TSTP Solution File: SWV897-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV897-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 : 0s
% DateTime : Wed Jul 20 16:29:05 EDT 2022
% Result : Unsatisfiable 27.63s 28.03s
% Output : Refutation 27.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV897-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Wed Jun 15 12:09:56 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.87/1.27 *** allocated 10000 integers for termspace/termends
% 0.87/1.27 *** allocated 10000 integers for clauses
% 0.87/1.27 *** allocated 10000 integers for justifications
% 0.87/1.27 Bliksem 1.12
% 0.87/1.27
% 0.87/1.27
% 0.87/1.27 Automatic Strategy Selection
% 0.87/1.27
% 0.87/1.27 Clauses:
% 0.87/1.27 [
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.87/1.27 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), Y ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.27 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), Y ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ],
% 0.87/1.27 [ =( hAPP( 'c_Fun_Ocomp'( 'v_f', 'v_g', 't_a', 't_b', 't_c' ), 'v_x' ),
% 0.87/1.27 hAPP( 'v_f', hAPP( 'v_g', 'v_x' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_Fun_Oinj__on'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ), hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( U ), hAPP( X, Y ) ), 'c_Set_Oimage'( X,
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Z, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.87/1.27 T, 'tc_bool' ) ), T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, Z, T, U ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 0.87/1.27 , V4 ) ) ],
% 0.87/1.27 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W ), ~(
% 0.87/1.27 'c_Natural_Oevaln'( Y, T, U, W ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevaln'( Z, Y, T, U ), ~(
% 0.87/1.27 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Z, W ), Y, T, U ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 0.87/1.27 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y,
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, X ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, U ), ~(
% 0.87/1.27 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), W, T, U ) ), ~(
% 0.87/1.27 'c_Natural_Oevaln'( Y, Z, T, W ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Option_Ooption_ONone'( X ), 'c_Option_Ooption_OSome'( Y, X )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Option_Ooption_ONone'( X ), 'c_Option_Ooption_OSome'( Y, X )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.87/1.27 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.27 , T, X ) ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.87/1.27 , T, X ) ) ), =( Z, T ) ],
% 0.87/1.27 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U ), ~(
% 0.87/1.27 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T, W ) )
% 0.87/1.27 ],
% 0.87/1.27 [ 'c_Com_OWT'( 'c_Com_Ocom_OSKIP' ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X, Y, Z
% 0.87/1.27 , T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.87/1.27 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ],
% 0.87/1.27 [ 'c_Com_OWT'( 'c_Com_Ocom_OAss'( X, Y ) ) ],
% 0.87/1.27 [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.87/1.27 'tc_bool' ) ), Y, Z ) ],
% 0.87/1.27 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 0.87/1.27 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), =( Y,
% 0.87/1.27 Z ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ) ],
% 0.87/1.27 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 0.87/1.27 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 0.87/1.27 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W
% 0.87/1.27 ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ), ~(
% 0.87/1.27 hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ) ],
% 0.87/1.27 [ 'c_Com_OWT'( 'c_Com_Ocom_OCall'( X, Y, Z ) ), ~( 'c_Com_OWT'( hAPP(
% 0.87/1.27 'c_Com_Ocom_OBODY', Y ) ) ) ],
% 0.87/1.27 [ 'c_Com_OWT'( hAPP( 'c_Com_Ocom_OBODY', X ) ), ~( 'c_Com_OWT'(
% 0.87/1.27 'c_Com_Ocom_OCall'( Y, X, Z ) ) ) ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.27 Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.87/1.27 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 0.87/1.27 Y, Z ) ) ],
% 0.87/1.27 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.87/1.27 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.27 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( =( 'c_COMBC'( 'c_in'( X ), Y, X, 'tc_fun'( X, 'tc_bool' ),
% 0.87/1.27 'tc_bool' ), 'c_COMBC'( 'c_in'( X ), Z, X, 'tc_fun'( X, 'tc_bool' ),
% 0.87/1.27 'tc_bool' ) ) ), =( Y, Z ) ],
% 0.87/1.27 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 0.87/1.27 ) ],
% 0.87/1.27 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.27 Z ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ), ~(
% 0.87/1.27 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y, T,
% 0.87/1.27 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.87/1.27 T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 0.87/1.27 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 0.87/1.27 T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T
% 0.87/1.27 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.87/1.27 ) ],
% 0.87/1.27 [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 0.87/1.27 , 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X
% 0.87/1.27 , Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ),
% 0.87/1.27 ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T,
% 0.87/1.27 'tc_bool' ) ), T, U ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 0.87/1.27 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z
% 0.87/1.27 ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.87/1.27 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 0.87/1.27 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 0.87/1.27 , 'c_Set_Oinsert'( hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'(
% 0.87/1.27 'tc_Com_Ostate' ), X ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 0.87/1.27 , 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ),
% 0.87/1.27 ~( 'c_Hoare__Mirabelle_Ohoare__valids'( 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 0.87/1.27 , 'c_Set_Oinsert'( hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'(
% 0.87/1.27 'tc_Com_Ostate' ), X ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 0.87/1.27 , 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ) )
% 0.87/1.27 , ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 0.87/1.27 , 'c_Set_Oinsert'( 'c_Hoare__Mirabelle_OMGT'( Y ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.27 'tc_Com_Ostate' ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.27 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ) ) ],
% 0.87/1.27 [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 0.87/1.27 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ],
% 0.87/1.27 [ 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ],
% 0.87/1.27 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Set_Oinsert'( Y
% 0.87/1.27 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( U ), Z ), W ) ) ), ~( 'c_lessequals'( 'c_Set_Oimage'( Y, W
% 0.87/1.27 , U, X ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 0.87/1.27 Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( Z ), Y ), X ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y, T, Z
% 0.87/1.27 ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.87/1.27 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.87/1.27 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.87/1.27 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.87/1.27 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, Z ), hBOOL(
% 0.87/1.27 hAPP( X, Z ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 0.87/1.27 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( T, 'c_Orderings_Otop__class_Otop'(
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), Z, U ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 0.87/1.27 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ],
% 0.87/1.27 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 0.87/1.27 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'(
% 0.87/1.27 Z, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) )
% 0.87/1.27 ) ],
% 0.87/1.27 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.87/1.27 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OSKIP', V2 ), X ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( Z, V2 )
% 0.87/1.27 , V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.87/1.27 , =( Z, W ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.87/1.27 , =( Y, U ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.87/1.27 , =( X, T ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( hAPP( T, V2 ), V3 )
% 0.87/1.27 , 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V2, V4 ) ),
% 0.87/1.27 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.27 [ 'c_Fun_Oinj__on'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T,
% 0.87/1.27 'tc_bool' ) ), T, U ), ~( 'c_Fun_Oinj__on'( X, Y, T, U ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 0.87/1.27 , 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Ovimage'( X
% 0.87/1.27 , Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X, Y, Z, T ), Z, T
% 0.87/1.27 ), Y, 'tc_fun'( T, 'tc_bool' ) ) ],
% 0.87/1.27 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oimage'( X, Y, Z, T ), Z, T ), Y ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Z, T ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.87/1.27 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.87/1.27 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( Y
% 0.87/1.27 , T ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( X
% 0.87/1.27 , Z ) ],
% 0.87/1.27 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 0.87/1.27 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 0.87/1.27 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 0.87/1.27 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 0.87/1.27 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 0.87/1.27 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.87/1.27 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 0.87/1.27 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.87/1.27 T, 'tc_bool' ) ), T ), X, T ) ) ) ],
% 0.87/1.27 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 0.87/1.27 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), Y, Z ) ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.27 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.87/1.27 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( Y,
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 0.87/1.27 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 0.87/1.27 X, T ), Y ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ) ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( T, Z, 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ) ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.87/1.27 , =( Z, W ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.87/1.27 , =( Y, U ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.87/1.27 , =( X, T ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.27 ) ],
% 0.87/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.87/1.27 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.87/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Otop__class_Otop'(
% 0.87/1.27 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Option_Ooption_OSome'( X, Y ), 'c_Option_Ooption_ONone'( Y )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Option_Ooption_OSome'( X, Y ), 'c_Option_Ooption_ONone'( Y )
% 0.87/1.27 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ ~( =( 'c_Option_Ooption_OSome'( X, Y ), 'c_Option_Ooption_OSome'( Z, Y
% 0.87/1.27 ) ) ), =( X, Z ) ],
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y, 'tc_bool' ) ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 0.87/1.27 ) ],
% 0.87/1.27 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 0.87/1.27 ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( U, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ), X, T ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 0.87/1.27 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( Y, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( U,
% 0.87/1.27 'tc_bool' ) ), U, X ) ) ],
% 0.87/1.27 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.27 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool' ) ), T, U ) ), =(
% 0.87/1.27 Y, Z ) ],
% 0.87/1.27 [ =( hAPP( 'c_Fun_Ofcomp'( 'v_f', 'v_g', 't_a', 't_b', 't_c' ), 'v_x' )
% 0.87/1.27 , hAPP( 'v_g', hAPP( 'v_f', 'v_x' ) ) ) ],
% 0.87/1.27 [ 'c_Com_OWT'( 'c_Com_Ocom_OCond'( X, Y, Z ) ), ~( 'c_Com_OWT'( Z ) ),
% 0.87/1.27 ~( 'c_Com_OWT'( Y ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OSKIP', V2 ), X ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 0.87/1.27 ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Z, T ) ), =( Y, U ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP(
% 0.87/1.27 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), 'c_Com_Ocom_OSemi'(
% 0.87/1.27 T, U ) ), W ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.87/1.27 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 0.87/1.27 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 0.87/1.27 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 0.87/1.27 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), V0 ), U ), W ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.27 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ), ~(
% 0.87/1.27 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 0.87/1.27 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), T ), V0 ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.27 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) ) ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.87/1.27 ) ), Y ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OLocal'( X, Y, Z ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 0.87/1.27 [ 'c_Natural_Oevaln'( X, Y, 'c_Suc'( Z ), T ), ~( 'c_Natural_Oevaln'( X
% 0.87/1.27 , Y, Z, T ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( Z, 'tc_bool'
% 0.87/1.27 ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 0.87/1.27 ), Y ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ],
% 0.87/1.27 [ ~( 'class_Orderings_Otop'( X ) ), =( hAPP(
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 0.87/1.27 [ 'c_Natural_Oevaln'( X, Y, Z, T ), hBOOL( hAPP( U, Y ) ), ~(
% 0.87/1.27 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( U, W, X ), Y, Z, T ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z )
% 0.87/1.27 , 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.87/1.27 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( T ), Y ), X ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.87/1.27 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( Z ), T ), X ) ) ],
% 0.87/1.27 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 0.87/1.27 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 0.87/1.27 ), X ), Y ) ), =( Y, T ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), 'c_Set_Ovimage'( X, U,
% 0.87/1.27 Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( T
% 0.87/1.27 , 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( 'c_Fun_Oid'( T )
% 0.87/1.27 , W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W, V0 ) ) ],
% 0.87/1.27 [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP( 'c_HOL_Ominus__class_Ominus'( Y
% 0.87/1.27 , Z, 'tc_fun'( 't_a', X ) ), 'v_x' ), 'c_HOL_Ominus__class_Ominus'( hAPP(
% 0.87/1.27 Y, 'v_x' ), hAPP( Z, 'v_x' ), X ) ) ],
% 0.87/1.27 [ =( 'c_Set_Ovimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( T, V2 ), V3 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( 'c_Set_Ovimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ),
% 0.87/1.27 'c_Set_Ovimage'( Y, 'c_Set_Ovimage'( X, W, Z, T ), U, Z ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 0.87/1.27 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 0.87/1.27 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 0.87/1.27 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 0.87/1.27 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 0.87/1.27 =( X, Z ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 0.87/1.27 =( Y, T ) ],
% 0.87/1.27 [ 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( X, Y ) ), ~( 'c_Com_OWT'( Y ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( Y, X ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 0.87/1.27 , V4 ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 0.87/1.27 , X ), Y ) ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ), ~(
% 0.87/1.27 'c_Fun_Oinj__on'( Y, W, U, Z ) ) ],
% 0.87/1.27 [ 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( X, Y, Z ) ), ~( 'c_Com_OWT'( Z ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( Y, Z, X ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.87/1.27 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), X ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( X, 'c_Suc'( 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y
% 0.87/1.27 , X, Z, T ) ) ), ~( 'c_Natural_Oevaln'( hAPP( 'c_Com_Ocom_OBODY', Y ), Z
% 0.87/1.27 , X, T ) ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y,
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( T, 'c_Set_Oinsert'( Z,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), 'tc_fun'(
% 0.87/1.27 U, 'tc_bool' ) ), U, X ) ) ) ), ~( 'c_Fun_Oinj__on'( Y, 'c_Set_Oinsert'(
% 0.87/1.27 Z, T, U ), U, X ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, 'c_Com_Ocom_OAss'(
% 0.87/1.27 V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ],
% 0.87/1.27 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.87/1.27 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 0.87/1.27 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.87/1.27 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.87/1.27 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( W, V2 ), V3 ),
% 0.87/1.27 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), U, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'( X, U, Z, T ),
% 0.87/1.27 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y, Z, X ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ),
% 0.87/1.27 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( Z ), X ), Y ) ) ],
% 0.87/1.27 [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z
% 0.87/1.27 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.87/1.27 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T,
% 0.87/1.27 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.27 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( hAPP( U,
% 0.87/1.27 V2 ), V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3,
% 0.87/1.27 V5 ) ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 ) ) ) ]
% 0.87/1.27 ,
% 0.87/1.27 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 0.87/1.27 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.87/1.27 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.27 T, X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.87/1.27 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 0.87/1.27 Y, X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 0.87/1.27 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 0.87/1.27 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.87/1.27 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.27 T, X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.87/1.27 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 0.87/1.27 Y, X ), Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 0.87/1.27 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 0.87/1.27 'c_lessequals'( Y, Z, X ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 0.87/1.27 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( X ), Y, X ),
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( X ), X ), 'c_Orderings_Otop__class_Otop'(
