TSTP Solution File: LCL640+1.001 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL640+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n012.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 16:22:52 EDT 2022
% Result : Theorem 0.41s 0.62s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL640+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 16:42:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.41/0.62 (* PROOF-FOUND *)
% 0.41/0.62 % SZS status Theorem
% 0.41/0.62 (* BEGIN-PROOF *)
% 0.41/0.62 % SZS output start Proof
% 0.41/0.62 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)))))))))))))))))))).
% 0.41/0.62 Proof.
% 0.41/0.62 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).
% 0.41/0.62 do 1 intro. intros zenon_H1 zenon_H2.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H1). zenon_intro zenon_H5. zenon_intro zenon_H4.
% 0.41/0.62 exact (zenon_H4 zenon_H2).
% 0.41/0.62 (* end of lemma zenon_L1_ *)
% 0.41/0.62 apply NNPP. intro zenon_G.
% 0.41/0.62 apply zenon_G. zenon_intro zenon_H6.
% 0.41/0.62 elim zenon_H6. zenon_intro zenon_TX_h. zenon_intro zenon_H8.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H8). zenon_intro zenon_Ha. zenon_intro zenon_H9.
% 0.41/0.62 apply zenon_Ha. zenon_intro zenon_Hb.
% 0.41/0.62 apply zenon_H9. zenon_intro zenon_Hc.
% 0.41/0.62 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_h 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_Hc); [ zenon_intro zenon_Hd; idtac ].
% 0.41/0.62 elim zenon_Hd. zenon_intro zenon_TY_o. zenon_intro zenon_Hf.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_Hf). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H12). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 0.41/0.62 apply zenon_H14. zenon_intro zenon_H16.
% 0.41/0.62 apply zenon_H11. zenon_intro zenon_H17.
% 0.41/0.62 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_o X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H15); [ zenon_intro zenon_H18; idtac ].
% 0.41/0.62 elim zenon_H18. zenon_intro zenon_TX_z. zenon_intro zenon_H1a.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 0.41/0.62 apply zenon_H1c. zenon_intro zenon_H1d.
% 0.41/0.62 apply zenon_H1b. zenon_intro zenon_H1e.
% 0.41/0.62 generalize (zenon_Hb zenon_TY_o). zenon_intro zenon_H1f.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.41/0.62 exact (zenon_H21 zenon_H17).
% 0.41/0.62 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.41/0.62 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.41/0.62 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.41/0.62 exact (zenon_H13 zenon_H29).
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 0.41/0.62 exact (zenon_H2b zenon_H2d).
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 0.41/0.62 exact (zenon_H15 zenon_H2f).
% 0.41/0.62 exact (zenon_H2e zenon_H16).
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ].
% 0.41/0.62 generalize (zenon_H27 zenon_TX_z). zenon_intro zenon_H32.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.41/0.62 exact (zenon_H34 zenon_H1d).
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.41/0.62 generalize (zenon_H31 zenon_TX_z). zenon_intro zenon_H37.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H34 | zenon_intro zenon_H38 ].
% 0.41/0.62 exact (zenon_H34 zenon_H1d).
% 0.41/0.62 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_z X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))) zenon_H38); [ zenon_intro zenon_H39; idtac ].
% 0.41/0.62 elim zenon_H39. zenon_intro zenon_TX_cg. zenon_intro zenon_H3b.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e.
% 0.41/0.62 apply zenon_H3d. zenon_intro zenon_H40.
% 0.41/0.62 generalize (zenon_H36 zenon_TX_cg). zenon_intro zenon_H41.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 0.41/0.62 exact (zenon_H43 zenon_H40).
% 0.41/0.62 exact (zenon_H3f zenon_H42).
% 0.41/0.62 exact (zenon_H35 zenon_H1e).
% 0.41/0.62 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_o 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_H30); [ zenon_intro zenon_H44; idtac ].
% 0.41/0.62 elim zenon_H44. zenon_intro zenon_TX_cr. zenon_intro zenon_H46.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 0.41/0.62 apply zenon_H4b. zenon_intro zenon_H4d.
% 0.41/0.62 apply zenon_H48. zenon_intro zenon_H4e.
% 0.41/0.62 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cr Y))\/(p1 Y))) zenon_H4a); [ zenon_intro zenon_H4f; idtac ].
% 0.41/0.62 elim zenon_H4f. zenon_intro zenon_TY_d. zenon_intro zenon_H50.
% 0.41/0.62 apply (zenon_notor_s _ _ zenon_H50). zenon_intro zenon_H51. zenon_intro zenon_H2.
% 0.41/0.62 apply zenon_H51. zenon_intro zenon_H52.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H26); [ zenon_intro zenon_H53 | zenon_intro zenon_H2e ].
% 0.41/0.62 generalize (zenon_H4d zenon_TY_d). zenon_intro zenon_H54.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 0.41/0.62 exact (zenon_H56 zenon_H52).
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H1 ].
% 0.41/0.62 generalize (zenon_H53 zenon_TX_cr). zenon_intro zenon_H58.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ].
% 0.41/0.62 exact (zenon_H5a zenon_H4e).
% 0.41/0.62 generalize (zenon_H59 zenon_TY_d). zenon_intro zenon_H5b.
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H56 | zenon_intro zenon_H5c ].
% 0.41/0.62 exact (zenon_H56 zenon_H52).
% 0.41/0.62 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ].
% 0.41/0.62 exact (zenon_H2 zenon_H5e).
% 0.41/0.62 exact (zenon_H5d zenon_H57).
% 0.41/0.62 apply (zenon_L1_ zenon_TY_d); trivial.
% 0.41/0.62 exact (zenon_H2e zenon_H16).
% 0.41/0.62 Qed.
% 0.41/0.62 % SZS output end Proof
% 0.41/0.62 (* END-PROOF *)
% 0.41/0.62 nodes searched: 4323
% 0.41/0.62 max branch formulas: 1618
% 0.41/0.62 proof nodes created: 463
% 0.41/0.62 formulas created: 24144
% 0.41/0.62
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