TSTP Solution File: COM013+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n026.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 01:52:59 EDT 2022
% Result : Theorem 129.27s 129.46s
% Output : Proof 129.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n026.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 : Thu Jun 16 17:19:53 EDT 2022
% 0.18/0.33 % CPUTime :
% 129.27/129.46 (* PROOF-FOUND *)
% 129.27/129.46 % SZS status Theorem
% 129.27/129.46 (* BEGIN-PROOF *)
% 129.27/129.46 % SZS output start Proof
% 129.27/129.46 Theorem m__ : (forall W0 : zenon_U, ((aElement0 W0)->((forall W1 : zenon_U, ((aElement0 W1)->((iLess0 W1 W0)->(exists W2 : zenon_U, ((aElement0 W2)/\(((W1 = W2)\/(((aReductOfIn0 W2 W1 (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 W1 (xR))/\(sdtmndtplgtdt0 W3 (xR) W2)))))/\(sdtmndtplgtdt0 W1 (xR) W2)))/\((sdtmndtasgtdt0 W1 (xR) W2)/\((~(exists W3 : zenon_U, (aReductOfIn0 W3 W2 (xR))))/\(aNormalFormOfIn0 W2 W1 (xR))))))))))->(exists W1 : zenon_U, (((aElement0 W1)/\(((W0 = W1)\/((aReductOfIn0 W1 W0 (xR))\/((exists W2 : zenon_U, ((aElement0 W2)/\((aReductOfIn0 W2 W0 (xR))/\(sdtmndtplgtdt0 W2 (xR) W1))))\/((sdtmndtplgtdt0 W0 (xR) W1)\/(sdtmndtasgtdt0 W0 (xR) W1)))))/\(~(exists W2 : zenon_U, (aReductOfIn0 W2 W1 (xR))))))\/(aNormalFormOfIn0 W1 W0 (xR))))))).
% 129.27/129.46 Proof.
% 129.27/129.46 assert (zenon_L1_ : forall (zenon_TW3_u : zenon_U) (zenon_TW0_v : zenon_U), (forall W1 : zenon_U, (((aElement0 zenon_TW0_v)/\(aRewritingSystem0 W1))->(forall W2 : zenon_U, ((aReductOfIn0 W2 zenon_TW0_v W1)->(aElement0 W2))))) -> (aElement0 zenon_TW0_v) -> (aRewritingSystem0 (xR)) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> (~(aElement0 zenon_TW3_u)) -> False).
% 129.27/129.46 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13.
% 129.27/129.46 generalize (zenon_Hf (xR)). zenon_intro zenon_H16.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 generalize (zenon_H17 zenon_TW3_u). zenon_intro zenon_H1b.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ].
% 129.27/129.46 exact (zenon_H1d zenon_H12).
% 129.27/129.46 exact (zenon_H13 zenon_H1c).
% 129.27/129.46 (* end of lemma zenon_L1_ *)
% 129.27/129.46 assert (zenon_L2_ : forall (zenon_TW0_v : zenon_U) (zenon_TW3_u : zenon_U), (~(aElement0 zenon_TW3_u)) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> (aRewritingSystem0 (xR)) -> (aElement0 zenon_TW0_v) -> False).
% 129.27/129.46 do 2 intro. intros zenon_H13 zenon_H12 zenon_H11 zenon_H10.
% 129.27/129.46 generalize (mReduct zenon_TW0_v). zenon_intro zenon_Hf.
% 129.27/129.46 apply (zenon_L1_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 (* end of lemma zenon_L2_ *)
% 129.27/129.46 assert (zenon_L3_ : forall (zenon_TW0_v : zenon_U) (zenon_TW3_u : zenon_U), (~((aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W3 (xR) zenon_TW3_u)))))) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> False).
% 129.27/129.46 do 2 intro. intros zenon_H1e zenon_H12.
% 129.27/129.46 apply (zenon_notor_s _ _ zenon_H1e). zenon_intro zenon_H1d. zenon_intro zenon_H1f.
% 129.27/129.46 exact (zenon_H1d zenon_H12).