% 0.87/1.27 X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.87/1.27 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.87/1.27 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.87/1.27 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.87/1.27 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.87/1.27 [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_lessequals'(
% 0.87/1.27 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 0.87/1.27 'tc_bool' ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 0.87/1.27 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ),
% 0.87/1.27 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 0.87/1.27 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 0.87/1.27 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.27 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.27 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.87/1.27 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ) ) ],
% 0.87/1.27 [ =( 'c_Set_Oimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ],
% 0.87/1.27 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.27 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 0.87/1.27 ) ), Z, X ) ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 0.87/1.27 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 0.87/1.27 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 0.87/1.27 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 0.87/1.27 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 0.87/1.27 ) ],
% 0.87/1.27 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 0.87/1.27 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.27 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.27 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.87/1.27 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.87/1.27 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.27 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.87/1.27 , 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.27 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.87/1.27 ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.87/1.27 'tc_bool' ) ), X ) ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.27 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 0.87/1.27 X, 'tc_bool' ) ), Y ) ],
% 0.87/1.27 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 0.87/1.27 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 0.87/1.27 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 0.87/1.27 'tc_bool' ) ) ) ) ) ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.27 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.87/1.27 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 0.87/1.27 ) ],
% 0.87/1.27 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 0.87/1.28 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 0.87/1.28 ) ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 0.87/1.28 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 0.87/1.28 'tc_bool' ) ), T ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 0.87/1.28 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), Z ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.87/1.28 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.87/1.28 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X
% 0.87/1.28 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 0.87/1.28 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.87/1.28 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.87/1.28 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W ), ~(
% 0.87/1.28 'c_Natural_Oevaln'( Z, T, U, W ) ), hBOOL( hAPP( X, T ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.87/1.28 'c_COMBC'( 'c_in'( Z ), X, Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ),
% 0.87/1.28 'c_COMBC'( 'c_in'( Z ), Y, Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ),
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_COMBC'( 'c_in'( X ), Y, X, 'tc_fun'( X, 'tc_bool' )
% 0.87/1.28 , 'tc_bool' ), 'c_COMBC'( 'c_in'( X ), Z, X, 'tc_fun'( X, 'tc_bool' ),
% 0.87/1.28 'tc_bool' ), 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'( Y, Z,
% 0.87/1.28 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ) ],
% 0.87/1.28 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 0.87/1.28 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 0.87/1.28 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.87/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.87/1.28 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.87/1.28 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.28 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ],
% 0.87/1.28 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.87/1.28 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 0.87/1.28 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.87/1.28 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 0.87/1.28 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.87/1.28 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 0.87/1.28 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.87/1.28 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( 'c_Natural_Oevaln'( T, U, W, Z )
% 0.87/1.28 ), ~( hBOOL( hAPP( hAPP( V0, Y ), U ) ) ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple__valid'( W, hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( 't_a' ), V0 ), T ), X ), 't_a' ) )
% 0.87/1.28 ],
% 0.87/1.28 [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' )
% 0.87/1.28 ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OAss'( X, Y ) ) ) ],
% 0.87/1.28 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( Y, X ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 0.87/1.28 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.87/1.28 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.87/1.28 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.28 'tc_fun'( X, 'tc_bool' ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.87/1.28 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 0.87/1.28 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.28 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( Z, V2 ), V3 )
% 0.87/1.28 , V4 ) ) ],
% 0.87/1.28 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.28 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( W, V2 ), V3 ) ) ],
% 0.87/1.28 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 0.87/1.28 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 0.87/1.28 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Otop__class_Otop'(
% 0.87/1.28 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ),
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y, hAPP( X, W ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 0.87/1.28 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) ) ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 0.87/1.28 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 0.87/1.28 'c_Orderings_Otop__class_Otop'( X ), X ) ],
% 0.87/1.28 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 0.87/1.28 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ), =( Y,
% 0.87/1.28 T ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ), =( X,
% 0.87/1.28 Z ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP(
% 0.87/1.28 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), 'c_Com_Ocom_OSKIP'
% 0.87/1.28 ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ],
% 0.87/1.28 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 0.87/1.28 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 0.87/1.28 hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.87/1.28 ), =( Z, W ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.87/1.28 ), =( Y, U ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.87/1.28 ), =( X, T ) ],
% 0.87/1.28 [ 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ), ~( 'c_Com_OWT'( Y ) ), ~(
% 0.87/1.28 'c_Com_OWT'( X ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCall'( X, Y, Z ) ) ) ],
% 0.87/1.28 [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X ) ],
% 0.87/1.28 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.87/1.28 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.87/1.28 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.87/1.28 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( hBOOL( hAPP(
% 0.87/1.28 hAPP( 'c_in'( Z ), X ), Y ) ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.28 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.87/1.28 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.28 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.28 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( 'c_lessequals'( T, Z,
% 0.87/1.28 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T )
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 0.87/1.28 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'( X,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.87/1.28 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 0.87/1.28 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, U, Z, T ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 0.87/1.28 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 0.87/1.28 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 0.87/1.28 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 0.87/1.28 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 0.87/1.28 [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T
% 0.87/1.28 , 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X
% 0.87/1.28 , Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ),
% 0.87/1.28 ~( 'c_lessequals'( Z, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'(
% 0.87/1.28 Y, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, W, T, U ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.87/1.28 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( U, V2 ), V3 ),
% 0.87/1.28 V4 ) ) ],
% 0.87/1.28 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 0.87/1.28 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 0.87/1.28 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 0.87/1.28 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 0.87/1.28 , V4 ), W ) ) ],
% 0.87/1.28 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 0.87/1.28 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 0.87/1.28 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 0.87/1.28 Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 0.87/1.28 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 0.87/1.28 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevaln'(
% 0.87/1.28 'c_Com_Ocom_OWhile'( X, T ), Y, U, Z ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 0.87/1.28 X, T, U ), Z ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 0.87/1.28 hAPP( X, U ) ) ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y, Z,
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Z, T ) ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y,
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 T ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.87/1.28 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), Z ), ~(
% 0.87/1.28 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 0.87/1.28 , X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.87/1.28 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.28 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 0.87/1.28 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_Natural_Oevaln'( X, Y, Z, T ), 'c_Natural_Oevaln'( U, Y, Z, T ),
% 0.87/1.28 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( W, U, X ), Y, Z, T ) ) ],
% 0.87/1.28 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.87/1.28 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, Z, X ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, X, Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z, U, V0 ),
% 0.87/1.28 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ],
% 0.87/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.87/1.28 'c_lessequals'( Z, Y, X ) ],
% 0.87/1.28 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.87/1.28 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.87/1.28 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.87/1.28 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.87/1.28 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 0.87/1.28 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X, Y, U, T
% 0.87/1.28 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( U, Y, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), Z, T ) ) ],
% 0.87/1.28 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, U, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), Z, T ) ) ],
% 0.87/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( 't_a' ) ), =(
% 0.87/1.28 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( 'v_x', 't_a' ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( 'v_x',
% 0.87/1.28 'c_HOL_Ozero__class_Ozero'( 't_a' ), 't_a' ) ) ],
% 0.87/1.28 [ =( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_COMBC'(
% 0.87/1.28 'c_in'( 't_a' ), X, 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ),
% 0.87/1.28 'c_COMBC'( 'c_in'( 't_a' ), Y, 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 0.87/1.28 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_x' ), hAPP( hAPP( 'c_in'(
% 0.87/1.28 't_a' ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.28 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 0.87/1.28 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ), hAPP( X, hAPP( Y
% 0.87/1.28 , 'v_x' ) ) ) ],
% 0.87/1.28 [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ],
% 0.87/1.28 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ), hAPP( Y, hAPP(
% 0.87/1.28 X, 'v_x' ) ) ) ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), hAPP( 'c_Com_Ocom_OBODY', Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, hAPP(
% 0.87/1.28 'c_Com_Ocom_OBODY', V2 ), V3 ), hAPP( V0, V2 ) ) ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OCond'( Y, Z, T ) ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), hAPP( 'c_Com_Ocom_OBODY', T ) ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OAss'( Y, Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), hAPP( 'c_Com_Ocom_OBODY', Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OLocal'( Y, Z, T ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OWhile'( Y, Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), hAPP( 'c_Com_Ocom_OBODY', T ) ) )
% 0.87/1.28 ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OSemi'( Y, Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), hAPP( 'c_Com_Ocom_OBODY', Z ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), hAPP( 'c_Com_Ocom_OBODY', T ) )
% 0.87/1.28 ) ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OCall'( Y, Z, T ) ) )
% 0.87/1.28 ],
% 0.87/1.28 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1, hAPP(
% 0.87/1.28 'c_Com_Ocom_OBODY', V2 ), V3 ), hAPP( V0, V2 ) ) ],
% 0.87/1.28 [ ~( =( 'c_Com_Ocom_OSKIP', hAPP( 'c_Com_Ocom_OBODY', X ) ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'c_HOL_Ozero__class_Ozero'(
% 0.87/1.28 'tc_nat' ), hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ),
% 0.87/1.28 Y ), hAPP( 'c_Com_Ocom_OBODY', Z ) ), T ), X ) ],
% 0.87/1.28 [ ~( hBOOL( hAPP( X, 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y, hAPP(
% 0.87/1.28 hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( 't_b' ), Z ), T ), U )
% 0.87/1.28 , 't_b', 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U
% 0.87/1.28 ) ) ) ],
% 0.87/1.28 [ ~( hBOOL( hAPP( X, 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y, hAPP(
% 0.87/1.28 hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( 't_b' ), Z ), T ), U )
% 0.87/1.28 , 't_b', 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U
% 0.87/1.28 ) ) ) ],
% 0.87/1.28 [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__rec'( X, hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), T ), U ), Y, W ), hAPP(
% 0.87/1.28 hAPP( hAPP( X, Z ), T ), U ) ) ],
% 0.87/1.28 [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( X, hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), T ), U ), Y, W ), hAPP(
% 0.87/1.28 hAPP( hAPP( X, Z ), T ), U ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( T, Y,
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~( 'c_lessequals'( Y,
% 0.87/1.28 T, 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Z ), 'tc_bool' ) ) ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~( 'c_lessequals'( T,
% 0.87/1.28 X, 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Z ), 'tc_bool' ) ) ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), Y ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, Z ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~( 'c_lessequals'( Y,
% 0.87/1.28 X, 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Z ), 'tc_bool' ) ) ) ],
% 0.87/1.28 [ 'c_Com_OWT'( hAPP( 'c_Com_Ocom_OBODY', X ) ), =( hAPP( 'c_Com_Obody',
% 0.87/1.28 X ), 'c_Option_Ooption_ONone'( 'tc_Com_Ocom' ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ), Z ) ), hBOOL(
% 0.87/1.28 hAPP( hAPP( hAPP( 'c_Natural_Oevalc', T ), Y ), Z ) ), ~( hBOOL( hAPP(
% 0.87/1.28 hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( U, T, X ) ), Y ), Z )
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Natural_Oevalc', 'c_Com_Ocom_OWhile'( X, T ) ), Y ), Z ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( X, Y
% 0.87/1.28 , Z ) ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', Z )
% 0.87/1.28 , T ), U ) ) ), hBOOL( hAPP( X, T ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ), Z ) ), hBOOL(
% 0.87/1.28 hAPP( T, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 0.87/1.28 'c_Com_Ocom_OCond'( T, U, X ) ), Y ), Z ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OSKIP' ), X )
% 0.87/1.28 , X ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OWhile'( X, Y
% 0.87/1.28 ) ), Z ), Z ) ), hBOOL( hAPP( X, Z ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OWhile'( X, Y
% 0.87/1.28 ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 0.87/1.28 'c_Com_Ocom_OWhile'( X, Y ) ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Natural_Oevalc', Y ), Z ), U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( X, Y
% 0.87/1.28 , Z ) ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', Y )
% 0.87/1.28 , T ), U ) ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.87/1.28 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Natural_Oevalc', Z ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( X, Z, U ) ), Y ), T ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OSemi'( X, Y
% 0.87/1.28 ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', Y ), U
% 0.87/1.28 ), T ) ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Z ), U
% 0.87/1.28 ) ) ) ],
% 0.87/1.28 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 0.87/1.28 'c_Com_Ocom_OSKIP' ), Y ), X ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ), Z ) ), ~(
% 0.87/1.28 'c_Natural_Oevaln'( X, Y, T, Z ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ), Z ) ), ~(
% 0.87/1.28 'c_Natural_Oevaln'( X, Y, T, Z ) ) ],
% 0.87/1.28 [ =( hAPP( 'c_Option_Othe'( X ), 'c_Option_Ooption_OSome'( Y, X ) ), Y )
% 0.87/1.28 ],
% 0.87/1.28 [ =( 'c_Hoare__Mirabelle_OMGT'( 'v_c' ), hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), 'c_fequal'(
% 0.87/1.28 'tc_Com_Ostate' ) ), 'v_c' ), hAPP( 'c_Natural_Oevalc', 'v_c' ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( 'class_Lattices_Olattice'( 't_b' ) ), =( hAPP(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( 'v_f', 'v_g', 'tc_fun'(
% 0.87/1.28 't_a', 't_b' ) ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 hAPP( 'v_f', 'v_x' ), hAPP( 'v_g', 'v_x' ), 't_b' ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.87/1.28 'c_Hoare__Mirabelle_OMGT'( hAPP( 'c_Com_Ocom_OBODY', Y ) ),
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 'tc_Com_Ostate' ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Set_Oinsert'(
% 0.87/1.28 'c_Hoare__Mirabelle_OMGT'( hAPP( 'c_Com_Ocom_OBODY', Y ) ), X,
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'c_Set_Oinsert'(
% 0.87/1.28 'c_Hoare__Mirabelle_OMGT'( hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 0.87/1.28 'c_Com_Obody', Y ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'c_Natural_Oevaln'( hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 0.87/1.28 'c_Com_Obody', X ) ), Y,
