TSTP Solution File: KRS151+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : KRS151+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.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 : Sun Jul 17 03:39:36 EDT 2022
% Result : Theorem 0.41s 0.60s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS151+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.12/0.35 % Computer : n024.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Tue Jun 7 14:32:19 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.41/0.60 (* PROOF-FOUND *)
% 0.41/0.60 % SZS status Theorem
% 0.41/0.60 (* BEGIN-PROOF *)
% 0.41/0.60 % SZS output start Proof
% 0.41/0.60 Theorem the_axiom : ((forall X : zenon_U, ((cowlThing X)/\(~(cowlNothing X))))/\((forall X : zenon_U, ((xsd_string X)<->(~(xsd_integer X))))/\((cowlThing (iV21026))/\((cC84 (iV21026))/\((cC16 (iV21026))/\((cC36 (iV21026))/\((cC42 (iV21026))/\((cC88 (iV21026))/\((cC86 (iV21026))/\((cC174 (iV21026))/\((cC20 (iV21026))/\((cC156 (iV21026))/\((cC60 (iV21026))/\((cC38 (iV21026))/\((cC158 (iV21026))/\((cC10 (iV21026))/\((cC134 (iV21026))/\((cC22 (iV21026))/\((cC168 (iV21026))/\((cC56 (iV21026))/\((cC78 (iV21026))/\((cC58 (iV21026))/\((cC152 (iV21026))/\((cC40 (iV21026))/\((cC132 (iV21026))/\((cC130 (iV21026))/\((cC62 (iV21026))/\((cC154 (iV21026))/\((cC80 (iV21026))/\((cC8 (iV21026))/\((cC136 (iV21026))/\((cC112 (iV21026))/\((cC180 (iV21026))/\((cC114 (iV21026))/\((cC64 (iV21026))/\((cC110 (iV21026))/\((cC116 (iV21026))/\((cC82 (iV21026))/\((cC138 (iV21026))/\((cC4 (iV21026))/\((cC108 (iV21026))/\((cC14 (iV21026))/\((cC90 (iV21026))/\((cowlThing (iV21027))/\((cC30 (iV21027))/\((cC24 (iV21027))/\((cowlThing (iV21029))/\((cC50 (iV21029))/\((cC44 (iV21029))/\((cowlThing (iV21030))/\((cC66 (iV21030))/\(cC72 (iV21030))))))))))))))))))))))))))))))))))))))))))))))))))))).
% 0.41/0.60 Proof.
% 0.41/0.60 assert (zenon_L1_ : (~(~(cC18 (iV21030)))) -> False).
% 0.41/0.60 do 0 intro. intros zenon_Hf3.
% 0.41/0.60 exact (zenon_Hf3 axiom_202).
% 0.41/0.60 (* end of lemma zenon_L1_ *)
% 0.41/0.60 assert (zenon_L2_ : (~(~(cC12 (iV21029)))) -> False).
% 0.41/0.60 do 0 intro. intros zenon_Hf4.
% 0.41/0.60 exact (zenon_Hf4 axiom_163).
% 0.41/0.60 (* end of lemma zenon_L2_ *)
% 0.41/0.60 assert (zenon_L3_ : (~(~(cC2 (iV21027)))) -> False).
% 0.41/0.60 do 0 intro. intros zenon_Hf5.
% 0.41/0.60 exact (zenon_Hf5 axiom_150).
% 0.41/0.60 (* end of lemma zenon_L3_ *)
% 0.41/0.60 assert (zenon_L4_ : (~((forall X : zenon_U, ((cowlThing X)/\(~(cowlNothing X))))/\((forall X : zenon_U, ((xsd_string X)<->(~(xsd_integer X))))/\((cowlThing (iV21026))/\((cC84 (iV21026))/\((cC16 (iV21026))/\((cC36 (iV21026))/\((cC42 (iV21026))/\((cC88 (iV21026))/\((cC86 (iV21026))/\((cC174 (iV21026))/\((cC20 (iV21026))/\((cC156 (iV21026))/\((cC60 (iV21026))/\((cC38 (iV21026))/\((cC158 (iV21026))/\((cC10 (iV21026))/\((cC134 (iV21026))/\((cC22 (iV21026))/\((cC168 (iV21026))/\((cC56 (iV21026))/\((cC78 (iV21026))/\((cC58 (iV21026))/\((cC152 (iV21026))/\((cC40 (iV21026))/\((cC132 (iV21026))/\((cC130 (iV21026))/\((cC62 (iV21026))/\((cC154 (iV21026))/\((cC80 (iV21026))/\((cC8 (iV21026))/\((cC136 (iV21026))/\((cC112 (iV21026))/\((cC180 (iV21026))/\((cC114 (iV21026))/\((cC64 (iV21026))/\((cC110 (iV21026))/\((cC116 (iV21026))/\((cC82 (iV21026))/\((cC138 (iV21026))/\((cC4 (iV21026))/\((cC108 (iV21026))/\((cC14 (iV21026))/\((cC90 (iV21026))/\((cowlThing (iV21027))/\((cC30 (iV21027))/\((cC24 (iV21027))/\((cowlThing (iV21029))/\((cC50 (iV21029))/\((cC44 (iV21029))/\((cowlThing (iV21030))/\((cC66 (iV21030))/\(cC72 (iV21030)))))))))))))))))))))))))))))))))))))))))))))))))))))) -> ((cC14 (iV21026))/\(cC10 (iV21026))) -> ((~(cC28 (iV21026)))/\(~(cC34 (iV21026)))) -> ((cC40 (iV21026))/\(cC38 (iV21026))) -> ((cC82 (iV21026))/\(cC84 (iV21026))) -> ((cC168 (iV21026))/\(~(cC172 (iV21026)))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC18 Y)))) -> ((cC154 (iV21026))/\(cC138 (iV21026))) -> ((cC58 (iV21026))/\(cC42 (iV21026))) -> ((cC36 (iV21026))/\(cTOP (iV21026))) -> ((cC22 (iV21026))/\(cC156 (iV21026))) -> ((cC8 (iV21026))/\(cC4 (iV21026))) -> ((cC132 (iV21026))/\(cC116 (iV21026))) -> ((cC16 (iV21026))/\(cC20 (iV21026))) -> ((~(cC166 (iV21026)))/\(~(cC162 (iV21026)))) -> ((~(cC48 (iV21026)))/\(~(cC54 (iV21026)))) -> ((~(cC70 (iV21026)))/\(~(cC76 (iV21026)))) -> ((cC56 (iV21026))/\(cTOP (iV21026))) -> ((~(cC150 (iV21026)))/\(~(cC144 (iV21026)))) -> ((cTOP (iV21026))/\(cC130 (iV21026))) -> ((~(cC122 (iV21026)))/\(~(cC128 (iV21026)))) -> ((cTOP (iV21026))/\(cC152 (iV21026))) -> ((cTOP (iV21026))/\(cC78 (iV21026))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC6 Y)))) -> ((cC90 (iV21026))/\(cC110 (iV21026))) -> ((~(cC178 (iV21026)))/\(cC174 (iV21026))) -> ((cC62 (iV21026))/\(cC60 (iV21026))) -> ((cC108 (iV21026))/\(cTOP (iV21026))) -> ((cC114 (iV21026))/\(cC112 (iV21026))) -> ((cC80 (iV21026))/\(cC64 (iV21026))) -> ((cC136 (iV21026))/\(cC134 (iV21026))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC2 Y)))) -> ((~(cC106 (iV21026)))/\(~(cC98 (iV21026)))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC12 Y)))) -> ((cC88 (iV21026))/\(cC86 (iV21026))) -> (exists Y : zenon_U, ((rR1 (iV21027) Y)/\(~(cC12 Y)))) -> (exists Y : zenon_U, ((rR1 (iV21027) Y)/\(~(cC2 Y)))) -> (exists Y : zenon_U, ((rR1 (iV21029) Y)/\(~(cC12 Y)))) -> (exists Y : zenon_U, ((rR1 (iV21029) Y)/\(~(cC2 Y)))) -> (exists Y : zenon_U, ((rR1 (iV21030) Y)/\(~(cC2 Y)))) -> (exists Y : zenon_U, ((rR1 (iV21030) Y)/\(~(cC12 Y)))) -> False).
