TSTP Solution File: SWV854-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV854-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n004.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 16:28:51 EDT 2022
% Result : Unsatisfiable 128.96s 129.50s
% Output : Refutation 129.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV854-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Thu Jun 16 05:13:38 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.96/1.32 *** allocated 10000 integers for termspace/termends
% 0.96/1.32 *** allocated 10000 integers for clauses
% 0.96/1.32 *** allocated 10000 integers for justifications
% 0.96/1.32 *** allocated 15000 integers for termspace/termends
% 0.96/1.32 Bliksem 1.12
% 0.96/1.32
% 0.96/1.32
% 0.96/1.32 Automatic Strategy Selection
% 0.96/1.32
% 0.96/1.32 Clauses:
% 0.96/1.32 [
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 T, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 0.96/1.32 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.96/1.32 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.96/1.32 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 0.96/1.32 'tc_nat' ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.96/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.96/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.96/1.32 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, Z ), hBOOL( hAPP(
% 0.96/1.32 X, Z ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.32 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.96/1.32 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 0.96/1.32 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.96/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.96/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.96/1.32 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( Y
% 0.96/1.32 , T ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( X
% 0.96/1.32 , Z ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.96/1.32 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.96/1.32 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.96/1.32 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 0.96/1.32 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_Fun_Oinj__on'( 'c_COMBI'( X ), Y, X, X ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.96/1.32 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc',
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 0.96/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( hAPP( T, V2 ), V3 )
% 0.96/1.32 , 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V2, V4 ) ),
% 0.96/1.32 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.96/1.32 , =( X, T ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.96/1.32 , =( Y, U ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.96/1.32 , =( Z, W ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.96/1.32 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( Z, V2 )
% 0.96/1.32 , V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 )
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OSKIP', V2 ), X ) ],
% 0.96/1.32 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ) ) ) ), hBOOL( hAPP( X, Y
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 Z, X ) ) ],
% 0.96/1.32 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ) ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.96/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 0.96/1.32 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, Z ), hBOOL(
% 0.96/1.32 hAPP( X, Z ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.96/1.32 ), Z ), Y ) ],
% 0.96/1.32 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.96/1.32 hBOOL( hAPP( X, Z ) ) ],
% 0.96/1.32 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 0.96/1.32 hBOOL( hAPP( X, Z ) ) ],
% 0.96/1.32 [ =( X, Y ), ~( hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.32 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 0.96/1.32 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.96/1.32 Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.96/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.32 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( 'c_Suc', Z ), X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 0.96/1.32 ) ), Y ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( 'c_Suc', Z ), X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Power_Opower_Opower'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 0.96/1.32 ) ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 0.96/1.32 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.96/1.32 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 0.96/1.32 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.96/1.32 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.96/1.32 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 0.96/1.32 ) ), 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, T, X ) ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, T, X ) ), 'c_Power_Opower_Opower'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X
% 0.96/1.32 ) ) ) ],
% 0.96/1.32 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ],
% 0.96/1.32 [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.96/1.32 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.32 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ) ), T ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ) ), T ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.32 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.96/1.32 [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ],
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 0.96/1.32 , V4 ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( Y, T, U, W ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.96/1.32 [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevaln'( Z, Y, T, U ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Z, W ), Y, T, U ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.96/1.32 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 0.96/1.32 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 0.96/1.32 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.96/1.32 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 0.96/1.32 [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) ) ) ],
% 0.96/1.32 [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y ) ) ],
% 0.96/1.32 [ =( hAPP( 'c_COMBI'( X ), Y ), Y ) ],
% 0.96/1.32 [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ],
% 0.96/1.32 [ =( 'c_COMBS'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), hAPP( Y, Z ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 0.96/1.32 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.96/1.32 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.96/1.32 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.32 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.96/1.32 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.96/1.32 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 0.96/1.32 ), Z ), T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 0.96/1.32 , X ) ), T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.96/1.32 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.96/1.32 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.96/1.32 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 0.96/1.32 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 0.96/1.32 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 0.96/1.32 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 0.96/1.32 X, T ), Y ) ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 0.96/1.32 hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 0.96/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 X, T, 'tc_nat' ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 0.96/1.32 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( hAPP( 'c_Fun_Ocomp'( 'c_COMBK'( X, Y, Z ), T, Z, Y, 't_a' ), 'v_x'
% 0.96/1.32 ), X ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.32 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.32 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.96/1.32 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.96/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.96/1.32 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.96/1.32 , =( Z, W ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.96/1.32 , =( Y, U ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.96/1.32 , =( X, T ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.32 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.96/1.32 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 0.96/1.32 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.96/1.32 T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.96/1.32 T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 0.96/1.32 T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 0.96/1.32 T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Option_Ooption_OSome'( X, Y ), 'c_Option_Ooption_ONone'( Y )
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( =( 'c_Option_Ooption_OSome'( X, Y ), 'c_Option_Ooption_ONone'( Y )
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), Z ), X ) ],
% 0.96/1.32 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), Z ), X ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ ~( =( 'c_Option_Ooption_OSome'( X, Y ), 'c_Option_Ooption_OSome'( Z, Y
% 0.96/1.32 ) ) ), =( X, Z ) ],
% 0.96/1.32 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 0.96/1.32 ) ],
% 0.96/1.32 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.96/1.32 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.96/1.32 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.32 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 0.96/1.32 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 0.96/1.32 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.32 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 0.96/1.32 X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.32 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 0.96/1.32 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 0.96/1.32 [ 'c_Com_OWT'( 'c_Com_Ocom_OCond'( X, Y, Z ) ), ~( 'c_Com_OWT'( Z ) ),
% 0.96/1.32 ~( 'c_Com_OWT'( Y ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OSKIP', V2 ), X ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.96/1.32 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 0.96/1.32 , Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 0.96/1.32 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.32 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OSemi'( Z, T ), U, W
% 0.96/1.32 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.96/1.32 'tc_Hoare__Mirabelle_Otriple'( W ), 'tc_bool' ) ),
% 0.96/1.32 'tc_Hoare__Mirabelle_Otriple'( W ) ), W ), ~(
% 0.96/1.32 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.32 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, U, W ),
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.32 W ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( W ) ), W ) ), ~(
% 0.96/1.32 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.32 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, V0, W ),
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.32 W ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( W ) ), W ) ) ],
% 0.96/1.32 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'( Y ), 'tc_bool' ) ), Y ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.96/1.32 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 0.96/1.32 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 0.96/1.32 ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.32 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 0.96/1.32 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.96/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.96/1.32 ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, U ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), W, T, U ) ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( Y, Z, T, W ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 0.96/1.32 [ ~( =( 'c_Option_Ooption_ONone'( X ), 'c_Option_Ooption_OSome'( Y, X )
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( =( 'c_Option_Ooption_ONone'( X ), 'c_Option_Ooption_OSome'( Y, X )
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), U, T ) ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( Y, Z, U ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 0.96/1.32 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.96/1.32 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.32 , T, X ) ) ), =( Y, Z ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.96/1.32 , T, X ) ) ), =( Z, T ) ],
% 0.96/1.32 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 0.96/1.32 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T, W ) )
% 0.96/1.32 ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.96/1.32 X ), X ), Y ) ],
% 0.96/1.32 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 0.96/1.32 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.32 [ 'c_Com_OWT'( 'c_Com_Ocom_OSKIP' ) ],
% 0.96/1.32 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( Y, T, U ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.96/1.32 [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevalc'( Z, Y, T ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Z, U ), Y, T ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_Com_OWT'( 'c_Com_Ocom_OAss'( X, Y ) ) ],
% 0.96/1.32 [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.96/1.32 'tc_bool' ) ), Y, Z ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.32 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.32 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_Com_OWT'( 'c_Com_Ocom_OCall'( X, Y, Z ) ), ~( 'c_Com_OWT'(
% 0.96/1.32 'c_Com_Ocom_OBODY'( Y ) ) ) ],
% 0.96/1.32 [ 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( X ) ), ~( 'c_Com_OWT'(
% 0.96/1.32 'c_Com_Ocom_OCall'( Y, X, Z ) ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 0.96/1.32 , X ), Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 0.96/1.32 , X ), Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 0.96/1.32 Z, Y, X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z ) ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 0.96/1.32 'tc_nat' ) ],
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.96/1.32 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.32 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 ) ), =( Y, Z ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 ) ), =( Y, Z ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 0.96/1.32 , T, X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 0.96/1.32 , Z, X ), X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.96/1.32 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( 'c_in'( X, Y, Z ) ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 0.96/1.32 ],
% 0.96/1.32 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.32 Z ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ), ~(
% 0.96/1.32 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y, T,
% 0.96/1.32 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP(
% 0.96/1.32 Y, hAPP( 'c_Suc', Z ) ), X ), ~( 'c_Orderings_Oorder__class_Omono'( Y,
% 0.96/1.32 'tc_nat', X ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.32 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 0.96/1.32 , 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.32 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.96/1.32 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.96/1.32 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 0.96/1.32 'tc_nat' ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ),
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.96/1.32 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 0.96/1.32 ) ],
% 0.96/1.32 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 0.96/1.32 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.96/1.32 , T, X ), X ), T, X ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.96/1.32 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.96/1.32 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 0.96/1.32 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 0.96/1.32 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.96/1.32 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.96/1.32 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.96/1.32 , V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.32 T, X, U, W, Y, V0 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.32 T, X, U, Y, W, V0 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.96/1.32 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.96/1.32 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.96/1.32 , V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.32 X, T, U, Y, W, V0 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.96/1.32 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.96/1.32 , V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.96/1.32 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.96/1.32 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 0.96/1.32 , V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.96/1.32 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.96/1.32 W, V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.96/1.32 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 0.96/1.32 W, V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.96/1.32 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.96/1.32 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 0.96/1.32 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.96/1.32 W, V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 0.96/1.32 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.96/1.32 , V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 0.96/1.32 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 0.96/1.32 W, V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 0.96/1.32 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 0.96/1.32 , V0, V1, V2 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.96/1.32 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 0.96/1.32 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.96/1.32 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 0.96/1.32 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 0.96/1.32 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 0.96/1.32 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 0.96/1.32 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.96/1.32 ) ), Y ) ) ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.96/1.32 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 0.96/1.32 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OLocal'( X, Y, Z ) ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.96/1.32 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.96/1.32 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.32 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 0.96/1.32 ) ],
% 0.96/1.32 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.32 'tc_nat' ) ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.96/1.32 , X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.32 , Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.32 , Y, X ) ) ],
% 0.96/1.32 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.96/1.32 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 0.96/1.32 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , X ), Y ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Y ), X ), 'tc_nat' ) ],
% 0.96/1.32 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , X ), Y ), 'tc_nat' ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ),
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevaln'( X, Y, Z, T ), hBOOL( hAPP( U, Y ) ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( U, W, X ), Y, Z, T ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W ), ~(
% 0.96/1.32 'c_Natural_Oevaln'( Z, T, U, W ) ), hBOOL( hAPP( X, T ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ) ],
% 0.96/1.32 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.96/1.32 ), =( Z, Y ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.32 ) ],
% 0.96/1.32 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 0.96/1.32 , Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.96/1.32 [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~( 'c_Natural_Oevalc'(
% 0.96/1.32 Z, T, Y ) ) ],
% 0.96/1.32 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 0.96/1.32 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 0.96/1.32 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 Y, X, 'tc_nat' ), =( Y, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.96/1.32 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.96/1.32 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.96/1.32 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.96/1.32 ) ],
% 0.96/1.32 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.96/1.32 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.96/1.32 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.96/1.32 X ), Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 , X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.32 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.32 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.96/1.32 T, X ) ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.32 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 0.96/1.32 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 0.96/1.32 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ],
% 0.96/1.32 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), X ), Z ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 0.96/1.32 Z, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.96/1.32 , X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.32 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.32 , X ) ) ],
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.96/1.32 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.96/1.32 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.96/1.32 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 0.96/1.32 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.96/1.32 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.32 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.96/1.32 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.96/1.32 'c_lessequals'( Z, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.32 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.96/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.96/1.32 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.96/1.32 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.32 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.96/1.32 'c_lessequals'( Z, T, X ) ) ],
% 0.96/1.32 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.32 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 0.96/1.32 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.96/1.32 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 0.96/1.32 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevalc'( X, Y, Z ), hBOOL( hAPP( T, Y ) ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( T, U, X ), Y, Z ) ) ],
% 0.96/1.32 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U ), ~(
% 0.96/1.32 'c_Natural_Oevalc'( Z, T, U ) ), hBOOL( hAPP( X, T ) ) ],
% 0.96/1.32 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 0.96/1.32 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 0.96/1.32 X, 'tc_nat' ) ), X ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 0.96/1.32 X, Y, 'tc_nat' ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 0.96/1.32 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OAss'( X, Y ) ) ) ],
% 0.96/1.32 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( Y, X ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 0.96/1.32 ), Z ), X ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 0.96/1.32 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.32 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 0.96/1.32 ) ) ],
% 0.96/1.32 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.96/1.32 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( Z, V2 ), V3 )
% 0.96/1.32 , V4 ) ) ],
% 0.96/1.32 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.32 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( W, V2 ), V3 ) ) ],
% 0.96/1.32 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 0.96/1.32 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 0.96/1.32 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ],
% 0.96/1.32 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y, hAPP( X, W ) )
% 0.96/1.32 ) ],
% 0.96/1.32 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.32 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.32 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 0.96/1.32 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ), =( Y,
% 0.96/1.32 T ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ), =( X,
% 0.96/1.32 Z ) ],
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 0.96/1.32 ,
% 0.96/1.32 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.32 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.32 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.32 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.32 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OSKIP', Y, Z ),
% 0.96/1.32 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.32 Z ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.96/1.32 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.32 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.32 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.96/1.32 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 0.96/1.33 ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.33 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X ) ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 0.96/1.33 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 0.96/1.33 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 0.96/1.33 ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.33 T, X, U, W, Z, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.33 T, X, U, W, Y, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.33 T, X, U, Z, W, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.33 T, X, U, Y, W, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 0.96/1.33 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 0.96/1.33 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 0.96/1.33 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.33 X, T, U, Z, W, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 0.96/1.33 X, T, U, Y, W, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 0.96/1.33 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 0.96/1.33 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 0.96/1.33 , V0, U, V1 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 0.96/1.33 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 0.96/1.33 , V0, U, V1 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 0.96/1.33 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 0.96/1.33 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 0.96/1.33 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 0.96/1.33 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 0.96/1.33 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( 'c_Fun_Oid'( T )
