TSTP Solution File: NUM535+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n028.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 : Mon Jul 18 15:56:36 EDT 2022
% Result : Theorem 0.37s 0.56s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM535+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n028.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 19:53:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.37/0.56 (* PROOF-FOUND *)
% 0.37/0.56 % SZS status Theorem
% 0.37/0.56 (* BEGIN-PROOF *)
% 0.37/0.56 % SZS output start Proof
% 0.37/0.56 Theorem m__ : ((((aSet0 (sdtmndt0 (xS) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (xS) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (xS))/\(~(W0 = (xx))))))))->(((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (sdtmndt0 (xS) (xx)))\/(W0 = (xx)))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (xS))->(aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))))\/(aSubsetOf0 (xS) (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))))/\(((aSet0 (sdtmndt0 (xS) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtmndt0 (xS) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (xS))/\(~(W0 = (xx))))))))->(((aSet0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))<->((aElement0 W0)/\((aElementOf0 W0 (sdtmndt0 (xS) (xx)))\/(W0 = (xx)))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))->(aElementOf0 W0 (xS))))\/(aSubsetOf0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)) (xS)))))).
% 0.37/0.56 Proof.
% 0.37/0.56 assert (zenon_L1_ : forall (zenon_TW0_v : zenon_U), (aElementOf0 zenon_TW0_v (xS)) -> (~(aElement0 zenon_TW0_v)) -> False).
% 0.37/0.56 do 1 intro. intros zenon_H13 zenon_H14.
% 0.37/0.56 generalize (mEOfElem (xS)). zenon_intro zenon_H16.
% 0.37/0.56 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 0.37/0.56 exact (zenon_H18 m__617).
% 0.37/0.56 generalize (zenon_H17 zenon_TW0_v). zenon_intro zenon_H19.
% 0.37/0.56 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ].
% 0.37/0.56 exact (zenon_H1b zenon_H13).
% 0.37/0.56 exact (zenon_H14 zenon_H1a).
% 0.37/0.56 (* end of lemma zenon_L1_ *)
% 0.37/0.56 assert (zenon_L2_ : (~((xS) = (xS))) -> False).
% 0.37/0.56 do 0 intro. intros zenon_H1c.
% 0.37/0.56 apply zenon_H1c. apply refl_equal.
% 0.37/0.56 (* end of lemma zenon_L2_ *)
% 0.37/0.56 assert (zenon_L3_ : forall (zenon_TW0_bf : zenon_U), ((aElement0 zenon_TW0_bf)/\((aElementOf0 zenon_TW0_bf (xS))/\(~(zenon_TW0_bf = (xx))))) -> (~(aElementOf0 zenon_TW0_bf (xS))) -> False).
% 0.37/0.56 do 1 intro. intros zenon_H1d zenon_H1e.
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.37/0.56 exact (zenon_H1e zenon_H23).
% 0.37/0.56 (* end of lemma zenon_L3_ *)
% 0.37/0.56 apply NNPP. intro zenon_G.
% 0.37/0.56 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H26). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.37/0.56 apply (zenon_notor_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a.
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2f. zenon_intro zenon_H2e.
% 0.37/0.56 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (xS))->(aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx))))) zenon_H2b); [ zenon_intro zenon_H30; idtac ].
% 0.37/0.56 elim zenon_H30. zenon_intro zenon_TW0_v. zenon_intro zenon_H31.
% 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H13. zenon_intro zenon_H32.
% 0.37/0.56 generalize (zenon_H2c zenon_TW0_v). zenon_intro zenon_H33.
% 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H32; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.37/0.56 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H14 | zenon_intro zenon_H37 ].
% 0.37/0.56 apply (zenon_L1_ zenon_TW0_v); trivial.
% 0.37/0.56 apply (zenon_notor_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 0.37/0.56 generalize (zenon_H2e zenon_TW0_v). zenon_intro zenon_H3a.
% 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H39; zenon_intro zenon_H3d | zenon_intro zenon_H3c; zenon_intro zenon_H3b ].
% 0.37/0.56 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H14 | zenon_intro zenon_H3e ].
% 0.37/0.56 apply (zenon_L1_ zenon_TW0_v); trivial.
% 0.37/0.56 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H1b | zenon_intro zenon_H3f ].
% 0.37/0.56 exact (zenon_H1b zenon_H13).
% 0.37/0.56 exact (zenon_H3f zenon_H38).
% 0.37/0.56 exact (zenon_H39 zenon_H3c).
% 0.37/0.56 exact (zenon_H32 zenon_H35).
% 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H40.
% 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H29. zenon_intro zenon_H41.
% 0.37/0.56 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2f. zenon_intro zenon_H2e.
% 0.37/0.56 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (sdtpldt0 (sdtmndt0 (xS) (xx)) (xx)))->(aElementOf0 W0 (xS)))) zenon_H43); [ zenon_intro zenon_H44; idtac ].
% 0.37/0.56 elim zenon_H44. zenon_intro zenon_TW0_bf. zenon_intro zenon_H45.
% 0.37/0.56 apply (zenon_notimply_s _ _ zenon_H45). zenon_intro zenon_H46. zenon_intro zenon_H1e.
% 0.37/0.56 generalize (zenon_H2e zenon_TW0_bf). zenon_intro zenon_H47.
% 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H47); [ zenon_intro zenon_H4a; zenon_intro zenon_H49 | zenon_intro zenon_H48; zenon_intro zenon_H1d ].
% 0.37/0.56 cut ((aElementOf0 (xx) (xS)) = (aElementOf0 zenon_TW0_bf (xS))).
% 0.37/0.56 intro zenon_D_pnotp.
% 0.37/0.56 apply zenon_H1e.
% 0.37/0.56 rewrite <- zenon_D_pnotp.
% 0.37/0.56 exact m__617_02.
% 0.37/0.56 cut (((xS) = (xS))); [idtac | apply NNPP; zenon_intro zenon_H1c].
% 0.37/0.56 cut (((xx) = zenon_TW0_bf)); [idtac | apply NNPP; zenon_intro zenon_H4b].
% 0.37/0.56 congruence.
% 0.37/0.56 generalize (zenon_H2c zenon_TW0_bf). zenon_intro zenon_H4c.
% 0.37/0.56 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H46; zenon_intro zenon_H4d ].
% 0.37/0.56 exact (zenon_H4f zenon_H46).
% 0.37/0.56 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H21. zenon_intro zenon_H50.
% 0.37/0.56 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H48 | zenon_intro zenon_H51 ].
% 0.37/0.56 exact (zenon_H4a zenon_H48).
% 0.37/0.56 apply zenon_H4b. apply sym_equal. exact zenon_H51.
% 0.37/0.56 apply zenon_H1c. apply refl_equal.
% 0.37/0.56 apply (zenon_L3_ zenon_TW0_bf); trivial.
% 0.37/0.56 Qed.
% 0.37/0.56 % SZS output end Proof
% 0.37/0.56 (* END-PROOF *)
% 0.37/0.56 nodes searched: 1480
% 0.37/0.56 max branch formulas: 433
% 0.37/0.56 proof nodes created: 81
% 0.37/0.56 formulas created: 6368
% 0.37/0.56
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