TSTP Solution File: SWV848-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV848-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.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 16:28:49 EDT 2022
% Result : Unsatisfiable 1.11s 1.47s
% Output : Refutation 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV848-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 11:44:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.11/1.47 *** allocated 10000 integers for termspace/termends
% 1.11/1.47 *** allocated 10000 integers for clauses
% 1.11/1.47 *** allocated 10000 integers for justifications
% 1.11/1.47 Bliksem 1.12
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 Automatic Strategy Selection
% 1.11/1.47
% 1.11/1.47 Clauses:
% 1.11/1.47 [
% 1.11/1.47 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.11/1.47 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( Y, T, U ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevalc'( Z, Y, T ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Z, U ), Y, T ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OAss'( X, Y ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_COMBI'( X ), Y ), Y ) ],
% 1.11/1.47 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.11/1.47 U ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.11/1.47 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 1.11/1.47 , V4 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.11/1.47 'tc_bool' ) ), X ) ],
% 1.11/1.47 [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 1.11/1.47 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 't_a', X )
% 1.11/1.47 ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( Y, 'v_x'
% 1.11/1.47 ), hAPP( Z, 'v_x' ), X ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Set_Oinsert'( Y
% 1.11/1.47 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 hAPP( Y, Z ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( T, Y
% 1.11/1.47 , U, X ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( Z, V2 )
% 1.11/1.47 , V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oimage'( 'c_COMBI'( X ), Y, X, X ), Y ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 1.11/1.47 , =( Z, W ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 1.11/1.47 , =( Y, U ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) ) )
% 1.11/1.47 , =( X, T ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( hAPP( T, V2 ), V3 )
% 1.11/1.47 , 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V2, V4 ) ),
% 1.11/1.47 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OLocal'( Y, Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.11/1.47 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 1.11/1.47 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), Z ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 1.11/1.47 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), T ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( Y
% 1.11/1.47 , T ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( X
% 1.11/1.47 , Z ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.11/1.47 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.11/1.47 T, 'tc_bool' ) ), T ), X, T ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.11/1.47 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.11/1.47 X, T ), Y ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z,
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ) ) ), =( hAPP( Y, U ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), X )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OAss'( Y, Z ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.11/1.47 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.11/1.47 ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.11/1.47 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( X, Y ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, X, T, 'tc_fun'(
% 1.11/1.47 U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, X, T, 'tc_fun'(
% 1.11/1.47 U, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.11/1.47 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.11/1.47 , X, V0, V1, V2, U, V3, V4, T ) ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.11/1.47 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X
% 1.11/1.47 , W, V0, V1, U, V2, V3, V4, T ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.11/1.47 , =( Z, W ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.11/1.47 , =( Y, U ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.11/1.47 , =( X, T ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.11/1.47 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OCond'( X, Y, Z ) ), ~( 'c_Com_OWT'( Z ) ),
% 1.11/1.47 ~( 'c_Com_OWT'( Y ) ) ],
% 1.11/1.47 [ =( 'c_Set_Ovimage'( 'c_COMBI'( X ), Y, X, X ), Y ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCond'( Y, Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, Z, T, 'tc_fun'(
% 1.11/1.47 X, 'tc_bool' ) ) ) ), =( hAPP( Z, U ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U ), Y )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.11/1.47 X, 'tc_bool' ) ), Y ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.11/1.47 'tc_bool' ) ), X ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, X,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), T ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), X ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.11/1.47 ) ), Y ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.11/1.47 , Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~( 'c_Natural_Oevalc'(
% 1.11/1.47 Z, T, Y ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.11/1.47 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.11/1.47 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.11/1.47 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.11/1.47 'c_lessequals'( Y, Z, X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.11/1.47 'c_lessequals'( Z, Y, X ) ) ],
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OCall'( X, Y, Z ) ), ~( 'c_Com_OWT'(
% 1.11/1.47 'c_Com_Ocom_OBODY'( Y ) ) ) ],
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( X ) ), ~( 'c_Com_OWT'(
% 1.11/1.47 'c_Com_Ocom_OCall'( Y, X, Z ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.11/1.47 [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, 'c_COMBC'( Z, T, T,
% 1.11/1.47 'tc_bool' ), 'c_COMBC'( U, T, T, 'tc_bool' ), W, V0, V1, V2, T ), ~(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, Z, U, V0, W, V2, V1, T )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.11/1.47 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCall'( Y, Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.11/1.47 , X, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.11/1.47 'tc_nat' ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 1.11/1.47 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z
% 1.11/1.47 ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.11/1.47 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.11/1.47 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ],
% 1.11/1.47 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.11/1.47 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.11/1.47 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.11/1.47 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.11/1.47 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.11/1.47 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( 'c_Fun_Oid'( T )
% 1.11/1.47 , W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W, V0 ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 T, Z, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.11/1.47 'c_lessequals'( Z, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 T, Z, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Set_Ovimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( T, V2 ), V3 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Set_Ovimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ),
% 1.11/1.47 'c_Set_Ovimage'( Y, 'c_Set_Ovimage'( X, W, Z, T ), U, Z ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) ) ), =( X, Y )
% 1.11/1.47 ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 1.11/1.47 , V4 ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.11/1.47 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.11/1.47 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.11/1.47 ) ), Z, X ) ) ],
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( X, Y, Z ) ), ~( 'c_Com_OWT'( Z ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( Y, Z, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ],
% 1.11/1.47 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.11/1.47 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X, Y, U, T
% 1.11/1.47 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.11/1.47 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, 'c_Com_Ocom_OAss'(
% 1.11/1.47 V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), Y ) ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( hAPP( U,
% 1.11/1.47 V2 ), V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3,
% 1.11/1.47 V5 ) ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.11/1.47 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Ovimage'( X, Y, U, T
% 1.11/1.47 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.11/1.47 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.11/1.47 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_SetInterval_Oord_OatLeastLessThan'( Z, T, U, W, X ) ) ), ~( hBOOL(
% 1.11/1.47 hAPP( hAPP( T, Y ), W ) ) ), ~( hBOOL( hAPP( hAPP( Z, U ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.11/1.47 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.11/1.47 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_SetInterval_Oord_OatLeastAtMost'( Z, T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( Z, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( Z, T ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.11/1.47 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__XbexE__1__1'( Y, X, Z ) ) )
% 1.11/1.47 , ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), Y )