% 0.96/1.33 , W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W, V0 ) ) ],
% 0.96/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.33 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 0.96/1.33 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.33 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( T, V2 ), V3 ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.96/1.33 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Olinorder'(
% 0.96/1.33 Y ) ), =( 'c_Orderings_Oord__class_Omin'( hAPP( Z, T ), hAPP( Z, U ), Y )
% 0.96/1.33 , hAPP( Z, 'c_Orderings_Oord__class_Omin'( T, U, X ) ) ), ~(
% 0.96/1.33 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 0.96/1.33 =( X, Z ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 0.96/1.33 =( Y, T ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 0.96/1.33 Z, Y, X ) ) ],
% 0.96/1.33 [ 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( X, Y ) ), ~( 'c_Com_OWT'( Y ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( Y, X ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 0.96/1.33 , V4 ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'class_Orderings_Oorder'( Y ) )
% 0.96/1.33 , 'c_lessequals'( hAPP( Z, T ), hAPP( Z, U ), Y ), ~( 'c_lessequals'( T,
% 0.96/1.33 U, X ) ), ~( 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.96/1.33 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 0.96/1.33 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.96/1.33 X ), X ), X ) ],
% 0.96/1.33 [ 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( X, Y, Z ) ), ~( 'c_Com_OWT'( Z ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( Y, Z, X ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.33 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.33 'tc_nat' ), 'tc_nat' ), X ) ],
% 0.96/1.33 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.33 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 0.96/1.33 X ), X ), Y ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.96/1.33 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, 'c_Com_Ocom_OAss'(
% 0.96/1.33 V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.33 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.96/1.33 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 0.96/1.33 ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 0.96/1.33 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 0.96/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( W, V2 ), V3 ),
% 0.96/1.33 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ],
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.96/1.33 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.96/1.33 Y ) ],
% 0.96/1.33 [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y, Z, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 0.96/1.33 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 0.96/1.33 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ],
% 0.96/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Y ), Z ), Z, X ), Y ) ],
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( hAPP( U,
% 0.96/1.33 V2 ), V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3,
% 0.96/1.33 V5 ) ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Olinorder'(
% 0.96/1.33 Y ) ), =( 'c_Orderings_Oord__class_Omax'( hAPP( Z, T ), hAPP( Z, U ), Y )
% 0.96/1.33 , hAPP( Z, 'c_Orderings_Oord__class_Omax'( T, U, X ) ) ), ~(
% 0.96/1.33 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.96/1.33 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y, X ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.96/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 0.96/1.33 , 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 0.96/1.33 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 0.96/1.33 , 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ), 't_a' ),
% 0.96/1.33 'c_Natural_Oevaln'( Z, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2'(
% 0.96/1.33 Y, T, Z, X ), X, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3'( Y, T
% 0.96/1.33 , Z, X ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ) ), ~( hBOOL( 'c_in'(
% 0.96/1.33 X, Z, T ) ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ) ), ~( hBOOL( 'c_in'(
% 0.96/1.33 X, Z, T ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.96/1.33 'tc_bool' ) ), Y ) ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_in'( Y,
% 0.96/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.96/1.33 'tc_bool' ) ), Y ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.96/1.33 'tc_bool' ) ), Y ) ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, Y, Z ) ), =( X, T ), ~( hBOOL( 'c_in'( X,
% 0.96/1.33 'c_Set_Oinsert'( T, Y, Z ), Z ) ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ],
% 0.96/1.33 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( Z, T, U ) ) )
% 0.96/1.33 , ~( hBOOL( 'c_in'( Y, T, U ) ) ), =( Y, Z ), ~( 'c_Fun_Oinj__on'( X, T,
% 0.96/1.33 U, W ) ) ],
% 0.96/1.33 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( Z, T, U ) ) )
% 0.96/1.33 , ~( hBOOL( 'c_in'( Y, T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W ) ),
% 0.96/1.33 =( Y, Z ) ],
% 0.96/1.33 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( Z, T, U ) ) )
% 0.96/1.33 , ~( hBOOL( 'c_in'( Y, T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W ) ),
% 0.96/1.33 =( Y, Z ) ],
% 0.96/1.33 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W
% 0.96/1.33 ) ), =( Y, Z ), ~( hBOOL( 'c_in'( Z, T, U ) ) ), ~( hBOOL( 'c_in'( Y, T
% 0.96/1.33 , U ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.96/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 0.96/1.33 hBOOL( 'c_in'( X, T, Z ) ), hBOOL( 'c_in'( X, Y, Z ) ), =( Y, T ) ],
% 0.96/1.33 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( 'c_in'( X, Y, Z ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 0.96/1.33 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 0.96/1.33 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 0.96/1.33 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 0.96/1.33 X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 0.96/1.33 ), Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 0.96/1.33 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 0.96/1.33 V0, V1 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 0.96/1.33 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 0.96/1.33 V0, V1 ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.33 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 0.96/1.33 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 0.96/1.33 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.33 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.33 'tc_nat' ), Z, X ), Z ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.96/1.33 ), =( Z, W ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.96/1.33 ), =( Y, U ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 0.96/1.33 ), =( X, T ) ],
% 0.96/1.33 [ 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ), ~( 'c_Com_OWT'( Y ) ), ~(
% 0.96/1.33 'c_Com_OWT'( X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.96/1.33 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.96/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCall'( X, Y, Z ) ) ) ],
% 0.96/1.33 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X ) ],
% 0.96/1.33 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 0.96/1.33 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.33 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 0.96/1.33 ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.96/1.33 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevalc'(
% 0.96/1.33 'c_Com_Ocom_OWhile'( X, T ), Y, Z ) ) ],
% 0.96/1.33 [ =( 'c_Power_Opower_Opower'( X, Y, Z, 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.33 'tc_nat' ), T ), X ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.33 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.96/1.33 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.96/1.33 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.33 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.96/1.33 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.96/1.33 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.33 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.33 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 0.96/1.33 ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.33 , Z ), Y ), 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 0.96/1.33 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 0.96/1.33 ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 0.96/1.33 , Y ) ) ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.33 'tc_nat' ) ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.33 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.96/1.33 ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.96/1.33 ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.96/1.33 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.96/1.33 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.96/1.33 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.96/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 0.96/1.33 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.96/1.33 [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U, Z, 'tc_nat' )
% 0.96/1.33 ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.33 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.96/1.33 , X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.33 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.96/1.33 , X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.96/1.33 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.96/1.33 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.96/1.33 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.33 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 0.96/1.33 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 0.96/1.33 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 0.96/1.33 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.96/1.33 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ) ) ],
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( U, V2 ), V3 ),
% 0.96/1.33 V4 ) ) ],
% 0.96/1.33 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 0.96/1.33 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 0.96/1.33 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 0.96/1.33 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 0.96/1.33 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 0.96/1.33 , V4 ), W ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevaln'(
% 0.96/1.33 'c_Com_Ocom_OWhile'( X, T ), Y, U, Z ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( T, Y,
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y, Z,
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Z, T ) ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y,
% 0.96/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.33 T ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 0.96/1.33 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.33 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 0.96/1.33 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.96/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.96/1.33 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.33 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.33 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.33 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.96/1.33 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.96/1.33 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Y ), T ), Z, X ) ) ],
% 0.96/1.33 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 0.96/1.33 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.96/1.33 , Y ), Z ), T, X ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, hAPP(
% 0.96/1.33 'c_Suc', Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_Natural_Oevaln'( X, Y, Z, T ), 'c_Natural_Oevaln'( U, Y, Z, T ),
% 0.96/1.33 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( W, U, X ), Y, Z, T ) ) ],
% 0.96/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.33 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 0.96/1.33 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 0.96/1.33 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.96/1.33 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.96/1.33 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.96/1.33 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 0.96/1.33 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.96/1.33 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 0.96/1.33 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 0.96/1.33 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 0.96/1.33 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.96/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 0.96/1.33 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.96/1.33 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.96/1.33 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) )
% 0.96/1.33 ) ],
% 0.96/1.33 [ 'c_Natural_Oevalc'( X, Y, Z ), 'c_Natural_Oevalc'( T, Y, Z ), ~(
% 0.96/1.33 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( U, T, X ), Y, Z ) ) ],
% 0.96/1.33 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, Z, X ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, X, Z ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z, U, V0 ),
% 0.96/1.33 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.96/1.33 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.33 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.96/1.33 'c_lessequals'( Z, Y, X ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.33 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.96/1.33 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 0.96/1.33 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 0.96/1.33 , V0, V1 ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 0.96/1.33 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 0.96/1.33 , V0, V1 ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.33 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Natural_Oevaln'( X, Y, hAPP( 'c_Suc', Z ), T ), ~(
% 0.96/1.33 'c_Natural_Oevaln'( X, Y, Z, T ) ) ],
% 0.96/1.33 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 0.96/1.33 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 0.96/1.33 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 0.96/1.33 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.96/1.33 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 0.96/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y
% 0.96/1.33 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ =( 'c_Nat_Onat_Onat__case'( X, Y, hAPP( 'c_Suc', Z ), T ), hAPP( Y, Z
% 0.96/1.33 ) ) ],
% 0.96/1.33 [ 'c_Orderings_Oorder__class_Omono'( 'c_Suc', 'tc_nat', 'tc_nat' ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_Power_Opower_Opower'( X, Y, Z, hAPP( 'c_Suc', T ), U ), hAPP(
% 0.96/1.33 hAPP( Y, Z ), 'c_Power_Opower_Opower'( X, Y, Z, T, U ) ) ) ],
% 0.96/1.33 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 0.96/1.33 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, hAPP( 'c_Suc', Z ), T ), hAPP( hAPP(
% 0.96/1.33 Y, Z ), 'c_Nat_Onat_Onat__rec'( X, Y, Z, T ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.96/1.33 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ) ) ) ],
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 0.96/1.33 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.96/1.33 'tc_nat' ), X ), Y ) ) ) ],
% 0.96/1.33 [ =( 'c_Orderings_Oord__class_Omax'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 0.96/1.33 Y ), 'tc_nat' ), hAPP( 'c_Suc', 'c_Orderings_Oord__class_Omax'( X, Y,
% 0.96/1.33 'tc_nat' ) ) ) ],
% 0.96/1.33 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 0.96/1.33 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 0.96/1.33 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.96/1.33 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, hAPP( 'c_Suc', Z ), T, X )
% 0.96/1.33 , 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 0.96/1.33 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 0.96/1.33 'c_Suc', Y ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, hAPP( 'c_Suc', T ),
% 0.96/1.33 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, hAPP( 'c_Suc', T ),
% 0.96/1.33 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 0.96/1.33 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 0.96/1.33 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 0.96/1.33 X, 'tc_nat' ) ],
% 0.96/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 0.96/1.33 'c_Suc', X ), Y, 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 0.96/1.33 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.96/1.33 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_Orderings_Oord__class_Omin'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 0.96/1.33 Y ), 'tc_nat' ), hAPP( 'c_Suc', 'c_Orderings_Oord__class_Omin'( X, Y,
% 0.96/1.33 'tc_nat' ) ) ) ],
% 0.96/1.33 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 0.96/1.33 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 0.96/1.33 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 0.96/1.33 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 0.96/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 0.96/1.33 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 0.96/1.33 'tc_nat' ) ) ],
% 0.96/1.33 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 0.96/1.33 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 0.96/1.33 [ =( X, hAPP( 'c_Suc',
% 0.96/1.33 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y, X, Z, T ) ) ),
% 0.96/1.33 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( Y ), Z, X, T ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ), hAPP( X, hAPP( Y
% 0.96/1.33 , 'v_x' ) ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ],
% 0.96/1.33 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ), hAPP( Y, hAPP(
% 0.96/1.33 X, 'v_x' ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCond'( Y, Z, T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OAss'( Y, Z ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OLocal'( Y, Z, T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OWhile'( Y, Z ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCall'( Y, Z, T ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 0.96/1.33 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, U, 't_b' ), 't_b', 't_a' ) )
% 0.96/1.33 ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ],
% 0.96/1.33 [ ~( hBOOL( hAPP( X, 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, U, 't_b' ), 't_b', 't_a' ) )
% 0.96/1.33 ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ],
% 0.96/1.33 [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__rec'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, U ), U, W ), hAPP( hAPP(
% 0.96/1.33 hAPP( X, Y ), Z ), T ) ) ],
% 0.96/1.33 [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, U ), U, W ), hAPP( hAPP(
% 0.96/1.33 hAPP( X, Y ), Z ), T ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_COMBI'( 't_a' ), 'v_P' ), 'v_P' ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ), 't_a' ), ~( hBOOL(
% 0.96/1.33 hAPP( hAPP( T, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1'( Y, T,
% 0.96/1.33 Z, X ) ), 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3'( Y, T, Z, X
% 0.96/1.33 ) ) ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ), 't_a' ), hBOOL(
% 0.96/1.33 hAPP( hAPP( Y, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1'( Y, T,
% 0.96/1.33 Z, X ) ), 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2'( Y, T, Z, X
% 0.96/1.33 ) ) ) ],
% 0.96/1.33 [ 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( X ) ), =( 'c_Com_Obody'( X ),
% 0.96/1.33 'c_Option_Ooption_ONone'( 'tc_Com_Ocom' ) ) ],
% 0.96/1.33 [ =( 'c_COMBB'( 'v_P', 'v_Q', 'v_R', 't_a', 't_b', 't_c' ), hAPP( 'v_P'
% 0.96/1.33 , hAPP( 'v_Q', 'v_R' ) ) ) ],
% 0.96/1.33 [ =( 'c_COMBS'( 'v_P', 'v_Q', 'v_R', 't_a', 't_b', 't_c' ), hAPP( hAPP(
% 0.96/1.33 'v_P', 'v_R' ), hAPP( 'v_Q', 'v_R' ) ) ) ],
% 0.96/1.33 [ =( 'c_COMBC'( 'v_P', 'v_Q', 'v_R', 't_a', 't_b', 't_c' ), hAPP( hAPP(
% 0.96/1.33 'v_P', 'v_R' ), 'v_Q' ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( 'c_in'(
% 0.96/1.33 Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), hBOOL( 'c_in'(
% 0.96/1.33 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), T,
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, 't_a' ),
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple__valid'(
% 0.96/1.33 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2'( X, Y ), Z, 't_a' ),
% 0.96/1.33 ~( hBOOL( 'c_in'( Z, X, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( 'c_in'(
% 0.96/1.33 Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 0.96/1.33 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), 't_a' ) ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ],
% 0.96/1.33 [ =( 'c_Option_Othe'( 'c_Option_Ooption_OSome'( X, Y ), Y ), X ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 0.96/1.33 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.33 U ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Set_Oinsert'(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 0.96/1.33 , X, 'tc_Hoare__Mirabelle_Otriple'( U ) ), 'c_Set_Oinsert'(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 0.96/1.33 Z ), 'tc_Com_Ocom' ), T, U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( U ), 'tc_bool' ) ),
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 0.96/1.33 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 0.96/1.33 U ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 0.96/1.33 Z ), 'tc_Com_Ocom' ), T, U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( U ), 'tc_bool' ) ),
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ) ) ],
% 0.96/1.33 [ 'c_Natural_Oevaln'( 'c_Option_Othe'( 'c_Com_Obody'( X ), 'tc_Com_Ocom'
% 0.96/1.33 ), Y, 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( X, Z, Y, T )
% 0.96/1.33 , T ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( X ), Y, Z, T ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' )
% 0.96/1.33 ), 'v_x' ), 'c_in'( 'v_x', 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.96/1.33 't_a', 'tc_bool' ) ), 't_a' ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( 'c_Natural_Oevaln'( T, U, W, Z )
% 0.96/1.33 ), ~( hBOOL( hAPP( hAPP( V0, Y ), U ) ) ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple__valid'( W,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, X, 't_a' ), 't_a' ) ) ],
% 0.96/1.33 [ =( hAPP( 'c_COMBK'( 'v_P', 't_a', 't_b' ), 'v_Q' ), 'v_P' ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( 'c_in'(
% 0.96/1.33 Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), hBOOL( 'c_in'(
% 0.96/1.33 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), Z,
% 0.96/1.33 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'c_HOL_Ozero__class_Ozero'(
% 0.96/1.33 'tc_nat' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( X, 'c_Com_Ocom_OBODY'(
% 0.96/1.33 Y ), Z, T ), T ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( 'c_in'(
% 0.96/1.33 Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ),
% 0.96/1.33 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), 't_a' ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ), Y, Z ), ~(
% 0.96/1.33 'c_Natural_Oevalc'( 'c_Option_Othe'( 'c_Com_Obody'( X ), 'tc_Com_Ocom' )
% 0.96/1.33 , Y, Z ) ) ],
% 0.96/1.33 [ 'c_Natural_Oevalc'( 'c_Option_Othe'( 'c_Com_Obody'( X ), 'tc_Com_Ocom'
% 0.96/1.33 ), Y, Z ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ), Y, Z ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( X ), Y, hAPP( 'c_Suc', Z ), T
% 0.96/1.33 ), ~( 'c_Natural_Oevaln'( 'c_Option_Othe'( 'c_Com_Obody'( X ),
% 0.96/1.33 'tc_Com_Ocom' ), Y, Z, T ) ) ],
% 0.96/1.33 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 0.96/1.33 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 0.96/1.33 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ],
% 0.96/1.33 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ],
% 0.96/1.33 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 0.96/1.33 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ), Y, Z ) ) ],
% 0.96/1.33 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( hAPP( Y, X ) ) ) ],
% 0.96/1.33 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_in'( Y, X, Z ) ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ),
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 0.96/1.33 , U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 0.96/1.33 Z ), 'tc_Com_Ocom' ), T, U ), U ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 0.96/1.33 Z ), 'tc_Com_Ocom' ), T, U ), U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'(
% 0.96/1.33 hAPP( 'c_Suc', X ), 'c_Hoare__Mirabelle_Otriple_Otriple'( Y,
% 0.96/1.33 'c_Com_Ocom_OBODY'( Z ), T, U ), U ) ) ],
% 0.96/1.33 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) ) ), =( X, Y )
% 0.96/1.33 ],
% 0.96/1.33 [ hBOOL( 'c_in'( 'v_x', 'v_Procs', 'tc_Com_Opname' ) ) ],
% 0.96/1.33 [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', 'v_na' ),
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', 'v_x' ),
% 0.96/1.33 'c_Com_Ocom_OBODY'( 'v_x' ), hAPP( 'v_Q', 'v_x' ), 't_a' ), 't_a' ) ) ]
% 0.96/1.33 ,
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na', X, 't_a' ), ~( hBOOL(
% 0.96/1.33 'c_in'( X, 'v_G', 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ),
% 0.96/1.33 'c_Com_Ocom_OBODY'( X ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ), ~( hBOOL(
% 0.96/1.33 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ],
% 0.96/1.33 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 0.96/1.33 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ), 'c_Option_Othe'(
% 0.96/1.33 'c_Com_Obody'( X ), 'tc_Com_Ocom' ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ),
% 0.96/1.33 ~( hBOOL( 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ],
% 0.96/1.33 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.96/1.33 'class_Orderings_Opreorder'( Y ) ) ],
% 0.96/1.33 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.96/1.33 'class_Orderings_Oorder'( Y ) ) ],
% 0.96/1.33 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 0.96/1.33 Y ) ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.96/1.33 ],
% 0.96/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.96/1.33 ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 0.96/1.33 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.96/1.33 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.96/1.33 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 0.96/1.33 [ 'c_fequal'( X, X, Y ) ],
% 0.96/1.33 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.96/1.33 ] .
