%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL644+1.010 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n012.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 01:32:33 PM UTC 2026 % Result : Theorem 0.07s 0.35s % Output : Proof 0.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL644+1.010 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.02 % Command : run_zenon %s %d % 0.02/0.30 % Computer : n012.cluster.edu % 0.02/0.30 % Model : x86_64 x86_64 % 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.02/0.30 % Memory : 8046.5625MB % 0.02/0.30 % OS : Linux 6.8.0-71-generic % 0.02/0.30 % CPULimit : 300 % 0.02/0.30 % WCLimit : 300 % 0.02/0.30 % DateTime : Fri Sep 4 13:06:57 UTC 2026 % 0.02/0.30 % CPUTime : % 0.07/0.35 (* PROOF-FOUND *) % 0.07/0.35 % SZS status Theorem % 0.07/0.35 (* BEGIN-PROOF *) % 0.07/0.35 % SZS output start Proof % 0.07/0.35 Theorem main : (~(exists X : zenon_U, (~((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p11 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p11 X)))))\/(p10 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p11 Y)\/(~((p10 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))/\(p10 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p11 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p11 Y)))))\/(p10 X))))\/((p11 Y)\/(~((p10 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))/\(p10 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p11 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p11 X)))))\/((p10 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p11 X)\/(~((p10 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p10 Y)))/\(p10 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p11 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p11 X)))))\/((p10 Y)\/((p11 Y)\/(~((p10 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))/\(p10 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p10 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))))\/(p9 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p10 Y)\/(~((p9 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p9 X)))/\(p9 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p10 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p10 Y)))))\/(p9 X))))\/((p10 Y)\/(~((p9 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p9 X)))/\(p9 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p10 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))))\/((p9 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p10 X)\/(~((p9 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p9 Y)))/\(p9 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p10 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))))\/((p9 Y)\/((p10 Y)\/(~((p9 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p9 X)))/\(p9 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p9 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p9 X)))))\/(p8 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p9 Y)\/(~((p8 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p8 X)))/\(p8 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p9 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p9 Y)))))\/(p8 X))))\/((p9 Y)\/(~((p8 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p8 X)))/\(p8 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p9 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p9 X)))))\/((p8 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p9 X)\/(~((p8 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p8 Y)))/\(p8 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p9 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p9 X)))))\/((p8 Y)\/((p9 Y)\/(~((p8 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p8 X)))/\(p8 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p8 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p8 X)))))\/(p7 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p8 Y)\/(~((p7 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p7 X)))/\(p7 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p8 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p8 Y)))))\/(p7 X))))\/((p8 Y)\/(~((p7 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p7 X)))/\(p7 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p8 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p8 X)))))\/((p7 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p8 X)\/(~((p7 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p7 Y)))/\(p7 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p8 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p8 X)))))\/((p7 Y)\/((p8 Y)\/(~((p7 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p7 X)))/\(p7 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p7 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p7 X)))))\/(p6 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p7 Y)\/(~((p6 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))/\(p6 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p7 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p7 Y)))))\/(p6 X))))\/((p7 Y)\/(~((p6 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))/\(p6 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p7 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p7 X)))))\/((p6 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p7 X)\/(~((p6 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p6 Y)))/\(p6 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p7 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p7 X)))))\/((p6 Y)\/((p7 Y)\/(~((p6 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))/\(p6 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p6 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))))\/(p5 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p6 Y)\/(~((p5 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p5 X)))/\(p5 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p6 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p6 Y)))))\/(p5 X))))\/((p6 Y)\/(~((p5 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p5 X)))/\(p5 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p6 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))))\/((p5 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p6 X)\/(~((p5 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))/\(p5 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p6 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))))\/((p5 Y)\/((p6 Y)\/(~((p5 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p5 X)))/\(p5 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p5 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p5 X)))))\/(p4 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p5 Y)\/(~((p4 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))/\(p4 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p5 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))))\/(p4 X))))\/((p5 Y)\/(~((p4 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))/\(p4 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p5 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p5 X)))))\/((p4 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p5 X)\/(~((p4 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p4 Y)))/\(p4 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p5 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p5 X)))))\/((p4 Y)\/((p5 Y)\/(~((p4 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))/\(p4 Y)))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p10 Y)\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))/\(p10 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p10 Y)\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))/\(p10 Y))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p4 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))))\/(p3 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p4 Y)\/(~((p3 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p3 X)))/\(p3 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p4 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p4 Y)))))\/(p3 X))))\/((p4 Y)\/(~((p3 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p3 X)))/\(p3 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p4 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))))\/((p3 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p4 X)\/(~((p3 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))/\(p3 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p4 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))))\/((p3 Y)\/((p4 Y)\/(~((p3 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p3 X)))/\(p3 Y)))))))))))))))\/((~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p3 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p3 X)))))\/(p2 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p3 Y)\/(~((p2 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))/\(p2 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p3 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))))\/(p2 X))))\/((p3 Y)\/(~((p2 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))/\(p2 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p3 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p3 X)))))\/((p2 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p3 X)\/(~((p2 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))/\(p2 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p3 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p3 X)))))\/((p2 Y)\/((p3 Y)\/(~((p2 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))/\(p2 Y)))))))))))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((~((p2 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))))\/(p1 Y))))\/((forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~((p1 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))/\(p1 Y)))))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/((~((p2 X)/\(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))))\/(p1 X))))\/((p2 Y)\/(~((p1 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))/\(p1 Y))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/((~((p2 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))))\/((p1 Y)\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~((p1 X)/\((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))/\(p1 X)))))))))))/\(forall Y : zenon_U, ((~(r1 X Y))\/((~((p2 Y)/\(forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))))\/((p1 Y)\/((p2 Y)\/(~((p1 Y)/\((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))/\(p1 Y))))))))))))))))))))))))))))). % 0.07/0.35 Proof. % 0.07/0.35 apply NNPP. intro zenon_G. % 0.07/0.35 apply zenon_G. zenon_intro zenon_H1. % 0.07/0.35 elim zenon_H1. zenon_intro zenon_TX_c. zenon_intro zenon_H3. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H3). zenon_intro zenon_H5. zenon_intro zenon_H4. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H4). zenon_intro zenon_H7. zenon_intro zenon_H6. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H6). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Hb. zenon_intro zenon_Ha. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_Hc). zenon_intro zenon_Hf. zenon_intro zenon_He. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H13. zenon_intro zenon_H14. % 0.07/0.35 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_c Y))\/((p10 Y)\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p10 X)))/\(p10 Y)))))) zenon_H13); [ zenon_intro zenon_H15; idtac ]. % 0.07/0.35 elim zenon_H15. zenon_intro zenon_TY_w. zenon_intro zenon_H17. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H17). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.07/0.35 apply (zenon_notor_s _ _ zenon_H18). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.07/0.35 apply zenon_H1a. zenon_intro zenon_H1c. % 0.07/0.35 apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.07/0.35 exact (zenon_H1b zenon_H1d). % 0.07/0.35 Qed. % 0.07/0.35 % SZS output end Proof % 0.07/0.35 (* END-PROOF *) % 0.07/0.35 nodes searched: 6 % 0.07/0.35 max branch formulas: 20 % 0.07/0.35 proof nodes created: 6 % 0.07/0.35 formulas created: 786 % 0.07/0.35 %------------------------------------------------------------------------------