% 1.11/1.47 ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z,
% 1.11/1.47 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T,
% 1.11/1.47 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.11/1.47 [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.11/1.47 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool'
% 1.11/1.47 ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ],
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 1.11/1.47 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.11/1.47 ), X ), Y ) ), =( Y, T ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.11/1.47 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.11/1.47 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.11/1.47 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.11/1.47 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.11/1.47 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.11/1.47 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.11/1.47 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.11/1.47 'c_lessequals'( Y, Z, X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.11/1.47 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.11/1.47 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( X, Y, Z ), hBOOL( hAPP( T, Y ) ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( T, U, X ), Y, Z ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( Z, T, U ) ), hBOOL( hAPP( X, T ) ) ],
% 1.11/1.47 [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.47 'c_Set_Oinsert'( X, Y, Z ), T, Z, 'tc_fun'( U, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( T, X ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, T, Z, 'tc_fun'(
% 1.11/1.47 U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ],
% 1.11/1.47 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ],
% 1.11/1.47 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( Y, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.47 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'( Y, Z, T, X ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( T, U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( X ), U ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.47 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'( Y, Z, T, X ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( T, U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( X ), U ), Z ) ) ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y ), hAPP( X
% 1.11/1.47 , Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W, X, V0, V1, V2
% 1.11/1.47 , U, V3, V4, T ) ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y ), hAPP( X
% 1.11/1.47 , Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, W, V0, V1, U,
% 1.11/1.47 V2, V3, V4, T ) ) ],
% 1.11/1.47 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.11/1.47 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( Z, V2 ), V3 )
% 1.11/1.47 , V4 ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.11/1.47 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.11/1.47 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.11/1.47 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y, hAPP( X, W ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ),
% 1.11/1.47 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.11/1.47 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 1.11/1.47 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ), =( Y,
% 1.11/1.47 T ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ), =( X,
% 1.11/1.47 Z ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OAss'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Set_Oinsert'( X,
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ), T ), 'c_Set_Oinsert'( X,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.11/1.47 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.11/1.47 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 1.11/1.47 ), =( Z, W ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 1.11/1.47 ), =( Y, U ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'( T, U, W ) )
% 1.11/1.47 ), =( X, T ) ],
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ), ~( 'c_Com_OWT'( Y ) ), ~(
% 1.11/1.47 'c_Com_OWT'( X ) ) ],
% 1.11/1.47 [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X ) ],
% 1.11/1.47 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ],
% 1.11/1.47 [ =( 'c_Set_Oimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T ),
% 1.11/1.47 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.11/1.47 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1
% 1.11/1.47 , Z, V2, Y ) ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.11/1.47 ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1
% 1.11/1.47 , V2, Z, Y ) ) ],
% 1.11/1.47 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.11/1.47 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.11/1.47 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.11/1.47 'tc_bool' ) ), X ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.11/1.47 Y, X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 T, X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.11/1.47 'c_lessequals'( Y, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.11/1.47 Y, X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.47 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 T, X ), Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( 't_a', X )
% 1.11/1.47 ), 'v_x' ), 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( Y, 'v_x'
% 1.11/1.47 ), hAPP( Z, 'v_x' ), X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.47 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.11/1.47 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.11/1.47 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.11/1.47 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ), ~(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1, V2, V3, Z )
% 1.11/1.47 ) ],
% 1.11/1.47 [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ), ~(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1, V2, V3, Z )
% 1.11/1.47 ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( U, V2 ), V3 ),
% 1.11/1.47 V4 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 1.11/1.47 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 1.11/1.47 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 1.11/1.47 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 1.11/1.47 , V4 ), W ) ) ],
% 1.11/1.47 [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 1.11/1.47 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 1.11/1.47 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, Z, 'tc_fun'( U, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, T, Z, 'tc_fun'(
% 1.11/1.47 U, 'tc_bool' ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.47 Y, T, Z, 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.11/1.47 X, T, U ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.11/1.47 hAPP( X, U ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.11/1.47 hAPP( X, T ) ) ) ],
% 1.11/1.47 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.11/1.47 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 1.11/1.47 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.11/1.47 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.11/1.47 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCall'( T, U, W ) )
% 1.11/1.47 ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( X, Y, Z ), 'c_Natural_Oevalc'( T, Y, Z ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( U, T, X ), Y, Z ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.11/1.47 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.47 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.11/1.47 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, Z, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, X, Z ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z, U, V0 ),
% 1.11/1.47 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ],
% 1.11/1.47 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.11/1.47 'c_lessequals'( Z, Y, X ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( U ), T ), Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y
% 1.11/1.47 , W, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( U ), Y ), T ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.11/1.47 , Z, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y
% 1.11/1.47 ), 'c_SetInterval_Oord_OatLeastAtMost'( X, U, Z, T ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Z
% 1.11/1.47 ), 'c_SetInterval_Oord_OatLeastAtMost'( X, Y, U, T ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'( Y, Z, X, T
% 1.11/1.47 ) ) ), ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U
% 1.11/1.47 ), Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'( Y, Z, X, T
% 1.11/1.47 ) ) ), ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), U
% 1.11/1.47 ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), 'c_ATP__Linkup_Osko__Set__XbexE__1__1'(
% 1.11/1.47 Y, Z, X ) ), Y ) ), ~( hBOOL( hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( X ), T ), Y ) ) ) ],
% 1.11/1.47 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.11/1.47 , X ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_SetInterval_Oord_OlessThan'( Z
% 1.11/1.47 , T, X ) ) ), ~( hBOOL( hAPP( hAPP( Z, Y ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y
% 1.11/1.47 ), 'c_SetInterval_Oord_OlessThan'( X, Z, T ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.47 T, 'tc_fun'( U, 'tc_bool' ) ) ), W ), V0 ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.11/1.47 Y, V1 ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), V1 ), X ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X
% 1.11/1.47 , Y, Z, 'tc_fun'( T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ),
% 1.11/1.47 U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.47 T, 'tc_fun'( U, 'tc_bool' ) ) ), W ), V0 ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.11/1.47 Y, V1 ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), V1 ), X ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ hBOOL( hAPP( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X