% 0.96/1.33
% 0.96/1.33
% 0.96/1.33 percentage equality = 0.325851, percentage horn = 0.912977
% 0.96/1.33 This is a problem with some equality
% 0.96/1.33
% 0.96/1.33
% 0.96/1.33
% 0.96/1.33 Options Used:
% 0.96/1.33
% 0.96/1.33 useres = 1
% 0.96/1.33 useparamod = 1
% 0.96/1.33 useeqrefl = 1
% 0.96/1.33 useeqfact = 1
% 0.96/1.33 usefactor = 1
% 0.96/1.33 usesimpsplitting = 0
% 0.96/1.33 usesimpdemod = 5
% 0.96/1.33 usesimpres = 3
% 0.96/1.33
% 0.96/1.33 resimpinuse = 1000
% 0.96/1.33 resimpclauses = 20000
% 0.96/1.33 substype = eqrewr
% 0.96/1.33 backwardsubs = 1
% 0.96/1.33 selectoldest = 5
% 0.96/1.33
% 0.96/1.33 litorderings [0] = split
% 0.96/1.33 litorderings [1] = extend the termordering, first sorting on arguments
% 0.96/1.33
% 0.96/1.33 termordering = kbo
% 0.96/1.33
% 0.96/1.33 litapriori = 0
% 0.96/1.33 termapriori = 1
% 0.96/1.33 litaposteriori = 0
% 0.96/1.33 termaposteriori = 0
% 0.96/1.33 demodaposteriori = 0
% 0.96/1.33 ordereqreflfact = 0
% 0.96/1.33
% 0.96/1.33 litselect = negord
% 0.96/1.33
% 0.96/1.33 maxweight = 15
% 0.96/1.33 maxdepth = 30000
% 0.96/1.33 maxlength = 115
% 0.96/1.33 maxnrvars = 195
% 0.96/1.33 excuselevel = 1
% 0.96/1.33 increasemaxweight = 1
% 0.96/1.33
% 0.96/1.33 maxselected = 10000000
% 0.96/1.33 maxnrclauses = 10000000
% 0.96/1.33
% 0.96/1.33 showgenerated = 0
% 0.96/1.33 showkept = 0
% 0.96/1.33 showselected = 0
% 0.96/1.33 showdeleted = 0
% 0.96/1.33 showresimp = 1
% 0.96/1.33 showstatus = 2000
% 0.96/1.33
% 0.96/1.33 prologoutput = 1
% 0.96/1.33 nrgoals = 5000000
% 0.96/1.33 totalproof = 1
% 0.96/1.33
% 0.96/1.33 Symbols occurring in the translation:
% 0.96/1.33
% 0.96/1.33 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.96/1.33 . [1, 2] (w:1, o:167, a:1, s:1, b:0),
% 0.96/1.33 ! [4, 1] (w:0, o:126, a:1, s:1, b:0),
% 0.96/1.33 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.33 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OWhile' [41, 2] (w:1, o:192, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OSKIP' [42, 0] (w:1, o:15, a:1, s:1, b:0),
% 0.96/1.33 'class_Orderings_Olinorder' [44, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.96/1.33 'c_Orderings_Oord__class_Omax' [47, 3] (w:1, o:203, a:1, s:1, b:0),
% 0.96/1.33 'c_HOL_Oord__class_Oless' [49, 3] (w:1, o:204, a:1, s:1, b:0),
% 0.96/1.33 'class_OrderedGroup_Opordered__ab__group__add' [50, 1] (w:1, o:132
% 0.96/1.33 , a:1, s:1, b:0),
% 0.96/1.33 'c_Orderings_Oord__class_Omin' [51, 3] (w:1, o:205, a:1, s:1, b:0),
% 0.96/1.33 'c_HOL_Ominus__class_Ominus' [52, 3] (w:1, o:206, a:1, s:1, b:0),
% 0.96/1.33 'tc_nat' [55, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.96/1.33 'c_HOL_Ozero__class_Ozero' [56, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.96/1.33 'c_lessequals' [57, 3] (w:1, o:207, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OLocal' [63, 3] (w:1, o:208, a:1, s:1, b:0),
% 0.96/1.33 'c_Natural_Oevalc' [66, 3] (w:1, o:202, a:1, s:1, b:0),
% 0.96/1.33 hAPP [67, 2] (w:1, o:193, a:1, s:1, b:0),
% 0.96/1.33 hBOOL [68, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.96/1.33 'c_Suc' [70, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.96/1.33 'c_HOL_Oplus__class_Oplus' [71, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.96/1.33 'class_Orderings_Obot' [74, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.96/1.33 'c_Orderings_Obot__class_Obot' [75, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OSemi' [78, 2] (w:1, o:194, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OCond' [81, 3] (w:1, o:209, a:1, s:1, b:0),
% 0.96/1.33 'c_Set_Oinsert' [83, 3] (w:1, o:210, a:1, s:1, b:0),
% 0.96/1.33 'tc_bool' [84, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.96/1.33 'tc_fun' [85, 2] (w:1, o:195, a:1, s:1, b:0),
% 0.96/1.33 'c_COMBI' [86, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.96/1.33 'c_Fun_Oinj__on' [87, 4] (w:1, o:220, a:1, s:1, b:0),
% 0.96/1.33 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [88, 1]
% 0.96/1.33 (w:1, o:139, a:1, s:1, b:0),
% 0.96/1.33 'class_OrderedGroup_Ocomm__monoid__add' [89, 1] (w:1, o:140, a:1, s:1
% 0.96/1.33 , b:0),
% 0.96/1.33 't_a' [91, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.96/1.33 'v_x' [92, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_Ocom__rec' [101, 10] (w:1, o:239, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OCall' [104, 3] (w:1, o:211, a:1, s:1, b:0),
% 0.96/1.33 'class_Divides_Osemiring__div' [107, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.96/1.33
% 0.96/1.33 'c_Divides_Odiv__class_Omod' [108, 3] (w:1, o:213, a:1, s:1, b:0),
% 0.96/1.33 'c_Com_Ocom_OAss' [109, 2] (w:1, o:196, a:1, s:1, b:0),
% 0.96/1.33 'c_Nat_Onat_Onat__case' [111, 4] (w:1, o:221, a:1, s:1, b:0),
% 0.96/1.33 'class_OrderedGroup_Olordered__ab__group__add' [112, 1] (w:1, o:143
% 0.96/1.33 , a:1, s:1, b:0),
% 0.96/1.33 'c_Natural_Oevaln' [114, 4] (w:1, o:222, a:1, s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Ogroup__add' [115, 1] (w:1, o:144, a:1, s:1, b:0)
% 4.37/4.81 ,
% 4.37/4.81 'c_in' [117, 3] (w:1, o:214, a:1, s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Opordered__ab__semigroup__add' [119, 1] (w:1, o:
% 4.37/4.81 145, a:1, s:1, b:0),
% 4.37/4.81 'c_Power_Opower_Opower' [120, 5] (w:1, o:232, a:1, s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Opordered__comm__monoid__add' [121, 1] (w:1, o:
% 4.37/4.81 146, a:1, s:1, b:0),
% 4.37/4.81 'c_Fun_Oid' [122, 1] (w:1, o:147, a:1, s:1, b:0),
% 4.37/4.81 'c_Fun_Ocomp' [123, 5] (w:1, o:233, a:1, s:1, b:0),
% 4.37/4.81 'class_Orderings_Opreorder' [125, 1] (w:1, o:149, a:1, s:1, b:0),
% 4.37/4.81 'class_Orderings_Oorder' [126, 1] (w:1, o:148, a:1, s:1, b:0),
% 4.37/4.81 'class_Ring__and__Field_Ocomm__semiring__1' [127, 1] (w:1, o:150, a:1
% 4.37/4.81 , s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Oab__group__add' [128, 1] (w:1, o:151, a:1, s:1
% 4.37/4.81 , b:0),
% 4.37/4.81 'class_OrderedGroup_Oab__semigroup__add' [129, 1] (w:1, o:152, a:1
% 4.37/4.81 , s:1, b:0),
% 4.37/4.81 'c_Com_Ocom_Ocom__case' [131, 10] (w:1, o:240, a:1, s:1, b:0),
% 4.37/4.81 'class_Divides_Oring__div' [137, 1] (w:1, o:141, a:1, s:1, b:0),
% 4.37/4.81 'c_COMBB' [141, 6] (w:1, o:235, a:1, s:1, b:0),
% 4.37/4.81 'c_COMBC' [142, 6] (w:1, o:236, a:1, s:1, b:0),
% 4.37/4.81 'c_COMBK' [143, 3] (w:1, o:212, a:1, s:1, b:0),
% 4.37/4.81 'c_COMBS' [144, 6] (w:1, o:237, a:1, s:1, b:0),
% 4.37/4.81 'class_Ring__and__Field_Oidom' [146, 1] (w:1, o:153, a:1, s:1, b:0),
% 4.37/4.81
% 4.37/4.81 'class_Int_Onumber__ring' [147, 1] (w:1, o:154, a:1, s:1, b:0),
% 4.37/4.81 'c_Groebner__Basis_Ogb__semiring' [155, 6] (w:1, o:238, a:1, s:1, b:0
% 4.37/4.81 ),
% 4.37/4.81 'c_Option_Ooption_OSome' [157, 2] (w:1, o:197, a:1, s:1, b:0),
% 4.37/4.81 'c_Option_Ooption_ONone' [158, 1] (w:1, o:155, a:1, s:1, b:0),
% 4.37/4.81 'class_Ring__and__Field_Oordered__idom' [162, 1] (w:1, o:156, a:1, s:
% 4.37/4.81 1, b:0),
% 4.37/4.81 'c_Com_OWT' [163, 1] (w:1, o:157, a:1, s:1, b:0),
% 4.37/4.81 'c_Hoare__Mirabelle_Otriple_Otriple' [165, 4] (w:1, o:223, a:1, s:1
% 4.37/4.81 , b:0),
% 4.37/4.81 'tc_Hoare__Mirabelle_Otriple' [166, 1] (w:1, o:158, a:1, s:1, b:0),
% 4.37/4.81 'c_Hoare__Mirabelle_Ohoare__derivs' [167, 3] (w:1, o:215, a:1, s:1
% 4.37/4.81 , b:0),
% 4.37/4.81 'c_Com_Ocom_OBODY' [174, 1] (w:1, o:160, a:1, s:1, b:0),
% 4.37/4.81 'c_Orderings_Oorder__class_Omono' [176, 3] (w:1, o:216, a:1, s:1, b:0
% 4.37/4.81 ),
% 4.37/4.81 'class_OrderedGroup_Ocancel__ab__semigroup__add' [177, 1] (w:1, o:161
% 4.37/4.81 , a:1, s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Ocancel__semigroup__add' [178, 1] (w:1, o:162, a:
% 4.37/4.81 1, s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [183, 1]
% 4.37/4.81 (w:1, o:163, a:1, s:1, b:0),
% 4.37/4.81 'c_Nat_Onat_Onat__rec' [184, 4] (w:1, o:224, a:1, s:1, b:0),
% 4.37/4.81 'c_Fun_Ofcomp' [186, 5] (w:1, o:234, a:1, s:1, b:0),
% 4.37/4.81 'class_OrderedGroup_Omonoid__add' [190, 1] (w:1, o:164, a:1, s:1, b:0
% 4.37/4.81 ),
% 4.37/4.81 'c_Hoare__Mirabelle_Otriple__valid' [191, 3] (w:1, o:217, a:1, s:1
% 4.37/4.81 , b:0),
% 4.37/4.81 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2' [192, 4] (w:1, o:
% 4.37/4.81 226, a:1, s:1, b:0),
% 4.37/4.81 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3' [193, 4] (w:1, o:
% 4.37/4.81 227, a:1, s:1, b:0),
% 4.37/4.81 'class_Ring__and__Field_Oordered__semidom' [195, 1] (w:1, o:165, a:1
% 4.37/4.81 , s:1, b:0),
% 4.37/4.81 'class_Ring__and__Field_Osemiring__1' [196, 1] (w:1, o:166, a:1, s:1
% 4.37/4.81 , b:0),
% 4.37/4.81 'c_Nat_Osemiring__1__class_Oof__nat__aux' [198, 4] (w:1, o:228, a:1
% 4.37/4.81 , s:1, b:0),
% 4.37/4.81 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1' [208, 4] (w:1
% 4.37/4.81 , o:229, a:1, s:1, b:0),
% 4.37/4.81 't_b' [211, 0] (w:1, o:112, a:1, s:1, b:0),
% 4.37/4.81 'c_Hoare__Mirabelle_Otriple_Otriple__case' [212, 4] (w:1, o:230, a:1
% 4.37/4.81 , s:1, b:0),
% 4.37/4.81 'c_Hoare__Mirabelle_Otriple_Otriple__rec' [215, 4] (w:1, o:231, a:1
% 4.37/4.81 , s:1, b:0),
% 4.37/4.81 'v_P' [216, 0] (w:1, o:113, a:1, s:1, b:0),
% 4.37/4.81 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1' [217, 4] (w:1, o:
% 4.37/4.81 225, a:1, s:1, b:0),
% 4.37/4.81 'c_Com_Obody' [218, 1] (w:1, o:159, a:1, s:1, b:0),
% 4.37/4.81 'tc_Com_Ocom' [219, 0] (w:1, o:114, a:1, s:1, b:0),
% 4.37/4.81 'v_Q' [220, 0] (w:1, o:116, a:1, s:1, b:0),
% 4.37/4.81 'v_R' [221, 0] (w:1, o:117, a:1, s:1, b:0),
% 4.37/4.81 't_c' [222, 0] (w:1, o:118, a:1, s:1, b:0),
% 4.37/4.81 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1' [224, 2] (w:1, o:
% 4.37/4.81 198, a:1, s:1, b:0),
% 20.45/20.88 'c_Hoare__Mirabelle_Ohoare__valids' [225, 3] (w:1, o:218, a:1, s:1
% 20.45/20.88 , b:0),
% 20.45/20.88 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2' [226, 2] (w:1, o:
% 20.45/20.88 199, a:1, s:1, b:0),
% 20.45/20.88 'c_Option_Othe' [228, 2] (w:1, o:200, a:1, s:1, b:0),
% 20.45/20.88 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1' [230, 2] (w:1, o:
% 20.45/20.88 201, a:1, s:1, b:0),
% 20.45/20.88 'v_Procs' [234, 0] (w:1, o:115, a:1, s:1, b:0),
% 20.45/20.88 'tc_Com_Opname' [235, 0] (w:1, o:121, a:1, s:1, b:0),
% 20.45/20.88 'v_na' [236, 0] (w:1, o:122, a:1, s:1, b:0),
% 20.45/20.88 'v_G' [237, 0] (w:1, o:123, a:1, s:1, b:0),
% 20.45/20.88 'c_fequal' [240, 3] (w:1, o:219, a:1, s:1, b:0).
