TSTP Solution File: COM022+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : COM022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n011.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 : Fri Jul 15 01:53:02 EDT 2022
% Result : Theorem 0.60s 0.82s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n011.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
% 0.13/0.34 % DateTime : Thu Jun 16 19:56:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.82 (* PROOF-FOUND *)
% 0.60/0.82 % SZS status Theorem
% 0.60/0.82 (* BEGIN-PROOF *)
% 0.60/0.82 % SZS output start Proof
% 0.60/0.82 Theorem m__ : ((((sdtmndtplgtdt0 (xa) (xR) (xb))/\(sdtmndtplgtdt0 (xa) (xR) (xc)))->(exists W0 : zenon_U, ((aElement0 W0)/\((aReductOfIn0 W0 (xa) (xR))/\((sdtmndtasgtdt0 W0 (xR) (xb))/\(exists W1 : zenon_U, ((aElement0 W1)/\((aReductOfIn0 W1 (xa) (xR))/\((sdtmndtasgtdt0 W1 (xR) (xc))/\(exists W2 : zenon_U, ((aElement0 W2)/\((sdtmndtasgtdt0 W0 (xR) W2)/\((sdtmndtasgtdt0 W1 (xR) W2)/\(exists W3 : zenon_U, ((aNormalFormOfIn0 W3 W2 (xR))/\((sdtmndtasgtdt0 (xb) (xR) W3)/\(sdtmndtasgtdt0 (xc) (xR) W3)))))))))))))))))->(((sdtmndtasgtdt0 (xa) (xR) (xb))/\(sdtmndtasgtdt0 (xa) (xR) (xc)))->(exists W0 : zenon_U, ((aElement0 W0)/\((sdtmndtasgtdt0 (xb) (xR) W0)/\(sdtmndtasgtdt0 (xc) (xR) W0)))))).
% 0.60/0.82 Proof.
% 0.60/0.82 assert (zenon_L1_ : (~((xc) = (xc))) -> False).
% 0.60/0.82 do 0 intro. intros zenon_H13.
% 0.60/0.82 apply zenon_H13. apply refl_equal.
% 0.60/0.82 (* end of lemma zenon_L1_ *)
% 0.60/0.82 assert (zenon_L2_ : (forall W2 : zenon_U, (((aElement0 (xc))/\((aRewritingSystem0 (xR))/\(aElement0 W2)))->((sdtmndtasgtdt0 (xc) (xR) W2)<->(((xc) = W2)\/(sdtmndtplgtdt0 (xc) (xR) W2))))) -> (aElement0 (xc)) -> (~(sdtmndtasgtdt0 (xc) (xR) (xc))) -> False).
% 0.60/0.82 do 0 intro. intros zenon_H14 zenon_H15 zenon_H16.
% 0.60/0.82 generalize (zenon_H14 (xc)). zenon_intro zenon_H17.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ].
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H16; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H13. zenon_intro zenon_H20.
% 0.60/0.82 apply zenon_H13. apply refl_equal.
% 0.60/0.82 exact (zenon_H16 zenon_H1e).
% 0.60/0.82 (* end of lemma zenon_L2_ *)
% 0.60/0.82 assert (zenon_L3_ : (~((xb) = (xb))) -> False).
% 0.60/0.82 do 0 intro. intros zenon_H21.
% 0.60/0.82 apply zenon_H21. apply refl_equal.
% 0.60/0.82 (* end of lemma zenon_L3_ *)
% 0.60/0.82 assert (zenon_L4_ : (~(((xc) = (xa))\/(sdtmndtplgtdt0 (xc) (xR) (xa)))) -> ((xa) = (xc)) -> False).
% 0.60/0.82 do 0 intro. intros zenon_H22 zenon_H23.
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.60/0.82 apply zenon_H25. apply sym_equal. exact zenon_H23.
% 0.60/0.82 (* end of lemma zenon_L4_ *)
% 0.60/0.82 apply NNPP. intro zenon_G.
% 0.60/0.82 apply (zenon_and_s _ _ m__731). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H28. zenon_intro zenon_H15.
% 0.60/0.82 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H2a. zenon_intro zenon_H29.
% 0.60/0.82 apply (zenon_notimply_s _ _ zenon_H29). zenon_intro zenon_H2c. zenon_intro zenon_H2b.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.60/0.82 generalize (mTCRDef (xa)). zenon_intro zenon_H33.