% 129.27/129.46 (* end of lemma zenon_L3_ *)
% 129.27/129.46 assert (zenon_L4_ : forall (zenon_TW3_u : zenon_U) (zenon_TW0_v : zenon_U), ((sdtmndtplgtdt0 zenon_TW0_v (xR) zenon_TW3_u)<->((aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W3 (xR) zenon_TW3_u)))))) -> (~(sdtmndtplgtdt0 zenon_TW0_v (xR) zenon_TW3_u)) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> False).
% 129.27/129.46 do 2 intro. intros zenon_H20 zenon_H21 zenon_H12.
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H21; zenon_intro zenon_H1e | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 129.27/129.46 apply (zenon_L3_ zenon_TW0_v zenon_TW3_u); trivial.
% 129.27/129.46 exact (zenon_H21 zenon_H23).
% 129.27/129.46 (* end of lemma zenon_L4_ *)
% 129.27/129.46 assert (zenon_L5_ : forall (zenon_TW3_u : zenon_U) (zenon_TW0_v : zenon_U), (forall W2 : zenon_U, (((aElement0 zenon_TW0_v)/\((aRewritingSystem0 (xR))/\(aElement0 W2)))->((sdtmndtplgtdt0 zenon_TW0_v (xR) W2)<->((aReductOfIn0 W2 zenon_TW0_v (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W3 (xR) W2)))))))) -> (aElement0 zenon_TW0_v) -> (aRewritingSystem0 (xR)) -> (forall W1 : zenon_U, (((aElement0 zenon_TW0_v)/\(aRewritingSystem0 W1))->(forall W2 : zenon_U, ((aReductOfIn0 W2 zenon_TW0_v W1)->(aElement0 W2))))) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> (~(sdtmndtplgtdt0 zenon_TW0_v (xR) zenon_TW3_u)) -> False).
% 129.27/129.46 do 2 intro. intros zenon_H24 zenon_H10 zenon_H11 zenon_Hf zenon_H12 zenon_H21.
% 129.27/129.46 generalize (zenon_H24 zenon_TW3_u). zenon_intro zenon_H25.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H26 | zenon_intro zenon_H20 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H1a | zenon_intro zenon_H27 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H19 | zenon_intro zenon_H13 ].
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 apply (zenon_L1_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 apply (zenon_L4_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 (* end of lemma zenon_L5_ *)
% 129.27/129.46 assert (zenon_L6_ : forall (zenon_TW3_u : zenon_U) (zenon_TW0_v : zenon_U), (~((zenon_TW0_v = zenon_TW3_u)\/(sdtmndtplgtdt0 zenon_TW0_v (xR) zenon_TW3_u))) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> (forall W1 : zenon_U, (((aElement0 zenon_TW0_v)/\(aRewritingSystem0 W1))->(forall W2 : zenon_U, ((aReductOfIn0 W2 zenon_TW0_v W1)->(aElement0 W2))))) -> (aRewritingSystem0 (xR)) -> (aElement0 zenon_TW0_v) -> (forall W2 : zenon_U, (((aElement0 zenon_TW0_v)/\((aRewritingSystem0 (xR))/\(aElement0 W2)))->((sdtmndtplgtdt0 zenon_TW0_v (xR) W2)<->((aReductOfIn0 W2 zenon_TW0_v (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W3 (xR) W2)))))))) -> False).
% 129.27/129.46 do 2 intro. intros zenon_H28 zenon_H12 zenon_Hf zenon_H11 zenon_H10 zenon_H24.
% 129.27/129.46 apply (zenon_notor_s _ _ zenon_H28). zenon_intro zenon_H29. zenon_intro zenon_H21.
% 129.27/129.46 apply (zenon_L5_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 (* end of lemma zenon_L6_ *)
% 129.27/129.46 assert (zenon_L7_ : forall (zenon_TW2_bv : zenon_U) (zenon_TW3_u : zenon_U) (zenon_TW0_v : zenon_U), (forall W1 : zenon_U, (forall W2 : zenon_U, (forall W3 : zenon_U, (((aElement0 zenon_TW0_v)/\((aRewritingSystem0 W1)/\((aElement0 W2)/\(aElement0 W3))))->(((sdtmndtasgtdt0 zenon_TW0_v W1 W2)/\(sdtmndtasgtdt0 W2 W1 W3))->(sdtmndtasgtdt0 zenon_TW0_v W1 W3)))))) -> (aElement0 zenon_TW0_v) -> (aRewritingSystem0 (xR)) -> (aReductOfIn0 zenon_TW3_u zenon_TW0_v (xR)) -> (aElement0 zenon_TW2_bv) -> (sdtmndtasgtdt0 zenon_TW0_v (xR) zenon_TW3_u) -> (sdtmndtasgtdt0 zenon_TW3_u (xR) zenon_TW2_bv) -> (~(sdtmndtasgtdt0 zenon_TW0_v (xR) zenon_TW2_bv)) -> False).
