%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n007.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 01:32:47 PM UTC 2026 % Result : Theorem 0.11s 0.42s % Output : Proof 0.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : run_zenon %s %d % 0.07/0.33 % Computer : n007.cluster.edu % 0.07/0.33 % Model : x86_64 x86_64 % 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.33 % Memory : 8046.5625MB % 0.07/0.33 % OS : Linux 6.8.0-71-generic % 0.07/0.33 % CPULimit : 300 % 0.07/0.33 % WCLimit : 300 % 0.07/0.33 % DateTime : Fri Sep 4 16:04:09 UTC 2026 % 0.07/0.34 % CPUTime : % 0.11/0.42 (* PROOF-FOUND *) % 0.11/0.42 % SZS status Theorem % 0.11/0.42 (* BEGIN-PROOF *) % 0.11/0.42 % SZS output start Proof % 0.11/0.42 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p16 X))))\/((~(forall X : zenon_U, ((~(r1 Y X))\/(p12 X))))\/((~(forall X : zenon_U, ((~(r1 Y X))\/(p14 X))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p12 X)))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p15 X)))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p13 X)))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p12 X)))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p11 X)))))))))))). % 0.11/0.42 Proof. % 0.11/0.42 apply NNPP. intro zenon_G. % 0.11/0.42 apply zenon_G. zenon_intro zenon_H3. % 0.11/0.42 elim zenon_H3. zenon_intro zenon_TX_e. zenon_intro zenon_H5. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H5). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H6). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.11/0.42 apply zenon_H7. zenon_intro zenon_He. % 0.11/0.42 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_e Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p12 X))))) zenon_Hd); [ zenon_intro zenon_Hf; idtac ]. % 0.11/0.42 elim zenon_Hf. zenon_intro zenon_TY_q. zenon_intro zenon_H11. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H11). zenon_intro zenon_H13. zenon_intro zenon_H12. % 0.11/0.42 apply zenon_H13. zenon_intro zenon_H14. % 0.11/0.42 generalize (zenon_He zenon_TY_q). zenon_intro zenon_H15. % 0.11/0.42 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 0.11/0.42 exact (zenon_H17 zenon_H14). % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H16). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H18). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.11/0.42 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.11/0.42 exact (zenon_H1b zenon_H12). % 0.11/0.42 Qed. % 0.11/0.42 % SZS output end Proof % 0.11/0.42 (* END-PROOF *) % 0.11/0.42 nodes searched: 84 % 0.11/0.42 max branch formulas: 96 % 0.11/0.42 proof nodes created: 16 % 0.11/0.42 formulas created: 541 % 0.11/0.42 %------------------------------------------------------------------------------