% 0.60/0.82 generalize (mTCRDef (xc)). zenon_intro zenon_H34.
% 0.60/0.82 generalize (zenon_H34 (xR)). zenon_intro zenon_H14.
% 0.60/0.82 apply zenon_H2b. exists (xc). apply NNPP. zenon_intro zenon_H35.
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H1b | zenon_intro zenon_H36 ].
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H37 | zenon_intro zenon_H16 ].
% 0.60/0.82 generalize (zenon_H33 (xR)). zenon_intro zenon_H38.
% 0.60/0.82 generalize (zenon_H38 (xb)). zenon_intro zenon_H39.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.60/0.82 exact (zenon_H3d zenon_H27).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H1c | zenon_intro zenon_H3e ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H41; zenon_intro zenon_H40 | zenon_intro zenon_H2e; zenon_intro zenon_H3f ].
% 0.60/0.82 exact (zenon_H41 zenon_H2e).
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 0.60/0.82 generalize (mTCRDef (xb)). zenon_intro zenon_H44.
% 0.60/0.82 generalize (mTCRTrans (xb)). zenon_intro zenon_H45.
% 0.60/0.82 generalize (zenon_H45 (xR)). zenon_intro zenon_H46.
% 0.60/0.82 generalize (zenon_H44 (xR)). zenon_intro zenon_H47.
% 0.60/0.82 generalize (zenon_H46 (xa)). zenon_intro zenon_H48.
% 0.60/0.82 generalize (zenon_H47 (xa)). zenon_intro zenon_H49.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4b); [ zenon_intro zenon_H3e | zenon_intro zenon_H4c ].
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H1c | zenon_intro zenon_H3d ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 exact (zenon_H3d zenon_H27).
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H50; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51.
% 0.60/0.82 apply zenon_H52. apply sym_equal. exact zenon_H43.
% 0.60/0.82 generalize (zenon_H48 (xc)). zenon_intro zenon_H53.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H3e | zenon_intro zenon_H56 ].
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H1c | zenon_intro zenon_H57 ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H3d | zenon_intro zenon_H1b ].
% 0.60/0.82 exact (zenon_H3d zenon_H27).
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H50 | zenon_intro zenon_H5a ].
% 0.60/0.82 exact (zenon_H50 zenon_H4e).
% 0.60/0.82 exact (zenon_H5a zenon_H2d).
% 0.60/0.82 exact (zenon_H37 zenon_H58).
% 0.60/0.82 exact (zenon_H32 zenon_H42).
% 0.60/0.82 apply (zenon_L2_); trivial.
% 0.60/0.82 generalize (mTCRDef (xa)). zenon_intro zenon_H33.
% 0.60/0.82 generalize (mTCRDef (xb)). zenon_intro zenon_H44.
% 0.60/0.82 generalize (zenon_H33 (xR)). zenon_intro zenon_H38.
% 0.60/0.82 apply zenon_H2b. exists (xb). apply NNPP. zenon_intro zenon_H5b.
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H5b); [ zenon_intro zenon_H3e | zenon_intro zenon_H5c ].
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H5e | zenon_intro zenon_H5d ].
% 0.60/0.82 generalize (zenon_H44 (xR)). zenon_intro zenon_H47.
% 0.60/0.82 generalize (zenon_H47 (xb)). zenon_intro zenon_H5f.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H3e | zenon_intro zenon_H3c ].
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H1c | zenon_intro zenon_H3e ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H5e; zenon_intro zenon_H64 | zenon_intro zenon_H63; zenon_intro zenon_H62 ].
% 0.60/0.82 apply (zenon_notor_s _ _ zenon_H64). zenon_intro zenon_H21. zenon_intro zenon_H65.
% 0.60/0.82 apply zenon_H21. apply refl_equal.
% 0.60/0.82 exact (zenon_H5e zenon_H63).
% 0.60/0.82 generalize (mTCRDef (xc)). zenon_intro zenon_H34.
% 0.60/0.82 generalize (zenon_H38 (xc)). zenon_intro zenon_H66.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H68); [ zenon_intro zenon_H3d | zenon_intro zenon_H1a ].
% 0.60/0.82 exact (zenon_H3d zenon_H27).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H5a; zenon_intro zenon_H6a | zenon_intro zenon_H2d; zenon_intro zenon_H69 ].
