%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 01:32:49 PM UTC 2026 % Result : Theorem 0.09s 0.45s % Output : Proof 0.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL686+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n006.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 09:50:31 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.45 (* PROOF-FOUND *) % 0.09/0.45 % SZS status Theorem % 0.09/0.45 (* BEGIN-PROOF *) % 0.09/0.45 % SZS output start Proof % 0.09/0.45 Theorem main : (~(exists X : zenon_U, (~((forall Y : zenon_U, ((~(r1 X Y))\/((~(p3 Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/False))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(((p2 Y)/\(~(p1 Y)))\/((~(p2 Y))/\(p1 Y)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((~(p1 Y))/\(~(p2 Y)))\/((p2 Y)/\(p1 Y)))))))))))))))))). % 0.09/0.45 Proof. % 0.09/0.45 assert (zenon_L1_ : forall (zenon_TY_h : zenon_U) (zenon_TY_i : zenon_U), (~(~(p2 zenon_TY_i))) -> (forall Y : zenon_U, ((~(r1 zenon_TY_h Y))\/(~(((p2 Y)/\(~(p1 Y)))\/((~(p2 Y))/\(p1 Y)))))) -> (r1 zenon_TY_h zenon_TY_i) -> (~((p2 zenon_TY_i)/\(p1 zenon_TY_i))) -> False). % 0.09/0.45 do 2 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 0.09/0.45 apply zenon_H3. zenon_intro zenon_H9. % 0.09/0.45 apply (zenon_notand_s _ _ zenon_H6); [ zenon_intro zenon_Hb | zenon_intro zenon_Ha ]. % 0.09/0.45 exact (zenon_Hb zenon_H9). % 0.09/0.45 generalize (zenon_H4 zenon_TY_i). zenon_intro zenon_Hc. % 0.09/0.45 apply (zenon_or_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 0.09/0.45 exact (zenon_He zenon_H5). % 0.09/0.45 apply (zenon_notor_s _ _ zenon_Hd). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.09/0.45 apply (zenon_notand_s _ _ zenon_H10); [ zenon_intro zenon_Hb | zenon_intro zenon_H11 ]. % 0.09/0.45 exact (zenon_Hb zenon_H9). % 0.09/0.45 exact (zenon_H11 zenon_Ha). % 0.09/0.45 (* end of lemma zenon_L1_ *) % 0.09/0.45 apply NNPP. intro zenon_G. % 0.09/0.45 apply zenon_G. zenon_intro zenon_H12. % 0.09/0.45 elim zenon_H12. zenon_intro zenon_TX_t. zenon_intro zenon_H14. % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.09/0.45 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_t Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/False))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(((p2 Y)/\(~(p1 Y)))\/((~(p2 Y))/\(p1 Y)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((~(p1 Y))/\(~(p2 Y)))\/((p2 Y)/\(p1 Y)))))))))))))) zenon_H15); [ zenon_intro zenon_H17; idtac ]. % 0.09/0.45 elim zenon_H17. zenon_intro zenon_TY_h. zenon_intro zenon_H18. % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H18). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.09/0.45 apply zenon_H19. zenon_intro zenon_H1b. % 0.09/0.45 generalize (zenon_H1b zenon_TY_h). zenon_intro zenon_H1c. % 0.09/0.45 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 0.09/0.45 generalize (reflexivity zenon_TY_h). zenon_intro zenon_H1f. % 0.09/0.45 exact (zenon_H1e zenon_H1f). % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22. % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24. % 0.09/0.45 apply zenon_H23. zenon_intro zenon_H4. % 0.09/0.45 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TY_h Y))\/(((~(p1 Y))/\(~(p2 Y)))\/((p2 Y)/\(p1 Y))))) zenon_H24); [ zenon_intro zenon_H26; idtac ]. % 0.09/0.45 elim zenon_H26. zenon_intro zenon_TY_i. zenon_intro zenon_H27. % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.09/0.45 apply (zenon_notor_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H6. % 0.09/0.45 apply zenon_H29. zenon_intro zenon_H5. % 0.09/0.45 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H11 | zenon_intro zenon_H3 ]. % 0.09/0.45 apply zenon_H11. zenon_intro zenon_H2b. % 0.09/0.45 generalize (zenon_H4 zenon_TY_i). zenon_intro zenon_Hc. % 0.09/0.45 apply (zenon_or_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 0.09/0.45 exact (zenon_He zenon_H5). % 0.09/0.45 apply (zenon_notor_s _ _ zenon_Hd). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.09/0.45 apply (zenon_notand_s _ _ zenon_Hf); [ zenon_intro zenon_H3 | zenon_intro zenon_Ha ]. % 0.09/0.45 apply (zenon_L1_ zenon_TY_h zenon_TY_i); trivial. % 0.09/0.45 exact (zenon_Ha zenon_H2b). % 0.09/0.45 apply (zenon_L1_ zenon_TY_h zenon_TY_i); trivial. % 0.09/0.45 Qed. % 0.09/0.45 % SZS output end Proof % 0.09/0.45 (* END-PROOF *) % 0.09/0.45 nodes searched: 144 % 0.09/0.45 max branch formulas: 69 % 0.09/0.45 proof nodes created: 59 % 0.09/0.45 formulas created: 571 % 0.09/0.45 %------------------------------------------------------------------------------