% 0.87/1.28 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( X, Z, Y, T ), T ),
% 0.87/1.28 ~( 'c_Natural_Oevaln'( hAPP( 'c_Com_Ocom_OBODY', X ), Y, Z, T ) ) ],
% 0.87/1.28 [ 'c_Natural_Oevaln'( hAPP( 'c_Com_Ocom_OBODY', X ), Y, 'c_Suc'( Z ), T
% 0.87/1.28 ), ~( 'c_Natural_Oevaln'( hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 0.87/1.28 'c_Com_Obody', X ) ), Y, Z, T ) ) ],
% 0.87/1.28 [ =( 'c_Set_Oimage'( 'c_COMBB'( X, Y, Z, T, U ),
% 0.87/1.28 'c_Orderings_Otop__class_Otop'( 'tc_fun'( U, 'tc_bool' ) ), U, T ),
% 0.87/1.28 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, 'c_Orderings_Otop__class_Otop'(
% 0.87/1.28 'tc_fun'( U, 'tc_bool' ) ), U, Z ), Z, T ) ) ],
% 0.87/1.28 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 0.87/1.28 ~( 'c_Fun_Oinj__on'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 U, 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), =( Y, U ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Com_Ocom_OBODY'
% 0.87/1.28 , T ) ), U ), Y ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X, hAPP( hAPP(
% 0.87/1.28 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 0.87/1.28 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ), Y )
% 0.87/1.28 ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Option_Othe'(
% 0.87/1.28 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ), Y ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Com_Ocom_OBODY'
% 0.87/1.28 , T ) ), U ), Y ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP(
% 0.87/1.28 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), hAPP( Z, T ) ), hAPP(
% 0.87/1.28 'c_Com_Ocom_OBODY', T ) ), hAPP( U, T ) ), 'c_Orderings_Obot__class_Obot'(
% 0.87/1.28 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 0.87/1.28 'tc_Com_Opname' ), T ), W ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 0.87/1.28 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 0.87/1.28 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), U, 'tc_Com_Opname', 'tc_fun'( Y,
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ) ), W, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 0.87/1.28 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 0.87/1.28 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 0.87/1.28 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 0.87/1.28 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), U
% 0.87/1.28 , 'tc_Com_Opname', 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 0.87/1.28 , 'tc_Hoare__Mirabelle_Otriple'( Y ) ), W, 'tc_Com_Opname',
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ],
% 0.87/1.28 [ =( 'c_Hoare__Mirabelle_OMGT'( X ), hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), 'c_fequal'(
% 0.87/1.28 'tc_Com_Ostate' ) ), X ), hAPP( 'c_Natural_Oevalc', X ) ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP(
% 0.87/1.28 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 0.87/1.28 'c_Com_Ocom_OBODY', T ) ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Com_Ocom_OBODY'
% 0.87/1.28 , T ) ), U ), X, 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'c_Set_Oinsert'(
% 0.87/1.28 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 0.87/1.28 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ),
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP(
% 0.87/1.28 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 0.87/1.28 'c_Com_Ocom_OBODY', T ) ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Option_Othe'(
% 0.87/1.28 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ),
% 0.87/1.28 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, 'c_Set_Oimage'( 'c_COMBS'(
% 0.87/1.28 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z,
% 0.87/1.28 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 0.87/1.28 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__valids'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 0.87/1.28 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 0.87/1.28 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 0.87/1.28 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 0.87/1.28 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 0.87/1.28 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 0.87/1.28 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T
% 0.87/1.28 , 'tc_Com_Opname', 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 0.87/1.28 , 'tc_Hoare__Mirabelle_Otriple'( Y ) ), U, 'tc_Com_Opname',
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oimage'( 'c_COMBS'(
% 0.87/1.28 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z,
% 0.87/1.28 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 0.87/1.28 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 0.87/1.28 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 0.87/1.28 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'tc_fun'(
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 0.87/1.28 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 0.87/1.28 , 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 0.87/1.28 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 0.87/1.28 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 0.87/1.28 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T
% 0.87/1.28 , 'tc_Com_Opname', 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 0.87/1.28 , 'tc_Hoare__Mirabelle_Otriple'( Y ) ), U, 'tc_Com_Opname',
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ],
% 0.87/1.28 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 0.87/1.28 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 0.87/1.28 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP( 'c_Com_Ocom_OBODY'
% 0.87/1.28 , X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 0.87/1.28 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', X ) ) ), Y ), Z )
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'(
% 0.87/1.28 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', X ) ) ), Y ), Z ) ), ~( hBOOL( hAPP(
% 0.87/1.28 hAPP( hAPP( 'c_Natural_Oevalc', hAPP( 'c_Com_Ocom_OBODY', X ) ), Y ), Z )
% 0.87/1.28 ) ) ],
% 0.87/1.28 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 0.87/1.28 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 0.87/1.28 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ],
% 0.87/1.28 [ ~( =( hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y )
% 0.87/1.28 , Z ), T ), hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ),
% 0.87/1.28 U ), W ), V0 ) ) ), =( T, V0 ) ],
% 0.87/1.28 [ ~( =( hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y )
% 0.87/1.28 , Z ), T ), hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ),
% 0.87/1.28 U ), W ), V0 ) ) ), =( Z, W ) ],
% 0.87/1.28 [ ~( =( hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y )
% 0.87/1.28 , Z ), T ), hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ),
% 0.87/1.28 U ), W ), V0 ) ) ), =( Y, U ) ],
% 0.87/1.28 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', Z ), T ), X
% 0.87/1.28 ) ) ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', Z ), T ), Y ) ) )
% 0.87/1.28 ],
% 0.87/1.28 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 0.87/1.28 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 0.87/1.28 'tc_bool' ) ), Y ) ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 't_a', X )
% 0.87/1.28 ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( Y, 'v_x'
% 0.87/1.28 ), hAPP( Z, 'v_x' ), X ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 0.87/1.28 'tc_bool' ) ), X ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 0.87/1.28 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 0.87/1.28 , W ) ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.87/1.28 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 0.87/1.28 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 0.87/1.28 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 0.87/1.28 [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), hAPP( 'c_Com_Ocom_OBODY', Y ) ) )
% 0.87/1.28 , =( X, Y ) ],
% 0.87/1.28 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.87/1.28 'tc_bool' ) ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.87/1.28 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.87/1.28 [ 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 0.87/1.28 'c_Lattices_Oupper__semilattice__class_Osup'( 'v_G', 'c_Set_Oimage'(
% 0.87/1.28 'c_COMBS'( 'c_COMBB'( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'(
% 0.87/1.28 'tc_Com_Ostate' ), 'c_fequal'( 'tc_Com_Ostate' ) ), 'c_Com_Ocom_OBODY',
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 0.87/1.28 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 'tc_Com_Ostate' ) ), 'tc_Com_Opname' ), 'c_COMBB'( 'c_Natural_Oevalc',
% 0.87/1.28 'c_Com_Ocom_OBODY', 'tc_Com_Ocom', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 0.87/1.28 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Opname' ), 'tc_Com_Opname',
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'v_Procs',
% 0.87/1.28 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 0.87/1.28 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 0.87/1.28 , 'c_Set_Oimage'( 'c_COMBS'( 'c_COMBB'( hAPP(
% 0.87/1.28 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), 'c_fequal'(
% 0.87/1.28 'tc_Com_Ostate' ) ), 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ),
% 0.87/1.28 'c_Com_Obody', 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom',
% 0.87/1.28 'tc_Com_Opname' ), 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 0.87/1.28 'tc_Com_Ostate' ) ), 'tc_Com_Opname' ), 'c_COMBB'( 'c_Natural_Oevalc',
% 0.87/1.28 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 0.87/1.28 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 0.87/1.28 'tc_Com_Ocom', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 0.87/1.28 'tc_bool' ) ), 'tc_Com_Opname' ), 'tc_Com_Opname', 'tc_fun'(
% 0.87/1.28 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 0.87/1.28 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'v_Procs',
% 0.87/1.28 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 0.87/1.28 'tc_Com_Ostate' ) ],
% 0.87/1.28 [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'(
% 0.87/1.28 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', 'v_pn' ) ) ), 'v_x' ), 'v_xa' ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 0.87/1.28 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ) ],
% 0.87/1.28 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.28 'class_Lattices_Olattice'( Y ) ) ],
% 0.87/1.28 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.28 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 0.87/1.28 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.28 'class_Orderings_Opreorder'( Y ) ) ],
% 0.87/1.28 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.28 'class_Lattices_Olattice'( Y ) ) ],
% 0.87/1.28 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.87/1.28 'class_Orderings_Oorder'( Y ) ) ],
% 0.87/1.28 [ 'class_Orderings_Otop'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Otop'(
% 0.87/1.28 Y ) ) ],
% 0.87/1.28 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 0.87/1.28 Y ) ) ],
% 0.87/1.28 [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Ominus'( Y ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_HOL_Ominus'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 0.87/1.28 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_Orderings_Otop'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_HOL_Ominus'( 'tc_bool' ) ],
% 0.87/1.28 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 0.87/1.28 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 0.87/1.28 , W ) ) ) ],
% 0.87/1.28 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 0.87/1.28 ,
% 0.87/1.28 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.87/1.28 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.87/1.28 ] .
% 0.87/1.28
% 0.87/1.28
% 0.87/1.28 percentage equality = 0.380774, percentage horn = 0.936652
% 0.87/1.28 This is a problem with some equality
% 0.87/1.28
% 0.87/1.28
% 0.87/1.28
% 0.87/1.28 Options Used:
% 0.87/1.28
% 0.87/1.28 useres = 1
% 0.87/1.28 useparamod = 1
% 0.87/1.28 useeqrefl = 1
% 0.87/1.28 useeqfact = 1
% 0.87/1.28 usefactor = 1
% 0.87/1.28 usesimpsplitting = 0
% 0.87/1.28 usesimpdemod = 5
% 0.87/1.28 usesimpres = 3
% 0.87/1.28
% 0.87/1.28 resimpinuse = 1000
% 0.87/1.28 resimpclauses = 20000
% 0.87/1.28 substype = eqrewr
% 0.87/1.28 backwardsubs = 1
% 0.87/1.28 selectoldest = 5
% 0.87/1.28
% 0.87/1.28 litorderings [0] = split
% 0.87/1.28 litorderings [1] = extend the termordering, first sorting on arguments
% 0.87/1.28
% 0.87/1.28 termordering = kbo
% 0.87/1.28
% 0.87/1.28 litapriori = 0
% 0.87/1.28 termapriori = 1
% 0.87/1.28 litaposteriori = 0
% 0.87/1.28 termaposteriori = 0
% 0.87/1.28 demodaposteriori = 0
% 0.87/1.28 ordereqreflfact = 0
% 0.87/1.28
% 0.87/1.28 litselect = negord
% 1.94/2.30
% 1.94/2.30 maxweight = 15
% 1.94/2.30 maxdepth = 30000
% 1.94/2.30 maxlength = 115
% 1.94/2.30 maxnrvars = 195
% 1.94/2.30 excuselevel = 1
% 1.94/2.30 increasemaxweight = 1
% 1.94/2.30
% 1.94/2.30 maxselected = 10000000
% 1.94/2.30 maxnrclauses = 10000000
% 1.94/2.30
% 1.94/2.30 showgenerated = 0
% 1.94/2.30 showkept = 0
% 1.94/2.30 showselected = 0
% 1.94/2.30 showdeleted = 0
% 1.94/2.30 showresimp = 1
% 1.94/2.30 showstatus = 2000
% 1.94/2.30
% 1.94/2.30 prologoutput = 1
% 1.94/2.30 nrgoals = 5000000
% 1.94/2.30 totalproof = 1
% 1.94/2.30
% 1.94/2.30 Symbols occurring in the translation:
% 1.94/2.30
% 1.94/2.30 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.94/2.30 . [1, 2] (w:1, o:150, a:1, s:1, b:0),
% 1.94/2.30 ! [4, 1] (w:0, o:114, a:1, s:1, b:0),
% 1.94/2.30 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.94/2.30 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.94/2.30 'class_OrderedGroup_Olordered__ab__group__add' [40, 1] (w:1, o:119
% 1.94/2.30 , a:1, s:1, b:0),
% 1.94/2.30 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt' [42, 2] (w:1
% 1.94/2.30 , o:175, a:1, s:1, b:0),
% 1.94/2.30 'c_HOL_Ozero__class_Ozero' [43, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.94/2.30 'c_lessequals' [44, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.94/2.30 'v_f' [45, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.94/2.30 'v_g' [46, 0] (w:1, o:12, a:1, s:1, b:0),
% 1.94/2.30 't_a' [47, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.94/2.30 't_b' [48, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.94/2.30 't_c' [49, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.94/2.30 'c_Fun_Ocomp' [50, 5] (w:1, o:199, a:1, s:1, b:0),
% 1.94/2.30 'v_x' [51, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.94/2.30 hAPP [52, 2] (w:1, o:176, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_OCall' [56, 3] (w:1, o:183, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_OSemi' [59, 2] (w:1, o:177, a:1, s:1, b:0),
% 1.94/2.30 'c_Set_Oinsert' [62, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.94/2.30 'c_Fun_Oinj__on' [64, 4] (w:1, o:192, a:1, s:1, b:0),
% 1.94/2.30 'c_in' [65, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.94/2.30 'tc_bool' [66, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.94/2.30 'tc_fun' [67, 2] (w:1, o:178, a:1, s:1, b:0),
% 1.94/2.30 'c_Orderings_Obot__class_Obot' [68, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.94/2.30 'c_HOL_Ominus__class_Ominus' [69, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.94/2.30 'c_Set_Oimage' [70, 4] (w:1, o:193, a:1, s:1, b:0),
% 1.94/2.30 hBOOL [71, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.94/2.30 'c_Fun_Oid' [74, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_Ocom__case' [86, 10] (w:1, o:204, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_OCond' [90, 3] (w:1, o:186, a:1, s:1, b:0),
% 1.94/2.30 'c_Natural_Oevaln' [94, 4] (w:1, o:194, a:1, s:1, b:0),
% 1.94/2.30 'c_COMBC' [102, 5] (w:1, o:201, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_OAss' [104, 2] (w:1, o:179, a:1, s:1, b:0),
% 1.94/2.30 'c_Orderings_Otop__class_Otop' [105, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.94/2.30
% 1.94/2.30 'c_Com_Ocom_OWhile' [107, 2] (w:1, o:180, a:1, s:1, b:0),
% 1.94/2.30 'c_Option_Ooption_ONone' [110, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.94/2.30 'c_Option_Ooption_OSome' [111, 2] (w:1, o:181, a:1, s:1, b:0),
% 1.94/2.30 'class_OrderedGroup_Oab__group__add' [114, 1] (w:1, o:127, a:1, s:1
% 1.94/2.30 , b:0),
% 1.94/2.30 'c_Com_Ocom_OSKIP' [117, 0] (w:1, o:71, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_OWT' [118, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_OBODY' [121, 0] (w:1, o:74, a:1, s:1, b:0),
% 1.94/2.30 'c_Lattices_Oupper__semilattice__class_Osup' [122, 3] (w:1, o:187, a:
% 1.94/2.30 1, s:1, b:0),
% 1.94/2.30 'class_Ring__and__Field_Oidom' [125, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.94/2.30
% 1.94/2.30 'class_Int_Onumber__ring' [126, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.94/2.30 'class_OrderedGroup_Ogroup__add' [127, 1] (w:1, o:133, a:1, s:1, b:0)
% 1.94/2.30 ,
% 1.94/2.30 'tc_Hoare__Mirabelle_Otriple' [129, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.94/2.30 'c_Hoare__Mirabelle_Ohoare__derivs' [130, 3] (w:1, o:188, a:1, s:1
% 1.94/2.30 , b:0),
% 1.94/2.30 'c_Com_Ocom_OLocal' [134, 3] (w:1, o:189, a:1, s:1, b:0),
% 1.94/2.30 'tc_Com_Ostate' [135, 0] (w:1, o:80, a:1, s:1, b:0),
% 1.94/2.30 'c_Hoare__Mirabelle_Otriple_Otriple' [136, 1] (w:1, o:135, a:1, s:1
% 1.94/2.30 , b:0),
% 1.94/2.30 'c_Hoare__Mirabelle_Ohoare__valids' [137, 3] (w:1, o:190, a:1, s:1
% 1.94/2.30 , b:0),
% 1.94/2.30 'c_Hoare__Mirabelle_OMGT' [138, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.94/2.30 'c_Com_Ocom_Ocom__rec' [140, 10] (w:1, o:205, a:1, s:1, b:0),
% 1.94/2.30 'class_Orderings_Obot' [141, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.94/2.30 'c_Set_Ovimage' [143, 4] (w:1, o:195, a:1, s:1, b:0),
% 1.94/2.30 'tc_nat' [144, 0] (w:1, o:88, a:1, s:1, b:0),
% 1.94/2.30 'c_Suc' [146, 1] (w:1, o:138, a:1, s:1, b:0),
% 9.57/9.94 'c_Hoare__Mirabelle_Otriple__valid' [149, 3] (w:1, o:191, a:1, s:1
% 9.57/9.94 , b:0),
% 9.57/9.94 'c_Fun_Ofcomp' [153, 5] (w:1, o:202, a:1, s:1, b:0),
% 9.57/9.94 'class_Orderings_Otop' [158, 1] (w:1, o:139, a:1, s:1, b:0),
% 9.57/9.94 'class_HOL_Ominus' [159, 1] (w:1, o:130, a:1, s:1, b:0),
% 9.57/9.94 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1' [161, 4] (w:1
% 9.57/9.94 , o:196, a:1, s:1, b:0),
% 9.57/9.94 'class_HOL_Oord' [162, 1] (w:1, o:131, a:1, s:1, b:0),
% 9.57/9.94 'class_Lattices_Oupper__semilattice' [163, 1] (w:1, o:140, a:1, s:1
% 9.57/9.94 , b:0),
% 9.57/9.94 'class_Lattices_Obounded__lattice' [165, 1] (w:1, o:141, a:1, s:1, b:
% 9.57/9.94 0),
% 9.57/9.94 'class_Lattices_Olattice' [166, 1] (w:1, o:142, a:1, s:1, b:0),
% 9.57/9.94 'class_Orderings_Oorder' [168, 1] (w:1, o:143, a:1, s:1, b:0),
% 9.57/9.94 'class_OrderedGroup_Opordered__ab__group__add' [169, 1] (w:1, o:144
% 9.57/9.94 , a:1, s:1, b:0),
% 9.57/9.94 'class_Orderings_Opreorder' [173, 1] (w:1, o:145, a:1, s:1, b:0),
% 9.57/9.94 'class_Orderings_Olinorder' [177, 1] (w:1, o:146, a:1, s:1, b:0),
% 9.57/9.94 'c_Hoare__Mirabelle_Otriple_Otriple__case' [180, 4] (w:1, o:197, a:1
% 9.57/9.94 , s:1, b:0),
% 9.57/9.94 'c_Hoare__Mirabelle_Otriple_Otriple__rec' [183, 4] (w:1, o:198, a:1
% 9.57/9.94 , s:1, b:0),
% 9.57/9.94 'c_Com_Obody' [186, 0] (w:1, o:70, a:1, s:1, b:0),
% 9.57/9.94 'tc_Com_Ocom' [187, 0] (w:1, o:104, a:1, s:1, b:0),
% 9.57/9.94 'c_Natural_Oevalc' [188, 0] (w:1, o:105, a:1, s:1, b:0),
% 9.57/9.94 'c_Option_Othe' [189, 1] (w:1, o:147, a:1, s:1, b:0),
% 9.57/9.94 'v_c' [190, 0] (w:1, o:106, a:1, s:1, b:0),
% 9.57/9.94 'c_fequal' [191, 1] (w:1, o:148, a:1, s:1, b:0),
% 9.57/9.94 'c_COMBB' [192, 5] (w:1, o:200, a:1, s:1, b:0),
% 9.57/9.94 'tc_Com_Opname' [193, 0] (w:1, o:107, a:1, s:1, b:0),
% 9.57/9.94 'c_COMBS' [195, 5] (w:1, o:203, a:1, s:1, b:0),
% 9.57/9.94 'tc_Option_Ooption' [196, 1] (w:1, o:149, a:1, s:1, b:0),
% 9.57/9.94 'v_G' [200, 0] (w:1, o:108, a:1, s:1, b:0),
% 9.57/9.94 'v_Procs' [201, 0] (w:1, o:109, a:1, s:1, b:0),
% 9.57/9.94 'v_pn' [202, 0] (w:1, o:110, a:1, s:1, b:0),
% 9.57/9.94 'v_xa' [203, 0] (w:1, o:111, a:1, s:1, b:0).