% 0.41/0.60 do 0 intro. intros zenon_G zenon_Hf6 zenon_Hf7 zenon_Hf8 zenon_Hf9 zenon_Hfa zenon_Hfb zenon_Hfc zenon_Hfd zenon_Hfe zenon_Hff zenon_H100 zenon_H101 zenon_H102 zenon_H103 zenon_H104 zenon_H105 zenon_H106 zenon_H107 zenon_H108 zenon_H109 zenon_H10a zenon_H10b zenon_H10c zenon_H10d zenon_H10e zenon_H10f zenon_H110 zenon_H111 zenon_H112 zenon_H113 zenon_H114 zenon_H115 zenon_H116 zenon_H117 zenon_H118 zenon_H119 zenon_H11a zenon_H11b zenon_H11c zenon_H11d.
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H11f | zenon_intro zenon_H11e ].
% 0.41/0.60 exact (zenon_H11f axiom_0).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H11e); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ].
% 0.41/0.60 exact (zenon_H121 axiom_1).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H120); [ zenon_intro zenon_H123 | zenon_intro zenon_H122 ].
% 0.41/0.60 exact (zenon_H123 axiom_120).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H122); [ zenon_intro zenon_H125 | zenon_intro zenon_H124 ].
% 0.41/0.60 generalize (axiom_79 (iV21026)). zenon_intro zenon_H126.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H126); [ zenon_intro zenon_H125; zenon_intro zenon_H128 | zenon_intro zenon_H127; zenon_intro axiom_88 ].
% 0.41/0.60 exact (zenon_H128 axiom_88).
% 0.41/0.60 exact (zenon_H125 zenon_H127).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H124); [ zenon_intro zenon_H12a | zenon_intro zenon_H129 ].
% 0.41/0.60 generalize (axiom_33 (iV21026)). zenon_intro zenon_H12b.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H12b); [ zenon_intro zenon_H12a; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_Hf6 ].
% 0.41/0.60 exact (zenon_H12d zenon_Hf6).
% 0.41/0.60 exact (zenon_H12a zenon_H12c).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H129); [ zenon_intro zenon_H12f | zenon_intro zenon_H12e ].
% 0.41/0.60 generalize (axiom_53 (iV21026)). zenon_intro zenon_H130.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H130); [ zenon_intro zenon_H12f; zenon_intro zenon_H132 | zenon_intro zenon_H131; zenon_intro zenon_Hf7 ].
% 0.41/0.60 exact (zenon_H132 zenon_Hf7).
% 0.41/0.60 exact (zenon_H12f zenon_H131).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H12e); [ zenon_intro zenon_H134 | zenon_intro zenon_H133 ].
% 0.41/0.60 generalize (axiom_57 (iV21026)). zenon_intro zenon_H135.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H135); [ zenon_intro zenon_H134; zenon_intro zenon_H137 | zenon_intro zenon_H136; zenon_intro zenon_Hf8 ].
% 0.41/0.60 exact (zenon_H137 zenon_Hf8).
% 0.41/0.60 exact (zenon_H134 zenon_H136).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H133); [ zenon_intro zenon_H139 | zenon_intro zenon_H138 ].
% 0.41/0.60 generalize (axiom_81 (iV21026)). zenon_intro zenon_H13a.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H13a); [ zenon_intro zenon_H139; zenon_intro zenon_H128 | zenon_intro zenon_H13b; zenon_intro axiom_88 ].
% 0.41/0.60 exact (zenon_H128 axiom_88).
% 0.41/0.60 exact (zenon_H139 zenon_H13b).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H138); [ zenon_intro zenon_H13d | zenon_intro zenon_H13c ].
% 0.41/0.60 generalize (axiom_80 (iV21026)). zenon_intro zenon_H13e.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H13e); [ zenon_intro zenon_H13d; zenon_intro zenon_H140 | zenon_intro zenon_H13f; zenon_intro zenon_Hf9 ].
% 0.41/0.60 exact (zenon_H140 zenon_Hf9).
% 0.41/0.60 exact (zenon_H13d zenon_H13f).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H13c); [ zenon_intro zenon_H142 | zenon_intro zenon_H141 ].
% 0.41/0.60 generalize (axiom_41 (iV21026)). zenon_intro zenon_H143.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H143); [ zenon_intro zenon_H142; zenon_intro zenon_H145 | zenon_intro zenon_H144; zenon_intro zenon_Hfa ].
% 0.41/0.60 exact (zenon_H145 zenon_Hfa).
% 0.41/0.60 exact (zenon_H142 zenon_H144).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H141); [ zenon_intro zenon_H147 | zenon_intro zenon_H146 ].
% 0.41/0.60 generalize (axiom_45 (iV21026)). zenon_intro zenon_H148.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H148); [ zenon_intro zenon_H147; zenon_intro zenon_H14a | zenon_intro zenon_H149; zenon_intro zenon_Hfb ].
% 0.41/0.60 exact (zenon_H14a zenon_Hfb).
% 0.41/0.60 exact (zenon_H147 zenon_H149).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H146); [ zenon_intro zenon_H14c | zenon_intro zenon_H14b ].
% 0.41/0.60 generalize (axiom_31 (iV21026)). zenon_intro zenon_H14d.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H14d); [ zenon_intro zenon_H14c; zenon_intro zenon_H14f | zenon_intro zenon_H14e; zenon_intro zenon_Hfc ].
% 0.41/0.60 exact (zenon_H14f zenon_Hfc).
% 0.41/0.60 exact (zenon_H14c zenon_H14e).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H151 | zenon_intro zenon_H150 ].
% 0.41/0.60 generalize (axiom_66 (iV21026)). zenon_intro zenon_H152.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H152); [ zenon_intro zenon_H151; zenon_intro zenon_H154 | zenon_intro zenon_H153; zenon_intro zenon_Hfd ].
% 0.41/0.60 exact (zenon_H154 zenon_Hfd).
% 0.41/0.60 exact (zenon_H151 zenon_H153).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H150); [ zenon_intro zenon_H156 | zenon_intro zenon_H155 ].
