%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------