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Starting Search:
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 4470
% 20.45/20.88 Kept: 2001
% 20.45/20.88 Inuse: 147
% 20.45/20.88 Deleted: 3
% 20.45/20.88 Deletedinuse: 0
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 9822
% 20.45/20.88 Kept: 4021
% 20.45/20.88 Inuse: 207
% 20.45/20.88 Deleted: 5
% 20.45/20.88 Deletedinuse: 0
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 14408
% 20.45/20.88 Kept: 6024
% 20.45/20.88 Inuse: 260
% 20.45/20.88 Deleted: 7
% 20.45/20.88 Deletedinuse: 0
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 20951
% 20.45/20.88 Kept: 8033
% 20.45/20.88 Inuse: 336
% 20.45/20.88 Deleted: 10
% 20.45/20.88 Deletedinuse: 0
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 30955
% 20.45/20.88 Kept: 11564
% 20.45/20.88 Inuse: 415
% 20.45/20.88 Deleted: 14
% 20.45/20.88 Deletedinuse: 2
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 36827
% 20.45/20.88 Kept: 13572
% 20.45/20.88 Inuse: 472
% 20.45/20.88 Deleted: 14
% 20.45/20.88 Deletedinuse: 2
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 45046
% 20.45/20.88 Kept: 15649
% 20.45/20.88 Inuse: 556
% 20.45/20.88 Deleted: 17
% 20.45/20.88 Deletedinuse: 2
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 51836
% 20.45/20.88 Kept: 17696
% 20.45/20.88 Inuse: 596
% 20.45/20.88 Deleted: 19
% 20.45/20.88 Deletedinuse: 4
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 59679
% 20.45/20.88 Kept: 19704
% 20.45/20.88 Inuse: 646
% 20.45/20.88 Deleted: 21
% 20.45/20.88 Deletedinuse: 5
% 20.45/20.88
% 20.45/20.88 Resimplifying clauses:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 70936
% 20.45/20.88 Kept: 22235
% 20.45/20.88 Inuse: 660
% 20.45/20.88 Deleted: 221
% 20.45/20.88 Deletedinuse: 5
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 80138
% 20.45/20.88 Kept: 24249
% 20.45/20.88 Inuse: 701
% 20.45/20.88 Deleted: 221
% 20.45/20.88 Deletedinuse: 5
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 89936
% 20.45/20.88 Kept: 26866
% 20.45/20.88 Inuse: 735
% 20.45/20.88 Deleted: 221
% 20.45/20.88 Deletedinuse: 5
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 101159
% 20.45/20.88 Kept: 29201
% 20.45/20.88 Inuse: 755
% 20.45/20.88 Deleted: 221
% 20.45/20.88 Deletedinuse: 5
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 109971
% 20.45/20.88 Kept: 31391
% 20.45/20.88 Inuse: 774
% 20.45/20.88 Deleted: 221
% 20.45/20.88 Deletedinuse: 5
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 122534
% 20.45/20.88 Kept: 33750
% 20.45/20.88 Inuse: 792
% 20.45/20.88 Deleted: 235
% 20.45/20.88 Deletedinuse: 6
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 133340
% 20.45/20.88 Kept: 35841
% 20.45/20.88 Inuse: 802
% 20.45/20.88 Deleted: 260
% 20.45/20.88 Deletedinuse: 6
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 140616
% 20.45/20.88 Kept: 37847
% 20.45/20.88 Inuse: 835
% 20.45/20.88 Deleted: 268
% 20.45/20.88 Deletedinuse: 6
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 150785
% 20.45/20.88 Kept: 40468
% 20.45/20.88 Inuse: 846
% 20.45/20.88 Deleted: 268
% 20.45/20.88 Deletedinuse: 6
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying clauses:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 158323
% 20.45/20.88 Kept: 42516
% 20.45/20.88 Inuse: 874
% 20.45/20.88 Deleted: 581
% 20.45/20.88 Deletedinuse: 6
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 174259
% 20.45/20.88 Kept: 45020
% 20.45/20.88 Inuse: 894
% 20.45/20.88 Deleted: 581
% 20.45/20.88 Deletedinuse: 6
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88 Resimplifying inuse:
% 20.45/20.88 Done
% 20.45/20.88
% 20.45/20.88
% 20.45/20.88 Intermediate Status:
% 20.45/20.88 Generated: 194756
% 20.45/20.88 Kept: 48364
% 20.45/20.88 Inuse: 914
% 20.45/20.88 Deleted: 581
% 50.93/51.35 Deletedinuse: 6
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 205406
% 50.93/51.35 Kept: 50377
% 50.93/51.35 Inuse: 957
% 50.93/51.35 Deleted: 588
% 50.93/51.35 Deletedinuse: 6
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 222373
% 50.93/51.35 Kept: 53270
% 50.93/51.35 Inuse: 976
% 50.93/51.35 Deleted: 590
% 50.93/51.35 Deletedinuse: 7
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 229254
% 50.93/51.35 Kept: 55424
% 50.93/51.35 Inuse: 979
% 50.93/51.35 Deleted: 596
% 50.93/51.35 Deletedinuse: 11
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 239989
% 50.93/51.35 Kept: 57611
% 50.93/51.35 Inuse: 1013
% 50.93/51.35 Deleted: 602
% 50.93/51.35 Deletedinuse: 11
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 256884
% 50.93/51.35 Kept: 60452
% 50.93/51.35 Inuse: 1043
% 50.93/51.35 Deleted: 603
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying clauses:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 274610
% 50.93/51.35 Kept: 62527
% 50.93/51.35 Inuse: 1053
% 50.93/51.35 Deleted: 947
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 292012
% 50.93/51.35 Kept: 64532
% 50.93/51.35 Inuse: 1065
% 50.93/51.35 Deleted: 948
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 304125
% 50.93/51.35 Kept: 66553
% 50.93/51.35 Inuse: 1079
% 50.93/51.35 Deleted: 948
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 312220
% 50.93/51.35 Kept: 68790
% 50.93/51.35 Inuse: 1098
% 50.93/51.35 Deleted: 948
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 319977
% 50.93/51.35 Kept: 70857
% 50.93/51.35 Inuse: 1117
% 50.93/51.35 Deleted: 948
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 334490
% 50.93/51.35 Kept: 73070
% 50.93/51.35 Inuse: 1137
% 50.93/51.35 Deleted: 948
% 50.93/51.35 Deletedinuse: 12
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 344435
% 50.93/51.35 Kept: 75163
% 50.93/51.35 Inuse: 1160
% 50.93/51.35 Deleted: 951
% 50.93/51.35 Deletedinuse: 13
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 354902
% 50.93/51.35 Kept: 78880
% 50.93/51.35 Inuse: 1180
% 50.93/51.35 Deleted: 951
% 50.93/51.35 Deletedinuse: 13
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying clauses:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 368465
% 50.93/51.35 Kept: 80917
% 50.93/51.35 Inuse: 1205
% 50.93/51.35 Deleted: 1305
% 50.93/51.35 Deletedinuse: 13
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 392486
% 50.93/51.35 Kept: 83448
% 50.93/51.35 Inuse: 1220
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 416389
% 50.93/51.35 Kept: 86817
% 50.93/51.35 Inuse: 1230
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 428790
% 50.93/51.35 Kept: 88953
% 50.93/51.35 Inuse: 1235
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 450291
% 50.93/51.35 Kept: 91186
% 50.93/51.35 Inuse: 1245
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 464304
% 50.93/51.35 Kept: 93569
% 50.93/51.35 Inuse: 1270
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 475839
% 50.93/51.35 Kept: 95579
% 50.93/51.35 Inuse: 1298
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 513205
% 50.93/51.35 Kept: 99295
% 50.93/51.35 Inuse: 1300
% 50.93/51.35 Deleted: 1306
% 50.93/51.35 Deletedinuse: 14
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 553096
% 50.93/51.35 Kept: 103224
% 50.93/51.35 Inuse: 1305
% 50.93/51.35 Deleted: 1307
% 50.93/51.35 Deletedinuse: 15
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying clauses:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 561688
% 50.93/51.35 Kept: 105244
% 50.93/51.35 Inuse: 1321
% 50.93/51.35 Deleted: 1628
% 50.93/51.35 Deletedinuse: 15
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 50.93/51.35 Done
% 50.93/51.35
% 50.93/51.35
% 50.93/51.35 Intermediate Status:
% 50.93/51.35 Generated: 568441
% 50.93/51.35 Kept: 107362
% 50.93/51.35 Inuse: 1335
% 50.93/51.35 Deleted: 1628
% 50.93/51.35 Deletedinuse: 15
% 50.93/51.35
% 50.93/51.35 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 575738
% 105.40/105.83 Kept: 109407
% 105.40/105.83 Inuse: 1347
% 105.40/105.83 Deleted: 1629
% 105.40/105.83 Deletedinuse: 16
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 582481
% 105.40/105.83 Kept: 111576
% 105.40/105.83 Inuse: 1358
% 105.40/105.83 Deleted: 1629
% 105.40/105.83 Deletedinuse: 16
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 589786
% 105.40/105.83 Kept: 113627
% 105.40/105.83 Inuse: 1373
% 105.40/105.83 Deleted: 1629
% 105.40/105.83 Deletedinuse: 16
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 602033
% 105.40/105.83 Kept: 117556
% 105.40/105.83 Inuse: 1390
% 105.40/105.83 Deleted: 1629
% 105.40/105.83 Deletedinuse: 16
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 620856
% 105.40/105.83 Kept: 122170
% 105.40/105.83 Inuse: 1400
% 105.40/105.83 Deleted: 1629
% 105.40/105.83 Deletedinuse: 16
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 636747
% 105.40/105.83 Kept: 126194
% 105.40/105.83 Inuse: 1405
% 105.40/105.83 Deleted: 1629
% 105.40/105.83 Deletedinuse: 16
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying clauses:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 647098
% 105.40/105.83 Kept: 128218
% 105.40/105.83 Inuse: 1424
% 105.40/105.83 Deleted: 1828
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 659559
% 105.40/105.83 Kept: 130776
% 105.40/105.83 Inuse: 1440
% 105.40/105.83 Deleted: 1828
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 670815
% 105.40/105.83 Kept: 133584
% 105.40/105.83 Inuse: 1455
% 105.40/105.83 Deleted: 1828
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 687480
% 105.40/105.83 Kept: 135588
% 105.40/105.83 Inuse: 1484
% 105.40/105.83 Deleted: 1828
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 706327
% 105.40/105.83 Kept: 140299
% 105.40/105.83 Inuse: 1490
% 105.40/105.83 Deleted: 1828
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 722876
% 105.40/105.83 Kept: 144352
% 105.40/105.83 Inuse: 1495
% 105.40/105.83 Deleted: 1828
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying clauses:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 737915
% 105.40/105.83 Kept: 146787
% 105.40/105.83 Inuse: 1530
% 105.40/105.83 Deleted: 2036
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 748788
% 105.40/105.83 Kept: 148835
% 105.40/105.83 Inuse: 1562
% 105.40/105.83 Deleted: 2036
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 759142
% 105.40/105.83 Kept: 150837
% 105.40/105.83 Inuse: 1586
% 105.40/105.83 Deleted: 2036
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 768773
% 105.40/105.83 Kept: 152843
% 105.40/105.83 Inuse: 1595
% 105.40/105.83 Deleted: 2036
% 105.40/105.83 Deletedinuse: 17
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 777459
% 105.40/105.83 Kept: 155029
% 105.40/105.83 Inuse: 1615
% 105.40/105.83 Deleted: 2037
% 105.40/105.83 Deletedinuse: 18
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 786010
% 105.40/105.83 Kept: 157492
% 105.40/105.83 Inuse: 1630
% 105.40/105.83 Deleted: 2037
% 105.40/105.83 Deletedinuse: 18
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 794950
% 105.40/105.83 Kept: 159508
% 105.40/105.83 Inuse: 1654
% 105.40/105.83 Deleted: 2037
% 105.40/105.83 Deletedinuse: 18
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 807144
% 105.40/105.83 Kept: 161825
% 105.40/105.83 Inuse: 1655
% 105.40/105.83 Deleted: 2037
% 105.40/105.83 Deletedinuse: 18
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 838421
% 105.40/105.83 Kept: 164635
% 105.40/105.83 Inuse: 1665
% 105.40/105.83 Deleted: 2037
% 105.40/105.83 Deletedinuse: 18
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying clauses:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 847869
% 105.40/105.83 Kept: 166712
% 105.40/105.83 Inuse: 1682
% 105.40/105.83 Deleted: 2188
% 105.40/105.83 Deletedinuse: 18
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 857449
% 105.40/105.83 Kept: 168951
% 105.40/105.83 Inuse: 1700
% 105.40/105.83 Deleted: 2196
% 105.40/105.83 Deletedinuse: 26
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 867353
% 105.40/105.83 Kept: 171253
% 105.40/105.83 Inuse: 1715
% 105.40/105.83 Deleted: 2196
% 105.40/105.83 Deletedinuse: 26
% 105.40/105.83
% 105.40/105.83 Resimplifying inuse:
% 105.40/105.83 Done
% 105.40/105.83
% 105.40/105.83
% 105.40/105.83 Intermediate Status:
% 105.40/105.83 Generated: 884857
% 128.96/129.49 Kept: 173690
% 128.96/129.49 Inuse: 1725
% 128.96/129.49 Deleted: 2196
% 128.96/129.49 Deletedinuse: 26
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49
% 128.96/129.49 Intermediate Status:
% 128.96/129.49 Generated: 900558
% 128.96/129.49 Kept: 175808
% 128.96/129.49 Inuse: 1730
% 128.96/129.49 Deleted: 2196
% 128.96/129.49 Deletedinuse: 26
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49
% 128.96/129.49 Intermediate Status:
% 128.96/129.49 Generated: 916516
% 128.96/129.49 Kept: 177898
% 128.96/129.49 Inuse: 1735
% 128.96/129.49 Deleted: 2196
% 128.96/129.49 Deletedinuse: 26
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49
% 128.96/129.49 Intermediate Status:
% 128.96/129.49 Generated: 926494
% 128.96/129.49 Kept: 179901
% 128.96/129.49 Inuse: 1751
% 128.96/129.49 Deleted: 2196
% 128.96/129.49 Deletedinuse: 26
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49
% 128.96/129.49 Intermediate Status:
% 128.96/129.49 Generated: 951696
% 128.96/129.49 Kept: 184573
% 128.96/129.49 Inuse: 1780
% 128.96/129.49 Deleted: 2196
% 128.96/129.49 Deletedinuse: 26
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49
% 128.96/129.49 Intermediate Status:
% 128.96/129.49 Generated: 961574
% 128.96/129.49 Kept: 186770
% 128.96/129.49 Inuse: 1800
% 128.96/129.49 Deleted: 2196
% 128.96/129.49 Deletedinuse: 26
% 128.96/129.49
% 128.96/129.49 Resimplifying clauses:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49 Resimplifying inuse:
% 128.96/129.49 Done
% 128.96/129.49
% 128.96/129.49
% 128.96/129.49 Intermediate Status:
% 128.96/129.49 Generated: 972612
% 128.96/129.50 Kept: 189154
% 128.96/129.50 Inuse: 1820
% 128.96/129.50 Deleted: 3135
% 128.96/129.50 Deletedinuse: 26
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 984795
% 128.96/129.50 Kept: 191229
% 128.96/129.50 Inuse: 1845
% 128.96/129.50 Deleted: 3135
% 128.96/129.50 Deletedinuse: 26
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 998348
% 128.96/129.50 Kept: 193265
% 128.96/129.50 Inuse: 1873
% 128.96/129.50 Deleted: 3135
% 128.96/129.50 Deletedinuse: 26
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1023795
% 128.96/129.50 Kept: 197884
% 128.96/129.50 Inuse: 1895
% 128.96/129.50 Deleted: 3135
% 128.96/129.50 Deletedinuse: 26
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1044860
% 128.96/129.50 Kept: 201859
% 128.96/129.50 Inuse: 1905
% 128.96/129.50 Deleted: 3135
% 128.96/129.50 Deletedinuse: 26
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1060141
% 128.96/129.50 Kept: 204106
% 128.96/129.50 Inuse: 1930
% 128.96/129.50 Deleted: 3136
% 128.96/129.50 Deletedinuse: 27
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1072615
% 128.96/129.50 Kept: 206134
% 128.96/129.50 Inuse: 1952
% 128.96/129.50 Deleted: 3138
% 128.96/129.50 Deletedinuse: 29
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1090502
% 128.96/129.50 Kept: 209345
% 128.96/129.50 Inuse: 1960
% 128.96/129.50 Deleted: 3138
% 128.96/129.50 Deletedinuse: 29
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying clauses:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1106650
% 128.96/129.50 Kept: 213379
% 128.96/129.50 Inuse: 1965
% 128.96/129.50 Deleted: 3434
% 128.96/129.50 Deletedinuse: 29
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1122082
% 128.96/129.50 Kept: 216111
% 128.96/129.50 Inuse: 1970
% 128.96/129.50 Deleted: 3434
% 128.96/129.50 Deletedinuse: 29
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1136674
% 128.96/129.50 Kept: 218319
% 128.96/129.50 Inuse: 2005
% 128.96/129.50 Deleted: 3434
% 128.96/129.50 Deletedinuse: 29
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1158766
% 128.96/129.50 Kept: 222001
% 128.96/129.50 Inuse: 2020
% 128.96/129.50 Deleted: 3434
% 128.96/129.50 Deletedinuse: 29
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1172090
% 128.96/129.50 Kept: 224158
% 128.96/129.50 Inuse: 2040
% 128.96/129.50 Deleted: 3435
% 128.96/129.50 Deletedinuse: 30
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1187970
% 128.96/129.50 Kept: 226546
% 128.96/129.50 Inuse: 2060
% 128.96/129.50 Deleted: 3435
% 128.96/129.50 Deletedinuse: 30
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1203450
% 128.96/129.50 Kept: 229059
% 128.96/129.50 Inuse: 2070
% 128.96/129.50 Deleted: 3435
% 128.96/129.50 Deletedinuse: 30
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying clauses:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1217831
% 128.96/129.50 Kept: 231339
% 128.96/129.50 Inuse: 2090
% 128.96/129.50 Deleted: 3906
% 128.96/129.50 Deletedinuse: 30
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1230042
% 128.96/129.50 Kept: 233513
% 128.96/129.50 Inuse: 2100
% 128.96/129.50 Deleted: 3907
% 128.96/129.50 Deletedinuse: 31
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1240493
% 128.96/129.50 Kept: 235806
% 128.96/129.50 Inuse: 2120
% 128.96/129.50 Deleted: 3907
% 128.96/129.50 Deletedinuse: 31
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1254765
% 128.96/129.50 Kept: 238218
% 128.96/129.50 Inuse: 2150
% 128.96/129.50 Deleted: 3907
% 128.96/129.50 Deletedinuse: 31
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1266010
% 128.96/129.50 Kept: 240219
% 128.96/129.50 Inuse: 2168
% 128.96/129.50 Deleted: 3907
% 128.96/129.50 Deletedinuse: 31
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1274988
% 128.96/129.50 Kept: 242833
% 128.96/129.50 Inuse: 2175
% 128.96/129.50 Deleted: 3908
% 128.96/129.50 Deletedinuse: 32
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1285116
% 128.96/129.50 Kept: 245289
% 128.96/129.50 Inuse: 2190
% 128.96/129.50 Deleted: 3909
% 128.96/129.50 Deletedinuse: 33
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1294681
% 128.96/129.50 Kept: 247299
% 128.96/129.50 Inuse: 2206
% 128.96/129.50 Deleted: 3909
% 128.96/129.50 Deletedinuse: 33
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1318705
% 128.96/129.50 Kept: 250475
% 128.96/129.50 Inuse: 2220
% 128.96/129.50 Deleted: 3909
% 128.96/129.50 Deletedinuse: 33
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying clauses:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1339324
% 128.96/129.50 Kept: 252478
% 128.96/129.50 Inuse: 2229
% 128.96/129.50 Deleted: 3996
% 128.96/129.50 Deletedinuse: 33
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1379012
% 128.96/129.50 Kept: 259188
% 128.96/129.50 Inuse: 2235
% 128.96/129.50 Deleted: 3996
% 128.96/129.50 Deletedinuse: 33
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1390034
% 128.96/129.50 Kept: 261223
% 128.96/129.50 Inuse: 2254
% 128.96/129.50 Deleted: 4011
% 128.96/129.50 Deletedinuse: 48
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1396275
% 128.96/129.50 Kept: 263229
% 128.96/129.50 Inuse: 2262
% 128.96/129.50 Deleted: 4013
% 128.96/129.50 Deletedinuse: 50
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Intermediate Status:
% 128.96/129.50 Generated: 1403289
% 128.96/129.50 Kept: 265384
% 128.96/129.50 Inuse: 2270
% 128.96/129.50 Deleted: 4013
% 128.96/129.50 Deletedinuse: 50
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50 Resimplifying inuse:
% 128.96/129.50 Done
% 128.96/129.50
% 128.96/129.50
% 128.96/129.50 Bliksems!, er is een bewijs:
% 128.96/129.50 % SZS status Unsatisfiable
% 128.96/129.50 % SZS output start Refutation
% 128.96/129.50
% 128.96/129.50 clause( 316, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 128.96/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 128.96/129.50 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 346, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 409, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( 'c_in'( X, Y,
% 129.08/129.50 Z ) ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 557, [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( hAPP( Y, X ) ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 559, [ 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ),
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 129.08/129.50 , U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.08/129.50 Z ), 'tc_Com_Ocom' ), T, U ), U ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 562, [ hBOOL( 'c_in'( 'v_x', 'v_Procs', 'tc_Com_Opname' ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 563, [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc',
% 129.08/129.50 'v_na' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', 'v_x' ),
% 129.08/129.50 'c_Com_Ocom_OBODY'( 'v_x' ), hAPP( 'v_Q', 'v_x' ), 't_a' ), 't_a' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 .
