TSTP Solution File: RNG092+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : RNG092+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n022.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 0.43s 0.60s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG092+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n022.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 : Mon May 30 20:16:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.60 (* PROOF-FOUND *)
% 0.43/0.60 % SZS status Theorem
% 0.43/0.60 (* BEGIN-PROOF *)
% 0.43/0.60 % SZS output start Proof
% 0.43/0.60 Theorem m__ : ((forall W0 : zenon_U, (forall W1 : zenon_U, (forall W2 : zenon_U, ((((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (xI))/\((aElementOf0 W4 (xJ))/\((sdtpldt0 W3 W4) = W0)))))\/(aElementOf0 W0 (sdtpldt1 (xI) (xJ))))/\(((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (xI))/\((aElementOf0 W4 (xJ))/\((sdtpldt0 W3 W4) = W1)))))\/(aElementOf0 W1 (sdtpldt1 (xI) (xJ))))/\(aElement0 W2)))->(exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (xI))/\((aElementOf0 W4 (xJ))/\((W0 = (sdtpldt0 W3 W4))/\(exists W5 : zenon_U, (exists W6 : zenon_U, ((aElementOf0 W5 (xI))/\((aElementOf0 W6 (xJ))/\((W1 = (sdtpldt0 W5 W6))/\((aElementOf0 (sdtpldt0 W3 W5) (xI))/\((aElementOf0 (sdtpldt0 W4 W6) (xJ))/\((aElementOf0 (sdtasdt0 W2 W3) (xI))/\((aElementOf0 (sdtasdt0 W2 W4) (xJ))/\(((sdtpldt0 W0 W1) = (sdtpldt0 (sdtpldt0 W3 W5) (sdtpldt0 W4 W6)))/\((exists W7 : zenon_U, (exists W8 : zenon_U, ((aElementOf0 W7 (xI))/\((aElementOf0 W8 (xJ))/\((sdtpldt0 W7 W8) = (sdtpldt0 W0 W1))))))/\((aElementOf0 (sdtpldt0 W0 W1) (sdtpldt1 (xI) (xJ)))/\((exists W7 : zenon_U, (exists W8 : zenon_U, ((aElementOf0 W7 (xI))/\((aElementOf0 W8 (xJ))/\((sdtpldt0 W7 W8) = (sdtasdt0 W2 W0))))))/\(aElementOf0 (sdtasdt0 W2 W0) (sdtpldt1 (xI) (xJ)))))))))))))))))))))))))->(((aSet0 (sdtpldt1 (xI) (xJ)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt1 (xI) (xJ)))<->(exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (xI))/\((aElementOf0 W4 (xJ))/\((sdtpldt0 W3 W4) = W0))))))))->((forall W0 : zenon_U, ((aElementOf0 W0 (sdtpldt1 (xI) (xJ)))->((forall W1 : zenon_U, ((aElementOf0 W1 (sdtpldt1 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W0 W1) (sdtpldt1 (xI) (xJ)))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (sdtpldt1 (xI) (xJ))))))))\/(aIdeal0 (sdtpldt1 (xI) (xJ)))))).
% 0.43/0.60 Proof.
% 0.43/0.60 assert (zenon_L1_ : forall (zenon_TW0_bc : zenon_U), (~((exists W3 : zenon_U, (exists W4 : zenon_U, ((aElementOf0 W3 (xI))/\((aElementOf0 W4 (xJ))/\((sdtpldt0 W3 W4) = zenon_TW0_bc)))))\/(aElementOf0 zenon_TW0_bc (sdtpldt1 (xI) (xJ))))) -> (aElementOf0 zenon_TW0_bc (sdtpldt1 (xI) (xJ))) -> False).
% 0.43/0.60 do 1 intro. intros zenon_H1a zenon_H1b.
% 0.43/0.60 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1e. zenon_intro zenon_H1d.
% 0.43/0.60 exact (zenon_H1d zenon_H1b).
% 0.43/0.60 (* end of lemma zenon_L1_ *)
% 0.43/0.60 apply NNPP. intro zenon_G.
% 0.43/0.60 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H20. zenon_intro zenon_H1f.
% 0.43/0.60 apply (zenon_notimply_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21.
% 0.43/0.60 apply (zenon_notor_s _ _ zenon_H21). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.43/0.60 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElementOf0 W0 (sdtpldt1 (xI) (xJ)))->((forall W1 : zenon_U, ((aElementOf0 W1 (sdtpldt1 (xI) (xJ)))->(aElementOf0 (sdtpldt0 W0 W1) (sdtpldt1 (xI) (xJ)))))/\(forall W1 : zenon_U, ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 W0) (sdtpldt1 (xI) (xJ)))))))) zenon_H24); [ zenon_intro zenon_H25; idtac ].