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Starting Search:
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 5786
% 9.57/9.94 Kept: 2248
% 9.57/9.94 Inuse: 162
% 9.57/9.94 Deleted: 4
% 9.57/9.94 Deletedinuse: 0
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 12146
% 9.57/9.94 Kept: 4747
% 9.57/9.94 Inuse: 217
% 9.57/9.94 Deleted: 5
% 9.57/9.94 Deletedinuse: 0
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 19859
% 9.57/9.94 Kept: 6780
% 9.57/9.94 Inuse: 299
% 9.57/9.94 Deleted: 9
% 9.57/9.94 Deletedinuse: 2
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 28855
% 9.57/9.94 Kept: 8945
% 9.57/9.94 Inuse: 329
% 9.57/9.94 Deleted: 9
% 9.57/9.94 Deletedinuse: 2
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 39493
% 9.57/9.94 Kept: 11732
% 9.57/9.94 Inuse: 374
% 9.57/9.94 Deleted: 9
% 9.57/9.94 Deletedinuse: 2
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 47198
% 9.57/9.94 Kept: 13795
% 9.57/9.94 Inuse: 403
% 9.57/9.94 Deleted: 9
% 9.57/9.94 Deletedinuse: 2
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 54008
% 9.57/9.94 Kept: 15801
% 9.57/9.94 Inuse: 430
% 9.57/9.94 Deleted: 11
% 9.57/9.94 Deletedinuse: 4
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 64109
% 9.57/9.94 Kept: 17996
% 9.57/9.94 Inuse: 454
% 9.57/9.94 Deleted: 11
% 9.57/9.94 Deletedinuse: 4
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 77147
% 9.57/9.94 Kept: 21152
% 9.57/9.94 Inuse: 488
% 9.57/9.94 Deleted: 13
% 9.57/9.94 Deletedinuse: 5
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying clauses:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 85634
% 9.57/9.94 Kept: 23218
% 9.57/9.94 Inuse: 514
% 9.57/9.94 Deleted: 164
% 9.57/9.94 Deletedinuse: 5
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 94721
% 9.57/9.94 Kept: 25334
% 9.57/9.94 Inuse: 536
% 9.57/9.94 Deleted: 165
% 9.57/9.94 Deletedinuse: 6
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94
% 9.57/9.94 Intermediate Status:
% 9.57/9.94 Generated: 101125
% 9.57/9.94 Kept: 27343
% 9.57/9.94 Inuse: 551
% 9.57/9.94 Deleted: 166
% 9.57/9.94 Deletedinuse: 7
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 9.57/9.94
% 9.57/9.94 Resimplifying inuse:
% 9.57/9.94 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 108560
% 27.63/28.02 Kept: 29352
% 27.63/28.02 Inuse: 561
% 27.63/28.02 Deleted: 166
% 27.63/28.02 Deletedinuse: 7
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 119897
% 27.63/28.02 Kept: 31374
% 27.63/28.02 Inuse: 586
% 27.63/28.02 Deleted: 166
% 27.63/28.02 Deletedinuse: 7
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 134543
% 27.63/28.02 Kept: 34801
% 27.63/28.02 Inuse: 618
% 27.63/28.02 Deleted: 166
% 27.63/28.02 Deletedinuse: 7
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 142447
% 27.63/28.02 Kept: 36801
% 27.63/28.02 Inuse: 626
% 27.63/28.02 Deleted: 166
% 27.63/28.02 Deletedinuse: 7
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 151194
% 27.63/28.02 Kept: 38817
% 27.63/28.02 Inuse: 654
% 27.63/28.02 Deleted: 167
% 27.63/28.02 Deletedinuse: 8
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 162254
% 27.63/28.02 Kept: 41056
% 27.63/28.02 Inuse: 693
% 27.63/28.02 Deleted: 168
% 27.63/28.02 Deletedinuse: 9
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying clauses:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 176317
% 27.63/28.02 Kept: 43057
% 27.63/28.02 Inuse: 759
% 27.63/28.02 Deleted: 246
% 27.63/28.02 Deletedinuse: 10
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 187928
% 27.63/28.02 Kept: 45602
% 27.63/28.02 Inuse: 788
% 27.63/28.02 Deleted: 248
% 27.63/28.02 Deletedinuse: 12
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 197524
% 27.63/28.02 Kept: 47604
% 27.63/28.02 Inuse: 816
% 27.63/28.02 Deleted: 248
% 27.63/28.02 Deletedinuse: 12
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 208550
% 27.63/28.02 Kept: 49627
% 27.63/28.02 Inuse: 853
% 27.63/28.02 Deleted: 248
% 27.63/28.02 Deletedinuse: 12
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 222639
% 27.63/28.02 Kept: 51667
% 27.63/28.02 Inuse: 908
% 27.63/28.02 Deleted: 248
% 27.63/28.02 Deletedinuse: 12
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 243142
% 27.63/28.02 Kept: 54165
% 27.63/28.02 Inuse: 933
% 27.63/28.02 Deleted: 249
% 27.63/28.02 Deletedinuse: 13
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 270943
% 27.63/28.02 Kept: 58058
% 27.63/28.02 Inuse: 948
% 27.63/28.02 Deleted: 249
% 27.63/28.02 Deletedinuse: 13
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 298115
% 27.63/28.02 Kept: 61272
% 27.63/28.02 Inuse: 953
% 27.63/28.02 Deleted: 250
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying clauses:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 310952
% 27.63/28.02 Kept: 63288
% 27.63/28.02 Inuse: 984
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 321328
% 27.63/28.02 Kept: 65289
% 27.63/28.02 Inuse: 1001
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 331245
% 27.63/28.02 Kept: 67548
% 27.63/28.02 Inuse: 1003
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 342260
% 27.63/28.02 Kept: 69956
% 27.63/28.02 Inuse: 1008
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 356289
% 27.63/28.02 Kept: 72528
% 27.63/28.02 Inuse: 1023
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 375689
% 27.63/28.02 Kept: 75290
% 27.63/28.02 Inuse: 1033
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 390116
% 27.63/28.02 Kept: 77562
% 27.63/28.02 Inuse: 1073
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 414347
% 27.63/28.02 Kept: 80929
% 27.63/28.02 Inuse: 1098
% 27.63/28.02 Deleted: 372
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying clauses:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 426455
% 27.63/28.02 Kept: 83171
% 27.63/28.02 Inuse: 1108
% 27.63/28.02 Deleted: 559
% 27.63/28.02 Deletedinuse: 14
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 441997
% 27.63/28.02 Kept: 85172
% 27.63/28.02 Inuse: 1141
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 454960
% 27.63/28.02 Kept: 87175
% 27.63/28.02 Inuse: 1162
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 467377
% 27.63/28.02 Kept: 90888
% 27.63/28.02 Inuse: 1169
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 487933
% 27.63/28.02 Kept: 95195
% 27.63/28.02 Inuse: 1197
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 502023
% 27.63/28.02 Kept: 97206
% 27.63/28.02 Inuse: 1218
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 515314
% 27.63/28.02 Kept: 100683
% 27.63/28.02 Inuse: 1234
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 529471
% 27.63/28.02 Kept: 102858
% 27.63/28.02 Inuse: 1258
% 27.63/28.02 Deleted: 560
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying clauses:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 550005
% 27.63/28.02 Kept: 105237
% 27.63/28.02 Inuse: 1261
% 27.63/28.02 Deleted: 863
% 27.63/28.02 Deletedinuse: 15
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 559185
% 27.63/28.02 Kept: 107741
% 27.63/28.02 Inuse: 1267
% 27.63/28.02 Deleted: 878
% 27.63/28.02 Deletedinuse: 16
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 566242
% 27.63/28.02 Kept: 109791
% 27.63/28.02 Inuse: 1271
% 27.63/28.02 Deleted: 889
% 27.63/28.02 Deletedinuse: 16
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 579238
% 27.63/28.02 Kept: 113816
% 27.63/28.02 Inuse: 1276
% 27.63/28.02 Deleted: 889
% 27.63/28.02 Deletedinuse: 16
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 587091
% 27.63/28.02 Kept: 115882
% 27.63/28.02 Inuse: 1286
% 27.63/28.02 Deleted: 895
% 27.63/28.02 Deletedinuse: 17
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 606543
% 27.63/28.02 Kept: 119213
% 27.63/28.02 Inuse: 1296
% 27.63/28.02 Deleted: 895
% 27.63/28.02 Deletedinuse: 17
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 614715
% 27.63/28.02 Kept: 121805
% 27.63/28.02 Inuse: 1306
% 27.63/28.02 Deleted: 895
% 27.63/28.02 Deletedinuse: 17
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 626685
% 27.63/28.02 Kept: 124260
% 27.63/28.02 Inuse: 1311
% 27.63/28.02 Deleted: 895
% 27.63/28.02 Deletedinuse: 17
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying clauses:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 634717
% 27.63/28.02 Kept: 126338
% 27.63/28.02 Inuse: 1321
% 27.63/28.02 Deleted: 939
% 27.63/28.02 Deletedinuse: 17
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 641520
% 27.63/28.02 Kept: 128424
% 27.63/28.02 Inuse: 1327
% 27.63/28.02 Deleted: 941
% 27.63/28.02 Deletedinuse: 19
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 656219
% 27.63/28.02 Kept: 130505
% 27.63/28.02 Inuse: 1333
% 27.63/28.02 Deleted: 941
% 27.63/28.02 Deletedinuse: 19
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 671313
% 27.63/28.02 Kept: 132611
% 27.63/28.02 Inuse: 1341
% 27.63/28.02 Deleted: 941
% 27.63/28.02 Deletedinuse: 19
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 679075
% 27.63/28.02 Kept: 134830
% 27.63/28.02 Inuse: 1351
% 27.63/28.02 Deleted: 941
% 27.63/28.02 Deletedinuse: 19
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 698750
% 27.63/28.02 Kept: 137083
% 27.63/28.02 Inuse: 1366
% 27.63/28.02 Deleted: 941
% 27.63/28.02 Deletedinuse: 19
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02 Resimplifying inuse:
% 27.63/28.02 Done
% 27.63/28.02
% 27.63/28.02
% 27.63/28.02 Intermediate Status:
% 27.63/28.02 Generated: 730025
% 27.63/28.03 Kept: 140463
% 27.63/28.03 Inuse: 1376
% 27.63/28.03 Deleted: 942
% 27.63/28.03 Deletedinuse: 20
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 Intermediate Status:
% 27.63/28.03 Generated: 749610
% 27.63/28.03 Kept: 142730
% 27.63/28.03 Inuse: 1386
% 27.63/28.03 Deleted: 942
% 27.63/28.03 Deletedinuse: 20
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03 Resimplifying clauses:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 Intermediate Status:
% 27.63/28.03 Generated: 762616
% 27.63/28.03 Kept: 144755
% 27.63/28.03 Inuse: 1408
% 27.63/28.03 Deleted: 1096
% 27.63/28.03 Deletedinuse: 20
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 Intermediate Status:
% 27.63/28.03 Generated: 780871
% 27.63/28.03 Kept: 146917
% 27.63/28.03 Inuse: 1436
% 27.63/28.03 Deleted: 1096
% 27.63/28.03 Deletedinuse: 20
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 Intermediate Status:
% 27.63/28.03 Generated: 805441
% 27.63/28.03 Kept: 151305
% 27.63/28.03 Inuse: 1451
% 27.63/28.03 Deleted: 1097
% 27.63/28.03 Deletedinuse: 21
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 Intermediate Status:
% 27.63/28.03 Generated: 822049
% 27.63/28.03 Kept: 153694
% 27.63/28.03 Inuse: 1461
% 27.63/28.03 Deleted: 1097
% 27.63/28.03 Deletedinuse: 21
% 27.63/28.03
% 27.63/28.03 Resimplifying inuse:
% 27.63/28.03 Done
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 Bliksems!, er is een bewijs:
% 27.63/28.03 % SZS status Unsatisfiable
% 27.63/28.03 % SZS output start Refutation
% 27.63/28.03
% 27.63/28.03 clause( 341, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 27.63/28.03 'c_Com_Obody', X ) ) ), Y ), Z ) ) ) ] )
% 27.63/28.03 .
% 27.63/28.03 clause( 369, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', 'v_pn' ) ) ),
% 27.63/28.03 'v_x' ), 'v_xa' ) ) ] )
% 27.63/28.03 .
% 27.63/28.03 clause( 370, [ ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ) ] )
% 27.63/28.03 .
% 27.63/28.03 clause( 153885, [] )
% 27.63/28.03 .
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 % SZS output end Refutation
% 27.63/28.03 found a proof!
