TSTP Solution File: RNG093+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : RNG093+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 20:48:26 EDT 2022
% Result : Theorem 0.50s 0.66s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG093+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % 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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 04:45:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.50/0.66 (* PROOF-FOUND *)
% 0.50/0.66 % SZS status Theorem
% 0.50/0.66 (* BEGIN-PROOF *)
% 0.50/0.66 % SZS output start Proof
% 0.50/0.66 Theorem m__ : (((aSet0 (sdtasasdt0 (xI) (xJ)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))->((forall W1 : zenon_U, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ)))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ))))))))\/(aIdeal0 (sdtasasdt0 (xI) (xJ))))).
% 0.50/0.66 Proof.
% 0.50/0.66 assert (zenon_L1_ : forall (zenon_TW0_be : zenon_U), (forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))) -> (aElementOf0 zenon_TW0_be (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW0_be (xI))) -> False).
% 0.50/0.66 do 1 intro. intros zenon_H1b zenon_H1c zenon_H1d.
% 0.50/0.66 generalize (zenon_H1b zenon_TW0_be). zenon_intro zenon_H1f.
% 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1c; zenon_intro zenon_H20 ].
% 0.50/0.66 exact (zenon_H22 zenon_H1c).
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.50/0.66 exact (zenon_H1d zenon_H24).
% 0.50/0.66 (* end of lemma zenon_L1_ *)
% 0.50/0.66 assert (zenon_L2_ : forall (zenon_TW0_be : zenon_U), (forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))) -> (aElementOf0 zenon_TW0_be (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 zenon_TW0_be (xJ))) -> False).
% 0.50/0.66 do 1 intro. intros zenon_H1b zenon_H1c zenon_H25.
% 0.50/0.66 generalize (zenon_H1b zenon_TW0_be). zenon_intro zenon_H1f.
% 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1c; zenon_intro zenon_H20 ].
% 0.50/0.66 exact (zenon_H22 zenon_H1c).
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.50/0.66 exact (zenon_H25 zenon_H23).
% 0.50/0.66 (* end of lemma zenon_L2_ *)
% 0.50/0.66 assert (zenon_L3_ : forall (zenon_TW1_bp : zenon_U) (zenon_TW0_be : zenon_U), (forall W0 : zenon_U, ((aElementOf0 W0 (xI))->((forall W1 : zenon_U, ((aElementOf0 W1 (xI))->(aElementOf0 (sdtpldt0 W0 W1) (xI))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (xI))))))) -> (forall W0 : zenon_U, ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))<->((aElementOf0 W0 (xI))/\(aElementOf0 W0 (xJ))))) -> (aElementOf0 zenon_TW0_be (sdtasasdt0 (xI) (xJ))) -> (~(aElementOf0 (sdtasdt0 zenon_TW1_bp zenon_TW0_be) (xI))) -> (aElement0 zenon_TW1_bp) -> False).
% 0.50/0.66 do 2 intro. intros zenon_H26 zenon_H1b zenon_H1c zenon_H27 zenon_H28.
% 0.50/0.66 generalize (zenon_H26 zenon_TW0_be). zenon_intro zenon_H2a.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H1d | zenon_intro zenon_H2b ].
% 0.50/0.66 apply (zenon_L1_ zenon_TW0_be); trivial.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 0.50/0.66 generalize (zenon_H2c zenon_TW1_bp). zenon_intro zenon_H2e.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.50/0.66 exact (zenon_H30 zenon_H28).
% 0.50/0.66 exact (zenon_H27 zenon_H2f).
% 0.50/0.66 (* end of lemma zenon_L3_ *)
% 0.50/0.66 assert (zenon_L4_ : forall (zenon_TW1_bp : zenon_U) (zenon_TW0_be : zenon_U), ((forall W1 : zenon_U, ((aElementOf0 W1 (xJ))->(aElementOf0 (sdtpldt0 zenon_TW0_be W1) (xJ))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 zenon_TW0_be) (xJ))))) -> (~(aElementOf0 (sdtasdt0 zenon_TW1_bp zenon_TW0_be) (xJ))) -> (aElement0 zenon_TW1_bp) -> False).
% 0.50/0.66 do 2 intro. intros zenon_H31 zenon_H32 zenon_H28.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.50/0.66 generalize (zenon_H33 zenon_TW1_bp). zenon_intro zenon_H35.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H30 | zenon_intro zenon_H36 ].
% 0.50/0.66 exact (zenon_H30 zenon_H28).
% 0.50/0.66 exact (zenon_H32 zenon_H36).
% 0.50/0.66 (* end of lemma zenon_L4_ *)
% 0.50/0.66 apply NNPP. intro zenon_G.
% 0.50/0.66 apply (zenon_and_s _ _ m__1150). zenon_intro zenon_H38. zenon_intro zenon_H37.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H26. zenon_intro zenon_H39.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e.