% 0.41/0.60 generalize (axiom_54 (iV21026)). zenon_intro zenon_H157.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H157); [ zenon_intro zenon_H156; zenon_intro zenon_H159 | zenon_intro zenon_H158; zenon_intro zenon_Hfe ].
% 0.41/0.60 exact (zenon_H159 zenon_Hfe).
% 0.41/0.60 exact (zenon_H156 zenon_H158).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H155); [ zenon_intro zenon_H15b | zenon_intro zenon_H15a ].
% 0.41/0.60 generalize (axiom_32 (iV21026)). zenon_intro zenon_H15c.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H15c); [ zenon_intro zenon_H15b; zenon_intro zenon_H15e | zenon_intro zenon_H15d; zenon_intro zenon_Hff ].
% 0.41/0.60 exact (zenon_H15e zenon_Hff).
% 0.41/0.60 exact (zenon_H15b zenon_H15d).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H15a); [ zenon_intro zenon_H160 | zenon_intro zenon_H15f ].
% 0.41/0.60 generalize (axiom_2 (iV21026)). zenon_intro zenon_H161.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H161); [ zenon_intro zenon_H160; zenon_intro zenon_H163 | zenon_intro zenon_H162; zenon_intro zenon_H100 ].
% 0.41/0.60 exact (zenon_H163 zenon_H100).
% 0.41/0.60 exact (zenon_H160 zenon_H162).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H15f); [ zenon_intro zenon_H165 | zenon_intro zenon_H164 ].
% 0.41/0.60 generalize (axiom_19 (iV21026)). zenon_intro zenon_H166.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H166); [ zenon_intro zenon_H165; zenon_intro zenon_H168 | zenon_intro zenon_H167; zenon_intro zenon_H101 ].
% 0.41/0.60 exact (zenon_H168 zenon_H101).
% 0.41/0.60 exact (zenon_H165 zenon_H167).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H164); [ zenon_intro zenon_H16a | zenon_intro zenon_H169 ].
% 0.41/0.60 generalize (axiom_46 (iV21026)). zenon_intro zenon_H16b.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H16b); [ zenon_intro zenon_H16a; zenon_intro zenon_H16d | zenon_intro zenon_H16c; zenon_intro zenon_H102 ].
% 0.41/0.60 exact (zenon_H16d zenon_H102).
% 0.41/0.60 exact (zenon_H16a zenon_H16c).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H169); [ zenon_intro zenon_H16f | zenon_intro zenon_H16e ].
% 0.41/0.60 generalize (axiom_38 (iV21026)). zenon_intro zenon_H170.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H170); [ zenon_intro zenon_H16f; zenon_intro zenon_H172 | zenon_intro zenon_H171; zenon_intro zenon_H103 ].
% 0.41/0.60 exact (zenon_H172 zenon_H103).
% 0.41/0.60 exact (zenon_H16f zenon_H171).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H16e); [ zenon_intro zenon_H174 | zenon_intro zenon_H173 ].
% 0.41/0.60 generalize (axiom_64 (iV21026)). zenon_intro zenon_H175.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H175); [ zenon_intro zenon_H174; zenon_intro zenon_H177 | zenon_intro zenon_H176; zenon_intro zenon_H104 ].
% 0.41/0.60 exact (zenon_H177 zenon_H104).
% 0.41/0.60 exact (zenon_H174 zenon_H176).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H173); [ zenon_intro zenon_H179 | zenon_intro zenon_H178 ].
% 0.41/0.60 generalize (axiom_75 (iV21026)). zenon_intro zenon_H17a.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H17a); [ zenon_intro zenon_H179; zenon_intro zenon_H17c | zenon_intro zenon_H17b; zenon_intro zenon_H105 ].
% 0.41/0.60 exact (zenon_H17c zenon_H105).
% 0.41/0.60 exact (zenon_H179 zenon_H17b).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H178); [ zenon_intro zenon_H17e | zenon_intro zenon_H17d ].
% 0.41/0.60 generalize (axiom_65 (iV21026)). zenon_intro zenon_H17f.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H17f); [ zenon_intro zenon_H17e; zenon_intro zenon_H181 | zenon_intro zenon_H180; zenon_intro zenon_H106 ].
% 0.41/0.60 exact (zenon_H181 zenon_H106).
% 0.41/0.60 exact (zenon_H17e zenon_H180).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H17d); [ zenon_intro zenon_H183 | zenon_intro zenon_H182 ].
% 0.41/0.60 generalize (axiom_29 (iV21026)). zenon_intro zenon_H184.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H184); [ zenon_intro zenon_H183; zenon_intro zenon_H186 | zenon_intro zenon_H185; zenon_intro zenon_H107 ].
% 0.41/0.60 exact (zenon_H186 zenon_H107).
% 0.41/0.60 exact (zenon_H183 zenon_H185).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H182); [ zenon_intro zenon_H188 | zenon_intro zenon_H187 ].
% 0.41/0.60 generalize (axiom_56 (iV21026)). zenon_intro zenon_H189.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H189); [ zenon_intro zenon_H188; zenon_intro zenon_H128 | zenon_intro zenon_H18a; zenon_intro axiom_88 ].
% 0.41/0.60 exact (zenon_H128 axiom_88).
% 0.41/0.60 exact (zenon_H188 zenon_H18a).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H187); [ zenon_intro zenon_H18c | zenon_intro zenon_H18b ].
% 0.41/0.60 generalize (axiom_18 (iV21026)). zenon_intro zenon_H18d.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H18d); [ zenon_intro zenon_H18c; zenon_intro zenon_H18f | zenon_intro zenon_H18e; zenon_intro zenon_H108 ].
% 0.41/0.60 exact (zenon_H18f zenon_H108).
% 0.41/0.60 exact (zenon_H18c zenon_H18e).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H18b); [ zenon_intro zenon_H191 | zenon_intro zenon_H190 ].
% 0.41/0.60 generalize (axiom_17 (iV21026)). zenon_intro zenon_H192.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H192); [ zenon_intro zenon_H191; zenon_intro zenon_H194 | zenon_intro zenon_H193; zenon_intro zenon_H109 ].
% 0.41/0.60 exact (zenon_H194 zenon_H109).
% 0.41/0.60 exact (zenon_H191 zenon_H193).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H190); [ zenon_intro zenon_H196 | zenon_intro zenon_H195 ].
% 0.41/0.60 generalize (axiom_67 (iV21026)). zenon_intro zenon_H197.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H197); [ zenon_intro zenon_H196; zenon_intro zenon_H128 | zenon_intro zenon_H198; zenon_intro axiom_88 ].
% 0.41/0.60 exact (zenon_H128 axiom_88).
% 0.41/0.60 exact (zenon_H196 zenon_H198).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H195); [ zenon_intro zenon_H19a | zenon_intro zenon_H199 ].
% 0.41/0.60 generalize (axiom_30 (iV21026)). zenon_intro zenon_H19b.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H19b); [ zenon_intro zenon_H19a; zenon_intro zenon_H19d | zenon_intro zenon_H19c; zenon_intro zenon_H10a ].
% 0.41/0.60 exact (zenon_H19d zenon_H10a).