% 0.60/0.82 exact (zenon_H5a zenon_H2d).
% 0.60/0.82 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H23 | zenon_intro zenon_H6b ].
% 0.60/0.82 generalize (zenon_H34 (xR)). zenon_intro zenon_H14.
% 0.60/0.82 generalize (mTCRTrans (xc)). zenon_intro zenon_H6c.
% 0.60/0.82 generalize (zenon_H14 (xa)). zenon_intro zenon_H6d.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H1b | zenon_intro zenon_H4c ].
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H4c); [ zenon_intro zenon_H1c | zenon_intro zenon_H3d ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 exact (zenon_H3d zenon_H27).
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_H6e); [ zenon_intro zenon_H72; zenon_intro zenon_H22 | zenon_intro zenon_H71; zenon_intro zenon_H70 ].
% 0.60/0.82 apply (zenon_L4_); trivial.
% 0.60/0.82 generalize (zenon_H6c (xR)). zenon_intro zenon_H73.
% 0.60/0.82 generalize (zenon_H73 (xa)). zenon_intro zenon_H74.
% 0.60/0.82 generalize (zenon_H74 (xb)). zenon_intro zenon_H75.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H1b | zenon_intro zenon_H78 ].
% 0.60/0.82 exact (zenon_H1b zenon_H15).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H1c | zenon_intro zenon_H79 ].
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H79); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ].
% 0.60/0.82 exact (zenon_H3d zenon_H27).
% 0.60/0.82 exact (zenon_H3e zenon_H28).
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H76); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H72 | zenon_intro zenon_H41 ].
% 0.60/0.82 exact (zenon_H72 zenon_H71).
% 0.60/0.82 exact (zenon_H41 zenon_H2e).
% 0.60/0.82 exact (zenon_H5d zenon_H7a).
% 0.60/0.82 exact (zenon_H31 zenon_H6b).
% 0.60/0.82 elim zenon_H2f. zenon_intro zenon_TW0_eu. zenon_intro zenon_H7d.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82.
% 0.60/0.82 elim zenon_H82. zenon_intro zenon_TW1_fc. zenon_intro zenon_H85.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H87. zenon_intro zenon_H86.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 0.60/0.82 elim zenon_H8a. zenon_intro zenon_TW2_fk. zenon_intro zenon_H8d.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H8f. zenon_intro zenon_H8e.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92.
% 0.60/0.82 elim zenon_H92. zenon_intro zenon_TW3_fs. zenon_intro zenon_H95.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H95). zenon_intro zenon_H97. zenon_intro zenon_H96.
% 0.60/0.82 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98.
% 0.60/0.82 apply zenon_H2b. exists zenon_TW3_fs. apply NNPP. zenon_intro zenon_H9a.
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H9a); [ zenon_intro zenon_H9c | zenon_intro zenon_H9b ].
% 0.60/0.82 generalize (mNFRDef zenon_TW2_fk). zenon_intro zenon_H9d.
% 0.60/0.82 generalize (zenon_H9d (xR)). zenon_intro zenon_H9e.
% 0.60/0.82 apply (zenon_imply_s _ _ zenon_H9e); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9f ].
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_Ha0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_H1c ].
% 0.60/0.82 exact (zenon_Ha1 zenon_H8f).
% 0.60/0.82 exact (zenon_H1c m__656).
% 0.60/0.82 generalize (zenon_H9f zenon_TW3_fs). zenon_intro zenon_Ha2.
% 0.60/0.82 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha5; zenon_intro zenon_Ha4 | zenon_intro zenon_H97; zenon_intro zenon_Ha3 ].
% 0.60/0.82 exact (zenon_Ha5 zenon_H97).
% 0.60/0.82 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6.
% 0.60/0.82 exact (zenon_H9c zenon_Ha7).
% 0.60/0.82 apply (zenon_notand_s _ _ zenon_H9b); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ].
% 0.60/0.82 exact (zenon_Ha9 zenon_H99).
% 0.60/0.82 exact (zenon_Ha8 zenon_H98).
% 0.60/0.82 Qed.
% 0.60/0.82 % SZS output end Proof
% 0.60/0.82 (* END-PROOF *)
% 0.60/0.82 nodes searched: 15345
% 0.60/0.82 max branch formulas: 2778
% 0.60/0.82 proof nodes created: 618
% 0.60/0.82 formulas created: 58533
% 0.60/0.82
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