% 1.11/1.47 , Y, Z, 'tc_fun'( T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ),
% 1.11/1.47 U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y
% 1.11/1.47 ), 'c_SetInterval_Oord_OatLeastLessThan'( U, X, W, Z, T ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Z
% 1.11/1.47 ), 'c_SetInterval_Oord_OatLeastLessThan'( X, U, Y, W, T ) ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.47 'c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1'( Y, Z, X ) ), Y ) ), ~( hBOOL(
% 1.11/1.47 hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1'( Y, X, Z )
% 1.11/1.47 ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T )
% 1.11/1.47 , Y ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.11/1.47 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.11/1.47 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.11/1.47 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( 'c_COMBC'(
% 1.11/1.47 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ),
% 1.11/1.47 hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 1.11/1.47 'tc_bool' ), Y ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_x' ), hAPP( hAPP(
% 1.11/1.47 'c_in'( 't_a' ), 'v_x' ), 'c_Lattices_Olower__semilattice__class_Oinf'( X
% 1.11/1.47 , Y, 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( 'c_COMBC'(
% 1.11/1.47 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ),
% 1.11/1.47 hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 1.11/1.47 'tc_bool' ), Y ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_x' ), hAPP( hAPP(
% 1.11/1.47 'c_in'( 't_a' ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 1.11/1.47 , Y, 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ), hAPP( X, hAPP( Y
% 1.11/1.47 , 'v_x' ) ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ],
% 1.11/1.47 [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ), hAPP( Y, hAPP(
% 1.11/1.47 X, 'v_x' ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCall'( X, Y, Z ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OAss'( X, Y ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OLocal'( X, Y, Z ) ) ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OSKIP', V2 ), X ) ],
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OSKIP', V2 ), X ) ],
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OSKIP' ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y, X ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevalc'(
% 1.11/1.47 'c_Com_Ocom_OWhile'( X, T ), Y, Z ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( W, V2 ), V3 ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OAss'( Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCall'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, Z ), hBOOL( hAPP(
% 1.11/1.47 X, Z ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T, U ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OWhile'( Y, Z ) ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), U, T ) ), ~(
% 1.11/1.47 'c_Natural_Oevalc'( Y, Z, U ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( X, Y ) ), ~( 'c_Com_OWT'( Y ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( Y, X ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( W, V2 ), V3 ),
% 1.11/1.47 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y, Z, T ), 'c_Natural_Oevaln'( U, Y, Z, T ),
% 1.11/1.47 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( W, U, X ), Y, Z, T ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U, Z, 'tc_nat' )
% 1.11/1.47 ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( Z, T, U, W ) ), hBOOL( hAPP( X, T ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y, Z, T ), hBOOL( hAPP( U, Y ) ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( U, W, X ), Y, Z, T ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y, 'c_Suc'( Z ), T ), ~( 'c_Natural_Oevaln'( X
% 1.11/1.47 , Y, Z, T ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y,
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( Z, X, T, Y, U, W ), W ),
% 1.11/1.47 ~( 'c_Natural_Oevaln'( X, Y, V0, W ) ), ~( 'c_Natural_Oevaln'( Z, T, V1,
% 1.11/1.47 U ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y,
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( X, Z, Y, T, U, W ), U ),
% 1.11/1.47 ~( 'c_Natural_Oevaln'( Z, T, V0, W ) ), ~( 'c_Natural_Oevaln'( X, Y, V1,
% 1.11/1.47 U ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( Y, T, U, W ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.11/1.47 [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevaln'( Z, Y, T, U ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Z, W ), Y, T, U ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T, W ) )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y, T, Z ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( hAPP( 'c_COMBI'( 't_a' ), 'v_P' ), 'v_P' ) ],
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), Y, Z ) ) ],
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ),
% 1.11/1.47 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ) ), T ) ), ~(
% 1.11/1.47 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ],
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ), ~(
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ),
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), 't_a' ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, 't_a' ),
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple__valid'(
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2'( X, Y ), Z, 't_a' ),
% 1.11/1.47 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Z
% 1.11/1.47 ), X ) ) ) ],
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ), ~(
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), 't_a' ) ), ~(
% 1.11/1.47 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ],
% 1.11/1.47 [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' )
% 1.11/1.47 ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ),
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( X, Y, Z, T, U ), Z
% 1.11/1.47 , U ), ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_Natural_Oevaln'(
% 1.11/1.47 'c_Com_Ocom_OWhile'( X, Y ), T, Z, U ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y, Z,
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( T, X, Z, Y, U ) ),
% 1.11/1.47 =( U, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( T, X ), Y, Z, U )
% 1.11/1.47 ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ),
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( X, Y, Z, T, U ), Z
% 1.11/1.47 , U ), =( U, T ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), T,
% 1.11/1.47 Z, U ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( X, Y, Z,
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( T, X, Z, Y, U ) ),
% 1.11/1.47 ~( hBOOL( hAPP( T, Y ) ) ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( T
% 1.11/1.47 , X ), Y, Z, U ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( 'c_Natural_Oevaln'( T, U, W, Z )
% 1.11/1.47 ), ~( hBOOL( hAPP( hAPP( V0, Y ), U ) ) ), ~(
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple__valid'( W,
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, X, 't_a' ), 't_a' ) ) ],
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~( hBOOL( hAPP(
% 1.11/1.47 hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y ), Z ) ) ),
% 1.11/1.47 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ),
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ) ), Z ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevaln'(
% 1.11/1.47 'c_Com_Ocom_OWhile'( X, T ), Y, U, Z ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, Z ), hBOOL(
% 1.11/1.47 hAPP( X, Z ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 1.11/1.47 ],
% 1.11/1.47 [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, U ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), W, T, U ) ), ~(
% 1.11/1.47 'c_Natural_Oevaln'( Y, Z, T, W ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 1.11/1.47 =( X, Z ) ],
% 1.11/1.47 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 1.11/1.47 =( Y, T ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y, Z, X ) ) ]
% 1.11/1.47 ,
% 1.11/1.47 [ =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'v_P', 'v_x' ), 'v_sa' ) ) ],
% 1.11/1.47 [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na', X, 't_a' ), ~( hBOOL(
% 1.11/1.47 hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), X ), 'v_G'
% 1.11/1.47 ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( 'v_b', 'v_sa' ) ), ~( hBOOL( hAPP( hAPP( 'v_P', 'v_x' ),
% 1.11/1.47 'v_sa' ) ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'v_P', X ), Y ) ), ~( 'c_Natural_Oevaln'( 'v_c', Z
% 1.11/1.47 , T, Y ) ), ~( hBOOL( hAPP( 'v_b', Z ) ) ), ~( hBOOL( hAPP( hAPP( 'v_P',
% 1.11/1.47 X ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.11/1.47 't_a' ) ), 'v_nb'( T ) ), 'v_G' ) ) ],
% 1.11/1.47 [ hBOOL( hAPP( hAPP( 'v_P', X ), Y ) ), ~( 'c_Natural_Oevaln'( 'v_c', Z
% 1.11/1.47 , T, Y ) ), ~( hBOOL( hAPP( 'v_b', Z ) ) ), ~( hBOOL( hAPP( hAPP( 'v_P',
% 1.11/1.47 X ), Z ) ) ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( T, 'v_nb'( T ),
% 1.11/1.47 't_a' ) ) ],
% 1.11/1.47 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ],
% 1.11/1.47 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Lattices_Olattice'( Y ) ) ],
% 1.11/1.47 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Lattices_Olattice'( Y ) ) ],
% 1.11/1.47 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.11/1.47 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.11/1.47 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Orderings_Opreorder'( Y ) ) ],
% 1.11/1.47 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Lattices_Olattice'( Y ) ) ],
% 1.11/1.47 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.47 'class_Orderings_Oorder'( Y ) ) ],
% 1.11/1.47 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.11/1.47 Y ) ) ],
% 1.11/1.47 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.11/1.47 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.11/1.47 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.11/1.47 [ 'c_fequal'( X, X, Y ) ],
% 1.11/1.47 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.11/1.47 ] .
