%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL660+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 01:32:39 PM UTC 2026 % Result : Theorem 0.20s 0.53s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL660+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n019.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Sat Sep 5 11:04:23 UTC 2026 % 0.08/0.35 % CPUTime : % 0.20/0.53 (* PROOF-FOUND *) % 0.20/0.53 % SZS status Theorem % 0.20/0.53 (* BEGIN-PROOF *) % 0.20/0.53 % SZS output start Proof % 0.20/0.53 Theorem main : (~(exists X : zenon_U, (~(((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p3 Y)))))/\((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p4 Y)))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/((p4 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p4 Y)))\/(~(p4 X))))))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(p3 X))))))))/\((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))\/(~(((((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))/\((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))))\/(~(((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))/\((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X 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)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))))))))))))))). % 0.20/0.53 Proof. % 0.20/0.53 assert (zenon_L1_ : forall (zenon_TY_g : zenon_U) (zenon_TX_h : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))) -> (r1 zenon_TX_h zenon_TY_g) -> (~(p2 zenon_TY_g)) -> (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))) -> False). % 0.20/0.53 do 2 intro. intros zenon_H2 zenon_H3 zenon_H4 zenon_H5. % 0.20/0.53 generalize (zenon_H2 zenon_TY_g). zenon_intro zenon_H8. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H8); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ]. % 0.20/0.53 exact (zenon_Ha zenon_H3). % 0.20/0.53 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 0.20/0.53 apply (zenon_or_s _ _ zenon_Hb); [ zenon_intro zenon_He | zenon_intro zenon_Hd ]. % 0.20/0.53 exact (zenon_H4 zenon_He). % 0.20/0.53 exact (zenon_Hd zenon_H5). % 0.20/0.53 (* end of lemma zenon_L1_ *) % 0.20/0.53 assert (zenon_L2_ : forall (zenon_TX_h : zenon_U), (~((forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))) -> False). % 0.20/0.53 do 1 intro. intros zenon_Hf zenon_H10. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_Hf). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.20/0.53 exact (zenon_H11 zenon_H10). % 0.20/0.53 (* end of lemma zenon_L2_ *) % 0.20/0.53 assert (zenon_L3_ : forall (zenon_TX_h : zenon_U), (~((p2 zenon_TX_h)\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_h Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H13 zenon_H14. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.20/0.53 exact (zenon_H15 zenon_H14). % 0.20/0.53 (* end of lemma zenon_L3_ *) % 0.20/0.53 assert (zenon_L4_ : forall (zenon_TX_ba : zenon_U), (~((forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/(p2 Y)))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y))))))))))))) -> ((((forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))/\((p2 zenon_TX_ba)\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_ba Y))\/((((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))))\/(~(((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))/\((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))))))))) -> False). % 0.20/0.53 do 1 intro. intros zenon_H17 zenon_H18 zenon_H19. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H17). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.20/0.53 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ba Y))\/(p2 Y))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ]. % 0.20/0.53 elim zenon_H1d. zenon_intro zenon_TY_be. zenon_intro zenon_H1f. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.20/0.53 apply zenon_H21. zenon_intro zenon_H22. % 0.20/0.53 apply zenon_H1b. zenon_intro zenon_H23. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H19); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ]. % 0.20/0.53 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.53 generalize (zenon_H29 zenon_TY_be). zenon_intro zenon_H2a. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 0.20/0.53 exact (zenon_H2c zenon_H22). % 0.20/0.53 generalize (zenon_H18 zenon_TY_be). zenon_intro zenon_H2d. % 0.20/0.53 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H2c | zenon_intro zenon_H2e ]. % 0.20/0.53 exact (zenon_H2c zenon_H22). % 0.20/0.53 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 0.20/0.53 exact (zenon_H20 zenon_H30). % 0.20/0.53 exact (zenon_H2f zenon_H2b). % 0.20/0.53 exact (zenon_H28 zenon_H23). % 0.20/0.53 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ba Y))\/((((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))/\((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))))\/(~(((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X)))))))))))/\((p2 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/(~(p2 Y)))))))))))))))) zenon_H24); [ zenon_intro zenon_H31; idtac ]. % 0.20/0.53 elim zenon_H31. zenon_intro zenon_TY_by. zenon_intro zenon_H33. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.20/0.53 apply zenon_H36. zenon_intro zenon_H38. % 0.20/0.53 apply zenon_H35. zenon_intro zenon_H39. % 0.20/0.53 apply (zenon_notand_s _ _ zenon_H37); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.20/0.53 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_by X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))))) zenon_H3d); [ zenon_intro zenon_H3e; idtac ]. % 0.20/0.53 elim zenon_H3e. zenon_intro zenon_TX_h. zenon_intro zenon_H3f. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H3f). zenon_intro zenon_H40. zenon_intro zenon_H10. % 0.20/0.53 apply zenon_H40. zenon_intro zenon_H41. % 0.20/0.53 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_h Y))\/((p2 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/(~(p2 X))))))))) zenon_H10); [ zenon_intro zenon_H42; idtac ]. % 0.20/0.53 elim zenon_H42. zenon_intro zenon_TY_g. zenon_intro zenon_H43. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 0.20/0.53 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H4. zenon_intro zenon_H46. % 0.20/0.53 apply zenon_H46. zenon_intro zenon_H5. % 0.20/0.53 apply zenon_H45. zenon_intro zenon_H3. % 0.20/0.53 apply zenon_H3c. zenon_intro zenon_H47. % 0.20/0.54 generalize (zenon_H47 zenon_TX_h). zenon_intro zenon_H48. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.20/0.54 exact (zenon_H4a zenon_H41). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H14 ]. % 0.20/0.54 generalize (zenon_H38 zenon_TX_h). zenon_intro zenon_H4c. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H4a | zenon_intro zenon_H4d ]. % 0.20/0.54 exact (zenon_H4a zenon_H41). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H2 | zenon_intro zenon_H4e ]. % 0.20/0.54 apply (zenon_L1_ zenon_TY_g zenon_TX_h); trivial. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_Hf | zenon_intro zenon_H13 ]. % 0.20/0.54 apply (zenon_L2_ zenon_TX_h); trivial. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.20/0.54 exact (zenon_H16 zenon_H4b). % 0.20/0.54 generalize (zenon_H38 zenon_TX_h). zenon_intro zenon_H4c. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H4a | zenon_intro zenon_H4d ]. % 0.20/0.54 exact (zenon_H4a zenon_H41). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H2 | zenon_intro zenon_H4e ]. % 0.20/0.54 apply (zenon_L1_ zenon_TY_g zenon_TX_h); trivial. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_Hf | zenon_intro zenon_H13 ]. % 0.20/0.54 apply (zenon_L2_ zenon_TX_h); trivial. % 0.20/0.54 apply (zenon_L3_ zenon_TX_h); trivial. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 0.20/0.54 apply zenon_H4f. zenon_intro zenon_H51. % 0.20/0.54 generalize (zenon_H23 zenon_TY_by). zenon_intro zenon_H52. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.20/0.54 exact (zenon_H54 zenon_H39). % 0.20/0.54 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.20/0.54 exact (zenon_H50 zenon_H56). % 0.20/0.54 exact (zenon_H55 zenon_H51). % 0.20/0.54 (* end of lemma zenon_L4_ *) % 0.20/0.54 apply NNPP. intro zenon_G. % 0.20/0.54 apply zenon_G. zenon_intro zenon_H57. % 0.20/0.54 elim zenon_H57. zenon_intro zenon_TX_ba. zenon_intro zenon_H58. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H58). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H59). zenon_intro zenon_H5c. zenon_intro zenon_H5b. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H5b). zenon_intro zenon_H5e. zenon_intro zenon_H5d. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H5d). zenon_intro zenon_H60. zenon_intro zenon_H5f. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H5f). zenon_intro zenon_H62. zenon_intro zenon_H61. % 0.20/0.54 apply (zenon_notor_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 0.20/0.54 apply zenon_H63. zenon_intro zenon_H65. % 0.20/0.54 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H66 | zenon_intro zenon_H17 ]. % 0.20/0.54 apply zenon_H66. zenon_intro zenon_H67. % 0.20/0.54 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H68 | zenon_intro zenon_H17 ]. % 0.20/0.54 apply zenon_H68. zenon_intro zenon_H69. % 0.20/0.54 generalize (zenon_H69 zenon_TX_ba). zenon_intro zenon_H6a. % 0.20/0.54 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.20/0.54 generalize (reflexivity zenon_TX_ba). zenon_intro zenon_H6d. % 0.20/0.54 exact (zenon_H6c zenon_H6d). % 0.20/0.54 exact (zenon_H6b zenon_H67). % 0.20/0.54 apply (zenon_L4_ zenon_TX_ba); trivial. % 0.20/0.54 apply (zenon_L4_ zenon_TX_ba); trivial. % 0.20/0.54 Qed. % 0.20/0.54 % SZS output end Proof % 0.20/0.54 (* END-PROOF *) % 0.20/0.54 nodes searched: 2466 % 0.20/0.54 max branch formulas: 616 % 0.20/0.54 proof nodes created: 415 % 0.20/0.54 formulas created: 12380 % 0.20/0.54 %------------------------------------------------------------------------------