% 27.63/28.03
% 27.63/28.03 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 27.63/28.03
% 27.63/28.03 initialclauses(
% 27.63/28.03 [ clause( 153887, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 27.63/28.03 ), =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), Y
% 27.63/28.03 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 27.63/28.03 , clause( 153888, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 27.63/28.03 ), ~( =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X )
% 27.63/28.03 , Y ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ] )
% 27.63/28.03 , clause( 153889, [ =( hAPP( 'c_Fun_Ocomp'( 'v_f', 'v_g', 't_a', 't_b',
% 27.63/28.03 't_c' ), 'v_x' ), hAPP( 'v_f', hAPP( 'v_g', 'v_x' ) ) ) ] )
% 27.63/28.03 , clause( 153890, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSemi'(
% 27.63/28.03 T, U ) ) ) ] )
% 27.63/28.03 , clause( 153891, [ 'c_Fun_Oinj__on'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U )
% 27.63/28.03 , hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( X, Y ) ), 'c_Set_Oimage'( X,
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Z, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, Z, T, U ) ) ] )
% 27.63/28.03 , clause( 153892, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y
% 27.63/28.03 , Z, X ) ) ) ] )
% 27.63/28.03 , clause( 153893, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y
% 27.63/28.03 , Z, X ) ) ) ] )
% 27.63/28.03 , clause( 153894, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y
% 27.63/28.03 , Z, X ) ) ) ] )
% 27.63/28.03 , clause( 153895, [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ] )
% 27.63/28.03 , clause( 153896, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 27.63/28.03 , V4 ) ) ] )
% 27.63/28.03 , clause( 153897, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U
% 27.63/28.03 , W ), ~( 'c_Natural_Oevaln'( Y, T, U, W ) ), ~( hBOOL( hAPP( X, T ) ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 153898, [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevaln'( Z, Y, T
% 27.63/28.03 , U ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Z, W ), Y, T, U ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 153899, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T )
% 27.63/28.03 , 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ] )
% 27.63/28.03 , clause( 153900, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 27.63/28.03 hAPP( Z, Y ) ) ) ] )
% 27.63/28.03 , clause( 153901, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z
% 27.63/28.03 ), Y ), X ) ) ) ] )
% 27.63/28.03 , clause( 153902, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X
% 27.63/28.03 , W ), Y ) ) ] )
% 27.63/28.03 , clause( 153903, [ =( 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153904, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ] )
% 27.63/28.03 , clause( 153905, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 27.63/28.03 'c_Set_Oimage'( Y, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T, 'tc_bool'
% 27.63/28.03 ) ), T, X ) ) ) ] )
% 27.63/28.03 , clause( 153906, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T,
% 27.63/28.03 U ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), W, T, U ) ), ~(
% 27.63/28.03 'c_Natural_Oevaln'( Y, Z, T, W ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 27.63/28.03 , clause( 153907, [ ~( =( 'c_Option_Ooption_ONone'( X ),
% 27.63/28.03 'c_Option_Ooption_OSome'( Y, X ) ) ) ] )
% 27.63/28.03 , clause( 153908, [ ~( =( 'c_Option_Ooption_ONone'( X ),
% 27.63/28.03 'c_Option_Ooption_OSome'( Y, X ) ) ) ] )
% 27.63/28.03 , clause( 153909, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 27.63/28.03 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ] )
% 27.63/28.03 , clause( 153910, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 27.63/28.03 , T, X ) ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153911, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 27.63/28.03 , T, X ) ) ), =( Z, T ) ] )
% 27.63/28.03 , clause( 153912, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U
% 27.63/28.03 ), ~( 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T
% 27.63/28.03 , W ) ) ] )
% 27.63/28.03 , clause( 153913, [ 'c_Com_OWT'( 'c_Com_Ocom_OSKIP' ) ] )
% 27.63/28.03 , clause( 153914, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 153915, [ 'c_Com_OWT'( 'c_Com_Ocom_OAss'( X, Y ) ) ] )
% 27.63/28.03 , clause( 153916, [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ) ] )
% 27.63/28.03 , clause( 153917, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP(
% 27.63/28.03 hAPP( 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 27.63/28.03 U ) ) ), =( Y, Z ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ) ] )
% 27.63/28.03 , clause( 153918, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP(
% 27.63/28.03 hAPP( 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 27.63/28.03 U ) ) ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153919, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP(
% 27.63/28.03 hAPP( 'c_in'( T ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 27.63/28.03 U ) ) ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153920, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~(
% 27.63/28.03 'c_Fun_Oinj__on'( X, T, U, W ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 27.63/28.03 U ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ) ] )
% 27.63/28.03 , clause( 153921, [ 'c_Com_OWT'( 'c_Com_Ocom_OCall'( X, Y, Z ) ), ~(
% 27.63/28.03 'c_Com_OWT'( hAPP( 'c_Com_Ocom_OBODY', Y ) ) ) ] )
% 27.63/28.03 , clause( 153922, [ 'c_Com_OWT'( hAPP( 'c_Com_Ocom_OBODY', X ) ), ~(
% 27.63/28.03 'c_Com_OWT'( 'c_Com_Ocom_OCall'( Y, X, Z ) ) ) ] )
% 27.63/28.03 , clause( 153923, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 153924, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 153925, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCall'( Z
% 27.63/28.03 , T, U ) ) ) ] )
% 27.63/28.03 , clause( 153926, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 153927, [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 27.63/28.03 , 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 27.63/28.03 Y, Z ) ) ] )
% 27.63/28.03 , clause( 153928, [ ~( =( 'c_Set_Oinsert'( X,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ),
% 27.63/28.03 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ), Y ) ) ), =( X, Z ) ] )
% 27.63/28.03 , clause( 153929, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 27.63/28.03 'c_in'( Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 27.63/28.03 ) ) ) ) ) ] )
% 27.63/28.03 , clause( 153930, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 27.63/28.03 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 27.63/28.03 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153931, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 27.63/28.03 ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153932, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 27.63/28.03 ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153933, [ ~( =( 'c_COMBC'( 'c_in'( X ), Y, X, 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ), 'tc_bool' ), 'c_COMBC'( 'c_in'( X ), Z, X, 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ), 'tc_bool' ) ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 153934, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( Z ), X ), Y ) ) ] )
% 27.63/28.03 , clause( 153935, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Z ), 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y, T,
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ] )
% 27.63/28.03 , clause( 153936, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 27.63/28.03 ), Z ) ) ) ] )
% 27.63/28.03 , clause( 153937, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y
% 27.63/28.03 ), Z ) ) ) ] )
% 27.63/28.03 , clause( 153938, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OLocal'( T, U, W ) ) ) ] )
% 27.63/28.03 , clause( 153939, [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 27.63/28.03 Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( T, 'tc_bool' ) ), T, U ) ) ] )
% 27.63/28.03 , clause( 153940, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_Set_Oinsert'( Y, T, X ), Z, 'tc_fun'( X, 'tc_bool' ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 153941, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OWhile'( T, U ) ) ) ] )
% 27.63/28.03 , clause( 153942, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~(
% 27.63/28.03 hBOOL( hAPP( Y, T ) ) ) ] )
% 27.63/28.03 , clause( 153943, [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z
% 27.63/28.03 , T, U ), U ), 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP(
% 27.63/28.03 'c_in'( T ), Y ), Z ) ) ) ] )
% 27.63/28.03 , clause( 153944, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 27.63/28.03 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 27.63/28.03 , clause( 153945, [ 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ), 'tc_bool' ) ), 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), X ), Y ), Z ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__valids'( 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 27.63/28.03 , 'c_Set_Oinsert'( hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ), X ), Y ), Z ), 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 27.63/28.03 , 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ) )
% 27.63/28.03 , ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 27.63/28.03 , 'c_Set_Oinsert'( 'c_Hoare__Mirabelle_OMGT'( Y ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ) ) ] )
% 27.63/28.03 , clause( 153946, [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 153947, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 153948, [ 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W
% 27.63/28.03 ), ~( 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ] )
% 27.63/28.03 , clause( 153949, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ),
% 27.63/28.03 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z ) ) ) ) ] )
% 27.63/28.03 , clause( 153950, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 27.63/28.03 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), W ) ) ), ~( 'c_lessequals'(
% 27.63/28.03 'c_Set_Oimage'( Y, W, U, X ), T, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153951, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X,
% 27.63/28.03 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool'
% 27.63/28.03 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) ), ~( 'c_lessequals'(
% 27.63/28.03 X, 'c_Set_Oinsert'( Y, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153952, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153953, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153954, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T,
% 27.63/28.03 Z ), hBOOL( hAPP( X, Z ) ) ] )
% 27.63/28.03 , clause( 153955, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U
% 27.63/28.03 ), 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( T,
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, U ) ) ] )
% 27.63/28.03 , clause( 153956, [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ),
% 27.63/28.03 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'(
% 27.63/28.03 X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 153957, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X
% 27.63/28.03 , 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ] )
% 27.63/28.03 , clause( 153958, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 27.63/28.03 T, U, W ) ) ) ] )
% 27.63/28.03 , clause( 153959, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y
% 27.63/28.03 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T
% 27.63/28.03 , 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T
% 27.63/28.03 ) ) ) ] )
% 27.63/28.03 , clause( 153960, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OCond'( T, U, W ) ) ) ] )
% 27.63/28.03 , clause( 153961, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 153962, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 153963, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OSKIP', V2 ), X ) ] )
% 27.63/28.03 , clause( 153964, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 27.63/28.03 , T ) ) ) ] )
% 27.63/28.03 , clause( 153965, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( Z, V2 )
% 27.63/28.03 , V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 153966, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 27.63/28.03 T, U, W ) ) ), =( Z, W ) ] )
% 27.63/28.03 , clause( 153967, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 27.63/28.03 T, U, W ) ) ), =( Y, U ) ] )
% 27.63/28.03 , clause( 153968, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 27.63/28.03 T, U, W ) ) ), =( X, T ) ] )
% 27.63/28.03 , clause( 153969, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( hAPP( T, V2 ), V3 )
% 27.63/28.03 , 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V2, V4 ) ),
% 27.63/28.03 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ] )
% 27.63/28.03 , clause( 153970, [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 27.63/28.03 , clause( 153971, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 153972, [ 'c_Fun_Oinj__on'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 27.63/28.03 , 'tc_fun'( T, 'tc_bool' ) ), T, U ), ~( 'c_Fun_Oinj__on'( X, Y, T, U ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 153973, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OLocal'(
% 27.63/28.03 Z, T, U ) ) ) ] )
% 27.63/28.03 , clause( 153974, [ =( 'c_Set_Ovimage'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 27.63/28.03 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ), 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 27.63/28.03 , 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153975, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 27.63/28.03 X ) ) ) ] )
% 27.63/28.03 , clause( 153976, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 27.63/28.03 X ) ) ) ] )
% 27.63/28.03 , clause( 153977, [ 'c_lessequals'( 'c_Set_Oimage'( X, 'c_Set_Ovimage'( X,
% 27.63/28.03 Y, Z, T ), Z, T ), Y, 'tc_fun'( T, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 153978, [ =( 'c_Set_Ovimage'( X, 'c_Set_Oimage'( X, Y, Z, T ), Z
% 27.63/28.03 , T ), Y ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ] )
% 27.63/28.03 , clause( 153979, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 27.63/28.03 ), =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 153980, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 153981, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 27.63/28.03 , clause( 153982, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 27.63/28.03 , T ) ) ), =( Y, T ) ] )
% 27.63/28.03 , clause( 153983, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 27.63/28.03 , T ) ) ), =( X, Z ) ] )
% 27.63/28.03 , clause( 153984, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153985, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'(
% 27.63/28.03 Z, T ) ) ) ] )
% 27.63/28.03 , clause( 153986, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y
% 27.63/28.03 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 27.63/28.03 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153987, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y
% 27.63/28.03 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 153988, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z
% 27.63/28.03 , T, U ) ) ) ] )
% 27.63/28.03 , clause( 153989, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ] )
% 27.63/28.03 , clause( 153990, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OLocal'(
% 27.63/28.03 Z, T, U ) ) ) ] )
% 27.63/28.03 , clause( 153991, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z
% 27.63/28.03 , 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), T ), X, T ) ) ) ] )
% 27.63/28.03 , clause( 153992, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), Y, Z ) ) ] )
% 27.63/28.03 , clause( 153993, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 27.63/28.03 ), ~( =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X )
% 27.63/28.03 , 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_lessequals'( Y,
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 27.63/28.03 , clause( 153994, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 27.63/28.03 ), =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( Y,
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 27.63/28.03 , clause( 153995, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z )
% 27.63/28.03 , 'c_Set_Oinsert'( X, Y, Z ) ) ] )
% 27.63/28.03 , clause( 153996, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OAss'(
% 27.63/28.03 T, U ) ) ) ] )
% 27.63/28.03 , clause( 153997, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 27.63/28.03 'c_Set_Oinsert'( Z, X, T ), Y ) ) ) ] )
% 27.63/28.03 , clause( 153998, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OWhile'( T, U ) ) ) ] )
% 27.63/28.03 , clause( 153999, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z, T,
% 27.63/28.03 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 27.63/28.03 , clause( 154000, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OLocal'( T, U, W ) ) ) ] )
% 27.63/28.03 , clause( 154001, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~(
% 27.63/28.03 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( T, Z,
% 27.63/28.03 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 27.63/28.03 , clause( 154002, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154003, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'(
% 27.63/28.03 T, U ) ) ) ] )
% 27.63/28.03 , clause( 154004, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 27.63/28.03 T, U, W ) ) ), =( Z, W ) ] )
% 27.63/28.03 , clause( 154005, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 27.63/28.03 T, U, W ) ) ), =( Y, U ) ] )
% 27.63/28.03 , clause( 154006, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 27.63/28.03 T, U, W ) ) ), =( X, T ) ] )
% 27.63/28.03 , clause( 154007, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154008, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154009, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154010, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154011, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 27.63/28.03 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 27.63/28.03 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 27.63/28.03 , clause( 154012, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ] )
% 27.63/28.03 , clause( 154013, [ ~( =( 'c_Option_Ooption_OSome'( X, Y ),
% 27.63/28.03 'c_Option_Ooption_ONone'( Y ) ) ) ] )
% 27.63/28.03 , clause( 154014, [ ~( =( 'c_Option_Ooption_OSome'( X, Y ),
% 27.63/28.03 'c_Option_Ooption_ONone'( Y ) ) ) ] )
% 27.63/28.03 , clause( 154015, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 27.63/28.03 T, U, W ) ) ) ] )
% 27.63/28.03 , clause( 154016, [ ~( =( 'c_Option_Ooption_OSome'( X, Y ),
% 27.63/28.03 'c_Option_Ooption_OSome'( Z, Y ) ) ), =( X, Z ) ] )
% 27.63/28.03 , clause( 154017, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ), X ) ] )
% 27.63/28.03 , clause( 154018, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154019, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X,
% 27.63/28.03 hAPP( Y, W ) ) ) ] )
% 27.63/28.03 , clause( 154020, [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y,
% 27.63/28.03 T, U, W ), Z ) ) ] )