% 129.08/129.50 clause( 566, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ), 'c_Option_Othe'(
% 129.08/129.50 'c_Com_Obody'( X ), 'tc_Com_Ocom' ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ),
% 129.08/129.50 ~( hBOOL( 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 627, [ ~( =( X, Y ) ), ~( =( 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X
% 129.08/129.50 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ),
% 129.08/129.50 'c_Set_Oinsert'( U, 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ) ), =( Y, Z ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 628, [ ~( =( X, Y ) ), =( Y, X ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 164826, [ =( 'c_Set_Oinsert'( 'v_x', 'v_Procs', 'tc_Com_Opname' ),
% 129.08/129.50 'v_Procs' ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 164968, [ hBOOL( hAPP( 'v_Procs', 'v_x' ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 165136, [ hBOOL( hAPP( X, 'v_x' ) ), ~( =( X, 'v_Procs' ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 259843, [ hBOOL( 'c_in'( 'v_x', X, Y ) ), ~( =( X, 'v_Procs' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 .
% 129.08/129.50 clause( 263401, [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', 'v_x' ),
% 129.08/129.50 'c_Option_Othe'( 'c_Com_Obody'( 'v_x' ), 'tc_Com_Ocom' ), hAPP( 'v_Q',
% 129.08/129.50 'v_x' ), 't_a' ), 't_a' ) ) ] )
% 129.08/129.50 .
% 129.08/129.50 clause( 267192, [] )
% 129.08/129.50 .
% 129.08/129.50
% 129.08/129.50
% 129.08/129.50 % SZS output end Refutation
% 129.08/129.50 found a proof!
% 129.08/129.50
% 129.08/129.50 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 129.08/129.50
% 129.08/129.50 initialclauses(
% 129.08/129.50 [ clause( 267194, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267195, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267196, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z
% 129.08/129.50 , X ), T, X ), 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 129.08/129.50 , T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267197, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267198, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267199, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267200, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267201, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267202, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 129.08/129.50 , clause( 267203, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 129.08/129.50 , clause( 267204, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OLocal'(
% 129.08/129.50 Z, T, U ) ) ) ] )
% 129.08/129.50 , clause( 267205, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, Z )
% 129.08/129.50 , hBOOL( hAPP( X, Z ) ) ] )
% 129.08/129.50 , clause( 267206, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267207, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267208, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267209, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267210, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 129.08/129.50 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267211, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 129.08/129.50 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267212, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 129.08/129.50 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267213, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 129.08/129.50 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267214, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 129.08/129.50 , clause( 267215, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 129.08/129.50 , clause( 267216, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 129.08/129.50 , clause( 267217, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 129.08/129.50 , T ) ) ), =( Y, T ) ] )
% 129.08/129.50 , clause( 267218, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 129.08/129.50 , T ) ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267219, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'(
% 129.08/129.50 Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267220, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 129.08/129.50 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267221, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267222, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z
% 129.08/129.50 , T, U ) ) ) ] )
% 129.08/129.50 , clause( 267223, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ] )
% 129.08/129.50 , clause( 267224, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OLocal'(
% 129.08/129.50 Z, T, U ) ) ) ] )
% 129.08/129.50 , clause( 267225, [ 'c_Fun_Oinj__on'( 'c_COMBI'( X ), Y, X, X ) ] )
% 129.08/129.50 , clause( 267226, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 129.08/129.50 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 129.08/129.50 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267227, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267228, [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 129.08/129.50 , clause( 267229, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( hAPP( T, V2 ), V3 )
% 129.08/129.50 , 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V2, V4 ) ),
% 129.08/129.50 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ] )
% 129.08/129.50 , clause( 267230, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 129.08/129.50 T, U, W ) ) ), =( X, T ) ] )
% 129.08/129.50 , clause( 267231, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 129.08/129.50 T, U, W ) ) ), =( Y, U ) ] )
% 129.08/129.50 , clause( 267232, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 129.08/129.50 T, U, W ) ) ), =( Z, W ) ] )
% 129.08/129.50 , clause( 267233, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 129.08/129.50 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 129.08/129.50 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267234, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267235, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 129.08/129.50 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267236, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( Z, V2 )
% 129.08/129.50 , V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 )
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267237, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSemi'( Z
% 129.08/129.50 , T ) ) ) ] )
% 129.08/129.50 , clause( 267238, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OSKIP', V2 ), X ) ] )
% 129.08/129.50 , clause( 267239, [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ) ) ) ), hBOOL( hAPP( X, Y
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267240, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267241, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267242, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267243, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 129.08/129.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 129.08/129.50 , clause( 267244, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 129.08/129.50 , clause( 267245, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OCond'( T, U, W ) ) ) ] )
% 129.08/129.50 , clause( 267246, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267247, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 129.08/129.50 T, U, W ) ) ) ] )
% 129.08/129.50 , clause( 267248, [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X
% 129.08/129.50 , 'c_Set_Oinsert'( U, Y, Z ), Z, T ) ) ] )
% 129.08/129.50 , clause( 267249, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T,
% 129.08/129.50 Z ), hBOOL( hAPP( X, Z ) ) ] )
% 129.08/129.50 , clause( 267250, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z
% 129.08/129.50 , X ) ), Z ), Y ) ] )
% 129.08/129.50 , clause( 267251, [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) )
% 129.08/129.50 ), hBOOL( hAPP( X, Z ) ) ] )
% 129.08/129.50 , clause( 267252, [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) )
% 129.08/129.50 ), hBOOL( hAPP( X, Z ) ) ] )
% 129.08/129.50 , clause( 267253, [ =( X, Y ), ~( hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267254, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 129.08/129.50 , Z ), T ), 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267255, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 129.08/129.50 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 129.08/129.50 Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 129.08/129.50 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267256, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( 'c_Suc', Z ), X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 129.08/129.50 ) ), Y ) ) ] )
% 129.08/129.50 , clause( 267257, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( 'c_Suc', Z ), X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Power_Opower_Opower'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267258, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 129.08/129.50 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267259, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267260, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267261, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267262, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267263, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267264, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 129.08/129.50 ) ), 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, T, X ) ) ) ] )
% 129.08/129.50 , clause( 267265, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, Y, 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267266, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, T, X ) ), 'c_Power_Opower_Opower'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267267, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267268, [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267269, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 129.08/129.50 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ] )
% 129.08/129.50 , clause( 267270, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 129.08/129.50 , clause( 267271, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 129.08/129.50 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267272, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 129.08/129.50 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 129.08/129.50 , clause( 267273, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSemi'(
% 129.08/129.50 T, U ) ) ) ] )
% 129.08/129.50 , clause( 267274, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 129.08/129.50 X ) ) ] )
% 129.08/129.50 , clause( 267275, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267276, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 129.08/129.50 X ) ) ] )
% 129.08/129.50 , clause( 267277, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), Z ) ), T ) ) ] )
% 129.08/129.50 , clause( 267278, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 129.08/129.50 , clause( 267279, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 129.08/129.50 , clause( 267280, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 129.08/129.50 , clause( 267281, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 129.08/129.50 , clause( 267282, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 129.08/129.50 , clause( 267283, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 129.08/129.50 , clause( 267284, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), Z ) ), T ) ) ] )
% 129.08/129.50 , clause( 267285, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), T ) ), Z ) ) ] )
% 129.08/129.50 , clause( 267286, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 129.08/129.50 , clause( 267287, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 129.08/129.50 , clause( 267288, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267289, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267290, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267291, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 129.08/129.50 , clause( 267292, [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ] )
% 129.08/129.50 , clause( 267293, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267294, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267295, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267296, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267297, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267298, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267299, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 129.08/129.50 , V4 ) ) ] )
% 129.08/129.50 , clause( 267300, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U
% 129.08/129.50 , W ), ~( 'c_Natural_Oevaln'( Y, T, U, W ) ), ~( hBOOL( hAPP( X, T ) ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267301, [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevaln'( Z, Y, T
% 129.08/129.50 , U ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Z, W ), Y, T, U ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267302, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 129.08/129.50 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 129.08/129.50 , clause( 267303, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 129.08/129.50 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 129.08/129.50 , clause( 267304, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T )
% 129.08/129.50 , 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ] )
% 129.08/129.50 , clause( 267305, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 129.08/129.50 X ) ) ] )
% 129.08/129.50 , clause( 267306, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267307, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 129.08/129.50 X ) ) ] )
% 129.08/129.50 , clause( 267308, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z
% 129.08/129.50 , X ), T, X ), 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 129.08/129.50 , T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267309, [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z )
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267310, [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267311, [ =( hAPP( 'c_COMBI'( X ), Y ), Y ) ] )
% 129.08/129.50 , clause( 267312, [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ] )
% 129.08/129.50 , clause( 267313, [ =( 'c_COMBS'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ),
% 129.08/129.50 hAPP( Y, Z ) ) ) ] )
% 129.08/129.50 , clause( 267314, [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 129.08/129.50 X, Y, 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267315, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ] )
% 129.08/129.50 , clause( 267316, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 129.08/129.50 , clause( 267317, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267318, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 129.08/129.50 , clause( 267319, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267320, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 129.08/129.50 , clause( 267321, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267322, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 129.08/129.50 , clause( 267323, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267324, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 129.08/129.50 ), Z ), T, X ) ) ] )
% 129.08/129.50 , clause( 267325, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 129.08/129.50 , X ) ), T, X ) ) ] )
% 129.08/129.50 , clause( 267326, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 129.08/129.50 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267327, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 129.08/129.50 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 129.08/129.50 Y, Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267328, [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267329, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267330, [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267331, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267332, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z )
% 129.08/129.50 , 'c_Set_Oinsert'( X, Y, Z ) ) ] )
% 129.08/129.50 , clause( 267333, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267334, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267335, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267336, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267337, [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267338, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OAss'(
% 129.08/129.50 T, U ) ) ) ] )
% 129.08/129.50 , clause( 267339, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 129.08/129.50 'c_Set_Oinsert'( Z, X, T ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267340, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OWhile'( T, U ) ) ) ] )
% 129.08/129.50 , clause( 267341, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y
% 129.08/129.50 , 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat'
% 129.08/129.50 ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267342, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OLocal'( T, U, W ) ) ) ] )
% 129.08/129.50 , clause( 267343, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267344, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267345, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 129.08/129.50 , clause( 267346, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 129.08/129.50 , clause( 267347, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267348, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T
% 129.08/129.50 ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, T, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267349, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 129.08/129.50 , clause( 267350, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 129.08/129.50 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267351, [ =( hAPP( 'c_Fun_Ocomp'( 'c_COMBK'( X, Y, Z ), T, Z, Y,
% 129.08/129.50 't_a' ), 'v_x' ), X ) ] )
% 129.08/129.50 , clause( 267352, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 129.08/129.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267353, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'(
% 129.08/129.50 T, U ) ) ) ] )
% 129.08/129.50 , clause( 267354, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 129.08/129.50 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267355, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267356, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267357, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 129.08/129.50 T, U, W ) ) ), =( Z, W ) ] )
% 129.08/129.50 , clause( 267358, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 129.08/129.50 T, U, W ) ) ), =( Y, U ) ] )
% 129.08/129.50 , clause( 267359, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 129.08/129.50 T, U, W ) ) ), =( X, T ) ] )
% 129.08/129.50 , clause( 267360, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267361, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267362, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267363, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267364, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 129.08/129.50 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 129.08/129.50 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267365, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267366, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 129.08/129.50 , clause( 267367, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 129.08/129.50 , clause( 267368, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 Y, Z ), U ) ), hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y,
% 129.08/129.50 V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267369, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X
% 129.08/129.50 ), X ) ) ] )
% 129.08/129.50 , clause( 267370, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X
% 129.08/129.50 ), X ) ) ] )
% 129.08/129.50 , clause( 267371, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267372, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267373, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267374, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267375, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X
% 129.08/129.50 ), X ) ) ] )
% 129.08/129.50 , clause( 267376, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X
% 129.08/129.50 ), X ) ) ] )
% 129.08/129.50 , clause( 267377, [ =( 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267378, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267379, [ ~( =( 'c_Option_Ooption_OSome'( X, Y ),
% 129.08/129.50 'c_Option_Ooption_ONone'( Y ) ) ) ] )
% 129.08/129.50 , clause( 267380, [ ~( =( 'c_Option_Ooption_OSome'( X, Y ),
% 129.08/129.50 'c_Option_Ooption_ONone'( Y ) ) ) ] )
% 129.08/129.50 , clause( 267381, [ =( 'c_Nat_Onat_Onat__case'( X, Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z ), X ) ] )
% 129.08/129.50 , clause( 267382, [ =( 'c_Nat_Onat_Onat__case'( X, Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z ), X ) ] )
% 129.08/129.50 , clause( 267383, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 129.08/129.50 T, U, W ) ) ) ] )
% 129.08/129.50 , clause( 267384, [ ~( =( 'c_Option_Ooption_OSome'( X, Y ),
% 129.08/129.50 'c_Option_Ooption_OSome'( Z, Y ) ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267385, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X,
% 129.08/129.50 hAPP( Y, W ) ) ) ] )
% 129.08/129.50 , clause( 267386, [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y,
% 129.08/129.50 T, U, W ), Z ) ) ] )
% 129.08/129.50 , clause( 267387, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267388, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267389, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267390, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267391, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267392, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OWhile'( Z
% 129.08/129.50 , T ) ) ) ] )
% 129.08/129.50 , clause( 267393, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267394, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267395, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OLocal'( Z
% 129.08/129.50 , T, U ) ) ) ] )
% 129.08/129.50 , clause( 267396, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 129.08/129.50 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267397, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267398, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 129.08/129.50 ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267399, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 129.08/129.50 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267400, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267401, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267402, [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 129.08/129.50 ) ) ), =( Y, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 129.08/129.50 =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267403, [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 129.08/129.50 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267404, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ),
% 129.08/129.50 Z, X ) ) ] )
% 129.08/129.50 , clause( 267405, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ),
% 129.08/129.50 Z, X ) ) ] )
% 129.08/129.50 , clause( 267406, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267407, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 Z, X ) ) ] )
% 129.08/129.50 , clause( 267408, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267409, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 Z, X ) ) ] )
% 129.08/129.50 , clause( 267410, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ),
% 129.08/129.50 Z, X ) ) ] )
% 129.08/129.50 , clause( 267411, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ),
% 129.08/129.50 Z, X ) ) ] )
% 129.08/129.50 , clause( 267412, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267413, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267414, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 129.08/129.50 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 129.08/129.50 , X ), X ) ) ] )
% 129.08/129.50 , clause( 267415, [ 'c_Com_OWT'( 'c_Com_Ocom_OCond'( X, Y, Z ) ), ~(
% 129.08/129.50 'c_Com_OWT'( Z ) ), ~( 'c_Com_OWT'( Y ) ) ] )
% 129.08/129.50 , clause( 267416, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OSKIP', V2 ), X ) ] )
% 129.08/129.50 , clause( 267417, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OWhile'( T, U ) ) ) ] )
% 129.08/129.50 , clause( 267418, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 129.08/129.50 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 129.08/129.50 ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267419, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267420, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z
% 129.08/129.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 129.08/129.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267421, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 129.08/129.50 , Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267422, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 129.08/129.50 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267423, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCond'( Z
% 129.08/129.50 , T, U ) ) ) ] )
% 129.08/129.50 , clause( 267424, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OSemi'( Z, T ), U, W
% 129.08/129.50 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( W ), 'tc_bool' ) ),
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( W ) ), W ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, U, W ),
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 W ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( W ) ), W ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, V0, W ),
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 W ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( W ) ), W ) ) ] )
% 129.08/129.50 , clause( 267425, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 Y ), 'tc_bool' ) ), Y ) ] )
