29 PM UTC 2026 % Result : Theorem 0.13s 0.45s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n008.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 13:22:38 UTC 2026 % 0.09/0.36 % CPUTime : % 0.13/0.45 (* PROOF-FOUND *) % 0.13/0.45 % SZS status Theorem % 0.13/0.45 (* BEGIN-PROOF *) % 0.13/0.45 % SZS output start Proof % 0.13/0.45 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)))))))))/\((((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(p2 Y))/\((~(p102 Y))/\(p101 Y)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((p2 Y)/\((~(p102 Y))/\(p101 Y))))))))\/(~((~(p101 X))/\(p100 X))))/\(((((forall Y : zenon_U, ((~(r1 X Y))\/((~(p2 Y))\/(~(p101 Y)))))\/(p2 X))/\((forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(p101 Y)))))\/(~(p2 X))))\/(~(p101 X)))/\(((((forall Y : zenon_U, ((~(r1 X Y))\/((~(p1 Y))\/(~(p100 Y)))))\/(p1 X))/\((forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(p100 Y)))))\/(~(p1 X))))\/(~(p100 X)))/\(((p101 X)\/(~(p102 X)))/\(((p100 X)\/(~(p101 X)))/\((~(p101 X))/\(p100 X))))))))))))). % 0.13/0.45 Proof. % 0.13/0.45 apply NNPP. intro zenon_G. % 0.13/0.45 apply zenon_G. zenon_intro zenon_H1. % 0.13/0.45 elim zenon_H1. zenon_intro zenon_TX_c. zenon_intro zenon_H3. % 0.13/0.45 apply (zenon_notor_s _ _ zenon_H3). zenon_intro zenon_H5. zenon_intro zenon_H4. % 0.13/0.45 apply zenon_H4. zenon_intro zenon_H6. % 0.13/0.45 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_H8. zenon_intro zenon_H7. % 0.13/0.45 apply (zenon_and_s _ _ zenon_H7). zenon_intro zenon_Ha. zenon_intro zenon_H9. % 0.13/0.45 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 0.13/0.45 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.13/0.45 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.13/0.45 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.13/0.45 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.13/0.45 apply zenon_H5. zenon_intro zenon_H15. % 0.13/0.45 apply (zenon_or_s _ _ zenon_Ha); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.13/0.45 apply (zenon_and_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.13/0.45 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_c Y))\/(~((~(p2 Y))/\((~(p102 Y))/\(p101 Y)))))) zenon_H19); [ zenon_intro zenon_H1a; idtac ]. % 0.13/0.45 elim zenon_H1a. zenon_intro zenon_TY_bb. zenon_intro zenon_H1c. % 0.13/0.45 apply (zenon_notor_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.13/0.45 apply zenon_H1d. zenon_intro zenon_H1f. % 0.13/0.45 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.13/0.45 apply zenon_H1e. zenon_intro zenon_H22. % 0.13/0.45 generalize (zenon_H15 zenon_TY_bb). zenon_intro zenon_H23. % 0.13/0.45 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.13/0.45 exact (zenon_H25 zenon_H22). % 0.13/0.45 exact (zenon_H21 zenon_H24). % 0.13/0.45 apply (zenon_notand_s _ _ zenon_H16); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ]. % 0.13/0.45 exact (zenon_H27 zenon_H14). % 0.13/0.45 exact (zenon_H26 zenon_H13). % 0.13/0.45 Qed. % 0.13/0.45 % SZS output end Proof % 0.13/0.45 (* END-PROOF *) % 0.13/0.45 nodes searched: 45 % 0.13/0.45 max branch formulas: 55 % 0.13/0.45 proof nodes created: 15 % 0.13/0.45 formulas created: 495 % 0.13/0.45 %------------------------------------------------------------------------------