% 27.63/28.03 , clause( 154021, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 27.63/28.03 ), ~( 'c_Fun_Oinj__on'( U, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), X, T ) ) ] )
% 27.63/28.03 , clause( 154022, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 27.63/28.03 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 27.63/28.03 , T ) ) ), ~( 'c_Fun_Oinj__on'( Y, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( U, 'tc_bool' ) ), U, X ) ) ] )
% 27.63/28.03 , clause( 154023, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 27.63/28.03 , clause( 154024, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 27.63/28.03 , clause( 154025, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OWhile'( Z
% 27.63/28.03 , T ) ) ) ] )
% 27.63/28.03 , clause( 154026, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OLocal'( Z
% 27.63/28.03 , T, U ) ) ) ] )
% 27.63/28.03 , clause( 154027, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~(
% 27.63/28.03 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), T, U ) ), =( Y, Z ) ] )
% 27.63/28.03 , clause( 154028, [ =( hAPP( 'c_Fun_Ofcomp'( 'v_f', 'v_g', 't_a', 't_b',
% 27.63/28.03 't_c' ), 'v_x' ), hAPP( 'v_g', hAPP( 'v_f', 'v_x' ) ) ) ] )
% 27.63/28.03 , clause( 154029, [ 'c_Com_OWT'( 'c_Com_Ocom_OCond'( X, Y, Z ) ), ~(
% 27.63/28.03 'c_Com_OWT'( Z ) ), ~( 'c_Com_OWT'( Y ) ) ] )
% 27.63/28.03 , clause( 154030, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OSKIP', V2 ), X ) ] )
% 27.63/28.03 , clause( 154031, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OWhile'( T, U ) ) ) ] )
% 27.63/28.03 , clause( 154032, [ =( 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 27.63/28.03 ) ) ) ] )
% 27.63/28.03 , clause( 154033, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X,
% 27.63/28.03 U, Z, T ) ) ), ~( 'c_Fun_Oinj__on'( X, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), =( Y, U ) ] )
% 27.63/28.03 , clause( 154034, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCond'( Z
% 27.63/28.03 , T, U ) ) ) ] )
% 27.63/28.03 , clause( 154035, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ),
% 27.63/28.03 'c_Com_Ocom_OSemi'( T, U ) ), W ), 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), V0 ), U ), W ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), T ), V0 ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154036, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154037, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( X, 'tc_bool' ) ), Y ) ) ) ] )
% 27.63/28.03 , clause( 154038, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OLocal'( X, Y, Z
% 27.63/28.03 ) ) ) ] )
% 27.63/28.03 , clause( 154039, [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154040, [ 'c_Natural_Oevaln'( X, Y, 'c_Suc'( Z ), T ), ~(
% 27.63/28.03 'c_Natural_Oevaln'( X, Y, Z, T ) ) ] )
% 27.63/28.03 , clause( 154041, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154042, [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154043, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ),
% 27.63/28.03 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154044, [ ~( 'class_Orderings_Otop'( X ) ), =( hAPP(
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 27.63/28.03 , clause( 154045, [ 'c_Natural_Oevaln'( X, Y, Z, T ), hBOOL( hAPP( U, Y ) )
% 27.63/28.03 , ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( U, W, X ), Y, Z, T ) ) ] )
% 27.63/28.03 , clause( 154046, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( Z ), T ), X ) ), ~( 'c_lessequals'( X,
% 27.63/28.03 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154047, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 27.63/28.03 hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 27.63/28.03 , clause( 154048, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) )
% 27.63/28.03 ), hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), X ) ) ] )
% 27.63/28.03 , clause( 154049, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T
% 27.63/28.03 , Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP(
% 27.63/28.03 'c_in'( Z ), X ), Y ) ), =( Y, T ) ] )
% 27.63/28.03 , clause( 154050, [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ),
% 27.63/28.03 'c_Set_Ovimage'( X, U, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( Y, U, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154051, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'(
% 27.63/28.03 'c_Fun_Oid'( T ), W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W
% 27.63/28.03 , V0 ) ) ] )
% 27.63/28.03 , clause( 154052, [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( hAPP( Y, 'v_x' ), hAPP( Z, 'v_x' ), X ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154053, [ =( 'c_Set_Ovimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154054, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( T, V2 ), V3 ) ) ] )
% 27.63/28.03 , clause( 154055, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OSemi'( T, U ) ) ) ] )
% 27.63/28.03 , clause( 154056, [ =( 'c_Set_Ovimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W,
% 27.63/28.03 U, T ), 'c_Set_Ovimage'( Y, 'c_Set_Ovimage'( X, W, Z, T ), U, Z ) ) ] )
% 27.63/28.03 , clause( 154057, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z
% 27.63/28.03 , T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154058, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z
% 27.63/28.03 , T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154059, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z
% 27.63/28.03 , T, X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154060, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 27.63/28.03 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154061, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ),
% 27.63/28.03 ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154062, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'(
% 27.63/28.03 Z, T ) ) ), =( X, Z ) ] )
% 27.63/28.03 , clause( 154063, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'(
% 27.63/28.03 Z, T ) ) ), =( Y, T ) ] )
% 27.63/28.03 , clause( 154064, [ 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( X, Y ) ), ~(
% 27.63/28.03 'c_Com_OWT'( Y ) ) ] )
% 27.63/28.03 , clause( 154065, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OWhile'(
% 27.63/28.03 Y, X ) ) ) ] )
% 27.63/28.03 , clause( 154066, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 27.63/28.03 , V4 ) ) ] )
% 27.63/28.03 , clause( 154067, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP(
% 27.63/28.03 hAPP( 'c_in'( Z ), X ), Y ) ) ) ] )
% 27.63/28.03 , clause( 154068, [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154069, [ 'c_Fun_Oinj__on'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U
% 27.63/28.03 , T ), ~( 'c_Fun_Oinj__on'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ),
% 27.63/28.03 ~( 'c_Fun_Oinj__on'( Y, W, U, Z ) ) ] )
% 27.63/28.03 , clause( 154070, [ 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( X, Y, Z ) ), ~(
% 27.63/28.03 'c_Com_OWT'( Z ) ) ] )
% 27.63/28.03 , clause( 154071, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OLocal'(
% 27.63/28.03 Y, Z, X ) ) ) ] )
% 27.63/28.03 , clause( 154072, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 27.63/28.03 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 27.63/28.03 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), X ) ] )
% 27.63/28.03 , clause( 154073, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP'
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154074, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'(
% 27.63/28.03 Z, T, U ) ) ) ] )
% 27.63/28.03 , clause( 154075, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCall'( Z
% 27.63/28.03 , T, U ) ) ) ] )
% 27.63/28.03 , clause( 154076, [ =( X, 'c_Suc'(
% 27.63/28.03 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y, X, Z, T ) ) ),
% 27.63/28.03 ~( 'c_Natural_Oevaln'( hAPP( 'c_Com_Ocom_OBODY', Y ), Z, X, T ) ) ] )
% 27.63/28.03 , clause( 154077, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 27.63/28.03 'c_Set_Oimage'( Y, 'c_HOL_Ominus__class_Ominus'( T, 'c_Set_Oinsert'( Z,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), 'tc_fun'(
% 27.63/28.03 U, 'tc_bool' ) ), U, X ) ) ) ), ~( 'c_Fun_Oinj__on'( Y, 'c_Set_Oinsert'(
% 27.63/28.03 Z, T, U ), U, X ) ) ] )
% 27.63/28.03 , clause( 154078, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ] )
% 27.63/28.03 , clause( 154079, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OAss'(
% 27.63/28.03 T, U ) ) ) ] )
% 27.63/28.03 , clause( 154080, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y
% 27.63/28.03 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 27.63/28.03 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ] )
% 27.63/28.03 , clause( 154081, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 27.63/28.03 ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154082, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( W, V2 ), V3 ),
% 27.63/28.03 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ] )
% 27.63/28.03 , clause( 154083, [ 'c_lessequals'( 'c_Set_Ovimage'( X, Y, Z, T ), U,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, 'c_Set_Oimage'( X, U, Z
% 27.63/28.03 , T ), 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ) ] )
% 27.63/28.03 , clause( 154084, [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y
% 27.63/28.03 , Z, X ) ) ] )
% 27.63/28.03 , clause( 154085, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y
% 27.63/28.03 , Z ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), hBOOL( hAPP( hAPP(
% 27.63/28.03 'c_in'( Z ), X ), Y ) ) ] )
% 27.63/28.03 , clause( 154086, [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ] )
% 27.63/28.03 , clause( 154087, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154088, [ 'c_lessequals'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ), Z,
% 27.63/28.03 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154089, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( hAPP( U,
% 27.63/28.03 V2 ), V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3,
% 27.63/28.03 V5 ) ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154090, [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z
% 27.63/28.03 ), hAPP( T, Z ), X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ] )
% 27.63/28.03 , clause( 154091, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 27.63/28.03 , clause( 154092, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 27.63/28.03 , clause( 154093, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 27.63/28.03 ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154094, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 27.63/28.03 ), X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 27.63/28.03 , clause( 154095, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 27.63/28.03 , clause( 154096, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 27.63/28.03 , clause( 154097, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 27.63/28.03 'c_lessequals'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154098, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 27.63/28.03 'c_lessequals'( Y, Z, X ) ] )
% 27.63/28.03 , clause( 154099, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 27.63/28.03 'c_lessequals'( Z, Y, X ) ) ] )
% 27.63/28.03 , clause( 154100, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ] )
% 27.63/28.03 , clause( 154101, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ] )
% 27.63/28.03 , clause( 154102, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( X ), Y, X ),
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( X ) ) ] )
% 27.63/28.03 , clause( 154103, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( X ), X ), 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 X ) ) ] )
% 27.63/28.03 , clause( 154104, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154105, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X
% 27.63/28.03 ), X ) ] )
% 27.63/28.03 , clause( 154106, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X
% 27.63/28.03 ), X ) ] )
% 27.63/28.03 , clause( 154107, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154108, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 27.63/28.03 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154109, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y
% 27.63/28.03 , 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ] )
% 27.63/28.03 , clause( 154110, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y
% 27.63/28.03 , 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ] )
% 27.63/28.03 , clause( 154111, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 27.63/28.03 , clause( 154112, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 27.63/28.03 , clause( 154113, [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 27.63/28.03 'c_lessequals'( 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U
% 27.63/28.03 ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154114, [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ),
% 27.63/28.03 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154115, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154116, [ =( 'c_Set_Oimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U
% 27.63/28.03 , T ), 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ) ] )
% 27.63/28.03 , clause( 154117, [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U
% 27.63/28.03 ), 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154118, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154119, [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154120, [ =( 'c_Set_Oimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154121, [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z, X ) ) ] )
% 27.63/28.03 , clause( 154122, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154123, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154124, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 27.63/28.03 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 27.63/28.03 , T ) ) ) ] )
% 27.63/28.03 , clause( 154125, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 27.63/28.03 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 27.63/28.03 , T ) ) ) ] )
% 27.63/28.03 , clause( 154126, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154127, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T, X,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154128, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, T,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154129, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 27.63/28.03 , clause( 154130, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 27.63/28.03 , clause( 154131, [ 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 27.63/28.03 Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z
% 27.63/28.03 , 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154132, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 Y, 'tc_fun'( Z, 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154133, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154134, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154135, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ), X ) ] )
% 27.63/28.03 , clause( 154136, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ), Y ) ] )
% 27.63/28.03 , clause( 154137, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP(
% 27.63/28.03 hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ) ) ) ) ] )
% 27.63/28.03 , clause( 154138, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154139, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool'
% 27.63/28.03 ) ) ) ] )
% 27.63/28.03 , clause( 154140, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 27.63/28.03 Y, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), T ) ) ] )
% 27.63/28.03 , clause( 154141, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 27.63/28.03 'c_Set_Oinsert'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 27.63/28.03 , clause( 154142, [ 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154143, [ 'c_lessequals'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154144, [ 'c_lessequals'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154145, [ 'c_lessequals'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154146, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U
% 27.63/28.03 , W ), ~( 'c_Natural_Oevaln'( Z, T, U, W ) ), hBOOL( hAPP( X, T ) ) ] )
% 27.63/28.03 , clause( 154147, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( 'c_COMBC'( 'c_in'( Z ), X, Z, 'tc_fun'( Z, 'tc_bool' ),
% 27.63/28.03 'tc_bool' ), 'c_COMBC'( 'c_in'( Z ), Y, Z, 'tc_fun'( Z, 'tc_bool' ),
% 27.63/28.03 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154148, [ 'c_lessequals'( 'c_COMBC'( 'c_in'( X ), Y, X, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ), 'tc_bool' ), 'c_COMBC'( 'c_in'( X ), Z, X, 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ), 'tc_bool' ), 'tc_fun'( X, 'tc_bool' ) ), ~( 'c_lessequals'(
% 27.63/28.03 Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154149, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCall'(
% 27.63/28.03 Z, T, U ) ) ) ] )
% 27.63/28.03 , clause( 154150, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OAss'( Z
% 27.63/28.03 , T ) ) ) ] )
% 27.63/28.03 , clause( 154151, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154152, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154153, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 27.63/28.03 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154154, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 27.63/28.03 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154155, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 27.63/28.03 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 27.63/28.03 , clause( 154156, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 27.63/28.03 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 27.63/28.03 , X ) ) ] )
% 27.63/28.03 , clause( 154157, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 27.63/28.03 ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154158, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OSKIP' ) ) ] )
% 27.63/28.03 , clause( 154159, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ] )
% 27.63/28.03 , clause( 154160, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 27.63/28.03 'tc_nat' ) ) ) ] )
% 27.63/28.03 , clause( 154161, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'(
% 27.63/28.03 'tc_nat' ) ) ) ] )
% 27.63/28.03 , clause( 154162, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 27.63/28.03 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ] )
% 27.63/28.03 , clause( 154163, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 27.63/28.03 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ] )
% 27.63/28.03 , clause( 154164, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 27.63/28.03 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 27.63/28.03 , clause( 154165, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 27.63/28.03 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ] )
% 27.63/28.03 , clause( 154166, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( 'c_Natural_Oevaln'(
% 27.63/28.03 T, U, W, Z ) ), ~( hBOOL( hAPP( hAPP( V0, Y ), U ) ) ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple__valid'( W, hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 't_a' ), V0 ), T ), X ), 't_a' ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154167, [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 't_a', 'tc_bool' ) ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ] )