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 percentage equality = 0.380000, percentage horn = 0.923833
% 1.11/1.47 This is a problem with some equality
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 Options Used:
% 1.11/1.47
% 1.11/1.47 useres = 1
% 1.11/1.47 useparamod = 1
% 1.11/1.47 useeqrefl = 1
% 1.11/1.47 useeqfact = 1
% 1.11/1.47 usefactor = 1
% 1.11/1.47 usesimpsplitting = 0
% 1.11/1.47 usesimpdemod = 5
% 1.11/1.47 usesimpres = 3
% 1.11/1.47
% 1.11/1.47 resimpinuse = 1000
% 1.11/1.47 resimpclauses = 20000
% 1.11/1.47 substype = eqrewr
% 1.11/1.47 backwardsubs = 1
% 1.11/1.47 selectoldest = 5
% 1.11/1.47
% 1.11/1.47 litorderings [0] = split
% 1.11/1.47 litorderings [1] = extend the termordering, first sorting on arguments
% 1.11/1.47
% 1.11/1.47 termordering = kbo
% 1.11/1.47
% 1.11/1.47 litapriori = 0
% 1.11/1.47 termapriori = 1
% 1.11/1.47 litaposteriori = 0
% 1.11/1.47 termaposteriori = 0
% 1.11/1.47 demodaposteriori = 0
% 1.11/1.47 ordereqreflfact = 0
% 1.11/1.47
% 1.11/1.47 litselect = negord
% 1.11/1.47
% 1.11/1.47 maxweight = 15
% 1.11/1.47 maxdepth = 30000
% 1.11/1.47 maxlength = 115
% 1.11/1.47 maxnrvars = 195
% 1.11/1.47 excuselevel = 1
% 1.11/1.47 increasemaxweight = 1
% 1.11/1.47
% 1.11/1.47 maxselected = 10000000
% 1.11/1.47 maxnrclauses = 10000000
% 1.11/1.47
% 1.11/1.47 showgenerated = 0
% 1.11/1.47 showkept = 0
% 1.11/1.47 showselected = 0
% 1.11/1.47 showdeleted = 0
% 1.11/1.47 showresimp = 1
% 1.11/1.47 showstatus = 2000
% 1.11/1.47
% 1.11/1.47 prologoutput = 1
% 1.11/1.47 nrgoals = 5000000
% 1.11/1.47 totalproof = 1
% 1.11/1.47
% 1.11/1.47 Symbols occurring in the translation:
% 1.11/1.47
% 1.11/1.47 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.11/1.47 . [1, 2] (w:1, o:145, a:1, s:1, b:0),
% 1.11/1.47 ! [4, 1] (w:0, o:120, a:1, s:1, b:0),
% 1.11/1.47 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.11/1.47 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.11/1.47 'tc_bool' [41, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.11/1.47 'tc_fun' [42, 2] (w:1, o:170, a:1, s:1, b:0),
% 1.11/1.47 'c_Orderings_Obot__class_Obot' [43, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.11/1.47 'c_Set_Oimage' [45, 4] (w:1, o:192, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OCond' [49, 3] (w:1, o:178, a:1, s:1, b:0),
% 1.11/1.47 'c_Natural_Oevalc' [52, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.11/1.47 hAPP [53, 2] (w:1, o:171, a:1, s:1, b:0),
% 1.11/1.47 hBOOL [54, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OSemi' [57, 2] (w:1, o:172, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OAss' [62, 2] (w:1, o:173, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_OWT' [63, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup' [67, 3] (w:1, o:180, a:1
% 1.11/1.47 , s:1, b:0),
% 1.11/1.47 'class_Lattices_Oupper__semilattice' [68, 1] (w:1, o:128, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'class_Lattices_Olattice' [72, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.11/1.47 'c_Set_Oinsert' [74, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_Ocom__case' [85, 10] (w:1, o:206, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OBODY' [89, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.11/1.47 'c_COMBI' [90, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.11/1.47 'c_COMBC' [93, 4] (w:1, o:193, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OCall' [97, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.11/1.47 'c_Fun_Oid' [100, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.11/1.47 'c_Fun_Ocomp' [102, 5] (w:1, o:200, a:1, s:1, b:0),
% 1.11/1.47 'class_Lattices_Odistrib__lattice' [103, 1] (w:1, o:133, a:1, s:1, b:
% 1.11/1.47 0),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf' [104, 3] (w:1, o:183, a:
% 1.11/1.47 1, s:1, b:0),
% 1.11/1.47 't_a' [105, 0] (w:1, o:70, a:1, s:1, b:0),
% 1.11/1.47 'v_x' [106, 0] (w:1, o:71, a:1, s:1, b:0),
% 1.11/1.47 'c_in' [107, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.11/1.47 'class_Complete__Lattice_Ocomplete__lattice' [108, 1] (w:1, o:135, a:
% 1.11/1.47 1, s:1, b:0),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR' [111, 4] (w:1
% 1.11/1.47 , o:194, a:1, s:1, b:0),
% 1.11/1.47 'c_lessequals' [112, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OLocal' [115, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_Ocom__rec' [118, 10] (w:1, o:207, a:1, s:1, b:0),
% 1.11/1.47 'class_Orderings_Obot' [120, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.11/1.47 'c_Set_Ovimage' [122, 4] (w:1, o:195, a:1, s:1, b:0),
% 1.11/1.47 'class_Lattices_Obounded__lattice' [125, 1] (w:1, o:137, a:1, s:1, b:
% 1.11/1.47 0),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice' [136, 9] (w:1, o:205, a:1
% 1.11/1.47 , s:1, b:0),
% 1.11/1.47 'c_Suc' [138, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.11/1.47 'class_Lattices_Olower__semilattice' [141, 1] (w:1, o:139, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'tc_nat' [144, 0] (w:1, o:97, a:1, s:1, b:0),
% 1.11/1.47 'class_Orderings_Oorder' [147, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.11/1.47 'c_SetInterval_Oord_OatLeastLessThan' [150, 5] (w:1, o:201, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'c_SetInterval_Oord_OatLeastAtMost' [151, 4] (w:1, o:196, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'c_ATP__Linkup_Osko__Set__XbexE__1__1' [152, 3] (w:1, o:186, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple_Otriple' [157, 4] (w:1, o:197, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3' [160, 4] (w:1, o:198, a:1
% 1.11/1.47 , s:1, b:0),
% 1.11/1.47 'c_Fun_Ofcomp' [161, 5] (w:1, o:202, a:1, s:1, b:0),
% 1.11/1.47 'class_Orderings_Opreorder' [165, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.11/1.47 'class_Orderings_Olinorder' [171, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.11/1.47 'c_SetInterval_Oord_OlessThan' [172, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.11/1.47
% 1.11/1.47 'c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1' [173, 3] (w:1, o:188, a:1
% 1.11/1.47 , s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OSKIP' [174, 0] (w:1, o:104, a:1, s:1, b:0),
% 1.11/1.47 'c_Com_Ocom_OWhile' [175, 2] (w:1, o:174, a:1, s:1, b:0),
% 1.11/1.47 'c_Natural_Oevaln' [176, 4] (w:1, o:199, a:1, s:1, b:0),
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__max2__1__1' [180, 6] (w:1, o:204
% 1.11/1.47 , a:1, s:1, b:0),
% 1.11/1.47 'v_P' [183, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.11/1.47 'c_Hoare__Mirabelle_Otriple__valid' [184, 3] (w:1, o:189, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'tc_Hoare__Mirabelle_Otriple' [186, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1' [189, 2] (w:1, o:
% 1.11/1.47 175, a:1, s:1, b:0),
% 1.11/1.47 'c_Hoare__Mirabelle_Ohoare__valids' [190, 3] (w:1, o:190, a:1, s:1
% 1.11/1.47 , b:0),
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1' [191, 2] (w:1, o:
% 1.11/1.47 176, a:1, s:1, b:0),
% 1.11/1.47 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2' [192, 2] (w:1, o:
% 1.11/1.47 177, a:1, s:1, b:0),
% 1.11/1.47 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1' [194, 5] (w:1
% 1.11/1.47 , o:203, a:1, s:1, b:0),
% 1.11/1.47 'v_b' [196, 0] (w:1, o:112, a:1, s:1, b:0),
% 1.11/1.47 'v_c' [197, 0] (w:1, o:113, a:1, s:1, b:0),
% 1.11/1.47 'v_sa' [198, 0] (w:1, o:114, a:1, s:1, b:0),
% 1.11/1.47 'v_na' [199, 0] (w:1, o:115, a:1, s:1, b:0),
% 1.11/1.47 'v_G' [200, 0] (w:1, o:116, a:1, s:1, b:0),
% 1.11/1.47 'v_nb' [201, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.11/1.47 'c_fequal' [207, 3] (w:1, o:191, a:1, s:1, b:0).
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 Starting Search:
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 Bliksems!, er is een bewijs:
% 1.11/1.47 % SZS status Unsatisfiable
% 1.11/1.47 % SZS output start Refutation
% 1.11/1.47
% 1.11/1.47 clause( 325, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ]
% 1.11/1.47 )