% 129.27/129.46 do 3 intro. intros zenon_H2a zenon_H10 zenon_H11 zenon_H12 zenon_H2b zenon_H2c zenon_H2d zenon_H2e.
% 129.27/129.46 generalize (zenon_H2a (xR)). zenon_intro zenon_H30.
% 129.27/129.46 generalize (zenon_H30 zenon_TW3_u). zenon_intro zenon_H31.
% 129.27/129.46 generalize (zenon_H31 zenon_TW2_bv). zenon_intro zenon_H32.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H1a | zenon_intro zenon_H35 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H19 | zenon_intro zenon_H36 ].
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H13 | zenon_intro zenon_H37 ].
% 129.27/129.46 apply (zenon_L2_ zenon_TW0_v zenon_TW3_u); trivial.
% 129.27/129.46 exact (zenon_H37 zenon_H2b).
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 129.27/129.46 exact (zenon_H3b zenon_H2c).
% 129.27/129.46 exact (zenon_H3a zenon_H2d).
% 129.27/129.46 exact (zenon_H2e zenon_H38).
% 129.27/129.46 (* end of lemma zenon_L7_ *)
% 129.27/129.46 assert (zenon_L8_ : forall (zenon_TW2_bv : zenon_U) (zenon_TW0_v : zenon_U), (~(exists W1 : zenon_U, (((aElement0 W1)/\(((zenon_TW0_v = W1)\/((aReductOfIn0 W1 zenon_TW0_v (xR))\/((exists W2 : zenon_U, ((aElement0 W2)/\((aReductOfIn0 W2 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W2 (xR) W1))))\/((sdtmndtplgtdt0 zenon_TW0_v (xR) W1)\/(sdtmndtasgtdt0 zenon_TW0_v (xR) W1)))))/\(~(exists W2 : zenon_U, (aReductOfIn0 W2 W1 (xR))))))\/(aNormalFormOfIn0 W1 zenon_TW0_v (xR))))) -> (aElement0 zenon_TW2_bv) -> (sdtmndtasgtdt0 zenon_TW0_v (xR) zenon_TW2_bv) -> (~(exists W3 : zenon_U, (aReductOfIn0 W3 zenon_TW2_bv (xR)))) -> (aRewritingSystem0 (xR)) -> (aElement0 zenon_TW0_v) -> False).
% 129.27/129.46 do 2 intro. intros zenon_H3c zenon_H2b zenon_H38 zenon_H3d zenon_H11 zenon_H10.
% 129.27/129.46 generalize (mNFRDef zenon_TW0_v). zenon_intro zenon_H3e.
% 129.27/129.46 generalize (zenon_H3e (xR)). zenon_intro zenon_H3f.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H18 | zenon_intro zenon_H40 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 generalize (zenon_H40 zenon_TW2_bv). zenon_intro zenon_H41.
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H45; zenon_intro zenon_H44 | zenon_intro zenon_H43; zenon_intro zenon_H42 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H37 | zenon_intro zenon_H46 ].
% 129.27/129.46 exact (zenon_H37 zenon_H2b).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H2e | zenon_intro zenon_H47 ].
% 129.27/129.46 exact (zenon_H2e zenon_H38).
% 129.27/129.46 exact (zenon_H47 zenon_H3d).
% 129.27/129.46 apply zenon_H3c. exists zenon_TW2_bv. apply NNPP. zenon_intro zenon_H48.
% 129.27/129.46 apply (zenon_notor_s _ _ zenon_H48). zenon_intro zenon_H49. zenon_intro zenon_H45.
% 129.27/129.46 exact (zenon_H45 zenon_H43).