% 27.63/28.03 , clause( 154168, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OAss'( X, Y ) ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154169, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( Y
% 27.63/28.03 , X ) ) ) ] )
% 27.63/28.03 , clause( 154170, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X
% 27.63/28.03 , Y ) ) ) ] )
% 27.63/28.03 , clause( 154171, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154172, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154173, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OAss'( Z
% 27.63/28.03 , T ) ) ) ] )
% 27.63/28.03 , clause( 154174, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 27.63/28.03 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ] )
% 27.63/28.03 , clause( 154175, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( Z, V2 ), V3 )
% 27.63/28.03 , V4 ) ) ] )
% 27.63/28.03 , clause( 154176, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( W, V2 ), V3 ) ) ] )
% 27.63/28.03 , clause( 154177, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 27.63/28.03 , clause( 154178, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 27.63/28.03 , clause( 154179, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z
% 27.63/28.03 ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154180, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 27.63/28.03 , clause( 154181, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 27.63/28.03 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154182, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y
% 27.63/28.03 , hAPP( X, W ) ) ) ] )
% 27.63/28.03 , clause( 154183, [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T )
% 27.63/28.03 , Y ), 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154184, [ 'c_lessequals'( X, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154185, [ ~( 'class_Orderings_Otop'( X ) ), 'c_lessequals'( Y,
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( X ), X ) ] )
% 27.63/28.03 , clause( 154186, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U
% 27.63/28.03 , V0, W ), 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154187, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z,
% 27.63/28.03 T ) ) ), =( Y, T ) ] )
% 27.63/28.03 , clause( 154188, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z,
% 27.63/28.03 T ) ) ), =( X, Z ) ] )
% 27.63/28.03 , clause( 154189, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OAss'(
% 27.63/28.03 T, U ) ) ) ] )
% 27.63/28.03 , clause( 154190, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154191, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ),
% 27.63/28.03 'c_Com_Ocom_OSKIP' ), Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ] )
% 27.63/28.03 , clause( 154192, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 27.63/28.03 , clause( 154193, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 27.63/28.03 ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ] )
% 27.63/28.03 , clause( 154194, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OLocal'( T, U, W ) ) ), =( Z, W ) ] )
% 27.63/28.03 , clause( 154195, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OLocal'( T, U, W ) ) ), =( Y, U ) ] )
% 27.63/28.03 , clause( 154196, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OLocal'( T, U, W ) ) ), =( X, T ) ] )
% 27.63/28.03 , clause( 154197, [ 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ), ~(
% 27.63/28.03 'c_Com_OWT'( Y ) ), ~( 'c_Com_OWT'( X ) ) ] )
% 27.63/28.03 , clause( 154198, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCall'( X, Y, Z )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154199, [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154200, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154201, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'(
% 27.63/28.03 Z, T ) ) ) ] )
% 27.63/28.03 , clause( 154202, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 27.63/28.03 , clause( 154203, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 27.63/28.03 , clause( 154204, [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 27.63/28.03 , 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( hBOOL( hAPP(
% 27.63/28.03 hAPP( 'c_in'( Z ), X ), Y ) ) ) ] )
% 27.63/28.03 , clause( 154205, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 27.63/28.03 Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154206, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 27.63/28.03 Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154207, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154208, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154209, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154210, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~(
% 27.63/28.03 'c_lessequals'( T, Z, 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP(
% 27.63/28.03 'c_in'( X ), Y ), T ) ) ) ] )
% 27.63/28.03 , clause( 154211, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, Z, 'tc_fun'(
% 27.63/28.03 X, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154212, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 27.63/28.03 , clause( 154213, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 27.63/28.03 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 27.63/28.03 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154214, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_lessequals'( Y, U
% 27.63/28.03 , 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Fun_Oinj__on'( X, U, Z, T ) ) ] )
% 27.63/28.03 , clause( 154215, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~(
% 27.63/28.03 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154216, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 27.63/28.03 Y, X ) ] )
% 27.63/28.03 , clause( 154217, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 27.63/28.03 Y, Y, X ) ] )
% 27.63/28.03 , clause( 154218, [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X,
% 27.63/28.03 'tc_fun'( T, 'tc_bool' ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ] )
% 27.63/28.03 , clause( 154219, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSKIP'
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154220, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z
% 27.63/28.03 , T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 27.63/28.03 , clause( 154221, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z
% 27.63/28.03 , T, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 27.63/28.03 , clause( 154222, [ =( 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 27.63/28.03 Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ), 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, W, 'tc_fun'( T, 'tc_bool' ) ) ),
% 27.63/28.03 ~( 'c_lessequals'( Y, W, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 27.63/28.03 'c_Fun_Oinj__on'( X, W, T, U ) ) ] )
% 27.63/28.03 , clause( 154223, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y
% 27.63/28.03 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154224, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( U, V2 ), V3 ),
% 27.63/28.03 V4 ) ) ] )
% 27.63/28.03 , clause( 154225, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W
% 27.63/28.03 , V0, V1, T, U ) ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2
% 27.63/28.03 ) ) ) ] )
% 27.63/28.03 , clause( 154226, [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) )
% 27.63/28.03 ) ), =( hAPP( 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP(
% 27.63/28.03 'c_Fun_Ocomp'( T, U, V3, V1, V4 ), W ) ) ] )
% 27.63/28.03 , clause( 154227, [ =( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), =( X,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 27.63/28.03 'c_lessequals'( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154228, [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T
% 27.63/28.03 ), 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 27.63/28.03 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154229, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevaln'(
% 27.63/28.03 'c_Com_Ocom_OWhile'( X, T ), Y, U, Z ) ) ] )
% 27.63/28.03 , clause( 154230, [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP(
% 27.63/28.03 'c_Set_Ovimage'( Y, X, T, U ), Z ) ) ) ] )
% 27.63/28.03 , clause( 154231, [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~(
% 27.63/28.03 hBOOL( hAPP( Y, hAPP( X, U ) ) ) ) ] )
% 27.63/28.03 , clause( 154232, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 Y, Z, 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Z, T ) ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 T ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ) ) ] )
% 27.63/28.03 , clause( 154233, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 T, 'tc_bool' ) ), Z ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' )
% 27.63/28.03 ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154234, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 27.63/28.03 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 27.63/28.03 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 27.63/28.03 , clause( 154235, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 27.63/28.03 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 27.63/28.03 ~( 'c_lessequals'( U, T, X ) ) ] )
% 27.63/28.03 , clause( 154236, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSKIP' ) )
% 27.63/28.03 ] )
% 27.63/28.03 , clause( 154237, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ),
% 27.63/28.03 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 27.63/28.03 Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154238, [ 'c_Natural_Oevaln'( X, Y, Z, T ), 'c_Natural_Oevaln'( U
% 27.63/28.03 , Y, Z, T ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( W, U, X ), Y, Z,
% 27.63/28.03 T ) ) ] )
% 27.63/28.03 , clause( 154239, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'(
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154240, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 27.63/28.03 'c_Com_Ocom_OCall'( T, U, W ) ) ) ] )
% 27.63/28.03 , clause( 154241, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y
% 27.63/28.03 , Z, X ) ) ) ] )
% 27.63/28.03 , clause( 154242, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y
% 27.63/28.03 , X, Z ) ) ) ] )
% 27.63/28.03 , clause( 154243, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W,
% 27.63/28.03 Z, U, V0 ), 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154244, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) )
% 27.63/28.03 ) ] )
% 27.63/28.03 , clause( 154245, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 27.63/28.03 Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 27.63/28.03 , clause( 154246, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154247, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154248, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154249, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154250, [ =( 'c_HOL_Ominus__class_Ominus'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Z, 'tc_bool' ) ),
% 27.63/28.03 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154251, [ =( 'c_Set_Ovimage'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), U, T ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 27.63/28.03 , 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154252, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X
% 27.63/28.03 , 'c_Lattices_Oupper__semilattice__class_Osup'( U, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z, T ) ) ] )
% 27.63/28.03 , clause( 154253, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X
% 27.63/28.03 , 'c_Lattices_Oupper__semilattice__class_Osup'( Y, U, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z, T ) ) ] )
% 27.63/28.03 , clause( 154254, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'(
% 27.63/28.03 't_a' ) ), =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 27.63/28.03 'v_x', 't_a' ), 'c_Lattices_Oupper__semilattice__class_Osup'( 'v_x',
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( 't_a' ), 't_a' ) ) ] )
% 27.63/28.03 , clause( 154255, [ =( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_COMBC'( 'c_in'( 't_a' ), X, 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 27.63/28.03 'tc_bool' ), 'c_COMBC'( 'c_in'( 't_a' ), Y, 't_a', 'tc_fun'( 't_a',
% 27.63/28.03 'tc_bool' ), 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_x' ), hAPP(
% 27.63/28.03 hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 't_a',
% 27.63/28.03 'tc_bool' ) ) ) ) ] )
% 27.63/28.03 , clause( 154256, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ),
% 27.63/28.03 hAPP( X, hAPP( Y, 'v_x' ) ) ) ] )
% 27.63/28.03 , clause( 154257, [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ] )
% 27.63/28.03 , clause( 154258, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ),
% 27.63/28.03 hAPP( Y, hAPP( X, 'v_x' ) ) ) ] )
% 27.63/28.03 , clause( 154259, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OSKIP'
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154260, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', Z ) ) ) ] )
% 27.63/28.03 , clause( 154261, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 hAPP( 'c_Com_Ocom_OBODY', V2 ), V3 ), hAPP( V0, V2 ) ) ] )
% 27.63/28.03 , clause( 154262, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OCond'(
% 27.63/28.03 Y, Z, T ) ) ) ] )
% 27.63/28.03 , clause( 154263, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', T ) ) ) ] )
% 27.63/28.03 , clause( 154264, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OAss'(
% 27.63/28.03 Y, Z ) ) ) ] )
% 27.63/28.03 , clause( 154265, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', Z ) ) ) ] )
% 27.63/28.03 , clause( 154266, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ),
% 27.63/28.03 'c_Com_Ocom_OLocal'( Y, Z, T ) ) ) ] )
% 27.63/28.03 , clause( 154267, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ),
% 27.63/28.03 'c_Com_Ocom_OWhile'( Y, Z ) ) ) ] )
% 27.63/28.03 , clause( 154268, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', T ) ) ) ] )
% 27.63/28.03 , clause( 154269, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OSemi'(
% 27.63/28.03 Y, Z ) ) ) ] )
% 27.63/28.03 , clause( 154270, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', Z ) ) ) ] )
% 27.63/28.03 , clause( 154271, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', T ) ) ) ] )
% 27.63/28.03 , clause( 154272, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), 'c_Com_Ocom_OCall'(
% 27.63/28.03 Y, Z, T ) ) ) ] )
% 27.63/28.03 , clause( 154273, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 27.63/28.03 hAPP( 'c_Com_Ocom_OBODY', V2 ), V3 ), hAPP( V0, V2 ) ) ] )
% 27.63/28.03 , clause( 154274, [ ~( =( 'c_Com_Ocom_OSKIP', hAPP( 'c_Com_Ocom_OBODY', X )
% 27.63/28.03 ) ) ] )
% 27.63/28.03 , clause( 154275, [ 'c_Hoare__Mirabelle_Otriple__valid'(
% 27.63/28.03 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y ), hAPP( 'c_Com_Ocom_OBODY'
% 27.63/28.03 , Z ) ), T ), X ) ] )
% 27.63/28.03 , clause( 154276, [ ~( hBOOL( hAPP( X,
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y, hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 't_b' ), Z ), T ), U ), 't_b',
% 27.63/28.03 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154277, [ ~( hBOOL( hAPP( X,
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y, hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 't_b' ), Z ), T ), U ), 't_b',
% 27.63/28.03 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154278, [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__rec'( X, hAPP(
% 27.63/28.03 hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), T ), U ), Y,
% 27.63/28.03 W ), hAPP( hAPP( hAPP( X, Z ), T ), U ) ) ] )
% 27.63/28.03 , clause( 154279, [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( X, hAPP(
% 27.63/28.03 hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), T ), U ), Y,
% 27.63/28.03 W ), hAPP( hAPP( hAPP( X, Z ), T ), U ) ) ] )
% 27.63/28.03 , clause( 154280, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( T, Y,
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ] )
% 27.63/28.03 , clause( 154281, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 27.63/28.03 'c_lessequals'( Y, T, 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Z ),
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ) ] )
% 27.63/28.03 , clause( 154282, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 27.63/28.03 'c_lessequals'( T, X, 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Z ),
% 27.63/28.03 'tc_bool' ) ) ), ~( 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ] )
% 27.63/28.03 , clause( 154283, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ), 'tc_bool' ) ), Y ) ] )
% 27.63/28.03 , clause( 154284, [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, Z ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ) ) ] )
% 27.63/28.03 , clause( 154285, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 27.63/28.03 'c_lessequals'( Y, X, 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Z ),
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154286, [ 'c_Com_OWT'( hAPP( 'c_Com_Ocom_OBODY', X ) ), =( hAPP(
% 27.63/28.03 'c_Com_Obody', X ), 'c_Option_Ooption_ONone'( 'tc_Com_Ocom' ) ) ] )
% 27.63/28.03 , clause( 154287, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ),
% 27.63/28.03 Z ) ), hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', T ), Y ), Z ) ), ~(
% 27.63/28.03 hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( U, T, X
% 27.63/28.03 ) ), Y ), Z ) ) ) ] )
% 27.63/28.03 , clause( 154288, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP(
% 27.63/28.03 hAPP( 'c_Natural_Oevalc', 'c_Com_Ocom_OWhile'( X, T ) ), Y ), Z ) ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154289, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OCond'( X, Y, Z ) ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', Z ), T ), U ) ) ), hBOOL( hAPP( X, T ) ) ] )
% 27.63/28.03 , clause( 154290, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ),
% 27.63/28.03 Z ) ), hBOOL( hAPP( T, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( T, U, X ) ), Y ), Z ) ) ) ] )
% 27.63/28.03 , clause( 154291, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OSKIP' ), X ), X ) ) ] )
% 27.63/28.03 , clause( 154292, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OWhile'( X, Y ) ), Z ), Z ) ), hBOOL( hAPP( X, Z ) ) ] )
% 27.63/28.03 , clause( 154293, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OWhile'( X, Y ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', 'c_Com_Ocom_OWhile'( X, Y ) ), U ), T ) ) ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Natural_Oevalc', Y ), Z ), U ) ) ), ~( hBOOL( hAPP(
% 27.63/28.03 X, Z ) ) ) ] )
% 27.63/28.03 , clause( 154294, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OCond'( X, Y, Z ) ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', Y ), T ), U ) ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 27.63/28.03 , clause( 154295, [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', Z ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', 'c_Com_Ocom_OCond'( X, Z, U ) ), Y ), T ) ) ) ] )
% 27.63/28.03 , clause( 154296, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OSemi'( X, Y ) ), Z ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', Y ), U ), T ) ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', X ), Z ), U ) ) ) ] )
% 27.63/28.03 , clause( 154297, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', 'c_Com_Ocom_OSKIP' ), Y ), X ) ) ) ] )