% 1.11/1.47 .
% 1.11/1.47 clause( 333, [ =( 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' ), 'c_Com_Ocom_OSKIP' )
% 1.11/1.47 ] )
% 1.11/1.47 .
% 1.11/1.47 clause( 413, [] )
% 1.11/1.47 .
% 1.11/1.47
% 1.11/1.47
% 1.11/1.47 % SZS output end Refutation
% 1.11/1.47 found a proof!
% 1.11/1.47
% 1.11/1.47 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.11/1.47
% 1.11/1.47 initialclauses(
% 1.11/1.47 [ clause( 415, [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.47 , clause( 416, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U )
% 1.11/1.47 , ~( 'c_Natural_Oevalc'( Y, T, U ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 1.11/1.47 , clause( 417, [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevalc'( Z, Y, T )
% 1.11/1.47 , ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Z, U ), Y, T ) ) ] )
% 1.11/1.47 , clause( 418, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T ),
% 1.11/1.47 ~( 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) ) ]
% 1.11/1.47 )
% 1.11/1.47 , clause( 419, [ 'c_Com_OWT'( 'c_Com_Ocom_OAss'( X, Y ) ) ] )
% 1.11/1.47 , clause( 420, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.11/1.47 , clause( 421, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.47 , clause( 422, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 1.11/1.47 , clause( 423, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 1.11/1.47 , clause( 424, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 1.11/1.47 , clause( 425, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.47 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ] )
% 1.11/1.47 , clause( 426, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ] )
% 1.11/1.47 , clause( 427, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z )
% 1.11/1.47 ) ) ] )
% 1.11/1.47 , clause( 428, [ =( hAPP( 'c_COMBI'( X ), Y ), Y ) ] )
% 1.11/1.47 , clause( 429, [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP(
% 1.11/1.47 hAPP( X, W ), U ) ) ] )
% 1.11/1.47 , clause( 430, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.11/1.47 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ] )
% 1.11/1.47 , clause( 431, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 1.11/1.47 , V4 ) ) ] )
% 1.11/1.47 , clause( 432, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T
% 1.11/1.47 , U ) ) ) ] )
% 1.11/1.47 , clause( 433, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ] )
% 1.11/1.47 , clause( 434, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X,
% 1.11/1.47 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 1.11/1.47 , clause( 435, [ =( 'c_Fun_Ocomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ] )
% 1.11/1.47 , clause( 436, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Oid'( Y ), Y, Z, Y ), X ) ] )
% 1.11/1.47 , clause( 437, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.11/1.47 , clause( 438, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.11/1.47 , clause( 439, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.11/1.47 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.11/1.47 , clause( 440, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.47 , clause( 441, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 1.11/1.47 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 't_a', X )
% 1.11/1.47 ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( Y, 'v_x'
% 1.11/1.47 ), hAPP( Z, 'v_x' ), X ) ) ] )
% 1.11/1.47 , clause( 442, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ),
% 1.11/1.47 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.47 'tc_bool' ) ), Z ) ) ) ) ] )
% 1.11/1.47 , clause( 443, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z )
% 1.11/1.47 ) ) ] )
% 1.11/1.47 , clause( 444, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCall'( T
% 1.11/1.47 , U, W ) ) ) ] )
% 1.11/1.47 , clause( 445, [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ),
% 1.11/1.47 'c_lessequals'( hAPP( Y, Z ),
% 1.11/1.47 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( T, Y, U, X ), X )
% 1.11/1.47 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ] )
% 1.11/1.47 , clause( 446, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCond'(
% 1.11/1.47 T, U, W ) ) ) ] )
% 1.11/1.47 , clause( 447, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T
% 1.11/1.47 ) ) ) ] )
% 1.11/1.47 , clause( 448, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T
% 1.11/1.47 ) ) ) ] )
% 1.11/1.47 , clause( 449, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( Z, V2 )
% 1.11/1.47 , V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 )
% 1.11/1.47 ) ) ] )
% 1.11/1.47 , clause( 450, [ =( 'c_Set_Oimage'( 'c_COMBI'( X ), Y, X, X ), Y ) ] )
% 1.11/1.47 , clause( 451, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T
% 1.11/1.47 , U, W ) ) ), =( Z, W ) ] )
% 1.11/1.47 , clause( 452, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T
% 1.11/1.47 , U, W ) ) ), =( Y, U ) ] )
% 1.11/1.47 , clause( 453, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCall'( T
% 1.11/1.47 , U, W ) ) ), =( X, T ) ] )
% 1.11/1.47 , clause( 454, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.47 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( hAPP( T, V2 ), V3 )
% 1.11/1.47 , 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V2, V4 ) ),
% 1.11/1.47 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ] )
% 1.11/1.47 , clause( 455, [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.11/1.47 , clause( 456, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OLocal'( Y, Z,
% 1.11/1.47 T ) ) ) ] )
% 1.11/1.47 , clause( 457, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.11/1.47 'tc_bool' ) ), 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z,
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.11/1.47 , clause( 458, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.47 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.47 'c_Set_Oinsert'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.11/1.47 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 1.11/1.47 , clause( 459, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.47 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 1.11/1.47 Y, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.11/1.47 'tc_bool' ) ), T ) ) ] )
% 1.11/1.47 , clause( 460, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) )
% 1.11/1.47 ) ] )
% 1.11/1.47 , clause( 461, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 1.11/1.47 , clause( 462, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T
% 1.11/1.47 ) ) ), =( Y, T ) ] )
% 1.11/1.47 , clause( 463, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T
% 1.11/1.47 ) ) ), =( X, Z ) ] )
% 1.11/1.47 , clause( 464, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z, T
% 1.11/1.47 , U ) ) ) ] )
% 1.11/1.47 , clause( 465, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.11/1.47 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ] )
% 1.11/1.47 , clause( 466, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OLocal'( Z,
% 1.11/1.47 T, U ) ) ) ] )
% 1.11/1.47 , clause( 467, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z,
% 1.11/1.47 'c_Set_Oinsert'( hAPP( Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.11/1.47 T, 'tc_bool' ) ), T ), X, T ) ) ) ] )
% 1.11/1.48 , clause( 468, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), Z ) ) ] )
% 1.11/1.48 , clause( 469, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.11/1.48 'c_Set_Oinsert'( X, Y, Z ) ) ] )
% 1.11/1.48 , clause( 470, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OAss'( T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 471, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.11/1.48 'c_Set_Oinsert'( Z, X, T ), Y ) ) ) ] )
% 1.11/1.48 , clause( 472, [ ~( =(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.48 T, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool'
% 1.11/1.48 ) ) ) ), =( hAPP( Y, U ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), X ) ) ) ] )