% 129.27/129.46 (* end of lemma zenon_L8_ *)
% 129.27/129.46 assert (zenon_L9_ : forall (zenon_TW0_v : zenon_U), (exists W3 : zenon_U, (aReductOfIn0 W3 zenon_TW0_v (xR))) -> (isTerminating0 (xR)) -> (~(exists W1 : zenon_U, (((aElement0 W1)/\(((zenon_TW0_v = W1)\/((aReductOfIn0 W1 zenon_TW0_v (xR))\/((exists W2 : zenon_U, ((aElement0 W2)/\((aReductOfIn0 W2 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W2 (xR) W1))))\/((sdtmndtplgtdt0 zenon_TW0_v (xR) W1)\/(sdtmndtasgtdt0 zenon_TW0_v (xR) W1)))))/\(~(exists W2 : zenon_U, (aReductOfIn0 W2 W1 (xR))))))\/(aNormalFormOfIn0 W1 zenon_TW0_v (xR))))) -> (forall W1 : zenon_U, (forall W2 : zenon_U, (forall W3 : zenon_U, (((aElement0 zenon_TW0_v)/\((aRewritingSystem0 W1)/\((aElement0 W2)/\(aElement0 W3))))->(((sdtmndtasgtdt0 zenon_TW0_v W1 W2)/\(sdtmndtasgtdt0 W2 W1 W3))->(sdtmndtasgtdt0 zenon_TW0_v W1 W3)))))) -> (forall W2 : zenon_U, (((aElement0 zenon_TW0_v)/\((aRewritingSystem0 (xR))/\(aElement0 W2)))->((sdtmndtasgtdt0 zenon_TW0_v (xR) W2)<->((zenon_TW0_v = W2)\/(sdtmndtplgtdt0 zenon_TW0_v (xR) W2))))) -> (forall W2 : zenon_U, (((aElement0 zenon_TW0_v)/\((aRewritingSystem0 (xR))/\(aElement0 W2)))->((sdtmndtplgtdt0 zenon_TW0_v (xR) W2)<->((aReductOfIn0 W2 zenon_TW0_v (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W3 (xR) W2)))))))) -> (aElement0 zenon_TW0_v) -> (forall W1 : zenon_U, ((aElement0 W1)->((iLess0 W1 zenon_TW0_v)->(exists W2 : zenon_U, ((aElement0 W2)/\(((W1 = W2)\/(((aReductOfIn0 W2 W1 (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 W1 (xR))/\(sdtmndtplgtdt0 W3 (xR) W2)))))/\(sdtmndtplgtdt0 W1 (xR) W2)))/\((sdtmndtasgtdt0 W1 (xR) W2)/\((~(exists W3 : zenon_U, (aReductOfIn0 W3 W2 (xR))))/\(aNormalFormOfIn0 W2 W1 (xR)))))))))) -> (aRewritingSystem0 (xR)) -> False).
% 129.27/129.46 do 1 intro. intros zenon_H4a zenon_H4b zenon_H3c zenon_H2a zenon_H4c zenon_H24 zenon_H10 zenon_H4d zenon_H11.
% 129.27/129.46 elim zenon_H4a. zenon_intro zenon_TW3_u. zenon_intro zenon_H12.
% 129.27/129.46 generalize (mTermin (xR)). zenon_intro zenon_H4e.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ].
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H4f); [ zenon_intro zenon_H52; zenon_intro zenon_H51 | zenon_intro zenon_H4b; zenon_intro zenon_H50 ].
% 129.27/129.46 exact (zenon_H52 zenon_H4b).
% 129.27/129.46 generalize (zenon_H50 zenon_TW0_v). zenon_intro zenon_H53.
% 129.27/129.46 generalize (zenon_H4d zenon_TW3_u). zenon_intro zenon_H54.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H13 | zenon_intro zenon_H55 ].
% 129.27/129.46 apply (zenon_L2_ zenon_TW0_v zenon_TW3_u); trivial.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 129.27/129.46 generalize (mReduct zenon_TW0_v). zenon_intro zenon_Hf.
% 129.27/129.46 generalize (zenon_H53 zenon_TW3_u). zenon_intro zenon_H58.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H1a | zenon_intro zenon_H13 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_L1_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H21 | zenon_intro zenon_H5b ].
% 129.27/129.46 apply (zenon_L5_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 exact (zenon_H57 zenon_H5b).