% 0.41/0.60 exact (zenon_H19a zenon_H19c).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H199); [ zenon_intro zenon_H19f | zenon_intro zenon_H19e ].
% 0.41/0.60 generalize (axiom_77 (iV21026)). zenon_intro zenon_H1a0.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1a0); [ zenon_intro zenon_H19f; zenon_intro zenon_H1a2 | zenon_intro zenon_H1a1; zenon_intro zenon_H10b ].
% 0.41/0.60 exact (zenon_H1a2 zenon_H10b).
% 0.41/0.60 exact (zenon_H19f zenon_H1a1).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H19e); [ zenon_intro zenon_H1a4 | zenon_intro zenon_H1a3 ].
% 0.41/0.60 generalize (axiom_76 (iV21026)). zenon_intro zenon_H1a5.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1a5); [ zenon_intro zenon_H1a4; zenon_intro zenon_H1a7 | zenon_intro zenon_H1a6; zenon_intro zenon_H10c ].
% 0.41/0.60 exact (zenon_H1a7 zenon_H10c).
% 0.41/0.60 exact (zenon_H1a4 zenon_H1a6).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1a3); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H1a8 ].
% 0.41/0.60 generalize (axiom_20 (iV21026)). zenon_intro zenon_H1aa.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1aa); [ zenon_intro zenon_H1a9; zenon_intro zenon_H128 | zenon_intro zenon_H1ab; zenon_intro axiom_88 ].
% 0.41/0.60 exact (zenon_H128 axiom_88).
% 0.41/0.60 exact (zenon_H1a9 zenon_H1ab).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1a8); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ac ].
% 0.41/0.60 generalize (axiom_8 (iV21026)). zenon_intro zenon_H1ae.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1ae); [ zenon_intro zenon_H1ad; zenon_intro zenon_H1b0 | zenon_intro zenon_H1af; zenon_intro zenon_H10d ].
% 0.41/0.60 exact (zenon_H1b0 zenon_H10d).
% 0.41/0.60 exact (zenon_H1ad zenon_H1af).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1ac); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H1b1 ].
% 0.41/0.60 generalize (axiom_44 (iV21026)). zenon_intro zenon_H1b3.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1b3); [ zenon_intro zenon_H1b2; zenon_intro zenon_H1b5 | zenon_intro zenon_H1b4; zenon_intro zenon_H10e ].
% 0.41/0.60 exact (zenon_H1b5 zenon_H10e).
% 0.41/0.60 exact (zenon_H1b2 zenon_H1b4).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1b1); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1b6 ].
% 0.41/0.60 generalize (axiom_9 (iV21026)). zenon_intro zenon_H1b8.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1b8); [ zenon_intro zenon_H1b7; zenon_intro zenon_H128 | zenon_intro zenon_H1b9; zenon_intro axiom_88 ].
% 0.41/0.60 exact (zenon_H128 axiom_88).
% 0.41/0.60 exact (zenon_H1b7 zenon_H1b9).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1b6); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1ba ].
% 0.41/0.60 generalize (axiom_68 (iV21026)). zenon_intro zenon_H1bc.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1bc); [ zenon_intro zenon_H1bb; zenon_intro zenon_H1be | zenon_intro zenon_H1bd; zenon_intro zenon_H10f ].
% 0.41/0.60 exact (zenon_H1be zenon_H10f).
% 0.41/0.60 exact (zenon_H1bb zenon_H1bd).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1ba); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H1bf ].
% 0.41/0.60 generalize (axiom_7 (iV21026)). zenon_intro zenon_H1c1.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1c1); [ zenon_intro zenon_H1c0; zenon_intro zenon_H1c3 | zenon_intro zenon_H1c2; zenon_intro zenon_H110 ].
% 0.41/0.60 exact (zenon_H1c3 zenon_H110).
% 0.41/0.60 exact (zenon_H1c0 zenon_H1c2).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1bf); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1c4 ].
% 0.41/0.60 generalize (axiom_10 (iV21026)). zenon_intro zenon_H1c6.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1c6); [ zenon_intro zenon_H1c5; zenon_intro zenon_H1c8 | zenon_intro zenon_H1c7; zenon_intro zenon_H111 ].
% 0.41/0.60 exact (zenon_H1c8 zenon_H111).
% 0.41/0.60 exact (zenon_H1c5 zenon_H1c7).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1c4); [ zenon_intro zenon_H1ca | zenon_intro zenon_H1c9 ].
% 0.41/0.60 generalize (axiom_78 (iV21026)). zenon_intro zenon_H1cb.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1cb); [ zenon_intro zenon_H1ca; zenon_intro zenon_H1cd | zenon_intro zenon_H1cc; zenon_intro zenon_H112 ].
% 0.41/0.60 exact (zenon_H1cd zenon_H112).
% 0.41/0.60 exact (zenon_H1ca zenon_H1cc).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1c9); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1ce ].
% 0.41/0.60 generalize (axiom_21 (iV21026)). zenon_intro zenon_H1d0.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1d0); [ zenon_intro zenon_H1cf; zenon_intro zenon_H1d2 | zenon_intro zenon_H1d1; zenon_intro zenon_H113 ].
% 0.41/0.60 exact (zenon_H1d2 zenon_H113).
% 0.41/0.60 exact (zenon_H1cf zenon_H1d1).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1ce); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H1d3 ].
% 0.41/0.60 generalize (axiom_55 (iV21026)). zenon_intro zenon_H1d5.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1d5); [ zenon_intro zenon_H1d4; zenon_intro zenon_H1d7 | zenon_intro zenon_H1d6; zenon_intro zenon_H114 ].
% 0.41/0.60 exact (zenon_H1d7 zenon_H114).
% 0.41/0.60 exact (zenon_H1d4 zenon_H1d6).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1d3); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H1d8 ].
% 0.41/0.60 generalize (axiom_6 (iV21026)). zenon_intro zenon_H1da.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1da); [ zenon_intro zenon_H1d9; zenon_intro zenon_H1dc | zenon_intro zenon_H1db; zenon_intro zenon_H115 ].
% 0.41/0.60 exact (zenon_H1dc zenon_H115).
% 0.41/0.60 exact (zenon_H1d9 zenon_H1db).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1d8); [ zenon_intro zenon_H1de | zenon_intro zenon_H1dd ].
% 0.41/0.60 generalize (axiom_22 (iV21026)). zenon_intro zenon_H1df.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1df); [ zenon_intro zenon_H1de; zenon_intro zenon_H1e1 | zenon_intro zenon_H1e0; zenon_intro zenon_H116 ].
% 0.41/0.60 exact (zenon_H1e1 zenon_H116).
% 0.41/0.60 exact (zenon_H1de zenon_H1e0).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1dd); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e2 ].
% 0.41/0.60 generalize (axiom_82 (iV21026)). zenon_intro zenon_H1e4.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1e4); [ zenon_intro zenon_H1e3; zenon_intro zenon_H1e6 | zenon_intro zenon_H1e5; zenon_intro zenon_H117 ].
% 0.41/0.60 exact (zenon_H1e6 zenon_H117).
% 0.41/0.60 exact (zenon_H1e3 zenon_H1e5).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1e2); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1e7 ].