% 1.11/1.48 , clause( 473, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OAss'( Y, Z ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 474, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OLocal'(
% 1.11/1.48 T, U, W ) ) ) ] )
% 1.11/1.48 , clause( 475, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 X ) ) ] )
% 1.11/1.48 , clause( 476, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.11/1.48 , clause( 477, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.11/1.48 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 478, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.11/1.48 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 479, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 480, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( X,
% 1.11/1.48 Y ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, X, T,
% 1.11/1.48 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ),
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, X, T, 'tc_fun'(
% 1.11/1.48 U, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z ) ) ) ] )
% 1.11/1.48 , clause( 481, [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.11/1.48 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.11/1.48 , X, V0, V1, V2, U, V3, V4, T ) ) ] )
% 1.11/1.48 , clause( 482, [ =( hAPP( X, 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( Z,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T ) ),
% 1.11/1.48 hAPP( hAPP( U, Y ), Z ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X
% 1.11/1.48 , W, V0, V1, U, V2, V3, V4, T ) ) ] )
% 1.11/1.48 , clause( 483, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T
% 1.11/1.48 , U, W ) ) ), =( Z, W ) ] )
% 1.11/1.48 , clause( 484, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T
% 1.11/1.48 , U, W ) ) ), =( Y, U ) ] )
% 1.11/1.48 , clause( 485, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T
% 1.11/1.48 , U, W ) ) ), =( X, T ) ] )
% 1.11/1.48 , clause( 486, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OCond'( T
% 1.11/1.48 , U, W ) ) ) ] )
% 1.11/1.48 , clause( 487, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X,
% 1.11/1.48 hAPP( Y, W ) ) ) ] )
% 1.11/1.48 , clause( 488, [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T,
% 1.11/1.48 U, W ), Z ) ) ] )
% 1.11/1.48 , clause( 489, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.11/1.48 , clause( 490, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 1.11/1.48 , clause( 491, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OLocal'( Z, T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 492, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL(
% 1.11/1.48 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), Y ) ) ) ] )
% 1.11/1.48 , clause( 493, [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ] )
% 1.11/1.48 , clause( 494, [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 1.11/1.48 , clause( 495, [ 'c_Com_OWT'( 'c_Com_Ocom_OCond'( X, Y, Z ) ), ~(
% 1.11/1.48 'c_Com_OWT'( Z ) ), ~( 'c_Com_OWT'( Y ) ) ] )
% 1.11/1.48 , clause( 496, [ =( 'c_Set_Ovimage'( 'c_COMBI'( X ), Y, X, X ), Y ) ] )
% 1.11/1.48 , clause( 497, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 498, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCond'( Y, Z, T
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 499, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 500, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 501, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 502, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 503, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 504, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 505, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y,
% 1.11/1.48 Z, T, 'tc_fun'( X, 'tc_bool' ) ) ) ), =( hAPP( Z, U ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( T ), U ), Y ) ) ) ] )
% 1.11/1.48 , clause( 506, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ] )
% 1.11/1.48 , clause( 507, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ] )
% 1.11/1.48 , clause( 508, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.11/1.48 X, 'tc_bool' ) ), Y ) ] )
% 1.11/1.48 , clause( 509, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.11/1.48 'tc_bool' ) ), X ) ] )
% 1.11/1.48 , clause( 510, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, X,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), T ) ] )
% 1.11/1.48 , clause( 511, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.11/1.48 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), X ) ] )
% 1.11/1.48 , clause( 512, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCond'( Z, T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 513, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.11/1.48 X, 'tc_bool' ) ), Y ) ) ) ] )
% 1.11/1.48 , clause( 514, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 515, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ] )
% 1.11/1.48 , clause( 516, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ] )
% 1.11/1.48 , clause( 517, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OAss'( Z, T
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 518, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 519, [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~(
% 1.11/1.48 'c_Natural_Oevalc'( Z, T, Y ) ) ] )
% 1.11/1.48 , clause( 520, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 521, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 522, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 523, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ] )
% 1.11/1.48 , clause( 524, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 525, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 526, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 527, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ] )
% 1.11/1.48 , clause( 528, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.11/1.48 'c_lessequals'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 529, [ 'c_Com_OWT'( 'c_Com_Ocom_OCall'( X, Y, Z ) ), ~(
% 1.11/1.48 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( Y ) ) ) ] )
% 1.11/1.48 , clause( 530, [ 'c_Com_OWT'( 'c_Com_Ocom_OBODY'( X ) ), ~( 'c_Com_OWT'(
% 1.11/1.48 'c_Com_Ocom_OCall'( Y, X, Z ) ) ) ] )
% 1.11/1.48 , clause( 531, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 532, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X
% 1.11/1.48 ), X ) ] )
% 1.11/1.48 , clause( 533, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X
% 1.11/1.48 ), X ) ] )
% 1.11/1.48 , clause( 534, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 535, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 536, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ] )
% 1.11/1.48 , clause( 537, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ] )
% 1.11/1.48 , clause( 538, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 539, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 540, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 541, [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, 'c_COMBC'(
% 1.11/1.48 Z, T, T, 'tc_bool' ), 'c_COMBC'( U, T, T, 'tc_bool' ), W, V0, V1, V2, T )
% 1.11/1.48 , ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, Z, U, V0, W, V2, V1
% 1.11/1.48 , T ) ) ] )
% 1.11/1.48 , clause( 542, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ] )
% 1.11/1.48 , clause( 543, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OCall'( Z, T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 544, [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Y, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X
% 1.11/1.48 , Z ) ] )
% 1.11/1.48 , clause( 545, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 546, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( Z ), X ), Y ) ) ] )
% 1.11/1.48 , clause( 547, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OBODY'(
% 1.11/1.48 T ) ) ) ] )
% 1.11/1.48 , clause( 548, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCall'( Y, Z, T