% 129.08/129.50 , clause( 267426, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267427, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267428, [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 129.08/129.50 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 129.08/129.50 , clause( 267429, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 129.08/129.50 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267430, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267431, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267432, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 129.08/129.50 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267433, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267434, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267435, [ =( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267436, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T,
% 129.08/129.50 U ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), W, T, U ) ), ~(
% 129.08/129.50 'c_Natural_Oevaln'( Y, Z, T, W ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 129.08/129.50 , clause( 267437, [ ~( =( 'c_Option_Ooption_ONone'( X ),
% 129.08/129.50 'c_Option_Ooption_OSome'( Y, X ) ) ) ] )
% 129.08/129.50 , clause( 267438, [ ~( =( 'c_Option_Ooption_ONone'( X ),
% 129.08/129.50 'c_Option_Ooption_OSome'( Y, X ) ) ) ] )
% 129.08/129.50 , clause( 267439, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T )
% 129.08/129.50 , ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), U, T ) ), ~(
% 129.08/129.50 'c_Natural_Oevalc'( Y, Z, U ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 129.08/129.50 , clause( 267440, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.08/129.50 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ] )
% 129.08/129.50 , clause( 267441, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 129.08/129.50 , T, X ) ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267442, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 129.08/129.50 , T, X ) ) ), =( Z, T ) ] )
% 129.08/129.50 , clause( 267443, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 129.08/129.50 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267444, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U
% 129.08/129.50 ), ~( 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T
% 129.08/129.50 , W ) ) ] )
% 129.08/129.50 , clause( 267445, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 129.08/129.50 X ), X ), Y ) ] )
% 129.08/129.50 , clause( 267446, [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 129.08/129.50 ) ) ), =( Y, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 129.08/129.50 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267447, [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 129.08/129.50 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP(
% 129.08/129.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267448, [ 'c_Com_OWT'( 'c_Com_Ocom_OSKIP' ) ] )
% 129.08/129.50 , clause( 267449, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U
% 129.08/129.50 ), ~( 'c_Natural_Oevalc'( Y, T, U ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 129.08/129.50 , clause( 267450, [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevalc'( Z, Y, T
% 129.08/129.50 ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Z, U ), Y, T ) ) ] )
% 129.08/129.50 , clause( 267451, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T )
% 129.08/129.50 , ~( 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267452, [ 'c_Com_OWT'( 'c_Com_Ocom_OAss'( X, Y ) ) ] )
% 129.08/129.50 , clause( 267453, [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ) ] )
% 129.08/129.50 , clause( 267454, [ =( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267455, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267456, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267457, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267458, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), hAPP( 'c_Suc', X ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267459, [ 'c_Com_OWT'( 'c_Com_Ocom_OCall'( X, Y, Z ) ), ~(
% 129.08/129.50 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( Y ) ) ) ] )
% 129.08/129.50 , clause( 267460, [ 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( X ) ), ~( 'c_Com_OWT'(
% 129.08/129.50 'c_Com_Ocom_OCall'( Y, X, Z ) ) ) ] )
% 129.08/129.50 , clause( 267461, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267462, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267463, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267464, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267465, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267466, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267467, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 Z, Y, X ) ) ] )
% 129.08/129.50 , clause( 267468, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z )
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267469, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCall'( Z
% 129.08/129.50 , T, U ) ) ) ] )
% 129.08/129.50 , clause( 267470, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267471, [ ~( =( 'c_Set_Oinsert'( X,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ),
% 129.08/129.50 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 129.08/129.50 'tc_bool' ) ), Y ) ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267472, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267473, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 129.08/129.50 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 129.08/129.50 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267474, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267475, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267476, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267477, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 129.08/129.50 , clause( 267478, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267479, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 129.08/129.50 , clause( 267480, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267481, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 129.08/129.50 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 129.08/129.50 , clause( 267482, [ =( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 129.08/129.50 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267483, [ =( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 129.08/129.50 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267484, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL(
% 129.08/129.50 'c_in'( X, Y, Z ) ) ] )
% 129.08/129.50 , clause( 267485, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 129.08/129.50 , X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267486, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( Z ), 'tc_bool' ) ),
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y, T,
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ] )
% 129.08/129.50 , clause( 267487, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 129.08/129.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 129.08/129.50 , clause( 267488, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 129.08/129.50 , clause( 267489, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 hAPP( Y, Z ), hAPP( Y, hAPP( 'c_Suc', Z ) ), X ), ~(
% 129.08/129.50 'c_Orderings_Oorder__class_Omono'( Y, 'tc_nat', X ) ) ] )
% 129.08/129.50 , clause( 267490, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 129.08/129.50 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267491, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OLocal'( T, U, W ) ) ) ] )
% 129.08/129.50 , clause( 267492, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OWhile'( T, U ) ) ) ] )
% 129.08/129.50 , clause( 267493, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~(
% 129.08/129.50 hBOOL( hAPP( Y, T ) ) ) ] )
% 129.08/129.50 , clause( 267494, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z
% 129.08/129.50 ) ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267495, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y
% 129.08/129.50 ) ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267496, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z
% 129.08/129.50 ) ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267497, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 129.08/129.50 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 129.08/129.50 , clause( 267498, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X
% 129.08/129.50 ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 129.08/129.50 , clause( 267499, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 129.08/129.50 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 129.08/129.50 , clause( 267500, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) )
% 129.08/129.50 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 129.08/129.50 , clause( 267501, [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 129.08/129.50 'tc_nat' ), X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267502, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ),
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 129.08/129.50 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267503, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ),
% 129.08/129.50 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267504, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 129.08/129.50 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 129.08/129.50 , T, X ), X ), T, X ) ) ] )
% 129.08/129.50 , clause( 267505, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP(
% 129.08/129.50 hAPP( Y, hAPP( hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267506, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP(
% 129.08/129.50 hAPP( Z, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267507, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ),
% 129.08/129.50 ~( 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267508, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 129.08/129.50 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267509, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, Y, V0 ) ) ] )
% 129.08/129.50 , clause( 267510, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( T, X, U, Y, W, V0 ) ) ] )
% 129.08/129.50 , clause( 267511, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ),
% 129.08/129.50 ~( 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267512, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 129.08/129.50 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267513, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, T, U, Y, W, V0 ) ) ] )
% 129.08/129.50 , clause( 267514, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 129.08/129.50 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267515, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ),
% 129.08/129.50 ~( 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267516, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 129.08/129.50 hAPP( X, hAPP( hAPP( X, Y ), T ) ), Z ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267517, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 129.08/129.50 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267518, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 129.08/129.50 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, U, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267519, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP(
% 129.08/129.50 X, T ), U ) ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z
% 129.08/129.50 ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267520, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 129.08/129.50 hAPP( X, Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267521, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP(
% 129.08/129.50 hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267522, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 129.08/129.50 hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267523, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP(
% 129.08/129.50 hAPP( X, hAPP( hAPP( X, Y ), T ) ), Z ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267524, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP(
% 129.08/129.50 X, T ), U ) ), hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z )
% 129.08/129.50 ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267525, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP(
% 129.08/129.50 X, T ), U ) ), hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T )
% 129.08/129.50 , U ) ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267526, [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP(
% 129.08/129.50 X, T ), U ) ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z
% 129.08/129.50 ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267527, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( X, 'tc_bool' ) ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267528, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267529, [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267530, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OLocal'( X, Y, Z
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267531, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 129.08/129.50 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267532, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 129.08/129.50 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 129.08/129.50 , clause( 267533, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267534, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X )
% 129.08/129.50 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267535, [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 129.08/129.50 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267536, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267537, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267538, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267539, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 129.08/129.50 , clause( 267540, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 129.08/129.50 , clause( 267541, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 129.08/129.50 , clause( 267542, [ ~( 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ), =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ] )
% 129.08/129.50 , clause( 267543, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 129.08/129.50 , clause( 267544, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267545, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 129.08/129.50 , clause( 267546, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267547, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267548, [ 'c_lessequals'( X, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267549, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ),
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267550, [ 'c_Natural_Oevaln'( X, Y, Z, T ), hBOOL( hAPP( U, Y ) )
% 129.08/129.50 , ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( U, W, X ), Y, Z, T ) ) ] )
% 129.08/129.50 , clause( 267551, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U
% 129.08/129.50 , W ), ~( 'c_Natural_Oevaln'( Z, T, U, W ) ), hBOOL( hAPP( X, T ) ) ] )
% 129.08/129.50 , clause( 267552, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCall'(
% 129.08/129.50 Z, T, U ) ) ) ] )
% 129.08/129.50 , clause( 267553, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ] )
% 129.08/129.50 , clause( 267554, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OAss'( Z
% 129.08/129.50 , T ) ) ) ] )
% 129.08/129.50 , clause( 267555, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 129.08/129.50 ), =( Z, Y ) ] )
% 129.08/129.50 , clause( 267556, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267557, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267558, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 129.08/129.50 , clause( 267559, [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~(
% 129.08/129.50 'c_Natural_Oevalc'( Z, T, Y ) ) ] )
% 129.08/129.50 , clause( 267560, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), =( Z, Y ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267561, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 129.08/129.50 , clause( 267562, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 129.08/129.50 , clause( 267563, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 129.08/129.50 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267564, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 129.08/129.50 ), =( Z, Y ) ] )
% 129.08/129.50 , clause( 267565, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 129.08/129.50 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267566, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 129.08/129.50 , clause( 267567, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 129.08/129.50 , clause( 267568, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267569, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 129.08/129.50 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 129.08/129.50 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 129.08/129.50 X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267570, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267571, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267572, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OSKIP' ) ) ] )
% 129.08/129.50 , clause( 267573, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 129.08/129.50 , clause( 267574, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 129.08/129.50 T, X ) ) ] )
% 129.08/129.50 , clause( 267575, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267576, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267577, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267578, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 129.08/129.50 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267579, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267580, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ] )
% 129.08/129.50 , clause( 267581, [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Z ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 129.08/129.50 Z, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267582, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267583, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267584, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.08/129.50 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ] )
% 129.08/129.50 , clause( 267585, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.08/129.50 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ] )
% 129.08/129.50 , clause( 267586, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.08/129.50 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 129.08/129.50 , clause( 267587, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.08/129.50 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ] )
% 129.08/129.50 , clause( 267588, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 129.08/129.50 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267589, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 129.08/129.50 , clause( 267590, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 129.08/129.50 'c_lessequals'( Z, T, X ) ) ] )
% 129.08/129.50 , clause( 267591, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 129.08/129.50 , clause( 267592, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 129.08/129.50 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 129.08/129.50 Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 129.08/129.50 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267593, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 129.08/129.50 X ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 129.08/129.50 Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 129.08/129.50 'c_lessequals'( Z, T, X ) ) ] )
% 129.08/129.50 , clause( 267594, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 129.08/129.50 , Z ), Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267595, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267596, [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 129.08/129.50 , X ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267597, [ 'c_Natural_Oevalc'( X, Y, Z ), hBOOL( hAPP( T, Y ) ),
% 129.08/129.50 ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( T, U, X ), Y, Z ) ) ] )
% 129.08/129.50 , clause( 267598, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U
% 129.08/129.50 ), ~( 'c_Natural_Oevalc'( Z, T, U ) ), hBOOL( hAPP( X, T ) ) ] )
% 129.08/129.50 , clause( 267599, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 129.08/129.50 X, 'tc_nat' ) ), X ) ) ] )
% 129.08/129.50 , clause( 267600, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~(
% 129.08/129.50 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267601, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 129.08/129.50 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267602, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OAss'( X, Y ) ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267603, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( Y
% 129.08/129.50 , X ) ) ) ] )
% 129.08/129.50 , clause( 267604, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X
% 129.08/129.50 , Y ) ) ) ] )
% 129.08/129.50 , clause( 267605, [ =( 'c_Nat_Onat_Onat__rec'( X, Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z ), X ) ] )
% 129.08/129.50 , clause( 267606, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OAss'( Z
% 129.08/129.50 , T ) ) ) ] )
% 129.08/129.50 , clause( 267607, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267608, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267609, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 129.08/129.50 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ] )
% 129.08/129.50 , clause( 267610, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( Z, V2 ), V3 )
% 129.08/129.50 , V4 ) ) ] )
% 129.08/129.50 , clause( 267611, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( W, V2 ), V3 ) ) ] )
% 129.08/129.50 , clause( 267612, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, T, Z ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( T, Y, Z ) ) ] )
% 129.08/129.50 , clause( 267613, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y
% 129.08/129.50 , hAPP( X, W ) ) ) ] )
% 129.08/129.50 , clause( 267614, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267615, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U
% 129.08/129.50 , V0, W ), 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267616, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z,
% 129.08/129.50 T ) ) ), =( Y, T ) ] )
% 129.08/129.50 , clause( 267617, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z,
% 129.08/129.50 T ) ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267618, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OAss'(
% 129.08/129.50 T, U ) ) ) ] )
% 129.08/129.50 , clause( 267619, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267620, [ ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267621, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OSKIP', Y, Z ),
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 Z ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ] )
% 129.08/129.50 , clause( 267622, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267623, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 129.08/129.50 , clause( 267624, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 129.08/129.50 ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 129.08/129.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X ) ) ) ] )
% 129.08/129.50 , clause( 267625, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 129.08/129.50 , clause( 267626, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 129.08/129.50 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267627, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, Z, V0 ) ) ] )
% 129.08/129.50 , clause( 267628, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, Y, V0 ) ) ] )
% 129.08/129.50 , clause( 267629, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( T, X, U, Z, W, V0 ) ) ] )
% 129.08/129.50 , clause( 267630, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( T, X, U, Y, W, V0 ) ) ] )
% 129.08/129.50 , clause( 267631, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP(
% 129.08/129.50 hAPP( Y, hAPP( hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267632, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ),
% 129.08/129.50 ~( 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267633, [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, T, U, Z, W, V0 ) ) ] )
% 129.08/129.50 , clause( 267634, [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, T, U, Y, W, V0 ) ) ] )
% 129.08/129.50 , clause( 267635, [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 129.08/129.50 X, T ), T ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T
% 129.08/129.50 , V0 ) ) ] )
% 129.08/129.50 , clause( 267636, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP(
% 129.08/129.50 hAPP( Z, hAPP( hAPP( X, T ), U ) ), Y ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, Z, W, V0, U, V1 ) ) ] )
% 129.08/129.50 , clause( 267637, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP(
% 129.08/129.50 hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, U, V1 ) ) ] )
% 129.08/129.50 , clause( 267638, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP(
% 129.08/129.50 Y, U ), T ) ), hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ] )
% 129.08/129.50 , clause( 267639, [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y
% 129.08/129.50 , 'tc_nat' ) ), Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X
% 129.08/129.50 ), Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267640, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'(
% 129.08/129.50 'c_Fun_Oid'( T ), W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W
% 129.08/129.50 , V0 ) ) ] )