% 129.27/129.46 elim zenon_H56. zenon_intro zenon_TW2_bv. zenon_intro zenon_H5c.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H2b. zenon_intro zenon_H5d.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H5d). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H2d. zenon_intro zenon_H60.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H3d. zenon_intro zenon_H61.
% 129.27/129.46 generalize (mReduct zenon_TW0_v). zenon_intro zenon_Hf.
% 129.27/129.46 generalize (zenon_H4c zenon_TW2_bv). zenon_intro zenon_H62.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H1a | zenon_intro zenon_H65 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H19 | zenon_intro zenon_H37 ].
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 exact (zenon_H37 zenon_H2b).
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H63); [ zenon_intro zenon_H2e; zenon_intro zenon_H67 | zenon_intro zenon_H38; zenon_intro zenon_H66 ].
% 129.27/129.46 generalize (zenon_H4c zenon_TW3_u). zenon_intro zenon_H68.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H26 | zenon_intro zenon_H69 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H26); [ zenon_intro zenon_H1a | zenon_intro zenon_H27 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_H19 | zenon_intro zenon_H13 ].
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 apply (zenon_L2_ zenon_TW0_v zenon_TW3_u); trivial.
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H69); [ zenon_intro zenon_H3b; zenon_intro zenon_H28 | zenon_intro zenon_H2c; zenon_intro zenon_H6a ].
% 129.27/129.46 apply (zenon_L6_ zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 apply (zenon_L7_ zenon_TW2_bv zenon_TW3_u zenon_TW0_v); trivial.
% 129.27/129.46 apply (zenon_L8_ zenon_TW2_bv zenon_TW0_v); trivial.
% 129.27/129.46 (* end of lemma zenon_L9_ *)
% 129.27/129.46 assert (zenon_L10_ : forall (zenon_TW0_v : zenon_U), (~(exists W1 : zenon_U, (((aElement0 W1)/\(((zenon_TW0_v = W1)\/((aReductOfIn0 W1 zenon_TW0_v (xR))\/((exists W2 : zenon_U, ((aElement0 W2)/\((aReductOfIn0 W2 zenon_TW0_v (xR))/\(sdtmndtplgtdt0 W2 (xR) W1))))\/((sdtmndtplgtdt0 zenon_TW0_v (xR) W1)\/(sdtmndtasgtdt0 zenon_TW0_v (xR) W1)))))/\(~(exists W2 : zenon_U, (aReductOfIn0 W2 W1 (xR))))))\/(aNormalFormOfIn0 W1 zenon_TW0_v (xR))))) -> (~(exists W3 : zenon_U, (aReductOfIn0 W3 zenon_TW0_v (xR)))) -> (aElement0 zenon_TW0_v) -> False).
% 129.27/129.46 do 1 intro. intros zenon_H3c zenon_H6b zenon_H10.
% 129.27/129.46 apply zenon_H3c. exists zenon_TW0_v. apply NNPP. zenon_intro zenon_H6c.
% 129.27/129.46 apply (zenon_notor_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_H1a | zenon_intro zenon_H6f ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ].
% 129.27/129.46 apply (zenon_notor_s _ _ zenon_H71). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 129.27/129.46 apply zenon_H73. apply refl_equal.
% 129.27/129.46 exact (zenon_H70 zenon_H6b).
% 129.27/129.46 (* end of lemma zenon_L10_ *)
% 129.27/129.46 apply NNPP. intro zenon_G.
% 129.27/129.46 apply (zenon_and_s _ _ m__587). zenon_intro zenon_H11. zenon_intro zenon_H74.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H74). zenon_intro zenon_H75. zenon_intro zenon_H4b.