% 0.41/0.60 exact (zenon_H1e8 axiom_151).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1e7); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1e9 ].
% 0.41/0.60 generalize (axiom_50 (iV21027)). zenon_intro zenon_H1eb.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1eb); [ zenon_intro zenon_H1ea; zenon_intro zenon_H1ed | zenon_intro zenon_H1ec; zenon_intro zenon_H118 ].
% 0.41/0.60 exact (zenon_H1ed zenon_H118).
% 0.41/0.60 exact (zenon_H1ea zenon_H1ec).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1e9); [ zenon_intro zenon_H1ef | zenon_intro zenon_H1ee ].
% 0.41/0.60 generalize (axiom_47 (iV21027)). zenon_intro zenon_H1f0.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1f0); [ zenon_intro zenon_H1ef; zenon_intro zenon_H1f2 | zenon_intro zenon_H1f1; zenon_intro zenon_H119 ].
% 0.41/0.60 exact (zenon_H1f2 zenon_H119).
% 0.41/0.60 exact (zenon_H1ef zenon_H1f1).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1ee); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H1f3 ].
% 0.41/0.60 exact (zenon_H1f4 axiom_180).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1f3); [ zenon_intro zenon_H1f6 | zenon_intro zenon_H1f5 ].
% 0.41/0.60 generalize (axiom_61 (iV21029)). zenon_intro zenon_H1f7.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1f7); [ zenon_intro zenon_H1f6; zenon_intro zenon_H1f9 | zenon_intro zenon_H1f8; zenon_intro zenon_H11a ].
% 0.41/0.60 exact (zenon_H1f9 zenon_H11a).
% 0.41/0.60 exact (zenon_H1f6 zenon_H1f8).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1f5); [ zenon_intro zenon_H1fb | zenon_intro zenon_H1fa ].
% 0.41/0.60 generalize (axiom_58 (iV21029)). zenon_intro zenon_H1fc.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1fc); [ zenon_intro zenon_H1fb; zenon_intro zenon_H1fe | zenon_intro zenon_H1fd; zenon_intro zenon_H11b ].
% 0.41/0.60 exact (zenon_H1fe zenon_H11b).
% 0.41/0.60 exact (zenon_H1fb zenon_H1fd).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1fa); [ zenon_intro zenon_H200 | zenon_intro zenon_H1ff ].
% 0.41/0.60 exact (zenon_H200 axiom_207).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1ff); [ zenon_intro zenon_H202 | zenon_intro zenon_H201 ].
% 0.41/0.60 generalize (axiom_69 (iV21030)). zenon_intro zenon_H203.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H203); [ zenon_intro zenon_H202; zenon_intro zenon_H205 | zenon_intro zenon_H204; zenon_intro zenon_H11c ].
% 0.41/0.60 exact (zenon_H205 zenon_H11c).
% 0.41/0.60 exact (zenon_H202 zenon_H204).
% 0.41/0.60 generalize (axiom_72 (iV21030)). zenon_intro zenon_H206.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H206); [ zenon_intro zenon_H201; zenon_intro zenon_H208 | zenon_intro zenon_H207; zenon_intro zenon_H11d ].
% 0.41/0.60 exact (zenon_H208 zenon_H11d).
% 0.41/0.60 exact (zenon_H201 zenon_H207).
% 0.41/0.60 (* end of lemma zenon_L4_ *)
% 0.41/0.60 assert (zenon_L5_ : (~((~(cC66 (iV21030)))/\(~(cC18 (iV21030))))) -> (~((~(cC12 (iV21029)))/\(~(cC44 (iV21029))))) -> (~((~(cC24 (iV21027)))/\(~(cC2 (iV21027))))) -> ((cC14 (iV21026))/\(cC10 (iV21026))) -> ((~(cC28 (iV21026)))/\(~(cC34 (iV21026)))) -> ((cC40 (iV21026))/\(cC38 (iV21026))) -> ((cC82 (iV21026))/\(cC84 (iV21026))) -> ((cC168 (iV21026))/\(~(cC172 (iV21026)))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC18 Y)))) -> ((cC154 (iV21026))/\(cC138 (iV21026))) -> ((cC58 (iV21026))/\(cC42 (iV21026))) -> ((cC36 (iV21026))/\(cTOP (iV21026))) -> ((cC22 (iV21026))/\(cC156 (iV21026))) -> ((cC8 (iV21026))/\(cC4 (iV21026))) -> ((cC132 (iV21026))/\(cC116 (iV21026))) -> ((cC16 (iV21026))/\(cC20 (iV21026))) -> ((~(cC166 (iV21026)))/\(~(cC162 (iV21026)))) -> ((~(cC48 (iV21026)))/\(~(cC54 (iV21026)))) -> ((~(cC70 (iV21026)))/\(~(cC76 (iV21026)))) -> ((cC56 (iV21026))/\(cTOP (iV21026))) -> ((~(cC150 (iV21026)))/\(~(cC144 (iV21026)))) -> ((cTOP (iV21026))/\(cC130 (iV21026))) -> ((~(cC122 (iV21026)))/\(~(cC128 (iV21026)))) -> ((cTOP (iV21026))/\(cC152 (iV21026))) -> ((cTOP (iV21026))/\(cC78 (iV21026))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC6 Y)))) -> ((cC90 (iV21026))/\(cC110 (iV21026))) -> ((~(cC178 (iV21026)))/\(cC174 (iV21026))) -> ((cC62 (iV21026))/\(cC60 (iV21026))) -> ((cC108 (iV21026))/\(cTOP (iV21026))) -> ((cC114 (iV21026))/\(cC112 (iV21026))) -> ((cC80 (iV21026))/\(cC64 (iV21026))) -> ((cC136 (iV21026))/\(cC134 (iV21026))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC2 Y)))) -> ((~(cC106 (iV21026)))/\(~(cC98 (iV21026)))) -> (exists Y : zenon_U, ((rR1 (iV21026) Y)/\(~(cC12 Y)))) -> ((cC88 (iV21026))/\(cC86 (iV21026))) -> (exists Y : zenon_U, ((rR1 (iV21030) Y)/\(~(cC12 Y)))) -> (~((forall X : zenon_U, ((cowlThing X)/\(~(cowlNothing X))))/\((forall X : zenon_U, ((xsd_string X)<->(~(xsd_integer X))))/\((cowlThing (iV21026))/\((cC84 (iV21026))/\((cC16 (iV21026))/\((cC36 (iV21026))/\((cC42 (iV21026))/\((cC88 (iV21026))/\((cC86 (iV21026))/\((cC174 (iV21026))/\((cC20 (iV21026))/\((cC156 (iV21026))/\((cC60 (iV21026))/\((cC38 (iV21026))/\((cC158 (iV21026))/\((cC10 (iV21026))/\((cC134 (iV21026))/\((cC22 (iV21026))/\((cC168 (iV21026))/\((cC56 (iV21026))/\((cC78 (iV21026))/\((cC58 (iV21026))/\((cC152 (iV21026))/\((cC40 (iV21026))/\((cC132 (iV21026))/\((cC130 (iV21026))/\((cC62 (iV21026))/\((cC154 (iV21026))/\((cC80 (iV21026))/\((cC8 (iV21026))/\((cC136 (iV21026))/\((cC112 (iV21026))/\((cC180 (iV21026))/\((cC114 (iV21026))/\((cC64 (iV21026))/\((cC110 (iV21026))/\((cC116 (iV21026))/\((cC82 (iV21026))/\((cC138 (iV21026))/\((cC4 (iV21026))/\((cC108 (iV21026))/\((cC14 (iV21026))/\((cC90 (iV21026))/\((cowlThing (iV21027))/\((cC30 (iV21027))/\((cC24 (iV21027))/\((cowlThing (iV21029))/\((cC50 (iV21029))/\((cC44 (iV21029))/\((cowlThing (iV21030))/\((cC66 (iV21030))/\(cC72 (iV21030)))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((~(cC2 (iV21027)))/\(~(cC30 (iV21027))))) -> (~((~(cC12 (iV21029)))/\(~(cC50 (iV21029))))) -> False).