% 0.50/0.66 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 0.50/0.66 apply (zenon_notor_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H1b.
% 0.50/0.66 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (sdtasasdt0 (xI) (xJ)))->((forall W1 : zenon_U, ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W0 W1) (sdtasasdt0 (xI) (xJ)))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (sdtasasdt0 (xI) (xJ)))))))) zenon_H43); [ zenon_intro zenon_H45; idtac ].
% 0.50/0.66 elim zenon_H45. zenon_intro zenon_TW0_be. zenon_intro zenon_H46.
% 0.50/0.66 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H1c. zenon_intro zenon_H47.
% 0.50/0.66 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 0.50/0.66 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElementOf0 W1 (sdtasasdt0 (xI) (xJ)))->(aElementOf0 (sdtpldt0 zenon_TW0_be W1) (sdtasasdt0 (xI) (xJ))))) zenon_H49); [ zenon_intro zenon_H4a; idtac ].
% 0.50/0.66 elim zenon_H4a. zenon_intro zenon_TW1_cx. zenon_intro zenon_H4c.
% 0.50/0.66 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 0.50/0.66 generalize (zenon_H1b (sdtpldt0 zenon_TW0_be zenon_TW1_cx)). zenon_intro zenon_H4f.
% 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H4d; zenon_intro zenon_H52 | zenon_intro zenon_H51; zenon_intro zenon_H50 ].
% 0.50/0.66 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 0.50/0.66 generalize (zenon_H26 zenon_TW0_be). zenon_intro zenon_H2a.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H1d | zenon_intro zenon_H2b ].
% 0.50/0.66 apply (zenon_L1_ zenon_TW0_be); trivial.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 0.50/0.66 generalize (zenon_H2d zenon_TW1_cx). zenon_intro zenon_H55.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 0.50/0.66 generalize (zenon_H1b zenon_TW1_cx). zenon_intro zenon_H58.
% 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H4e; zenon_intro zenon_H59 ].
% 0.50/0.66 exact (zenon_H5b zenon_H4e).
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.50/0.66 exact (zenon_H57 zenon_H5d).
% 0.50/0.66 exact (zenon_H54 zenon_H56).
% 0.50/0.66 generalize (zenon_H3f zenon_TW0_be). zenon_intro zenon_H5e.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H25 | zenon_intro zenon_H31 ].
% 0.50/0.66 apply (zenon_L2_ zenon_TW0_be); trivial.
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.50/0.66 generalize (zenon_H34 zenon_TW1_cx). zenon_intro zenon_H5f.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 0.50/0.66 generalize (zenon_H1b zenon_TW1_cx). zenon_intro zenon_H58.
% 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H4e; zenon_intro zenon_H59 ].
% 0.50/0.66 exact (zenon_H5b zenon_H4e).
% 0.50/0.66 apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.50/0.66 exact (zenon_H61 zenon_H5c).
% 0.50/0.66 exact (zenon_H53 zenon_H60).
% 0.50/0.66 exact (zenon_H4d zenon_H51).
% 0.50/0.66 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 zenon_TW0_be) (sdtasasdt0 (xI) (xJ))))) zenon_H48); [ zenon_intro zenon_H62; idtac ].
% 0.50/0.66 elim zenon_H62. zenon_intro zenon_TW1_bp. zenon_intro zenon_H63.
% 0.50/0.66 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H28. zenon_intro zenon_H64.
% 0.50/0.66 generalize (zenon_H1b (sdtasdt0 zenon_TW1_bp zenon_TW0_be)). zenon_intro zenon_H65.
% 0.50/0.66 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H64; zenon_intro zenon_H68 | zenon_intro zenon_H67; zenon_intro zenon_H66 ].
% 0.50/0.66 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H27 | zenon_intro zenon_H32 ].
% 0.50/0.66 apply (zenon_L3_ zenon_TW1_bp zenon_TW0_be); trivial.
% 0.50/0.66 generalize (zenon_H3f zenon_TW0_be). zenon_intro zenon_H5e.
% 0.50/0.66 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H25 | zenon_intro zenon_H31 ].
% 0.50/0.66 apply (zenon_L2_ zenon_TW0_be); trivial.
% 0.50/0.66 apply (zenon_L4_ zenon_TW1_bp zenon_TW0_be); trivial.
% 0.50/0.66 exact (zenon_H64 zenon_H67).
% 0.50/0.66 Qed.
% 0.50/0.66 % SZS output end Proof
% 0.50/0.66 (* END-PROOF *)
% 0.50/0.66 nodes searched: 3605
% 0.50/0.66 max branch formulas: 693
% 0.50/0.66 proof nodes created: 191
% 0.50/0.66 formulas created: 17535
% 0.50/0.66
%------------------------------------------------------------------------------