TSTP Solution File: LCL658+1.001 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 16:23:21 EDT 2022
% Result : Theorem 0.46s 0.64s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL658+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 16:03:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.64 (* PROOF-FOUND *)
% 0.46/0.64 % SZS status Theorem
% 0.46/0.64 (* BEGIN-PROOF *)
% 0.46/0.64 % SZS output start Proof
% 0.46/0.64 Theorem main : (~(exists X : zenon_U, (~((~(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))\/(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)))))))))))))))))))).
% 0.46/0.64 Proof.
% 0.46/0.64 assert (zenon_L1_ : forall (zenon_TY_g : zenon_U), ((p1 zenon_TY_g)\/((forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_g X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))) -> (~(p1 zenon_TY_g)) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False).
% 0.46/0.64 do 1 intro. intros zenon_H2 zenon_H3 zenon_H4 zenon_H5.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H2); [ zenon_intro zenon_H8 | zenon_intro zenon_H7 ].
% 0.46/0.64 exact (zenon_H3 zenon_H8).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H7); [ zenon_intro zenon_Ha | zenon_intro zenon_H9 ].
% 0.46/0.64 exact (zenon_H4 zenon_Ha).
% 0.46/0.64 exact (zenon_H9 zenon_H5).
% 0.46/0.64 (* end of lemma zenon_L1_ *)
% 0.46/0.64 assert (zenon_L2_ : forall (zenon_TX_o : zenon_U) (zenon_TY_g : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))) -> (r1 zenon_TY_g zenon_TX_o) -> (forall Y : zenon_U, ((~(r1 zenon_TX_o Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))) -> False).
% 0.46/0.64 do 2 intro. intros zenon_Hb zenon_Hc zenon_Hd.
% 0.46/0.64 generalize (zenon_Hb zenon_TX_o). zenon_intro zenon_Hf.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_Hf); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 0.46/0.64 exact (zenon_H11 zenon_Hc).
% 0.46/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_o X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))) zenon_H10); [ zenon_intro zenon_H12; idtac ].
% 0.46/0.64 elim zenon_H12. zenon_intro zenon_TX_t. zenon_intro zenon_H14.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17.
% 0.46/0.64 apply zenon_H16. zenon_intro zenon_H19.
% 0.46/0.64 generalize (zenon_Hd zenon_TX_t). zenon_intro zenon_H1a.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.46/0.64 exact (zenon_H1c zenon_H19).
% 0.46/0.64 exact (zenon_H18 zenon_H1b).
% 0.46/0.64 (* end of lemma zenon_L2_ *)
% 0.46/0.64 assert (zenon_L3_ : forall (zenon_TY_bf : zenon_U), (~((forall X : zenon_U, ((~(r1 zenon_TY_bf X))\/(p1 X)))\/(~(p1 zenon_TY_bf)))) -> (~(p1 zenon_TY_bf)) -> False).
% 0.46/0.64 do 1 intro. intros zenon_H1d zenon_H1e.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.46/0.64 exact (zenon_H20 zenon_H1e).
% 0.46/0.64 (* end of lemma zenon_L3_ *)
% 0.46/0.64 assert (zenon_L4_ : forall (zenon_TY_g : zenon_U), (~(forall X : zenon_U, ((~(r1 zenon_TY_g 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))))))))))))) -> ((forall X : zenon_U, ((~(r1 zenon_TY_g 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_g 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_g X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False).
% 0.46/0.64 do 1 intro. intros zenon_H22 zenon_H23 zenon_H5.
% 0.46/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_g 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_H22); [ zenon_intro zenon_H24; idtac ].
% 0.46/0.64 elim zenon_H24. zenon_intro zenon_TX_bl. zenon_intro zenon_H26.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H27.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H27). zenon_intro zenon_H2a. zenon_intro zenon_H29.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H29). zenon_intro zenon_H2c. zenon_intro zenon_H2b.
% 0.46/0.64 apply zenon_H2b. zenon_intro zenon_H2d.
% 0.46/0.64 apply zenon_H28. zenon_intro zenon_H2e.
% 0.46/0.64 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bl Y))\/(p1 Y))) zenon_H2a); [ zenon_intro zenon_H2f; idtac ].