% 129.27/129.46 apply (zenon_notallex_s (fun W0 : zenon_U => ((aElement0 W0)->((forall W1 : zenon_U, ((aElement0 W1)->((iLess0 W1 W0)->(exists W2 : zenon_U, ((aElement0 W2)/\(((W1 = W2)\/(((aReductOfIn0 W2 W1 (xR))\/(exists W3 : zenon_U, ((aElement0 W3)/\((aReductOfIn0 W3 W1 (xR))/\(sdtmndtplgtdt0 W3 (xR) W2)))))/\(sdtmndtplgtdt0 W1 (xR) W2)))/\((sdtmndtasgtdt0 W1 (xR) W2)/\((~(exists W3 : zenon_U, (aReductOfIn0 W3 W2 (xR))))/\(aNormalFormOfIn0 W2 W1 (xR))))))))))->(exists W1 : zenon_U, (((aElement0 W1)/\(((W0 = W1)\/((aReductOfIn0 W1 W0 (xR))\/((exists W2 : zenon_U, ((aElement0 W2)/\((aReductOfIn0 W2 W0 (xR))/\(sdtmndtplgtdt0 W2 (xR) W1))))\/((sdtmndtplgtdt0 W0 (xR) W1)\/(sdtmndtasgtdt0 W0 (xR) W1)))))/\(~(exists W2 : zenon_U, (aReductOfIn0 W2 W1 (xR))))))\/(aNormalFormOfIn0 W1 W0 (xR))))))) zenon_G); [ zenon_intro zenon_H76; idtac ].
% 129.27/129.46 elim zenon_H76. zenon_intro zenon_TW0_v. zenon_intro zenon_H77.
% 129.27/129.46 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H10. zenon_intro zenon_H78.
% 129.27/129.46 apply (zenon_notimply_s _ _ zenon_H78). zenon_intro zenon_H4d. zenon_intro zenon_H3c.
% 129.27/129.46 generalize (mTCRDef zenon_TW0_v). zenon_intro zenon_H79.
% 129.27/129.46 generalize (mTCDef zenon_TW0_v). zenon_intro zenon_H7a.
% 129.27/129.46 generalize (zenon_H7a (xR)). zenon_intro zenon_H24.
% 129.27/129.46 generalize (mTCRTrans zenon_TW0_v). zenon_intro zenon_H2a.
% 129.27/129.46 generalize (zenon_H79 (xR)). zenon_intro zenon_H4c.
% 129.27/129.46 generalize (zenon_H4c zenon_TW0_v). zenon_intro zenon_H7b.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H7d); [ zenon_intro zenon_H1a | zenon_intro zenon_H7e ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H19 | zenon_intro zenon_H1a ].
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H82; zenon_intro zenon_H81 | zenon_intro zenon_H80; zenon_intro zenon_H7f ].
% 129.27/129.46 apply (zenon_notor_s _ _ zenon_H81). zenon_intro zenon_H73. zenon_intro zenon_H83.
% 129.27/129.46 apply zenon_H73. apply refl_equal.
% 129.27/129.46 generalize (mNFRDef zenon_TW0_v). zenon_intro zenon_H3e.
% 129.27/129.46 generalize (zenon_H3e (xR)). zenon_intro zenon_H3f.
% 129.27/129.46 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H18 | zenon_intro zenon_H40 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 exact (zenon_H19 zenon_H11).
% 129.27/129.46 generalize (zenon_H40 zenon_TW0_v). zenon_intro zenon_H84.
% 129.27/129.46 apply (zenon_equiv_s _ _ zenon_H84); [ zenon_intro zenon_H6d; zenon_intro zenon_H87 | zenon_intro zenon_H86; zenon_intro zenon_H85 ].
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H1a | zenon_intro zenon_H88 ].
% 129.27/129.46 exact (zenon_H1a zenon_H10).
% 129.27/129.46 apply (zenon_notand_s _ _ zenon_H88); [ zenon_intro zenon_H82 | zenon_intro zenon_H70 ].
% 129.27/129.46 exact (zenon_H82 zenon_H80).
% 129.27/129.46 apply zenon_H70. zenon_intro zenon_H4a.
% 129.27/129.46 apply (zenon_L9_ zenon_TW0_v); trivial.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H10. zenon_intro zenon_H89.
% 129.27/129.46 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H80. zenon_intro zenon_H6b.
% 129.27/129.46 apply (zenon_L10_ zenon_TW0_v); trivial.
% 129.27/129.46 Qed.
% 129.27/129.46 % SZS output end Proof
% 129.27/129.46 (* END-PROOF *)
% 129.27/129.46 nodes searched: 801409
% 129.27/129.46 max branch formulas: 12738
% 129.27/129.46 proof nodes created: 30352
% 129.27/129.46 formulas created: 1697507
% 129.27/129.46
%------------------------------------------------------------------------------