% 0.41/0.60 do 0 intro. intros zenon_H209 zenon_H20a zenon_H20b zenon_Hf6 zenon_Hf7 zenon_Hf8 zenon_Hf9 zenon_Hfa zenon_Hfb zenon_Hfc zenon_Hfd zenon_Hfe zenon_Hff zenon_H100 zenon_H101 zenon_H102 zenon_H103 zenon_H104 zenon_H105 zenon_H106 zenon_H107 zenon_H108 zenon_H109 zenon_H10a zenon_H10b zenon_H10c zenon_H10d zenon_H10e zenon_H10f zenon_H110 zenon_H111 zenon_H112 zenon_H113 zenon_H114 zenon_H115 zenon_H116 zenon_H117 zenon_H11d zenon_G zenon_H20c zenon_H20d.
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H209); [ zenon_intro zenon_H20e | zenon_intro zenon_Hf3 ].
% 0.41/0.60 apply zenon_H20e. zenon_intro zenon_H204.
% 0.41/0.60 generalize (axiom_69 (iV21030)). zenon_intro zenon_H203.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H203); [ zenon_intro zenon_H202; zenon_intro zenon_H205 | zenon_intro zenon_H204; zenon_intro zenon_H11c ].
% 0.41/0.60 exact (zenon_H202 zenon_H204).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H20d); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H20f ].
% 0.41/0.60 exact (zenon_Hf4 axiom_163).
% 0.41/0.60 apply zenon_H20f. zenon_intro zenon_H1f8.
% 0.41/0.60 generalize (axiom_61 (iV21029)). zenon_intro zenon_H1f7.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1f7); [ zenon_intro zenon_H1f6; zenon_intro zenon_H1f9 | zenon_intro zenon_H1f8; zenon_intro zenon_H11a ].
% 0.41/0.60 exact (zenon_H1f6 zenon_H1f8).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H20a); [ zenon_intro zenon_Hf4 | zenon_intro zenon_H210 ].
% 0.41/0.60 exact (zenon_Hf4 axiom_163).
% 0.41/0.60 apply zenon_H210. zenon_intro zenon_H1fd.
% 0.41/0.60 generalize (axiom_58 (iV21029)). zenon_intro zenon_H1fc.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1fc); [ zenon_intro zenon_H1fb; zenon_intro zenon_H1fe | zenon_intro zenon_H1fd; zenon_intro zenon_H11b ].
% 0.41/0.60 exact (zenon_H1fb zenon_H1fd).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H20c); [ zenon_intro zenon_Hf5 | zenon_intro zenon_H211 ].
% 0.41/0.60 exact (zenon_Hf5 axiom_150).
% 0.41/0.60 apply zenon_H211. zenon_intro zenon_H1ec.
% 0.41/0.60 generalize (axiom_50 (iV21027)). zenon_intro zenon_H1eb.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1eb); [ zenon_intro zenon_H1ea; zenon_intro zenon_H1ed | zenon_intro zenon_H1ec; zenon_intro zenon_H118 ].
% 0.41/0.60 exact (zenon_H1ea zenon_H1ec).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H20b); [ zenon_intro zenon_H212 | zenon_intro zenon_Hf5 ].
% 0.41/0.60 apply zenon_H212. zenon_intro zenon_H1f1.
% 0.41/0.60 generalize (axiom_47 (iV21027)). zenon_intro zenon_H1f0.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1f0); [ zenon_intro zenon_H1ef; zenon_intro zenon_H1f2 | zenon_intro zenon_H1f1; zenon_intro zenon_H119 ].
% 0.41/0.60 exact (zenon_H1ef zenon_H1f1).
% 0.41/0.60 apply (zenon_L4_); trivial.
% 0.41/0.60 exact (zenon_Hf5 axiom_150).
% 0.41/0.60 exact (zenon_Hf3 axiom_202).
% 0.41/0.60 (* end of lemma zenon_L5_ *)
% 0.41/0.60 apply NNPP. intro zenon_G.
% 0.41/0.60 generalize (axiom_86 (iV21026)). zenon_intro zenon_H213.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H213); [ zenon_intro zenon_H216; zenon_intro zenon_H215 | zenon_intro axiom_89; zenon_intro zenon_H214 ].
% 0.41/0.60 exact (zenon_H216 axiom_89).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H214). zenon_intro zenon_H15d. zenon_intro zenon_H1b4.
% 0.41/0.60 generalize (axiom_32 (iV21026)). zenon_intro zenon_H15c.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H15c); [ zenon_intro zenon_H15b; zenon_intro zenon_H15e | zenon_intro zenon_H15d; zenon_intro zenon_Hff ].
% 0.41/0.60 exact (zenon_H15b zenon_H15d).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hff). zenon_intro zenon_H16c. zenon_intro zenon_H14e.
% 0.41/0.60 generalize (axiom_46 (iV21026)). zenon_intro zenon_H16b.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H16b); [ zenon_intro zenon_H16a; zenon_intro zenon_H16d | zenon_intro zenon_H16c; zenon_intro zenon_H102 ].
% 0.41/0.60 exact (zenon_H16a zenon_H16c).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H102). zenon_intro zenon_H12c. zenon_intro zenon_H149.
% 0.41/0.60 generalize (axiom_33 (iV21026)). zenon_intro zenon_H12b.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H12b); [ zenon_intro zenon_H12a; zenon_intro zenon_H12d | zenon_intro zenon_H12c; zenon_intro zenon_Hf6 ].
% 0.41/0.60 exact (zenon_H12a zenon_H12c).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hf6). zenon_intro zenon_H1e0. zenon_intro zenon_H162.
% 0.41/0.60 generalize (axiom_22 (iV21026)). zenon_intro zenon_H1df.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1df); [ zenon_intro zenon_H1de; zenon_intro zenon_H1e1 | zenon_intro zenon_H1e0; zenon_intro zenon_H116 ].
% 0.41/0.60 exact (zenon_H1de zenon_H1e0).
% 0.41/0.60 generalize (axiom_2 (iV21026)). zenon_intro zenon_H161.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H161); [ zenon_intro zenon_H160; zenon_intro zenon_H163 | zenon_intro zenon_H162; zenon_intro zenon_H100 ].