% 0.46/0.64 elim zenon_H2f. zenon_intro zenon_TY_bf. zenon_intro zenon_H30.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H1e.
% 0.46/0.64 apply zenon_H31. zenon_intro zenon_H32.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H33 | zenon_intro zenon_H9 ].
% 0.46/0.64 generalize (zenon_H2d zenon_TY_bf). zenon_intro zenon_H34.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.46/0.64 exact (zenon_H36 zenon_H32).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H1d ].
% 0.46/0.64 generalize (zenon_H33 zenon_TX_bl). zenon_intro zenon_H38.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 0.46/0.64 exact (zenon_H3a zenon_H2e).
% 0.46/0.64 generalize (zenon_H39 zenon_TY_bf). zenon_intro zenon_H3b.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H36 | zenon_intro zenon_H3c ].
% 0.46/0.64 exact (zenon_H36 zenon_H32).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 0.46/0.64 exact (zenon_H1e zenon_H3e).
% 0.46/0.64 exact (zenon_H3d zenon_H37).
% 0.46/0.64 apply (zenon_L3_ zenon_TY_bf); trivial.
% 0.46/0.64 exact (zenon_H9 zenon_H5).
% 0.46/0.64 (* end of lemma zenon_L4_ *)
% 0.46/0.64 apply NNPP. intro zenon_G.
% 0.46/0.64 apply zenon_G. zenon_intro zenon_H3f.
% 0.46/0.64 elim zenon_H3f. zenon_intro zenon_TX_cm. zenon_intro zenon_H41.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 0.46/0.64 apply zenon_H43. zenon_intro zenon_H44.
% 0.46/0.64 apply zenon_H42. zenon_intro zenon_H45.
% 0.46/0.64 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cm 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_H45); [ zenon_intro zenon_H46; idtac ].
% 0.46/0.64 elim zenon_H46. zenon_intro zenon_TY_g. zenon_intro zenon_H47.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H48). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H4a). zenon_intro zenon_H4. zenon_intro zenon_H4c.
% 0.46/0.64 apply zenon_H4c. zenon_intro zenon_H5.
% 0.46/0.64 apply zenon_H49. zenon_intro zenon_H4d.
% 0.46/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_g X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H4); [ zenon_intro zenon_H4e; idtac ].
% 0.46/0.64 elim zenon_H4e. zenon_intro zenon_TX_o. zenon_intro zenon_H4f.
% 0.46/0.64 apply (zenon_notor_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50.
% 0.46/0.64 apply zenon_H51. zenon_intro zenon_Hc.
% 0.46/0.64 apply zenon_H50. zenon_intro zenon_H52.
% 0.46/0.64 generalize (zenon_H44 zenon_TY_g). zenon_intro zenon_H53.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.46/0.64 exact (zenon_H55 zenon_H4d).
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H57. zenon_intro zenon_H56.
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H2. zenon_intro zenon_H58.
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H59. zenon_intro zenon_H23.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ].
% 0.46/0.64 exact (zenon_H4b zenon_H5b).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H3 | zenon_intro zenon_H5c ].
% 0.46/0.64 apply (zenon_L1_ zenon_TY_g); trivial.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_Hb | zenon_intro zenon_H22 ].
% 0.46/0.64 generalize (zenon_H59 zenon_TX_o). zenon_intro zenon_H5d.
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H11 | zenon_intro zenon_H5e ].
% 0.46/0.64 exact (zenon_H11 zenon_Hc).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_Hd | zenon_intro zenon_H5f ].
% 0.46/0.64 apply (zenon_L2_ zenon_TX_o zenon_TY_g); trivial.
% 0.46/0.64 exact (zenon_H5f zenon_H52).
% 0.46/0.64 apply (zenon_L4_ zenon_TY_g); trivial.
% 0.46/0.64 Qed.
% 0.46/0.64 % SZS output end Proof
% 0.46/0.64 (* END-PROOF *)
% 0.46/0.64 nodes searched: 4652
% 0.46/0.64 max branch formulas: 1331
% 0.46/0.64 proof nodes created: 530
% 0.46/0.64 formulas created: 22670
% 0.46/0.64
%------------------------------------------------------------------------------