% 129.08/129.50 , clause( 267641, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 129.08/129.50 , =( Y, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267642, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 129.08/129.50 , =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267643, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( T, V2 ), V3 ) ) ] )
% 129.08/129.50 , clause( 267644, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OSemi'( T, U ) ) ) ] )
% 129.08/129.50 , clause( 267645, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267646, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'class_Orderings_Olinorder'( Y ) ), =( 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 hAPP( Z, T ), hAPP( Z, U ), Y ), hAPP( Z, 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 T, U, X ) ) ), ~( 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ] )
% 129.08/129.50 , clause( 267647, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'(
% 129.08/129.50 Z, T ) ) ), =( X, Z ) ] )
% 129.08/129.50 , clause( 267648, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'(
% 129.08/129.50 Z, T ) ) ), =( Y, T ) ] )
% 129.08/129.50 , clause( 267649, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 Z, Y, X ) ) ] )
% 129.08/129.50 , clause( 267650, [ 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( X, Y ) ), ~(
% 129.08/129.50 'c_Com_OWT'( Y ) ) ] )
% 129.08/129.50 , clause( 267651, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OWhile'(
% 129.08/129.50 Y, X ) ) ) ] )
% 129.08/129.50 , clause( 267652, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 129.08/129.50 , V4 ) ) ] )
% 129.08/129.50 , clause( 267653, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 129.08/129.50 'class_Orderings_Oorder'( Y ) ), 'c_lessequals'( hAPP( Z, T ), hAPP( Z, U
% 129.08/129.50 ), Y ), ~( 'c_lessequals'( T, U, X ) ), ~(
% 129.08/129.50 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ] )
% 129.08/129.50 , clause( 267654, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 129.08/129.50 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 129.08/129.50 X ), X ), X ) ] )
% 129.08/129.50 , clause( 267655, [ 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( X, Y, Z ) ), ~(
% 129.08/129.50 'c_Com_OWT'( Z ) ) ] )
% 129.08/129.50 , clause( 267656, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OLocal'(
% 129.08/129.50 Y, Z, X ) ) ) ] )
% 129.08/129.50 , clause( 267657, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267658, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 129.08/129.50 , clause( 267659, [ =( 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 129.08/129.50 , clause( 267660, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 129.08/129.50 X ), X ), Y ) ] )
% 129.08/129.50 , clause( 267661, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'(
% 129.08/129.50 Z, T, U ) ) ) ] )
% 129.08/129.50 , clause( 267662, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 129.08/129.50 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267663, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCall'( Z
% 129.08/129.50 , T, U ) ) ) ] )
% 129.08/129.50 , clause( 267664, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ] )
% 129.08/129.50 , clause( 267665, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OAss'(
% 129.08/129.50 T, U ) ) ) ] )
% 129.08/129.50 , clause( 267666, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 129.08/129.50 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267667, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 129.08/129.50 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267668, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267669, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( W, V2 ), V3 ),
% 129.08/129.50 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ] )
% 129.08/129.50 , clause( 267670, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 129.08/129.50 , clause( 267671, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 X ) ), Y ), Y ) ] )
% 129.08/129.50 , clause( 267672, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267673, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 129.08/129.50 , clause( 267674, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 129.08/129.50 , clause( 267675, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 129.08/129.50 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267676, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 129.08/129.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 129.08/129.50 , clause( 267677, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 129.08/129.50 , Y ), Y ) ] )
% 129.08/129.50 , clause( 267678, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 129.08/129.50 ) ), Y ) ] )
% 129.08/129.50 , clause( 267679, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 129.08/129.50 , clause( 267680, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 129.08/129.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y ) ] )
% 129.08/129.50 , clause( 267681, [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y
% 129.08/129.50 , Z, X ) ) ] )
% 129.08/129.50 , clause( 267682, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267683, [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z,
% 129.08/129.50 V0 ) ) ] )
% 129.08/129.50 , clause( 267684, [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ] )
% 129.08/129.50 , clause( 267685, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ] )
% 129.08/129.50 , clause( 267686, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ] )
% 129.08/129.50 , clause( 267687, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), Z, X ), Y ) ] )
% 129.08/129.50 , clause( 267688, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( hAPP( U,
% 129.08/129.50 V2 ), V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3,
% 129.08/129.50 V5 ) ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 ) ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267689, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'class_Orderings_Olinorder'( Y ) ), =( 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 hAPP( Z, T ), hAPP( Z, U ), Y ), hAPP( Z, 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 T, U, X ) ) ), ~( 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ] )
% 129.08/129.50 , clause( 267690, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267691, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 129.08/129.50 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267692, [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267693, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 129.08/129.50 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267694, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 129.08/129.50 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267695, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 129.08/129.50 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 129.08/129.50 , clause( 267696, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 129.08/129.50 , clause( 267697, [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X
% 129.08/129.50 , Y, T, Z ) ) ] )
% 129.08/129.50 , clause( 267698, [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X
% 129.08/129.50 , Y, T, Z ) ) ] )
% 129.08/129.50 , clause( 267699, [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ), 't_a' ),
% 129.08/129.50 'c_Natural_Oevaln'( Z, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2'(
% 129.08/129.50 Y, T, Z, X ), X, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3'( Y, T
% 129.08/129.50 , Z, X ) ) ] )
% 129.08/129.50 , clause( 267700, [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ) ),
% 129.08/129.50 ~( hBOOL( 'c_in'( X, Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267701, [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ) ),
% 129.08/129.50 ~( hBOOL( 'c_in'( X, Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267702, [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267703, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_in'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ] )
% 129.08/129.50 , clause( 267704, [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267705, [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'(
% 129.08/129.50 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267706, [ hBOOL( 'c_in'( X, Y, Z ) ), =( X, T ), ~( hBOOL( 'c_in'(
% 129.08/129.50 X, 'c_Set_Oinsert'( T, Y, Z ), Z ) ) ) ] )
% 129.08/129.50 , clause( 267707, [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267708, [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267709, [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267710, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'(
% 129.08/129.50 Z, T, U ) ) ), ~( hBOOL( 'c_in'( Y, T, U ) ) ), =( Y, Z ), ~(
% 129.08/129.50 'c_Fun_Oinj__on'( X, T, U, W ) ) ] )
% 129.08/129.50 , clause( 267711, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'(
% 129.08/129.50 Z, T, U ) ) ), ~( hBOOL( 'c_in'( Y, T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, T
% 129.08/129.50 , U, W ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267712, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'(
% 129.08/129.50 Z, T, U ) ) ), ~( hBOOL( 'c_in'( Y, T, U ) ) ), ~( 'c_Fun_Oinj__on'( X, T
% 129.08/129.50 , U, W ) ), =( Y, Z ) ] )
% 129.08/129.50 , clause( 267713, [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~(
% 129.08/129.50 'c_Fun_Oinj__on'( X, T, U, W ) ), =( Y, Z ), ~( hBOOL( 'c_in'( Z, T, U )
% 129.08/129.50 ) ), ~( hBOOL( 'c_in'( Y, T, U ) ) ) ] )
% 129.08/129.50 , clause( 267714, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( 'c_in'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ] )
% 129.08/129.50 , clause( 267715, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T
% 129.08/129.50 , Z ) ) ), hBOOL( 'c_in'( X, T, Z ) ), hBOOL( 'c_in'( X, Y, Z ) ), =( Y,
% 129.08/129.50 T ) ] )
% 129.08/129.50 , clause( 267716, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( 'c_in'( X
% 129.08/129.50 , Y, Z ) ) ) ] )
% 129.08/129.50 , clause( 267717, [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y )
% 129.08/129.50 , 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267718, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 129.08/129.50 hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267719, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 129.08/129.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267720, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267721, [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y
% 129.08/129.50 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc',
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267722, [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267723, [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 129.08/129.50 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267724, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 129.08/129.50 hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267725, [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP(
% 129.08/129.50 T, Y ), hAPP( hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 129.08/129.50 U, T, X, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267726, [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP(
% 129.08/129.50 T, Y ), hAPP( hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 129.08/129.50 U, T, X, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267727, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 129.08/129.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267728, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267729, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 129.08/129.50 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), Z, X ), Z ) ] )
% 129.08/129.50 , clause( 267730, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OLocal'( T, U, W ) ) ), =( Z, W ) ] )
% 129.08/129.50 , clause( 267731, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OLocal'( T, U, W ) ) ), =( Y, U ) ] )
% 129.08/129.50 , clause( 267732, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OLocal'( T, U, W ) ) ), =( X, T ) ] )
% 129.08/129.50 , clause( 267733, [ 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ), ~(
% 129.08/129.50 'c_Com_OWT'( Y ) ), ~( 'c_Com_OWT'( X ) ) ] )
% 129.08/129.50 , clause( 267734, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y )
% 129.08/129.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267735, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 129.08/129.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267736, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCall'( X, Y, Z )
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267737, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267738, [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267739, [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267740, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267741, [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267742, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'(
% 129.08/129.50 Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267743, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 129.08/129.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267744, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 129.08/129.50 'tc_nat' ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267745, [ 'c_HOL_Oord__class_Oless'( X,
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267746, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevalc'(
% 129.08/129.50 'c_Com_Ocom_OWhile'( X, T ), Y, Z ) ) ] )
% 129.08/129.50 , clause( 267747, [ =( 'c_Power_Opower_Opower'( X, Y, Z,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T ), X ) ] )
% 129.08/129.50 , clause( 267748, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267749, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267750, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 129.08/129.50 , clause( 267751, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 129.08/129.50 , clause( 267752, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 129.08/129.50 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 129.08/129.50 , clause( 267753, [ ~(
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 129.08/129.50 , clause( 267754, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267755, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 129.08/129.50 , Z ), Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267756, [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267757, [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 129.08/129.50 , Y ) ) ] )
% 129.08/129.50 , clause( 267758, [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 129.08/129.50 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267759, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 129.08/129.50 Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267760, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 129.08/129.50 , clause( 267761, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 129.08/129.50 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 129.08/129.50 , clause( 267762, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 129.08/129.50 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 129.08/129.50 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 129.08/129.50 , clause( 267763, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267764, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267765, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z
% 129.08/129.50 , Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267766, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267767, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y,
% 129.08/129.50 Y, X ) ] )
% 129.08/129.50 , clause( 267768, [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U
% 129.08/129.50 , Z, 'tc_nat' ) ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ] )
% 129.08/129.50 , clause( 267769, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Y, X ) ] )
% 129.08/129.50 , clause( 267770, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 129.08/129.50 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267771, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 129.08/129.50 , clause( 267772, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 129.08/129.50 T ), X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP(
% 129.08/129.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ] )
% 129.08/129.50 , clause( 267773, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSKIP'
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267774, [ =( 'c_Orderings_Oord__class_Omin'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 129.08/129.50 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267775, [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 129.08/129.50 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X
% 129.08/129.50 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ] )
% 129.08/129.50 , clause( 267776, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267777, [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267778, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( U, V2 ), V3 ),
% 129.08/129.50 V4 ) ) ] )
% 129.08/129.50 , clause( 267779, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP(
% 129.08/129.50 'c_Suc', Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267780, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W
% 129.08/129.50 , V0, V1, T, U ) ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267781, [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) )
% 129.08/129.50 ) ), =( hAPP( 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP(
% 129.08/129.50 'c_Fun_Ocomp'( T, U, V3, V1, V4 ), W ) ) ] )
% 129.08/129.50 , clause( 267782, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevaln'(
% 129.08/129.50 'c_Com_Ocom_OWhile'( X, T ), Y, U, Z ) ) ] )
% 129.08/129.50 , clause( 267783, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267784, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 129.08/129.50 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267785, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Y, Z ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( T, Y,
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( Z ) ), Z ) ) ] )
% 129.08/129.50 , clause( 267786, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 Y, Z, 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, Z, T ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'( Y,
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 T ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( T ) ), T ) ) ] )
% 129.08/129.50 , clause( 267787, [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP(
% 129.08/129.50 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267788, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267789, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 129.08/129.50 , clause( 267790, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 129.08/129.50 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 129.08/129.50 , clause( 267791, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 129.08/129.50 ~( 'c_lessequals'( U, T, X ) ) ] )
% 129.08/129.50 , clause( 267792, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 129.08/129.50 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267793, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X )
% 129.08/129.50 ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 129.08/129.50 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 129.08/129.50 , clause( 267794, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSKIP' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267795, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), T ), Z, X ) ) ] )
% 129.08/129.50 , clause( 267796, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 129.08/129.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 129.08/129.50 , Y ), Z ), T, X ) ) ] )
% 129.08/129.50 , clause( 267797, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267798, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 X, hAPP( 'c_Suc', Y ), 'tc_nat' ), X, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267799, [ 'c_Natural_Oevaln'( X, Y, Z, T ), 'c_Natural_Oevaln'( U
% 129.08/129.50 , Y, Z, T ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( W, U, X ), Y, Z,
% 129.08/129.50 T ) ) ] )
% 129.08/129.50 , clause( 267800, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 129.08/129.50 , =( Y, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 129.08/129.50 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267801, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 129.08/129.50 ), X ), Y ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 129.08/129.50 , =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267802, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 129.08/129.50 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267803, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 129.08/129.50 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 129.08/129.50 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 129.08/129.50 , clause( 267804, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267805, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 129.08/129.50 Z, Y ) ] )
% 129.08/129.50 , clause( 267806, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y )
% 129.08/129.50 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267807, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 129.08/129.50 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267808, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y )
% 129.08/129.50 , ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267809, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267810, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267811, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 129.08/129.50 , X ) ) ] )
% 129.08/129.50 , clause( 267812, [ ~( 'class_Orderings_Oorder'( X ) ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 129.08/129.50 Y, Z ) ] )
% 129.08/129.50 , clause( 267813, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 129.08/129.50 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 129.08/129.50 , clause( 267814, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 129.08/129.50 , clause( 267815, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OCall'( T, U, W ) ) ) ] )
% 129.08/129.50 , clause( 267816, [ 'c_Natural_Oevalc'( X, Y, Z ), 'c_Natural_Oevalc'( T, Y
% 129.08/129.50 , Z ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( U, T, X ), Y, Z ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267817, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y
% 129.08/129.50 , Z, X ) ) ) ] )
% 129.08/129.50 , clause( 267818, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y
% 129.08/129.50 , X, Z ) ) ) ] )
% 129.08/129.50 , clause( 267819, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W,
% 129.08/129.50 Z, U, V0 ), 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0
% 129.08/129.50 ) ) ] )
% 129.08/129.50 , clause( 267820, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267821, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 129.08/129.50 Y, X ) ) ] )
% 129.08/129.50 , clause( 267822, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 129.08/129.50 Y, X ) ) ] )
% 129.08/129.50 , clause( 267823, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X
% 129.08/129.50 , 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267824, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 129.08/129.50 Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 129.08/129.50 , clause( 267825, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 129.08/129.50 Y, X ) ) ] )
% 129.08/129.50 , clause( 267826, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 129.08/129.50 Y, X ) ) ] )
% 129.08/129.50 , clause( 267827, [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP(
% 129.08/129.50 hAPP( Y, Z ), hAPP( 'c_Suc', T ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267828, [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP(
% 129.08/129.50 hAPP( Z, Y ), hAPP( 'c_Suc', T ) ) ), ~(
% 129.08/129.50 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0, V1 ) ) ] )
% 129.08/129.50 , clause( 267829, [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y,
% 129.08/129.50 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267830, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ),
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267831, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ),
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267832, [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267833, [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'(
% 129.08/129.50 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267834, [ 'c_Natural_Oevaln'( X, Y, hAPP( 'c_Suc', Z ), T ), ~(
% 129.08/129.50 'c_Natural_Oevaln'( X, Y, Z, T ) ) ] )
% 129.08/129.50 , clause( 267835, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP(
% 129.08/129.50 'c_Suc', Y ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267836, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP(
% 129.08/129.50 'c_Suc', X ), 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267837, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 129.08/129.50 , ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267838, [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ),
% 129.08/129.50 hAPP( 'c_Suc', Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y,
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267839, [ =( 'c_Nat_Onat_Onat__case'( X, Y, hAPP( 'c_Suc', Z ), T
% 129.08/129.50 ), hAPP( Y, Z ) ) ] )
% 129.08/129.50 , clause( 267840, [ 'c_Orderings_Oorder__class_Omono'( 'c_Suc', 'tc_nat',
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267841, [ =( 'c_Power_Opower_Opower'( X, Y, Z, hAPP( 'c_Suc', T )
% 129.08/129.50 , U ), hAPP( hAPP( Y, Z ), 'c_Power_Opower_Opower'( X, Y, Z, T, U ) ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267842, [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267843, [ =( 'c_Nat_Onat_Onat__rec'( X, Y, hAPP( 'c_Suc', Z ), T
% 129.08/129.50 ), hAPP( hAPP( Y, Z ), 'c_Nat_Onat_Onat__rec'( X, Y, Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267844, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 129.08/129.50 'c_Suc', X ) ) ) ] )