% 0.41/0.60 exact (zenon_H160 zenon_H162).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_H1a6. zenon_intro zenon_H1d6.
% 0.41/0.60 generalize (axiom_76 (iV21026)). zenon_intro zenon_H1a5.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1a5); [ zenon_intro zenon_H1a4; zenon_intro zenon_H1a7 | zenon_intro zenon_H1a6; zenon_intro zenon_H10c ].
% 0.41/0.60 exact (zenon_H1a4 zenon_H1a6).
% 0.41/0.60 generalize (axiom_55 (iV21026)). zenon_intro zenon_H1d5.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1d5); [ zenon_intro zenon_H1d4; zenon_intro zenon_H1d7 | zenon_intro zenon_H1d6; zenon_intro zenon_H114 ].
% 0.41/0.60 exact (zenon_H1d4 zenon_H1d6).
% 0.41/0.60 generalize (axiom_45 (iV21026)). zenon_intro zenon_H148.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H148); [ zenon_intro zenon_H147; zenon_intro zenon_H14a | zenon_intro zenon_H149; zenon_intro zenon_Hfb ].
% 0.41/0.60 exact (zenon_H147 zenon_H149).
% 0.41/0.60 generalize (axiom_31 (iV21026)). zenon_intro zenon_H14d.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H14d); [ zenon_intro zenon_H14c; zenon_intro zenon_H14f | zenon_intro zenon_H14e; zenon_intro zenon_Hfc ].
% 0.41/0.60 exact (zenon_H14c zenon_H14e).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hfc). zenon_intro zenon_H19c. zenon_intro zenon_H1d1.
% 0.41/0.60 generalize (axiom_30 (iV21026)). zenon_intro zenon_H19b.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H19b); [ zenon_intro zenon_H19a; zenon_intro zenon_H19d | zenon_intro zenon_H19c; zenon_intro zenon_H10a ].
% 0.41/0.60 exact (zenon_H19a zenon_H19c).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H10a). zenon_intro axiom_88. zenon_intro zenon_H185.
% 0.41/0.60 generalize (axiom_29 (iV21026)). zenon_intro zenon_H184.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H184); [ zenon_intro zenon_H183; zenon_intro zenon_H186 | zenon_intro zenon_H185; zenon_intro zenon_H107 ].
% 0.41/0.60 exact (zenon_H183 zenon_H185).
% 0.41/0.60 generalize (axiom_21 (iV21026)). zenon_intro zenon_H1d0.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1d0); [ zenon_intro zenon_H1cf; zenon_intro zenon_H1d2 | zenon_intro zenon_H1d1; zenon_intro zenon_H113 ].
% 0.41/0.60 exact (zenon_H1cf zenon_H1d1).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H113). zenon_intro zenon_H1ab. zenon_intro zenon_H167.
% 0.41/0.60 generalize (axiom_19 (iV21026)). zenon_intro zenon_H166.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H166); [ zenon_intro zenon_H165; zenon_intro zenon_H168 | zenon_intro zenon_H167; zenon_intro zenon_H101 ].
% 0.41/0.60 exact (zenon_H165 zenon_H167).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H101). zenon_intro zenon_H18e. zenon_intro zenon_H1c7.
% 0.41/0.60 generalize (axiom_18 (iV21026)). zenon_intro zenon_H18d.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H18d); [ zenon_intro zenon_H18c; zenon_intro zenon_H18f | zenon_intro zenon_H18e; zenon_intro zenon_H108 ].
% 0.41/0.60 exact (zenon_H18c zenon_H18e).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H108). zenon_intro axiom_88. zenon_intro zenon_H193.
% 0.41/0.60 generalize (axiom_17 (iV21026)). zenon_intro zenon_H192.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H192); [ zenon_intro zenon_H191; zenon_intro zenon_H194 | zenon_intro zenon_H193; zenon_intro zenon_H109 ].
% 0.41/0.60 exact (zenon_H191 zenon_H193).
% 0.41/0.60 generalize (axiom_10 (iV21026)). zenon_intro zenon_H1c6.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1c6); [ zenon_intro zenon_H1c5; zenon_intro zenon_H1c8 | zenon_intro zenon_H1c7; zenon_intro zenon_H111 ].
% 0.41/0.60 exact (zenon_H1c5 zenon_H1c7).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H111). zenon_intro zenon_H1b9. zenon_intro zenon_H1af.
% 0.41/0.60 generalize (axiom_8 (iV21026)). zenon_intro zenon_H1ae.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1ae); [ zenon_intro zenon_H1ad; zenon_intro zenon_H1b0 | zenon_intro zenon_H1af; zenon_intro zenon_H10d ].
% 0.41/0.60 exact (zenon_H1ad zenon_H1af).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H10d). zenon_intro zenon_H1e5. zenon_intro zenon_H1c2.
% 0.41/0.60 generalize (axiom_82 (iV21026)). zenon_intro zenon_H1e4.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1e4); [ zenon_intro zenon_H1e3; zenon_intro zenon_H1e6 | zenon_intro zenon_H1e5; zenon_intro zenon_H117 ].
% 0.41/0.60 exact (zenon_H1e3 zenon_H1e5).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H117). zenon_intro zenon_H13b. zenon_intro zenon_H13f.
% 0.41/0.60 generalize (axiom_80 (iV21026)). zenon_intro zenon_H13e.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H13e); [ zenon_intro zenon_H13d; zenon_intro zenon_H140 | zenon_intro zenon_H13f; zenon_intro zenon_Hf9 ].
% 0.41/0.60 exact (zenon_H13d zenon_H13f).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hf9). zenon_intro zenon_H1cc. zenon_intro zenon_H127.
% 0.41/0.60 generalize (axiom_78 (iV21026)). zenon_intro zenon_H1cb.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1cb); [ zenon_intro zenon_H1ca; zenon_intro zenon_H1cd | zenon_intro zenon_H1cc; zenon_intro zenon_H112 ].
% 0.41/0.60 exact (zenon_H1ca zenon_H1cc).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H112). zenon_intro zenon_H1a1. zenon_intro zenon_H1bd.
% 0.41/0.60 generalize (axiom_77 (iV21026)). zenon_intro zenon_H1a0.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1a0); [ zenon_intro zenon_H19f; zenon_intro zenon_H1a2 | zenon_intro zenon_H1a1; zenon_intro zenon_H10b ].
% 0.41/0.60 exact (zenon_H19f zenon_H1a1).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H10b). zenon_intro axiom_88. zenon_intro zenon_H17b.
% 0.41/0.60 generalize (axiom_75 (iV21026)). zenon_intro zenon_H17a.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H17a); [ zenon_intro zenon_H179; zenon_intro zenon_H17c | zenon_intro zenon_H17b; zenon_intro zenon_H105 ].
% 0.41/0.60 exact (zenon_H179 zenon_H17b).
% 0.41/0.60 generalize (axiom_68 (iV21026)). zenon_intro zenon_H1bc.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1bc); [ zenon_intro zenon_H1bb; zenon_intro zenon_H1be | zenon_intro zenon_H1bd; zenon_intro zenon_H10f ].