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 549, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OLocal'(
% 1.11/1.48 T, U, W ) ) ) ] )
% 1.11/1.48 , clause( 550, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 551, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.11/1.48 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 1.11/1.48 , clause( 552, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL(
% 1.11/1.48 hAPP( Y, T ) ) ) ] )
% 1.11/1.48 , clause( 553, [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T
% 1.11/1.48 , U ), U ), 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.11/1.48 T ), Y ), Z ) ) ) ] )
% 1.11/1.48 , clause( 554, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.48 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ] )
% 1.11/1.48 , clause( 555, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ] )
% 1.11/1.48 , clause( 556, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 557, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 558, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.11/1.48 , clause( 559, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 1.11/1.48 , clause( 560, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'(
% 1.11/1.48 'c_Fun_Oid'( T ), W, T, T, U ) ) ), =( hAPP( X, hAPP( Y, V0 ) ), hAPP( W
% 1.11/1.48 , V0 ) ) ] )
% 1.11/1.48 , clause( 561, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 562, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 1.11/1.48 , clause( 563, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 T, X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.11/1.48 , clause( 564, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 T, X ), ~( 'c_lessequals'( Z, T, X ) ) ] )
% 1.11/1.48 , clause( 565, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 566, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 1.11/1.48 , clause( 567, [ =( 'c_Set_Ovimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ] )
% 1.11/1.48 , clause( 568, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OSemi'( V2, V3 ), V4 ), hAPP( hAPP( T, V2 ), V3 ) ) ] )
% 1.11/1.48 , clause( 569, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSemi'(
% 1.11/1.48 T, U ) ) ) ] )
% 1.11/1.48 , clause( 570, [ =( 'c_Set_Ovimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U,
% 1.11/1.48 T ), 'c_Set_Ovimage'( Y, 'c_Set_Ovimage'( X, W, Z, T ), U, Z ) ) ] )
% 1.11/1.48 , clause( 571, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 572, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 573, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 1.11/1.48 , clause( 574, [ =( 'c_Set_Oimage'( 'c_Fun_Oid'( X ), Y, X, X ), Y ) ] )
% 1.11/1.48 , clause( 575, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) ) )
% 1.11/1.48 , =( X, Y ) ] )
% 1.11/1.48 , clause( 576, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OCall'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( V1, V2 ), V3 )
% 1.11/1.48 , V4 ) ) ] )
% 1.11/1.48 , clause( 577, [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 578, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 579, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 580, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 581, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 582, [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.11/1.48 ) ), 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), Z, X ) ) ] )
% 1.11/1.48 , clause( 583, [ 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( X, Y, Z ) ), ~(
% 1.11/1.48 'c_Com_OWT'( Z ) ) ] )
% 1.11/1.48 , clause( 584, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OLocal'( Y,
% 1.11/1.48 Z, X ) ) ) ] )
% 1.11/1.48 , clause( 585, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ] )
% 1.11/1.48 , clause( 586, [ =( 'c_Set_Ovimage'( X,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), U, T ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 1.11/1.48 , 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 587, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCall'( Z, T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 588, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 1.11/1.48 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 589, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OAss'( V2, V3 ), V4 ), hAPP( hAPP( Y, V2 ), V3 ) ) ] )
% 1.11/1.48 , clause( 590, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OAss'( T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 591, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), Y ) ) ) ] )
% 1.11/1.48 , clause( 592, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), Y ) ) ) ] )
% 1.11/1.48 , clause( 593, [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ] )
% 1.11/1.48 , clause( 594, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( hAPP( hAPP( U,
% 1.11/1.48 V2 ), V3 ), V4 ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3,
% 1.11/1.48 V5 ) ), 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V4, V5 ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 595, [ =( 'c_Set_Ovimage'( X,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), U, T ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Set_Ovimage'( X, Y, U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U
% 1.11/1.48 , 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 596, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.11/1.48 , clause( 597, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.11/1.48 , clause( 598, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_SetInterval_Oord_OatLeastLessThan'( Z, T, U, W, X ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( T, Y ), W ) ) ), ~( hBOOL( hAPP( hAPP( Z, U ), Y ) ) ) ] )
% 1.11/1.48 , clause( 599, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T
% 1.11/1.48 , X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.11/1.48 , clause( 600, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T
% 1.11/1.48 , X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.11/1.48 , clause( 601, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_SetInterval_Oord_OatLeastAtMost'( Z, T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.11/1.48 hAPP( Z, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( Z, T ), Y ) ) ) ] )
% 1.11/1.48 , clause( 602, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ] )
% 1.11/1.48 , clause( 603, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ] )
% 1.11/1.48 , clause( 604, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.11/1.48 , clause( 605, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.11/1.48 Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 606, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.11/1.48 , clause( 607, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.11/1.48 , clause( 608, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 609, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP(
% 1.11/1.48 hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ) ) ] )
% 1.11/1.48 , clause( 610, [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__XbexE__1__1'( Y
% 1.11/1.48 , X, Z ) ) ), ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.11/1.48 ), T ), Y ) ) ) ] )
% 1.11/1.48 , clause( 611, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z
% 1.11/1.48 , X ) ) ) ] )
% 1.11/1.48 , clause( 612, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z
% 1.11/1.48 , X ) ) ) ] )
% 1.11/1.48 , clause( 613, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z
% 1.11/1.48 , X ) ) ) ] )
% 1.11/1.48 , clause( 614, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.11/1.48 hAPP( 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( T,
% 1.11/1.48 Z, 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.11/1.48 , clause( 615, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.11/1.48 hAPP( 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.11/1.48 T, 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ] )