% 27.63/28.03 , clause( 154298, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ),
% 27.63/28.03 Z ) ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ] )
% 27.63/28.03 , clause( 154299, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', X ), Y ),
% 27.63/28.03 Z ) ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ] )
% 27.63/28.03 , clause( 154300, [ =( hAPP( 'c_Option_Othe'( X ), 'c_Option_Ooption_OSome'(
% 27.63/28.03 Y, X ) ), Y ) ] )
% 27.63/28.03 , clause( 154301, [ =( 'c_Hoare__Mirabelle_OMGT'( 'v_c' ), hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), 'c_fequal'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'v_c' ), hAPP( 'c_Natural_Oevalc', 'v_c' ) ) ) ] )
% 27.63/28.03 , clause( 154302, [ ~( 'class_Lattices_Olattice'( 't_b' ) ), =( hAPP(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( 'v_f', 'v_g', 'tc_fun'(
% 27.63/28.03 't_a', 't_b' ) ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 hAPP( 'v_f', 'v_x' ), hAPP( 'v_g', 'v_x' ), 't_b' ) ) ] )
% 27.63/28.03 , clause( 154303, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 'c_Hoare__Mirabelle_OMGT'( hAPP( 'c_Com_Ocom_OBODY', Y ) ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Set_Oinsert'(
% 27.63/28.03 'c_Hoare__Mirabelle_OMGT'( hAPP( 'c_Com_Ocom_OBODY', Y ) ), X,
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'c_Set_Oinsert'(
% 27.63/28.03 'c_Hoare__Mirabelle_OMGT'( hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 27.63/28.03 'c_Com_Obody', Y ) ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'tc_Com_Ostate' ) ) ]
% 27.63/28.03 )
% 27.63/28.03 , clause( 154304, [ 'c_Natural_Oevaln'( hAPP( 'c_Option_Othe'(
% 27.63/28.03 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', X ) ), Y,
% 27.63/28.03 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( X, Z, Y, T ), T ),
% 27.63/28.03 ~( 'c_Natural_Oevaln'( hAPP( 'c_Com_Ocom_OBODY', X ), Y, Z, T ) ) ] )
% 27.63/28.03 , clause( 154305, [ 'c_Natural_Oevaln'( hAPP( 'c_Com_Ocom_OBODY', X ), Y,
% 27.63/28.03 'c_Suc'( Z ), T ), ~( 'c_Natural_Oevaln'( hAPP( 'c_Option_Othe'(
% 27.63/28.03 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', X ) ), Y, Z, T ) ) ] )
% 27.63/28.03 , clause( 154306, [ =( 'c_Set_Oimage'( 'c_COMBB'( X, Y, Z, T, U ),
% 27.63/28.03 'c_Orderings_Otop__class_Otop'( 'tc_fun'( U, 'tc_bool' ) ), U, T ),
% 27.63/28.03 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, 'c_Orderings_Otop__class_Otop'(
% 27.63/28.03 'tc_fun'( U, 'tc_bool' ) ), U, Z ), Z, T ) ) ] )
% 27.63/28.03 , clause( 154307, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X,
% 27.63/28.03 U, Z, T ) ) ), ~( 'c_Fun_Oinj__on'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, U, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), Z, T ) ), =( Y, U ) ] )
% 27.63/28.03 , clause( 154308, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), hAPP(
% 27.63/28.03 hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', T ) ), U ), Y ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple__valid'( X, hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Option_Othe'(
% 27.63/28.03 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ), Y ) ) ] )
% 27.63/28.03 , clause( 154309, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, hAPP( hAPP(
% 27.63/28.03 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 27.63/28.03 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ), Y )
% 27.63/28.03 , ~( 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Com_Ocom_OBODY'
% 27.63/28.03 , T ) ), U ), Y ) ) ] )
% 27.63/28.03 , clause( 154310, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), hAPP( Z, T )
% 27.63/28.03 ), hAPP( 'c_Com_Ocom_OBODY', T ) ), hAPP( U, T ) ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~( hBOOL(
% 27.63/28.03 hAPP( hAPP( 'c_in'( 'tc_Com_Opname' ), T ), W ) ) ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 27.63/28.03 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), U, 'tc_Com_Opname', 'tc_fun'( Y,
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ) ), W, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 27.63/28.03 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 27.63/28.03 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 27.63/28.03 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), U
% 27.63/28.03 , 'tc_Com_Opname', 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 27.63/28.03 , 'tc_Hoare__Mirabelle_Otriple'( Y ) ), W, 'tc_Com_Opname',
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154311, [ =( 'c_Hoare__Mirabelle_OMGT'( X ), hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), 'c_fequal'(
% 27.63/28.03 'tc_Com_Ostate' ) ), X ), hAPP( 'c_Natural_Oevalc', X ) ) ) ] )
% 27.63/28.03 , clause( 154312, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', T ) ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Com_Ocom_OBODY'
% 27.63/28.03 , T ) ), U ), X, 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'c_Set_Oinsert'(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 27.63/28.03 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154313, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 27.63/28.03 hAPP( hAPP( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', T ) ), U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( Y ), Z ), hAPP( 'c_Option_Othe'(
% 27.63/28.03 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', T ) ) ), U ),
% 27.63/28.03 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154314, [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 27.63/28.03 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__valids'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 27.63/28.03 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 27.63/28.03 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 27.63/28.03 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 27.63/28.03 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T
% 27.63/28.03 , 'tc_Com_Opname', 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 27.63/28.03 , 'tc_Hoare__Mirabelle_Otriple'( Y ) ), U, 'tc_Com_Opname',
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154315, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 27.63/28.03 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_Com_Ocom_OBODY', 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'(
% 27.63/28.03 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T, 'tc_Com_Opname', 'tc_fun'( Y,
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 Y ) ), U, 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( Y ) ), 'tc_fun'(
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_Hoare__Mirabelle_Otriple_Otriple'( Y
% 27.63/28.03 ), Z, 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), 'tc_Com_Opname' )
% 27.63/28.03 , 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 27.63/28.03 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 27.63/28.03 'tc_Com_Opname', 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 27.63/28.03 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Y ) ) ), T
% 27.63/28.03 , 'tc_Com_Opname', 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 27.63/28.03 , 'tc_Hoare__Mirabelle_Otriple'( Y ) ), U, 'tc_Com_Opname',
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( Y ) ), Y ) ) ] )
% 27.63/28.03 , clause( 154316, [ =( 'c_Set_Oimage'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154317, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 27.63/28.03 'c_Com_Obody', X ) ) ), Y ), Z ) ) ) ] )
% 27.63/28.03 , clause( 154318, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', X ) ) ), Y ), Z )
% 27.63/28.03 ), ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', X ) ), Y ), Z ) ) ) ] )
% 27.63/28.03 , clause( 154319, [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U,
% 27.63/28.03 W ), 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ] )
% 27.63/28.03 , clause( 154320, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 27.63/28.03 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ] )
% 27.63/28.03 , clause( 154321, [ ~( =( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y ), Z ), T ), hAPP( hAPP(
% 27.63/28.03 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), U ), W ), V0 ) ) ), =( T
% 27.63/28.03 , V0 ) ] )
% 27.63/28.03 , clause( 154322, [ ~( =( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y ), Z ), T ), hAPP( hAPP(
% 27.63/28.03 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), U ), W ), V0 ) ) ), =( Z
% 27.63/28.03 , W ) ] )
% 27.63/28.03 , clause( 154323, [ ~( =( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), Y ), Z ), T ), hAPP( hAPP(
% 27.63/28.03 hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'( X ), U ), W ), V0 ) ) ), =( Y
% 27.63/28.03 , U ) ] )
% 27.63/28.03 , clause( 154324, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', Z ), T ), X ) ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', Z ), T ), Y ) ) ) ] )
% 27.63/28.03 , clause( 154325, [ hBOOL( hAPP(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 27.63/28.03 , clause( 154326, [ hBOOL( hAPP(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ] )
% 27.63/28.03 , clause( 154327, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL(
% 27.63/28.03 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), Y ) ) ) ] )
% 27.63/28.03 , clause( 154328, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 't_a', X )
% 27.63/28.03 ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( Y, 'v_x'
% 27.63/28.03 ), hAPP( Z, 'v_x' ), X ) ) ] )
% 27.63/28.03 , clause( 154329, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X,
% 27.63/28.03 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 27.63/28.03 , clause( 154330, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ] )
% 27.63/28.03 , clause( 154331, [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP(
% 27.63/28.03 Y, W ) ) ) ] )
% 27.63/28.03 , clause( 154332, [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X
% 27.63/28.03 , W ), hAPP( Y, W ) ) ) ] )
% 27.63/28.03 , clause( 154333, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154334, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154335, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 27.63/28.03 , clause( 154336, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 27.63/28.03 , clause( 154337, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 27.63/28.03 , clause( 154338, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 27.63/28.03 , clause( 154339, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 27.63/28.03 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 27.63/28.03 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154340, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 27.63/28.03 , clause( 154341, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 27.63/28.03 , clause( 154342, [ ~( =( hAPP( 'c_Com_Ocom_OBODY', X ), hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', Y ) ) ), =( X, Y ) ] )
% 27.63/28.03 , clause( 154343, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 27.63/28.03 'tc_bool' ) ) ) ] )
% 27.63/28.03 , clause( 154344, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154345, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 27.63/28.03 , clause( 154346, [ 'c_Hoare__Mirabelle_Ohoare__derivs'(
% 27.63/28.03 'c_Lattices_Oupper__semilattice__class_Osup'( 'v_G', 'c_Set_Oimage'(
% 27.63/28.03 'c_COMBS'( 'c_COMBB'( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ), 'c_fequal'( 'tc_Com_Ostate' ) ), 'c_Com_Ocom_OBODY',
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 27.63/28.03 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'tc_Com_Opname' ), 'c_COMBB'( 'c_Natural_Oevalc',
% 27.63/28.03 'c_Com_Ocom_OBODY', 'tc_Com_Ocom', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 27.63/28.03 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Opname' ), 'tc_Com_Opname',
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'v_Procs',
% 27.63/28.03 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 27.63/28.03 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ), 'tc_bool' ) )
% 27.63/28.03 , 'c_Set_Oimage'( 'c_COMBS'( 'c_COMBB'( hAPP(
% 27.63/28.03 'c_Hoare__Mirabelle_Otriple_Otriple'( 'tc_Com_Ostate' ), 'c_fequal'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ),
% 27.63/28.03 'c_Com_Obody', 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom',
% 27.63/28.03 'tc_Com_Opname' ), 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'(
% 27.63/28.03 'tc_Com_Ostate' ) ), 'tc_Com_Opname' ), 'c_COMBB'( 'c_Natural_Oevalc',
% 27.63/28.03 'c_COMBB'( 'c_Option_Othe'( 'tc_Com_Ocom' ), 'c_Com_Obody',
% 27.63/28.03 'tc_Option_Ooption'( 'tc_Com_Ocom' ), 'tc_Com_Ocom', 'tc_Com_Opname' ),
% 27.63/28.03 'tc_Com_Ocom', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 27.63/28.03 'tc_bool' ) ), 'tc_Com_Opname' ), 'tc_Com_Opname', 'tc_fun'(
% 27.63/28.03 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 27.63/28.03 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ), 'v_Procs',
% 27.63/28.03 'tc_Com_Opname', 'tc_Hoare__Mirabelle_Otriple'( 'tc_Com_Ostate' ) ),
% 27.63/28.03 'tc_Com_Ostate' ) ] )
% 27.63/28.03 , clause( 154347, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', 'v_pn' ) ) ),
% 27.63/28.03 'v_x' ), 'v_xa' ) ) ] )
% 27.63/28.03 , clause( 154348, [ ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ) ] )
% 27.63/28.03 , clause( 154349, [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y )
% 27.63/28.03 ), ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 27.63/28.03 , clause( 154350, [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) )
% 27.63/28.03 , ~( 'class_Lattices_Obounded__lattice'( Y ) ) ] )
% 27.63/28.03 , clause( 154351, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_Orderings_Opreorder'( Y ) ) ] )
% 27.63/28.03 , clause( 154352, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_Lattices_Olattice'( Y ) ) ] )
% 27.63/28.03 , clause( 154353, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_Orderings_Oorder'( Y ) ) ] )
% 27.63/28.03 , clause( 154354, [ 'class_Orderings_Otop'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_Orderings_Otop'( Y ) ) ] )
% 27.63/28.03 , clause( 154355, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_Orderings_Obot'( Y ) ) ] )
% 27.63/28.03 , clause( 154356, [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_HOL_Ominus'( Y ) ) ] )
% 27.63/28.03 , clause( 154357, [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~(
% 27.63/28.03 'class_HOL_Oord'( Y ) ) ] )
% 27.63/28.03 , clause( 154358, [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154359, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154360, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154361, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154362, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154363, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154364, [ 'class_HOL_Ominus'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154365, [ 'class_HOL_Oord'( 'tc_nat' ) ] )
% 27.63/28.03 , clause( 154366, [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154367, [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154368, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154369, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154370, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154371, [ 'class_Orderings_Otop'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154372, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154373, [ 'class_HOL_Ominus'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154374, [ 'class_HOL_Oord'( 'tc_bool' ) ] )
% 27.63/28.03 , clause( 154375, [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X
% 27.63/28.03 , W ), hAPP( Y, W ) ) ) ] )
% 27.63/28.03 , clause( 154376, [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X
% 27.63/28.03 , W ), Y ) ) ] )
% 27.63/28.03 , clause( 154377, [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP(
% 27.63/28.03 Y, W ) ) ) ] )
% 27.63/28.03 , clause( 154378, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 27.63/28.03 , clause( 154379, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ),
% 27.63/28.03 Y ) ) ) ] )
% 27.63/28.03 ] ).
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03
% 27.63/28.03 subsumption(
% 27.63/28.03 clause( 341, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.63/28.03 'c_Com_Ocom_OBODY', X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.63/28.03 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 27.69/28.04 'c_Com_Obody', X ) ) ), Y ), Z ) ) ) ] )
% 27.69/28.04 , clause( 154317, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.69/28.04 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 27.69/28.04 'c_Com_Obody', X ) ) ), Y ), Z ) ) ) ] )
% 27.69/28.04 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 27.69/28.04 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 subsumption(
% 27.69/28.04 clause( 369, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', 'v_pn' ) ) ),
% 27.69/28.04 'v_x' ), 'v_xa' ) ) ] )
% 27.69/28.04 , clause( 154347, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', 'v_pn' ) ) ),
% 27.69/28.04 'v_x' ), 'v_xa' ) ) ] )
% 27.69/28.04 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 subsumption(
% 27.69/28.04 clause( 370, [ ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ) ] )
% 27.69/28.04 , clause( 154348, [ ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ) ] )
% 27.69/28.04 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 resolution(
% 27.69/28.04 clause( 155453, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ] )
% 27.69/28.04 , clause( 341, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', X ) ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 27.69/28.04 'c_Natural_Oevalc', hAPP( 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP(
% 27.69/28.04 'c_Com_Obody', X ) ) ), Y ), Z ) ) ) ] )
% 27.69/28.04 , 1, clause( 369, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Option_Othe'( 'tc_Com_Ocom' ), hAPP( 'c_Com_Obody', 'v_pn' ) ) ),
% 27.69/28.04 'v_x' ), 'v_xa' ) ) ] )
% 27.69/28.04 , 0, substitution( 0, [ :=( X, 'v_pn' ), :=( Y, 'v_x' ), :=( Z, 'v_xa' )] )
% 27.69/28.04 , substitution( 1, [] )).
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 resolution(
% 27.69/28.04 clause( 155454, [] )
% 27.69/28.04 , clause( 370, [ ~( hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ) ] )
% 27.69/28.04 , 0, clause( 155453, [ hBOOL( hAPP( hAPP( hAPP( 'c_Natural_Oevalc', hAPP(
% 27.69/28.04 'c_Com_Ocom_OBODY', 'v_pn' ) ), 'v_x' ), 'v_xa' ) ) ] )
% 27.69/28.04 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 subsumption(
% 27.69/28.04 clause( 153885, [] )
% 27.69/28.04 , clause( 155454, [] )
% 27.69/28.04 , substitution( 0, [] ), permutation( 0, [] ) ).
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 end.
% 27.69/28.04
% 27.69/28.04 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 27.69/28.04
% 27.69/28.04 Memory use:
% 27.69/28.04
% 27.69/28.04 space for terms: 5324641
% 27.69/28.04 space for clauses: 7724274
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 clauses generated: 824587
% 27.69/28.04 clauses kept: 153886
% 27.69/28.04 clauses selected: 1466
% 27.69/28.04 clauses deleted: 1097
% 27.69/28.04 clauses inuse deleted: 21
% 27.69/28.04
% 27.69/28.04 subsentry: 7279000
% 27.69/28.04 literals s-matched: 4070390
% 27.69/28.04 literals matched: 3856523
% 27.69/28.04 full subsumption: 2618085
% 27.69/28.04
% 27.69/28.04 checksum: -1026994446
% 27.69/28.04
% 27.69/28.04
% 27.69/28.04 Bliksem ended
%------------------------------------------------------------------------------