% 0.41/0.60 exact (zenon_H1bb zenon_H1bd).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H10f). zenon_intro zenon_H198. zenon_intro zenon_H153.
% 0.41/0.60 generalize (axiom_66 (iV21026)). zenon_intro zenon_H152.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H152); [ zenon_intro zenon_H151; zenon_intro zenon_H154 | zenon_intro zenon_H153; zenon_intro zenon_Hfd ].
% 0.41/0.60 exact (zenon_H151 zenon_H153).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hfd). zenon_intro zenon_H180. zenon_intro zenon_H136.
% 0.41/0.60 generalize (axiom_65 (iV21026)). zenon_intro zenon_H17f.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H17f); [ zenon_intro zenon_H17e; zenon_intro zenon_H181 | zenon_intro zenon_H180; zenon_intro zenon_H106 ].
% 0.41/0.60 exact (zenon_H17e zenon_H180).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H106). zenon_intro zenon_H176. zenon_intro axiom_88.
% 0.41/0.60 generalize (axiom_64 (iV21026)). zenon_intro zenon_H175.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H175); [ zenon_intro zenon_H174; zenon_intro zenon_H177 | zenon_intro zenon_H176; zenon_intro zenon_H104 ].
% 0.41/0.60 exact (zenon_H174 zenon_H176).
% 0.41/0.60 generalize (axiom_57 (iV21026)). zenon_intro zenon_H135.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H135); [ zenon_intro zenon_H134; zenon_intro zenon_H137 | zenon_intro zenon_H136; zenon_intro zenon_Hf8 ].
% 0.41/0.60 exact (zenon_H134 zenon_H136).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hf8). zenon_intro zenon_H18a. zenon_intro zenon_H158.
% 0.41/0.60 generalize (axiom_54 (iV21026)). zenon_intro zenon_H157.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H157); [ zenon_intro zenon_H156; zenon_intro zenon_H159 | zenon_intro zenon_H158; zenon_intro zenon_Hfe ].
% 0.41/0.60 exact (zenon_H156 zenon_H158).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H131. zenon_intro axiom_88.
% 0.41/0.60 generalize (axiom_53 (iV21026)). zenon_intro zenon_H130.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H130); [ zenon_intro zenon_H12f; zenon_intro zenon_H132 | zenon_intro zenon_H131; zenon_intro zenon_Hf7 ].
% 0.41/0.60 exact (zenon_H12f zenon_H131).
% 0.41/0.60 generalize (axiom_7 (iV21026)). zenon_intro zenon_H1c1.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1c1); [ zenon_intro zenon_H1c0; zenon_intro zenon_H1c3 | zenon_intro zenon_H1c2; zenon_intro zenon_H110 ].
% 0.41/0.60 exact (zenon_H1c0 zenon_H1c2).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H110). zenon_intro zenon_H1db. zenon_intro axiom_88.
% 0.41/0.60 generalize (axiom_6 (iV21026)). zenon_intro zenon_H1da.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1da); [ zenon_intro zenon_H1d9; zenon_intro zenon_H1dc | zenon_intro zenon_H1db; zenon_intro zenon_H115 ].
% 0.41/0.60 exact (zenon_H1d9 zenon_H1db).
% 0.41/0.60 generalize (axiom_44 (iV21026)). zenon_intro zenon_H1b3.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H1b3); [ zenon_intro zenon_H1b2; zenon_intro zenon_H1b5 | zenon_intro zenon_H1b4; zenon_intro zenon_H10e ].
% 0.41/0.60 exact (zenon_H1b2 zenon_H1b4).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H10e). zenon_intro axiom_99. zenon_intro zenon_H144.
% 0.41/0.60 generalize (axiom_41 (iV21026)). zenon_intro zenon_H143.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H143); [ zenon_intro zenon_H142; zenon_intro zenon_H145 | zenon_intro zenon_H144; zenon_intro zenon_Hfa ].
% 0.41/0.60 exact (zenon_H142 zenon_H144).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hfa). zenon_intro zenon_H171. zenon_intro axiom_116.
% 0.41/0.60 generalize (axiom_38 (iV21026)). zenon_intro zenon_H170.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H170); [ zenon_intro zenon_H16f; zenon_intro zenon_H172 | zenon_intro zenon_H171; zenon_intro zenon_H103 ].
% 0.41/0.60 exact (zenon_H16f zenon_H171).
% 0.41/0.60 generalize (axiom_48 (iV21027)). zenon_intro zenon_H217.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H217); [ zenon_intro axiom_126; zenon_intro zenon_H20b | zenon_intro zenon_H219; zenon_intro zenon_H218 ].
% 0.41/0.60 generalize (axiom_51 (iV21027)). zenon_intro zenon_H21a.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H21a); [ zenon_intro axiom_136; zenon_intro zenon_H20c | zenon_intro zenon_H21c; zenon_intro zenon_H21b ].
% 0.41/0.60 generalize (axiom_59 (iV21029)). zenon_intro zenon_H21d.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H21d); [ zenon_intro axiom_157; zenon_intro zenon_H20a | zenon_intro zenon_H21f; zenon_intro zenon_H21e ].
% 0.41/0.60 generalize (axiom_62 (iV21029)). zenon_intro zenon_H220.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H220); [ zenon_intro axiom_168; zenon_intro zenon_H20d | zenon_intro zenon_H222; zenon_intro zenon_H221 ].
% 0.41/0.60 generalize (axiom_70 (iV21030)). zenon_intro zenon_H223.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H223); [ zenon_intro axiom_191; zenon_intro zenon_H209 | zenon_intro zenon_H225; zenon_intro zenon_H224 ].
% 0.41/0.60 generalize (axiom_73 (iV21030)). zenon_intro zenon_H226.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H226); [ zenon_intro axiom_192; zenon_intro zenon_H229 | zenon_intro zenon_H228; zenon_intro zenon_H227 ].
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H229); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H22a ].
% 0.41/0.60 exact (zenon_Hf3 axiom_202).
% 0.41/0.60 apply zenon_H22a. zenon_intro zenon_H207.
% 0.41/0.60 generalize (axiom_72 (iV21030)). zenon_intro zenon_H206.
% 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H206); [ zenon_intro zenon_H201; zenon_intro zenon_H208 | zenon_intro zenon_H207; zenon_intro zenon_H11d ].
% 0.41/0.60 exact (zenon_H201 zenon_H207).
% 0.41/0.60 apply (zenon_L5_); trivial.
% 0.41/0.60 exact (axiom_192 zenon_H228).
% 0.41/0.60 exact (axiom_191 zenon_H225).
% 0.41/0.60 exact (axiom_168 zenon_H222).
% 0.41/0.60 exact (axiom_157 zenon_H21f).
% 0.41/0.60 exact (axiom_136 zenon_H21c).
% 0.41/0.60 exact (axiom_126 zenon_H219).
% 0.41/0.60 Qed.
% 0.41/0.60 % SZS output end Proof
% 0.41/0.60 (* END-PROOF *)
% 0.41/0.60 nodes searched: 360
% 0.41/0.60 max branch formulas: 371
% 0.41/0.60 proof nodes created: 204
% 0.41/0.60 formulas created: 2642
% 0.41/0.60
%------------------------------------------------------------------------------