%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL640+1.010 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 31.04s 31.37s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL640+1.010 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.37 % Computer : n004.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 5 16:05:29 UTC 2026 % 0.09/0.37 % CPUTime : % 31.04/31.37 (* PROOF-FOUND *) % 31.04/31.37 % SZS status Theorem % 31.04/31.37 (* BEGIN-PROOF *) % 31.04/31.37 % SZS output start Proof % 31.04/31.37 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))\/(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))\/(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)))))))))))))))))))))))))))\/((~(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))\/(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))\/(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))\/(~(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 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))\/(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 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((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))\/(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))\/(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))\/((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))\/(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))))))\/(~(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 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))\/(((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 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))))))))))))))))))))))). % 31.04/31.37 Proof. % 31.04/31.37 assert (zenon_L1_ : forall (zenon_TX_d : zenon_U), (~((forall Y : zenon_U, ((~(r1 zenon_TX_d Y))\/(p1 Y)))\/(~(p1 zenon_TX_d)))) -> (~(p1 zenon_TX_d)) -> False). % 31.04/31.37 do 1 intro. intros zenon_H1 zenon_H2. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H1). zenon_intro zenon_H5. zenon_intro zenon_H4. % 31.04/31.37 exact (zenon_H4 zenon_H2). % 31.04/31.37 (* end of lemma zenon_L1_ *) % 31.04/31.37 assert (zenon_L2_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U), (((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))\/((~(p1 zenon_TX_n))\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 zenon_TX_n)\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n 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_TX_n 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 Y : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n 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 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 2 intro. intros zenon_H6 zenon_H7 zenon_H8 zenon_H9 zenon_Ha zenon_Hb. % 31.04/31.37 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He. % 31.04/31.37 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10. % 31.04/31.37 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12. % 31.04/31.37 apply (zenon_or_s _ _ zenon_Hf); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 31.04/31.37 exact (zenon_H7 zenon_H15). % 31.04/31.37 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ]. % 31.04/31.37 exact (zenon_H17 zenon_H8). % 31.04/31.37 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ]. % 31.04/31.37 generalize (zenon_H13 zenon_TY_m). zenon_intro zenon_H1a. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ]. % 31.04/31.37 exact (zenon_H1c zenon_Ha). % 31.04/31.37 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ]. % 31.04/31.37 generalize (zenon_H19 zenon_TY_m). zenon_intro zenon_H1f. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H1c | zenon_intro zenon_H20 ]. % 31.04/31.37 exact (zenon_H1c zenon_Ha). % 31.04/31.37 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TY_m Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))) zenon_H20); [ zenon_intro zenon_H21; idtac ]. % 31.04/31.37 elim zenon_H21. zenon_intro zenon_TY_bi. zenon_intro zenon_H23. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26. % 31.04/31.37 apply zenon_H25. zenon_intro zenon_H28. % 31.04/31.37 generalize (zenon_H1e zenon_TY_bi). zenon_intro zenon_H29. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 31.04/31.37 exact (zenon_H2b zenon_H28). % 31.04/31.37 exact (zenon_H27 zenon_H2a). % 31.04/31.37 exact (zenon_H1d zenon_H9). % 31.04/31.37 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_n 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))) zenon_H18); [ zenon_intro zenon_H2c; idtac ]. % 31.04/31.37 elim zenon_H2c. zenon_intro zenon_TY_bt. zenon_intro zenon_H2e. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 31.04/31.37 apply zenon_H33. zenon_intro zenon_H35. % 31.04/31.37 apply zenon_H30. zenon_intro zenon_H36. % 31.04/31.37 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_bt X))\/(p1 X))) zenon_H32); [ zenon_intro zenon_H37; idtac ]. % 31.04/31.37 elim zenon_H37. zenon_intro zenon_TX_d. zenon_intro zenon_H38. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H38). zenon_intro zenon_H39. zenon_intro zenon_H2. % 31.04/31.37 apply zenon_H39. zenon_intro zenon_H3a. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 31.04/31.37 generalize (zenon_H35 zenon_TX_d). zenon_intro zenon_H3d. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 31.04/31.37 exact (zenon_H3f zenon_H3a). % 31.04/31.37 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H1 ]. % 31.04/31.37 generalize (zenon_H3c zenon_TY_bt). zenon_intro zenon_H41. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 31.04/31.37 exact (zenon_H43 zenon_H36). % 31.04/31.37 generalize (zenon_H42 zenon_TX_d). zenon_intro zenon_H44. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3f | zenon_intro zenon_H45 ]. % 31.04/31.37 exact (zenon_H3f zenon_H3a). % 31.04/31.37 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 31.04/31.37 exact (zenon_H2 zenon_H47). % 31.04/31.37 exact (zenon_H46 zenon_H40). % 31.04/31.37 apply (zenon_L1_ zenon_TX_d); trivial. % 31.04/31.37 exact (zenon_H3b zenon_Hb). % 31.04/31.37 (* end of lemma zenon_L2_ *) % 31.04/31.37 assert (zenon_L3_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_cw 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 3 intro. intros zenon_H48 zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb. % 31.04/31.37 generalize (zenon_H48 zenon_TX_n). zenon_intro zenon_H4b. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ]. % 31.04/31.37 exact (zenon_H4c zenon_H49). % 31.04/31.37 apply (zenon_L2_ zenon_TY_m zenon_TX_n); trivial. % 31.04/31.37 (* end of lemma zenon_L3_ *) % 31.04/31.37 assert (zenon_L4_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_db 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 4 intro. intros zenon_H4d zenon_H4e zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb. % 31.04/31.37 generalize (zenon_H4d zenon_TY_cw). zenon_intro zenon_H50. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H48 ]. % 31.04/31.37 exact (zenon_H51 zenon_H4e). % 31.04/31.37 apply (zenon_L3_ zenon_TY_m zenon_TX_n zenon_TY_cw); trivial. % 31.04/31.37 (* end of lemma zenon_L4_ *) % 31.04/31.37 assert (zenon_L5_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_dg 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 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 5 intro. intros zenon_H52 zenon_H53 zenon_H4e zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb. % 31.04/31.37 generalize (zenon_H52 zenon_TX_db). zenon_intro zenon_H55. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H4d ]. % 31.04/31.37 exact (zenon_H56 zenon_H53). % 31.04/31.37 apply (zenon_L4_ zenon_TY_m zenon_TX_n zenon_TY_cw zenon_TX_db); trivial. % 31.04/31.37 (* end of lemma zenon_L5_ *) % 31.04/31.37 assert (zenon_L6_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_dl Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 6 intro. intros zenon_H57 zenon_H58 zenon_H53 zenon_H4e zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb. % 31.04/31.37 generalize (zenon_H57 zenon_TY_dg). zenon_intro zenon_H5a. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H52 ]. % 31.04/31.37 exact (zenon_H5b zenon_H58). % 31.04/31.37 apply (zenon_L5_ zenon_TY_m zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg); trivial. % 31.04/31.37 (* end of lemma zenon_L6_ *) % 31.04/31.37 assert (zenon_L7_ : forall (zenon_TX_ds : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U), ((p1 zenon_TX_n)\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n 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_m X))\/(p1 X))) -> (r1 zenon_TX_n zenon_TY_m) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TY_cw zenon_TX_n) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_ds zenon_TY_dt) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((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 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 8 intro. intros zenon_H11 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4e zenon_H53 zenon_H58 zenon_H5c zenon_H5d zenon_H5e zenon_H5f zenon_Hb. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H8 | zenon_intro zenon_H62 ]. % 31.04/31.37 generalize (zenon_H5e zenon_TY_dt). zenon_intro zenon_H63. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 31.04/31.37 exact (zenon_H65 zenon_H5d). % 31.04/31.37 generalize (zenon_H64 zenon_TX_dl). zenon_intro zenon_H66. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H57 ]. % 31.04/31.37 exact (zenon_H67 zenon_H5c). % 31.04/31.37 apply (zenon_L6_ zenon_TY_m zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg zenon_TX_dl); trivial. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H68 | zenon_intro zenon_H3b ]. % 31.04/31.37 exact (zenon_H5f zenon_H68). % 31.04/31.37 exact (zenon_H3b zenon_Hb). % 31.04/31.37 (* end of lemma zenon_L7_ *) % 31.04/31.37 assert (zenon_L8_ : forall (zenon_TX_ds : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U), (((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))\/((~(p1 zenon_TX_n))\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 zenon_TX_n)\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n 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_TX_n 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 Y : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n 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_m X))\/(p1 X))) -> (r1 zenon_TX_n zenon_TY_m) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TY_cw zenon_TX_n) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_ds zenon_TY_dt) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((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 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False). % 31.04/31.37 do 8 intro. intros zenon_H6 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4e zenon_H53 zenon_H58 zenon_H5c zenon_H5d zenon_H5e zenon_H5f zenon_Hb. % 31.04/31.37 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He. % 31.04/31.37 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10. % 31.04/31.37 apply (zenon_L7_ zenon_TX_ds zenon_TY_dt zenon_TX_dl zenon_TY_dg zenon_TX_db zenon_TY_cw zenon_TY_m zenon_TX_n); trivial. % 31.04/31.37 (* end of lemma zenon_L8_ *) % 31.04/31.37 assert (zenon_L9_ : forall (zenon_TY_m : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_cw 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False). % 31.04/31.37 do 8 intro. intros zenon_H48 zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H58 zenon_H53 zenon_H4e zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f. % 31.04/31.37 generalize (zenon_H48 zenon_TX_n). zenon_intro zenon_H4b. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ]. % 31.04/31.37 exact (zenon_H4c zenon_H49). % 31.04/31.37 apply (zenon_L8_ zenon_TX_ds zenon_TY_dt zenon_TX_dl zenon_TY_dg zenon_TX_db zenon_TY_cw zenon_TY_m zenon_TX_n); trivial. % 31.04/31.37 (* end of lemma zenon_L9_ *) % 31.04/31.37 assert (zenon_L10_ : forall (zenon_TY_m : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_db 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False). % 31.04/31.37 do 8 intro. intros zenon_H4d zenon_H4e zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H58 zenon_H53 zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f. % 31.04/31.37 generalize (zenon_H4d zenon_TY_cw). zenon_intro zenon_H50. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H48 ]. % 31.04/31.37 exact (zenon_H51 zenon_H4e). % 31.04/31.37 apply (zenon_L9_ zenon_TY_m zenon_TX_db zenon_TY_dg zenon_TX_dl zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw); trivial. % 31.04/31.37 (* end of lemma zenon_L10_ *) % 31.04/31.37 assert (zenon_L11_ : forall (zenon_TY_m : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_dg 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 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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_dl zenon_TY_dg) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False). % 31.04/31.37 do 8 intro. intros zenon_H52 zenon_H53 zenon_H4e zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H58 zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f. % 31.04/31.37 generalize (zenon_H52 zenon_TX_db). zenon_intro zenon_H55. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H4d ]. % 31.04/31.37 exact (zenon_H56 zenon_H53). % 31.04/31.37 apply (zenon_L10_ zenon_TY_m zenon_TY_dg zenon_TX_dl zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw zenon_TX_db); trivial. % 31.04/31.37 (* end of lemma zenon_L11_ *) % 31.04/31.37 assert (zenon_L12_ : forall (zenon_TY_m : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_dl Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(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 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 Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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))\/((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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False). % 31.04/31.37 do 8 intro. intros zenon_H57 zenon_H58 zenon_H53 zenon_H4e zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f. % 31.04/31.37 generalize (zenon_H57 zenon_TY_dg). zenon_intro zenon_H5a. % 31.04/31.37 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H52 ]. % 31.04/31.37 exact (zenon_H5b zenon_H58). % 31.04/31.37 apply (zenon_L11_ zenon_TY_m zenon_TX_dl zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg); trivial. % 31.04/31.37 (* end of lemma zenon_L12_ *) % 31.04/31.37 apply NNPP. intro zenon_G. % 31.04/31.37 apply zenon_G. zenon_intro zenon_H69. % 31.04/31.37 elim zenon_H69. zenon_intro zenon_TX_ds. zenon_intro zenon_H6a. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H6a). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71. % 31.04/31.37 apply zenon_H71. zenon_intro zenon_H73. % 31.04/31.37 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H75. zenon_intro zenon_H74. % 31.04/31.37 apply zenon_H72. zenon_intro zenon_H5e. % 31.04/31.37 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))) zenon_H75); [ zenon_intro zenon_H76; idtac ]. % 31.04/31.37 elim zenon_H76. zenon_intro zenon_TY_dt. zenon_intro zenon_H77. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78. % 31.04/31.37 apply zenon_H79. zenon_intro zenon_H5d. % 31.04/31.37 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dt 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))) zenon_H78); [ zenon_intro zenon_H7a; idtac ]. % 31.04/31.37 elim zenon_H7a. zenon_intro zenon_TX_dl. zenon_intro zenon_H7b. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7d. zenon_intro zenon_H7c. % 31.04/31.37 apply zenon_H7d. zenon_intro zenon_H5c. % 31.04/31.37 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_dl Y))\/(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))\/(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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))) zenon_H7c); [ zenon_intro zenon_H7e; idtac ]. % 31.04/31.37 elim zenon_H7e. zenon_intro zenon_TY_dg. zenon_intro zenon_H7f. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 31.04/31.37 apply zenon_H81. zenon_intro zenon_H58. % 31.04/31.37 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dg 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 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)))))))))))))))))) zenon_H80); [ zenon_intro zenon_H82; idtac ]. % 31.04/31.37 elim zenon_H82. zenon_intro zenon_TX_db. zenon_intro zenon_H83. % 31.04/31.37 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84. % 0.15/31.49 apply zenon_H85. zenon_intro zenon_H53. % 0.15/31.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_db Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))) zenon_H84); [ zenon_intro zenon_H86; idtac ]. % 0.15/31.49 elim zenon_H86. zenon_intro zenon_TY_cw. zenon_intro zenon_H87. % 0.15/31.49 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H89. zenon_intro zenon_H88. % 0.15/31.49 apply zenon_H89. zenon_intro zenon_H4e. % 0.15/31.49 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_cw X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(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))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))) zenon_H88); [ zenon_intro zenon_H8a; idtac ]. % 0.15/31.49 elim zenon_H8a. zenon_intro zenon_TX_n. zenon_intro zenon_H8b. % 0.15/31.49 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 0.15/31.49 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H7. zenon_intro zenon_H8e. % 0.15/31.49 apply (zenon_notor_s _ _ zenon_H8e). zenon_intro zenon_H5f. zenon_intro zenon_H8f. % 0.15/31.49 apply zenon_H8f. zenon_intro zenon_Hb. % 0.15/31.49 apply zenon_H8d. zenon_intro zenon_H49. % 0.15/31.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))) zenon_H5f); [ zenon_intro zenon_H90; idtac ]. % 0.15/31.49 elim zenon_H90. zenon_intro zenon_TY_m. zenon_intro zenon_H91. % 0.15/31.49 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H93. zenon_intro zenon_H92. % 0.15/31.49 apply zenon_H93. zenon_intro zenon_Ha. % 0.15/31.49 apply zenon_H92. zenon_intro zenon_H9. % 0.15/31.49 generalize (zenon_H5e zenon_TY_dt). zenon_intro zenon_H63. % 0.15/31.49 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ]. % 0.15/31.49 exact (zenon_H65 zenon_H5d). % 0.15/31.49 generalize (zenon_H64 zenon_TX_dl). zenon_intro zenon_H66. % 0.15/31.49 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H57 ]. % 0.15/31.49 exact (zenon_H67 zenon_H5c). % 0.15/31.49 apply (zenon_L12_ zenon_TY_m zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg zenon_TX_dl); trivial. % 0.15/31.49 Qed. % 0.15/31.49 % SZS output end Proof % 0.15/31.49 (* END-PROOF *) % 0.15/31.49 nodes searched: 225545 % 0.15/31.49 max branch formulas: 57572 % 0.15/31.49 proof nodes created: 12637 % 0.15/31.49 formulas created: 1618065 % 0.15/31.49 %------------------------------------------------------------------------------