% 0.43/0.60 elim zenon_H25. zenon_intro zenon_TW0_bc. zenon_intro zenon_H26.
% 0.43/0.60 apply (zenon_notimply_s _ _ zenon_H26). zenon_intro zenon_H1b. zenon_intro zenon_H27.
% 0.43/0.60 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.43/0.60 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElementOf0 W1 (sdtpldt1 (xI) (xJ)))->(aElementOf0 (sdtpldt0 zenon_TW0_bc W1) (sdtpldt1 (xI) (xJ))))) zenon_H29); [ zenon_intro zenon_H2a; idtac ].
% 0.43/0.60 elim zenon_H2a. zenon_intro zenon_TW1_br. zenon_intro zenon_H2c.
% 0.43/0.60 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.43/0.60 generalize (zenon_H20 zenon_TW0_bc). zenon_intro zenon_H2f.
% 0.43/0.60 generalize (zenon_H2f zenon_TW1_br). zenon_intro zenon_H30.
% 0.43/0.60 generalize (zenon_H30 (sz10)). zenon_intro zenon_H31.
% 0.43/0.60 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.43/0.60 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H1a | zenon_intro zenon_H34 ].
% 0.43/0.60 apply (zenon_L1_ zenon_TW0_bc); trivial.
% 0.43/0.60 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.43/0.60 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H38. zenon_intro zenon_H37.
% 0.43/0.60 exact (zenon_H37 zenon_H2e).
% 0.43/0.60 exact (zenon_H35 mSortsC_01).
% 0.43/0.60 elim zenon_H32. zenon_intro zenon_TW3_cf. zenon_intro zenon_H3a.
% 0.43/0.60 elim zenon_H3a. zenon_intro zenon_TW4_ch. zenon_intro zenon_H3c.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 0.43/0.60 elim zenon_H41. zenon_intro zenon_TW5_cp. zenon_intro zenon_H44.
% 0.43/0.60 elim zenon_H44. zenon_intro zenon_TW6_cr. zenon_intro zenon_H46.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59.
% 0.43/0.60 exact (zenon_H2d zenon_H5a).
% 0.43/0.60 apply (zenon_notallex_s (fun W1 : zenon_U => ((aElement0 W1)->(aElementOf0 (sdtasdt0 W1 zenon_TW0_bc) (sdtpldt1 (xI) (xJ))))) zenon_H28); [ zenon_intro zenon_H5b; idtac ].
% 0.43/0.60 elim zenon_H5b. zenon_intro zenon_TW1_do. zenon_intro zenon_H5d.
% 0.43/0.60 apply (zenon_notimply_s _ _ zenon_H5d). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 0.43/0.60 generalize (zenon_H20 zenon_TW0_bc). zenon_intro zenon_H2f.
% 0.43/0.60 generalize (zenon_H2f zenon_TW0_bc). zenon_intro zenon_H60.
% 0.43/0.60 generalize (zenon_H60 zenon_TW1_do). zenon_intro zenon_H61.
% 0.43/0.60 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ].
% 0.43/0.60 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H1a | zenon_intro zenon_H64 ].
% 0.43/0.60 apply (zenon_L1_ zenon_TW0_bc); trivial.
% 0.43/0.60 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H1a | zenon_intro zenon_H65 ].
% 0.43/0.60 apply (zenon_L1_ zenon_TW0_bc); trivial.
% 0.43/0.60 exact (zenon_H65 zenon_H5f).
% 0.43/0.60 elim zenon_H62. zenon_intro zenon_TW3_dy. zenon_intro zenon_H67.
% 0.43/0.60 elim zenon_H67. zenon_intro zenon_TW4_ea. zenon_intro zenon_H69.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H6a.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 0.43/0.60 elim zenon_H6e. zenon_intro zenon_TW5_ei. zenon_intro zenon_H71.
% 0.43/0.60 elim zenon_H71. zenon_intro zenon_TW6_ek. zenon_intro zenon_H73.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H79. zenon_intro zenon_H78.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7d. zenon_intro zenon_H7c.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86.
% 0.43/0.60 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88.
% 0.43/0.60 exact (zenon_H5e zenon_H88).
% 0.43/0.60 Qed.
% 0.43/0.60 % SZS output end Proof
% 0.43/0.60 (* END-PROOF *)
% 0.43/0.60 nodes searched: 1515
% 0.43/0.60 max branch formulas: 626
% 0.43/0.60 proof nodes created: 94
% 0.43/0.60 formulas created: 16235
% 0.43/0.60
%------------------------------------------------------------------------------