% 129.08/129.50 , clause( 267845, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 129.08/129.50 'c_Suc', X ) ) ) ] )
% 129.08/129.50 , clause( 267846, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 hAPP( 'c_Suc', X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267847, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 X ), hAPP( 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 129.08/129.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ] )
% 129.08/129.50 , clause( 267848, [ =( 'c_Orderings_Oord__class_Omax'( hAPP( 'c_Suc', X ),
% 129.08/129.50 hAPP( 'c_Suc', Y ), 'tc_nat' ), hAPP( 'c_Suc',
% 129.08/129.50 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267849, [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y
% 129.08/129.50 , 'tc_nat' ), hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat'
% 129.08/129.50 ) ) ), =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' )
% 129.08/129.50 ), Y ) ] )
% 129.08/129.50 , clause( 267850, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 129.08/129.50 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, hAPP( 'c_Suc', Z ), T, X )
% 129.08/129.50 , 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267851, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 129.08/129.50 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 129.08/129.50 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ) ) ] )
% 129.08/129.50 , clause( 267852, [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, hAPP(
% 129.08/129.50 'c_Suc', T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267853, [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, hAPP(
% 129.08/129.50 'c_Suc', T ), 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267854, [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y,
% 129.08/129.50 'tc_nat' ), =( hAPP( 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X,
% 129.08/129.50 Y, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267855, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_lessequals'( hAPP( 'c_Suc', Y ), X, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267856, [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 129.08/129.50 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267857, [ =( 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), hAPP(
% 129.08/129.50 'c_Suc', Z ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 129.08/129.50 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267858, [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X )
% 129.08/129.50 , 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267859, [ =( 'c_Orderings_Oord__class_Omin'( hAPP( 'c_Suc', X ),
% 129.08/129.50 hAPP( 'c_Suc', Y ), 'tc_nat' ), hAPP( 'c_Suc',
% 129.08/129.50 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) ) ] )
% 129.08/129.50 , clause( 267860, [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y,
% 129.08/129.50 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267861, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 129.08/129.50 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267862, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267863, [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 129.08/129.50 'tc_nat' ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267864, [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP(
% 129.08/129.50 'c_Suc', Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267865, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 129.08/129.50 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 129.08/129.50 'tc_nat' ) ) ] )
% 129.08/129.50 , clause( 267866, [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP(
% 129.08/129.50 'c_Suc', Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267867, [ =( X, hAPP( 'c_Suc',
% 129.08/129.50 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y, X, Z, T ) ) ),
% 129.08/129.50 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( Y ), Z, X, T ) ) ] )
% 129.08/129.50 , clause( 267868, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ),
% 129.08/129.50 hAPP( X, hAPP( Y, 'v_x' ) ) ) ] )
% 129.08/129.50 , clause( 267869, [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ] )
% 129.08/129.50 , clause( 267870, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ),
% 129.08/129.50 hAPP( Y, hAPP( X, 'v_x' ) ) ) ] )
% 129.08/129.50 , clause( 267871, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267872, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OBODY'(
% 129.08/129.50 Z ) ) ) ] )
% 129.08/129.50 , clause( 267873, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ] )
% 129.08/129.50 , clause( 267874, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCond'( Y, Z
% 129.08/129.50 , T ) ) ) ] )
% 129.08/129.50 , clause( 267875, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OBODY'(
% 129.08/129.50 T ) ) ) ] )
% 129.08/129.50 , clause( 267876, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OAss'( Y, Z
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267877, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OBODY'( Z
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267878, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OLocal'( Y,
% 129.08/129.50 Z, T ) ) ) ] )
% 129.08/129.50 , clause( 267879, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OWhile'( Y,
% 129.08/129.50 Z ) ) ) ] )
% 129.08/129.50 , clause( 267880, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OBODY'(
% 129.08/129.50 T ) ) ) ] )
% 129.08/129.50 , clause( 267881, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267882, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267883, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ),
% 129.08/129.50 'c_Com_Ocom_OBODY'( T ) ) ) ] )
% 129.08/129.50 , clause( 267884, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCall'( Y, Z
% 129.08/129.50 , T ) ) ) ] )
% 129.08/129.50 , clause( 267885, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 129.08/129.50 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ] )
% 129.08/129.50 , clause( 267886, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267887, [ ~( hBOOL( hAPP( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, U, 't_b' ), 't_b', 't_a' ) )
% 129.08/129.50 ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ] )
% 129.08/129.50 , clause( 267888, [ ~( hBOOL( hAPP( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, U, 't_b' ), 't_b', 't_a' ) )
% 129.08/129.50 ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ] )
% 129.08/129.50 , clause( 267889, [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__rec'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, U ), U, W ), hAPP( hAPP(
% 129.08/129.50 hAPP( X, Y ), Z ), T ) ) ] )
% 129.08/129.50 , clause( 267890, [ =( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, U ), U, W ), hAPP( hAPP(
% 129.08/129.50 hAPP( X, Y ), Z ), T ) ) ] )
% 129.08/129.50 , clause( 267891, [ =( hAPP( 'c_COMBI'( 't_a' ), 'v_P' ), 'v_P' ) ] )
% 129.08/129.50 , clause( 267892, [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ), 't_a' ), ~( hBOOL(
% 129.08/129.50 hAPP( hAPP( T, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1'( Y, T,
% 129.08/129.50 Z, X ) ), 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3'( Y, T, Z, X
% 129.08/129.50 ) ) ) ) ] )
% 129.08/129.50 , clause( 267893, [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, Z, T, 't_a' ), 't_a' ), hBOOL(
% 129.08/129.50 hAPP( hAPP( Y, 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1'( Y, T,
% 129.08/129.50 Z, X ) ), 'v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2'( Y, T, Z, X
% 129.08/129.50 ) ) ) ] )
% 129.08/129.50 , clause( 267894, [ 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( X ) ), =(
% 129.08/129.50 'c_Com_Obody'( X ), 'c_Option_Ooption_ONone'( 'tc_Com_Ocom' ) ) ] )
% 129.08/129.50 , clause( 267895, [ =( 'c_COMBB'( 'v_P', 'v_Q', 'v_R', 't_a', 't_b', 't_c'
% 129.08/129.50 ), hAPP( 'v_P', hAPP( 'v_Q', 'v_R' ) ) ) ] )
% 129.08/129.50 , clause( 267896, [ =( 'c_COMBS'( 'v_P', 'v_Q', 'v_R', 't_a', 't_b', 't_c'
% 129.08/129.50 ), hAPP( hAPP( 'v_P', 'v_R' ), hAPP( 'v_Q', 'v_R' ) ) ) ] )
% 129.08/129.50 , clause( 267897, [ =( 'c_COMBC'( 'v_P', 'v_Q', 'v_R', 't_a', 't_b', 't_c'
% 129.08/129.50 ), hAPP( hAPP( 'v_P', 'v_R' ), 'v_Q' ) ) ] )
% 129.08/129.50 , clause( 267898, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 129.08/129.50 hBOOL( 'c_in'( Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), hBOOL(
% 129.08/129.50 'c_in'( 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), T,
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ] )
% 129.08/129.50 , clause( 267899, [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, 't_a' ),
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple__valid'(
% 129.08/129.50 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2'( X, Y ), Z, 't_a' ),
% 129.08/129.50 ~( hBOOL( 'c_in'( Z, X, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ) ] )
% 129.08/129.50 , clause( 267900, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 129.08/129.50 hBOOL( 'c_in'( Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), 't_a' ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ] )
% 129.08/129.50 , clause( 267901, [ =( 'c_Option_Othe'( 'c_Option_Ooption_OSome'( X, Y ), Y
% 129.08/129.50 ), X ) ] )
% 129.08/129.50 , clause( 267902, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 129.08/129.50 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 U ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 129.08/129.50 , X, 'tc_Hoare__Mirabelle_Otriple'( U ) ), 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.08/129.50 Z ), 'tc_Com_Ocom' ), T, U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( U ), 'tc_bool' ) ),
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ) ) ] )
% 129.08/129.50 , clause( 267903, [ 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 129.08/129.50 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_Hoare__Mirabelle_Otriple'(
% 129.08/129.50 U ), 'tc_bool' ) ), 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Ohoare__derivs'( X, 'c_Set_Oinsert'(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.08/129.50 Z ), 'tc_Com_Ocom' ), T, U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( U ), 'tc_bool' ) ),
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( U ) ), U ) ) ] )
% 129.08/129.50 , clause( 267904, [ 'c_Natural_Oevaln'( 'c_Option_Othe'( 'c_Com_Obody'( X )
% 129.08/129.50 , 'tc_Com_Ocom' ), Y,
% 129.08/129.50 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( X, Z, Y, T ), T ),
% 129.08/129.50 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( X ), Y, Z, T ) ) ] )
% 129.08/129.50 , clause( 267905, [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 129.08/129.50 't_a', 'tc_bool' ) ), 'v_x' ), 'c_in'( 'v_x',
% 129.08/129.50 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267906, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( 'c_Natural_Oevaln'(
% 129.08/129.50 T, U, W, Z ) ), ~( hBOOL( hAPP( hAPP( V0, Y ), U ) ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple__valid'( W,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, X, 't_a' ), 't_a' ) ) ] )
% 129.08/129.50 , clause( 267907, [ =( hAPP( 'c_COMBK'( 'v_P', 't_a', 't_b' ), 'v_Q' ),
% 129.08/129.50 'v_P' ) ] )
% 129.08/129.50 , clause( 267908, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 129.08/129.50 hBOOL( 'c_in'( Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), hBOOL(
% 129.08/129.50 'c_in'( 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), Z,
% 129.08/129.50 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ] )
% 129.08/129.50 , clause( 267909, [ 'c_Hoare__Mirabelle_Otriple__valid'(
% 129.08/129.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( X, 'c_Com_Ocom_OBODY'( Y ), Z, T )
% 129.08/129.50 , T ) ] )
% 129.08/129.50 , clause( 267910, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 129.08/129.50 hBOOL( 'c_in'( Y, Z, 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) ) ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ),
% 129.08/129.50 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), 't_a' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267911, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X ), Y, Z ),
% 129.08/129.50 ~( 'c_Natural_Oevalc'( 'c_Option_Othe'( 'c_Com_Obody'( X ), 'tc_Com_Ocom'
% 129.08/129.50 ), Y, Z ) ) ] )
% 129.08/129.50 , clause( 267912, [ 'c_Natural_Oevalc'( 'c_Option_Othe'( 'c_Com_Obody'( X )
% 129.08/129.50 , 'tc_Com_Ocom' ), Y, Z ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OBODY'( X )
% 129.08/129.50 , Y, Z ) ) ] )
% 129.08/129.50 , clause( 267913, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OBODY'( X ), Y, hAPP(
% 129.08/129.50 'c_Suc', Z ), T ), ~( 'c_Natural_Oevaln'( 'c_Option_Othe'( 'c_Com_Obody'(
% 129.08/129.50 X ), 'tc_Com_Ocom' ), Y, Z, T ) ) ] )
% 129.08/129.50 , clause( 267914, [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ] )
% 129.08/129.50 , clause( 267915, [ ~( =( hAPP( 'c_Suc', X ), X ) ) ] )
% 129.08/129.50 , clause( 267916, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T
% 129.08/129.50 ), 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267917, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T
% 129.08/129.50 ), 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267918, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T
% 129.08/129.50 ), 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267919, [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X
% 129.08/129.50 , Y ) ] )
% 129.08/129.50 , clause( 267920, [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X
% 129.08/129.50 , Y ) ] )
% 129.08/129.50 , clause( 267921, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ), Y, Z ) ) ] )
% 129.08/129.50 , clause( 267922, [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( hAPP( Y, X ) ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267923, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_in'( Y, X, Z ) ) )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267924, [ 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X )
% 129.08/129.50 , 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U
% 129.08/129.50 ), U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.08/129.50 Z ), 'tc_Com_Ocom' ), T, U ), U ) ) ] )
% 129.08/129.50 , clause( 267925, [ 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.08/129.50 Z ), 'tc_Com_Ocom' ), T, U ), U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'(
% 129.08/129.50 hAPP( 'c_Suc', X ), 'c_Hoare__Mirabelle_Otriple_Otriple'( Y,
% 129.08/129.50 'c_Com_Ocom_OBODY'( Z ), T, U ), U ) ) ] )
% 129.08/129.50 , clause( 267926, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y )
% 129.08/129.50 ) ), =( X, Y ) ] )
% 129.08/129.50 , clause( 267927, [ hBOOL( 'c_in'( 'v_x', 'v_Procs', 'tc_Com_Opname' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267928, [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc',
% 129.08/129.50 'v_na' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', 'v_x' ),
% 129.08/129.50 'c_Com_Ocom_OBODY'( 'v_x' ), hAPP( 'v_Q', 'v_x' ), 't_a' ), 't_a' ) ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267929, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na', X, 't_a' )
% 129.08/129.50 , ~( hBOOL( 'c_in'( X, 'v_G', 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ) )
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267930, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ),
% 129.08/129.50 'c_Com_Ocom_OBODY'( X ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ), ~( hBOOL(
% 129.08/129.50 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ] )
% 129.08/129.50 , clause( 267931, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 129.08/129.50 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ), 'c_Option_Othe'(
% 129.08/129.50 'c_Com_Obody'( X ), 'tc_Com_Ocom' ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ),
% 129.08/129.50 ~( hBOOL( 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ] )
% 129.08/129.50 , clause( 267932, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 129.08/129.50 'class_Orderings_Opreorder'( Y ) ) ] )
% 129.08/129.50 , clause( 267933, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 129.08/129.50 'class_Orderings_Oorder'( Y ) ) ] )
% 129.08/129.50 , clause( 267934, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 129.08/129.50 'class_Orderings_Obot'( Y ) ) ] )
% 129.08/129.50 , clause( 267935, [
% 129.08/129.50 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267936, [
% 129.08/129.50 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267937, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267938, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267939, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 129.08/129.50 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267940, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat'
% 129.08/129.50 ) ] )
% 129.08/129.50 , clause( 267941, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267942, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 129.08/129.50 ] )
% 129.08/129.50 , clause( 267943, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267944, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ]
% 129.08/129.50 )
% 129.08/129.50 , clause( 267945, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267946, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267947, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267948, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 129.08/129.50 , clause( 267949, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 129.10/129.52 , clause( 267950, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 129.10/129.52 , clause( 267951, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 129.10/129.52 , clause( 267952, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 129.10/129.52 , clause( 267953, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 129.10/129.52 , clause( 267954, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 129.10/129.52 , clause( 267955, [ 'c_fequal'( X, X, Y ) ] )
% 129.10/129.52 , clause( 267956, [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ] )
% 129.10/129.52 ] ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 316, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.10/129.52 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 129.10/129.52 , clause( 267586, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.10/129.52 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 129.10/129.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 129.10/129.52 , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 ), ==>( 2, 2 )] )
% 129.10/129.52 ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 346, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 129.10/129.52 , clause( 267625, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 129.10/129.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 129.10/129.52 permutation( 0, [ ==>( 0, 0 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 409, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( 'c_in'( X, Y,
% 129.10/129.52 Z ) ) ) ] )
% 129.10/129.52 , clause( 267716, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( 'c_in'( X
% 129.10/129.52 , Y, Z ) ) ) ] )
% 129.10/129.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 129.10/129.52 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 557, [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( hAPP( Y, X ) ) ) ] )
% 129.10/129.52 , clause( 267922, [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( hAPP( Y, X ) ) )
% 129.10/129.52 ] )
% 129.10/129.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z )] ),
% 129.10/129.52 permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 559, [ 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X ),
% 129.10/129.52 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U )
% 129.10/129.52 , U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.10/129.52 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.10/129.52 Z ), 'tc_Com_Ocom' ), T, U ), U ) ) ] )
% 129.10/129.52 , clause( 267924, [ 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc', X )
% 129.10/129.52 , 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, U
% 129.10/129.52 ), U ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 129.10/129.52 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Option_Othe'( 'c_Com_Obody'(
% 129.10/129.52 Z ), 'tc_Com_Ocom' ), T, U ), U ) ) ] )
% 129.10/129.52 , substitution( 0, [ :=( X, X ), :=( Y, Y ), :=( Z, Z ), :=( T, T ), :=( U
% 129.10/129.52 , U )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 562, [ hBOOL( 'c_in'( 'v_x', 'v_Procs', 'tc_Com_Opname' ) ) ] )
% 129.10/129.52 , clause( 267927, [ hBOOL( 'c_in'( 'v_x', 'v_Procs', 'tc_Com_Opname' ) ) ]
% 129.10/129.52 )
% 129.10/129.52 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 563, [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc',
% 129.10/129.52 'v_na' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', 'v_x' ),
% 129.10/129.52 'c_Com_Ocom_OBODY'( 'v_x' ), hAPP( 'v_Q', 'v_x' ), 't_a' ), 't_a' ) ) ]
% 129.10/129.52 )
% 129.10/129.52 , clause( 267928, [ ~( 'c_Hoare__Mirabelle_Otriple__valid'( hAPP( 'c_Suc',
% 129.10/129.52 'v_na' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', 'v_x' ),
% 129.10/129.52 'c_Com_Ocom_OBODY'( 'v_x' ), hAPP( 'v_Q', 'v_x' ), 't_a' ), 't_a' ) ) ]
% 129.10/129.52 )
% 129.10/129.52 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 subsumption(
% 129.10/129.52 clause( 566, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 129.10/129.52 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ), 'c_Option_Othe'(
% 129.10/129.52 'c_Com_Obody'( X ), 'tc_Com_Ocom' ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ),
% 129.10/129.52 ~( hBOOL( 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ] )
% 129.10/129.52 , clause( 267931, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na',
% 129.10/129.52 'c_Hoare__Mirabelle_Otriple_Otriple'( hAPP( 'v_P', X ), 'c_Option_Othe'(
% 129.10/129.52 'c_Com_Obody'( X ), 'tc_Com_Ocom' ), hAPP( 'v_Q', X ), 't_a' ), 't_a' ),
% 129.10/129.52 ~( hBOOL( 'c_in'( X, 'v_Procs', 'tc_Com_Opname' ) ) ) ] )
% 129.10/129.52 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1,
% 129.10/129.52 1 )] ) ).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 eqswap(
% 129.10/129.52 clause( 272295, [ =( Y, X ), ~( =( 'c_Set_Oinsert'( Z, 'c_Set_Oinsert'( X,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ),
% 129.10/129.52 'c_Set_Oinsert'( U, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ) ), =( Z, Y ) ] )
% 129.10/129.52 , clause( 316, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.10/129.52 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 129.10/129.52 , 2, substitution( 0, [ :=( X, Z ), :=( Y, X ), :=( Z, T ), :=( T, U ),
% 129.10/129.52 :=( U, Y )] )).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 eqswap(
% 129.10/129.52 clause( 272297, [ =( Y, X ), =( Y, Z ), ~( =( 'c_Set_Oinsert'( X,
% 129.10/129.52 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 129.10/129.52 'tc_bool' ) ), T ), T ), 'c_Set_Oinsert'( U, 'c_Set_Oinsert'( Y,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ) )
% 129.10/129.52 ] )
% 129.10/129.52 , clause( 272295, [ =( Y, X ), ~( =( 'c_Set_Oinsert'( Z, 'c_Set_Oinsert'( X
% 129.10/129.52 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ),
% 129.10/129.52 'c_Set_Oinsert'( U, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ) ), =( Z, Y ) ] )
% 129.10/129.52 , 2, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, X ), :=( T, T ),
% 129.10/129.52 :=( U, U )] )).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 eqswap(
% 129.10/129.52 clause( 272298, [ ~( =( 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.10/129.52 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( U, X ), =( U, Y ) ] )
% 129.10/129.52 , clause( 272297, [ =( Y, X ), =( Y, Z ), ~( =( 'c_Set_Oinsert'( X,
% 129.10/129.52 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 129.10/129.52 'tc_bool' ) ), T ), T ), 'c_Set_Oinsert'( U, 'c_Set_Oinsert'( Y,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ) )
% 129.10/129.52 ] )
% 129.10/129.52 , 2, substitution( 0, [ :=( X, X ), :=( Y, U ), :=( Z, Y ), :=( T, Z ),
% 129.10/129.52 :=( U, T )] )).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 eqfact(
% 129.10/129.52 clause( 272341, [ ~( =( X, Y ) ), ~( =( 'c_Set_Oinsert'( Z, 'c_Set_Oinsert'(
% 129.10/129.52 T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), U ),
% 129.10/129.52 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( U, 'tc_bool' ) ), U ), U ) ) ), =( T, Y ) ] )
% 129.10/129.52 , clause( 272298, [ ~( =( 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.10/129.52 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( U, X ), =( U, Y ) ] )
% 129.10/129.52 , 2, 1, substitution( 0, [ :=( X, Y ), :=( Y, X ), :=( Z, U ), :=( T, Z ),
% 129.10/129.52 :=( U, T )] )).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 eqswap(
% 129.10/129.52 clause( 272344, [ =( Y, X ), ~( =( Z, Y ) ), ~( =( 'c_Set_Oinsert'( T,
% 129.10/129.52 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U,
% 129.10/129.52 'tc_bool' ) ), U ), U ), 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), U ) ) )
% 129.10/129.52 ] )
% 129.10/129.52 , clause( 272341, [ ~( =( X, Y ) ), ~( =( 'c_Set_Oinsert'( Z,
% 129.10/129.52 'c_Set_Oinsert'( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U,
% 129.10/129.52 'tc_bool' ) ), U ), U ), 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), U ) ) )
% 129.10/129.52 , =( T, Y ) ] )
% 129.10/129.52 , 2, substitution( 0, [ :=( X, Z ), :=( Y, Y ), :=( Z, T ), :=( T, X ),
% 129.10/129.52 :=( U, U )] )).
% 129.10/129.52
% 129.10/129.52
% 129.10/129.52 eqswap(
% 129.10/129.52 clause( 272346, [ ~( =( 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 129.10/129.52 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 129.10/129.52 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( T, Y ), ~( =( U, T ) ) ] )
% 129.10/129.52 , clause( 272344, [ =( Y, X ), ~( =( Z, Y ) ), ~( =( 'c_Set_Oinsert'( T,
% 129.10/129.52 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U,
% 129.10/129.52 'tc_bool' ) ), U ), U ), 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 129.10/129.52 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), UCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------