%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL640+1.005 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 01:32:31 PM UTC 2026 % Result : Theorem 9.94s 10.26s % Output : Proof 9.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL640+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.36 % Computer : n026.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 % 0.02/0.36 % CPULimit : 300 % 0.02/0.36 % WCLimit : 300 % 0.02/0.36 % DateTime : Sat Sep 5 01:30:25 UTC 2026 % 0.02/0.36 % CPUTime : % 9.94/10.26 (* PROOF-FOUND *) % 9.94/10.26 % SZS status Theorem % 9.94/10.26 (* BEGIN-PROOF *) % 9.94/10.26 % SZS output start Proof % 9.94/10.26 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(((p1 X)\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(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))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 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))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(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)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X 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))\/(((p1 X)\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(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))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))))/\(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))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))))))))). % 9.94/10.26 Proof. % 9.94/10.26 assert (zenon_L1_ : forall (zenon_TY_d : zenon_U), (~((forall X : zenon_U, ((~(r1 zenon_TY_d X))\/(p1 X)))\/(~(p1 zenon_TY_d)))) -> (~(p1 zenon_TY_d)) -> False). % 9.94/10.26 do 1 intro. intros zenon_H1 zenon_H2. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H1). zenon_intro zenon_H5. zenon_intro zenon_H4. % 9.94/10.26 exact (zenon_H4 zenon_H2). % 9.94/10.26 (* end of lemma zenon_L1_ *) % 9.94/10.26 assert (zenon_L2_ : forall (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U), (((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))\/((~(p1 zenon_TY_n))\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 zenon_TY_n)\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall Y : zenon_U, ((~(r1 zenon_TY_n Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(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 X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (p1 zenon_TY_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (r1 zenon_TY_n zenon_TX_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False). % 9.94/10.26 do 2 intro. intros zenon_H6 zenon_H7 zenon_H8 zenon_H9 zenon_Ha zenon_Hb. % 9.94/10.26 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He. % 9.94/10.26 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10. % 9.94/10.26 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12. % 9.94/10.26 apply (zenon_or_s _ _ zenon_Hf); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 9.94/10.26 exact (zenon_H7 zenon_H15). % 9.94/10.26 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 9.94/10.26 exact (zenon_H17 zenon_H8). % 9.94/10.26 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 9.94/10.26 generalize (zenon_H13 zenon_TX_m). zenon_intro zenon_H1a. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 9.94/10.26 exact (zenon_H1c zenon_Ha). % 9.94/10.26 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 9.94/10.26 generalize (zenon_H19 zenon_TX_m). zenon_intro zenon_H1f. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H1c | zenon_intro zenon_H20 ]. % 9.94/10.26 exact (zenon_H1c zenon_Ha). % 9.94/10.26 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_m X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))) zenon_H20); [ zenon_intro zenon_H21; idtac ]. % 9.94/10.26 elim zenon_H21. zenon_intro zenon_TX_bi. zenon_intro zenon_H23. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26. % 9.94/10.26 apply zenon_H25. zenon_intro zenon_H28. % 9.94/10.26 generalize (zenon_H1e zenon_TX_bi). zenon_intro zenon_H29. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 9.94/10.26 exact (zenon_H2b zenon_H28). % 9.94/10.26 exact (zenon_H27 zenon_H2a). % 9.94/10.26 exact (zenon_H1d zenon_H9). % 9.94/10.26 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_n 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))) zenon_H18); [ zenon_intro zenon_H2c; idtac ]. % 9.94/10.26 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 9.94/10.26 apply zenon_H33. zenon_intro zenon_H35. % 9.94/10.26 apply zenon_H30. zenon_intro zenon_H36. % 9.94/10.26 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bt Y))\/(p1 Y))) zenon_H32); [ zenon_intro zenon_H37; idtac ]. % 9.94/10.26 elim zenon_H37. zenon_intro zenon_TY_d. zenon_intro zenon_H38. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H38). zenon_intro zenon_H39. zenon_intro zenon_H2. % 9.94/10.26 apply zenon_H39. zenon_intro zenon_H3a. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 9.94/10.26 generalize (zenon_H35 zenon_TY_d). zenon_intro zenon_H3d. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 9.94/10.26 exact (zenon_H3f zenon_H3a). % 9.94/10.26 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H1 ]. % 9.94/10.26 generalize (zenon_H3c zenon_TX_bt). zenon_intro zenon_H41. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 9.94/10.26 exact (zenon_H43 zenon_H36). % 9.94/10.26 generalize (zenon_H42 zenon_TY_d). zenon_intro zenon_H44. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3f | zenon_intro zenon_H45 ]. % 9.94/10.26 exact (zenon_H3f zenon_H3a). % 9.94/10.26 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 9.94/10.26 exact (zenon_H2 zenon_H47). % 9.94/10.26 exact (zenon_H46 zenon_H40). % 9.94/10.26 apply (zenon_L1_ zenon_TY_d); trivial. % 9.94/10.26 exact (zenon_H3b zenon_Hb). % 9.94/10.26 (* end of lemma zenon_L2_ *) % 9.94/10.26 assert (zenon_L3_ : forall (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U) (zenon_TX_cw : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_cw Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(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)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))) -> (r1 zenon_TX_cw zenon_TY_n) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (p1 zenon_TY_n) -> (r1 zenon_TY_n zenon_TX_m) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False). % 9.94/10.26 do 3 intro. intros zenon_H48 zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb. % 9.94/10.26 generalize (zenon_H48 zenon_TY_n). zenon_intro zenon_H4b. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ]. % 9.94/10.26 exact (zenon_H4c zenon_H49). % 9.94/10.26 apply (zenon_L2_ zenon_TX_m zenon_TY_n); trivial. % 9.94/10.26 (* end of lemma zenon_L3_ *) % 9.94/10.26 assert (zenon_L4_ : forall (zenon_TX_dd : zenon_U) (zenon_TY_de : zenon_U) (zenon_TX_cw : zenon_U) (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U), ((p1 zenon_TY_n)\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (r1 zenon_TY_n zenon_TX_m) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (r1 zenon_TX_cw zenon_TY_n) -> (r1 zenon_TY_de zenon_TX_cw) -> (r1 zenon_TX_dd zenon_TY_de) -> (forall Y : zenon_U, ((~(r1 zenon_TX_dd Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(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)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))))))) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False). % 9.94/10.26 do 5 intro. intros zenon_H11 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4d zenon_H4e zenon_H4f zenon_H50 zenon_Hb. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H8 | zenon_intro zenon_H53 ]. % 9.94/10.26 generalize (zenon_H4f zenon_TY_de). zenon_intro zenon_H54. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 9.94/10.26 exact (zenon_H56 zenon_H4e). % 9.94/10.26 generalize (zenon_H55 zenon_TX_cw). zenon_intro zenon_H57. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H48 ]. % 9.94/10.26 exact (zenon_H58 zenon_H4d). % 9.94/10.26 apply (zenon_L3_ zenon_TX_m zenon_TY_n zenon_TX_cw); trivial. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H59 | zenon_intro zenon_H3b ]. % 9.94/10.26 exact (zenon_H50 zenon_H59). % 9.94/10.26 exact (zenon_H3b zenon_Hb). % 9.94/10.26 (* end of lemma zenon_L4_ *) % 9.94/10.26 assert (zenon_L5_ : forall (zenon_TX_dd : zenon_U) (zenon_TY_de : zenon_U) (zenon_TX_cw : zenon_U) (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U), (((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))\/((~(p1 zenon_TY_n))\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 zenon_TY_n)\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall Y : zenon_U, ((~(r1 zenon_TY_n Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(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 X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (r1 zenon_TY_n zenon_TX_m) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (r1 zenon_TX_cw zenon_TY_n) -> (r1 zenon_TY_de zenon_TX_cw) -> (r1 zenon_TX_dd zenon_TY_de) -> (forall Y : zenon_U, ((~(r1 zenon_TX_dd Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(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)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))))))) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False). % 9.94/10.26 do 5 intro. intros zenon_H6 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4d zenon_H4e zenon_H4f zenon_H50 zenon_Hb. % 9.94/10.26 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He. % 9.94/10.26 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10. % 9.94/10.26 apply (zenon_L4_ zenon_TX_dd zenon_TY_de zenon_TX_cw zenon_TX_m zenon_TY_n); trivial. % 9.94/10.26 (* end of lemma zenon_L5_ *) % 9.94/10.26 assert (zenon_L6_ : forall (zenon_TX_m : zenon_U) (zenon_TY_de : zenon_U) (zenon_TX_dd : zenon_U) (zenon_TY_n : zenon_U) (zenon_TX_cw : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_cw Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(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)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))) -> (r1 zenon_TX_cw zenon_TY_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_dd Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))\/(~((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 Y)\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))/\((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))\/(~(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)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))))))) -> (r1 zenon_TX_dd zenon_TY_de) -> (r1 zenon_TY_de zenon_TX_cw) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (r1 zenon_TY_n zenon_TX_m) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> False). % 9.94/10.26 do 5 intro. intros zenon_H48 zenon_H49 zenon_H4f zenon_H4e zenon_H4d zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H50. % 9.94/10.26 generalize (zenon_H48 zenon_TY_n). zenon_intro zenon_H4b. % 9.94/10.26 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ]. % 9.94/10.26 exact (zenon_H4c zenon_H49). % 9.94/10.26 apply (zenon_L5_ zenon_TX_dd zenon_TY_de zenon_TX_cw zenon_TX_m zenon_TY_n); trivial. % 9.94/10.26 (* end of lemma zenon_L6_ *) % 9.94/10.26 apply NNPP. intro zenon_G. % 9.94/10.26 apply zenon_G. zenon_intro zenon_H5a. % 9.94/10.26 elim zenon_H5a. zenon_intro zenon_TX_dd. zenon_intro zenon_H5b. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 9.94/10.26 apply zenon_H5e. zenon_intro zenon_H60. % 9.94/10.26 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 9.94/10.26 apply zenon_H5f. zenon_intro zenon_H4f. % 9.94/10.26 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_dd Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))))) zenon_H62); [ zenon_intro zenon_H63; idtac ]. % 9.94/10.26 elim zenon_H63. zenon_intro zenon_TY_de. zenon_intro zenon_H64. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H65. % 9.94/10.26 apply zenon_H66. zenon_intro zenon_H4e. % 9.94/10.26 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_de X))\/(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))))) zenon_H65); [ zenon_intro zenon_H67; idtac ]. % 9.94/10.26 elim zenon_H67. zenon_intro zenon_TX_cw. zenon_intro zenon_H68. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 9.94/10.26 apply zenon_H6a. zenon_intro zenon_H4d. % 9.94/10.26 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cw Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ]. % 9.94/10.26 elim zenon_H6b. zenon_intro zenon_TY_n. zenon_intro zenon_H6c. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H6d). zenon_intro zenon_H7. zenon_intro zenon_H6f. % 9.94/10.26 apply (zenon_notor_s _ _ zenon_H6f). zenon_intro zenon_H50. zenon_intro zenon_H70. % 9.94/10.26 apply zenon_H70. zenon_intro zenon_Hb. % 9.94/10.26 apply zenon_H6e. zenon_intro zenon_H49. % 9.94/10.26 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H50); [ zenon_intro zenon_H71; idtac ]. % 9.94/10.26 elim zenon_H71. zenon_intro zenon_TX_m. zenon_intro zenon_H72. % 9.94/10.29 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73. % 9.94/10.29 apply zenon_H74. zenon_intro zenon_Ha. % 9.94/10.29 apply zenon_H73. zenon_intro zenon_H9. % 9.94/10.29 generalize (zenon_H4f zenon_TY_de). zenon_intro zenon_H54. % 9.94/10.29 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 9.94/10.29 exact (zenon_H56 zenon_H4e). % 9.94/10.29 generalize (zenon_H55 zenon_TX_cw). zenon_intro zenon_H57. % 9.94/10.29 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H48 ]. % 9.94/10.29 exact (zenon_H58 zenon_H4d). % 9.94/10.29 apply (zenon_L6_ zenon_TX_m zenon_TY_de zenon_TX_dd zenon_TY_n zenon_TX_cw); trivial. % 9.94/10.29 Qed. % 9.94/10.29 % SZS output end Proof % 9.94/10.29 (* END-PROOF *) % 9.94/10.29 nodes searched: 118259 % 9.94/10.29 max branch formulas: 36809 % 9.94/10.29 proof nodes created: 3805 % 9.94/10.29 formulas created: 921000 % 9.94/10.29 %------------------------------------------------------------------------------