% 1.11/1.48 , clause( 616, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.11/1.48 Z ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 617, [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ), 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.11/1.48 X, 'tc_bool' ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ] )
% 1.11/1.48 , clause( 618, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z
% 1.11/1.48 ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( Z ), X ), Y ) ), =( Y, T ) ] )
% 1.11/1.48 , clause( 619, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.11/1.48 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.11/1.48 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ] )
% 1.11/1.48 , clause( 620, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Z, T, U, 'tc_fun'(
% 1.11/1.48 X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( T, W
% 1.11/1.48 ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), Z ) ) ) ] )
% 1.11/1.48 , clause( 621, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T
% 1.11/1.48 , X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 622, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T
% 1.11/1.48 , X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 623, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T
% 1.11/1.48 , X, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 624, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 625, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ] )
% 1.11/1.48 , clause( 626, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.11/1.48 'c_lessequals'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 627, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.48 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ] )
% 1.11/1.48 , clause( 628, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.48 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ] )
% 1.11/1.48 , clause( 629, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.48 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 1.11/1.48 , clause( 630, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.11/1.48 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ] )
% 1.11/1.48 , clause( 631, [ 'c_Natural_Oevalc'( X, Y, Z ), hBOOL( hAPP( T, Y ) ), ~(
% 1.11/1.48 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( T, U, X ), Y, Z ) ) ] )
% 1.11/1.48 , clause( 632, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U )
% 1.11/1.48 , ~( 'c_Natural_Oevalc'( Z, T, U ) ), hBOOL( hAPP( X, T ) ) ] )
% 1.11/1.48 , clause( 633, [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.48 'c_Set_Oinsert'( X, Y, Z ), T, Z, 'tc_fun'( U, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( T, X ),
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( Y, T, Z, 'tc_fun'(
% 1.11/1.48 U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 634, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ] )
% 1.11/1.48 , clause( 635, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ] )
% 1.11/1.48 , clause( 636, [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ] )
% 1.11/1.48 , clause( 637, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( Y, X
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 638, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 639, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.48 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'( Y, Z, T, X ) ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( T, U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( X ), U ), Y ) ) ) ] )
% 1.11/1.48 , clause( 640, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.48 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'( Y, Z, T, X ) ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( T, U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( X ), U ), Z ) ) ) ] )
% 1.11/1.48 , clause( 641, [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y
% 1.11/1.48 ), hAPP( X, Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W, X,
% 1.11/1.48 V0, V1, V2, U, V3, V4, T ) ) ] )
% 1.11/1.48 , clause( 642, [ =( hAPP( X, 'c_Set_Oinsert'( Y, Z, T ) ), hAPP( hAPP( U, Y
% 1.11/1.48 ), hAPP( X, Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, W,
% 1.11/1.48 V0, V1, U, V2, V3, V4, T ) ) ] )
% 1.11/1.48 , clause( 643, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ] )
% 1.11/1.48 , clause( 644, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OLocal'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( Z, V2 ), V3 )
% 1.11/1.48 , V4 ) ) ] )
% 1.11/1.48 , clause( 645, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X )
% 1.11/1.48 , T ) ) ) ] )
% 1.11/1.48 , clause( 646, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.48 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 1.11/1.48 Y, 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 647, [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.11/1.48 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ] )
% 1.11/1.48 , clause( 648, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W ), hAPP( Y,
% 1.11/1.48 hAPP( X, W ) ) ) ] )
% 1.11/1.48 , clause( 649, [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y
% 1.11/1.48 ), 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Z,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( U, 'tc_bool' ) ), U ), T, U ) )
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 650, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ] )
% 1.11/1.48 , clause( 651, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ] )
% 1.11/1.48 , clause( 652, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 653, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 654, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 655, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 Z, X ) ] )
% 1.11/1.48 , clause( 656, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.11/1.48 Y, X ) ] )
% 1.11/1.48 , clause( 657, [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0
% 1.11/1.48 , W ), 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 658, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T )
% 1.11/1.48 ) ), =( Y, T ) ] )
% 1.11/1.48 , clause( 659, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OAss'( Z, T )
% 1.11/1.48 ) ), =( X, Z ) ] )
% 1.11/1.48 , clause( 660, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OAss'( T
% 1.11/1.48 , U ) ) ) ] )
% 1.11/1.48 , clause( 661, [ =( 'c_Set_Oinsert'( X,
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Z, Y,
% 1.11/1.48 'tc_fun'( T, 'tc_bool' ) ), T ), 'c_Set_Oinsert'( X,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ) ) ] )
% 1.11/1.48 , clause( 662, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 663, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.11/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 664, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 665, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 1.11/1.48 , clause( 666, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.11/1.48 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 667, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 668, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 1.11/1.48 , clause( 669, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 670, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 671, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 672, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 673, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'(
% 1.11/1.48 T, U, W ) ) ), =( Z, W ) ] )
% 1.11/1.48 , clause( 674, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'(
% 1.11/1.48 T, U, W ) ) ), =( Y, U ) ] )
% 1.11/1.48 , clause( 675, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OLocal'(
% 1.11/1.48 T, U, W ) ) ), =( X, T ) ] )
% 1.11/1.48 , clause( 676, [ 'c_Com_OWT'( 'c_Com_Ocom_OSemi'( X, Y ) ), ~( 'c_Com_OWT'(
% 1.11/1.48 Y ) ), ~( 'c_Com_OWT'( X ) ) ] )
% 1.11/1.48 , clause( 677, [ =( 'c_Fun_Ofcomp'( X, 'c_Fun_Oid'( Y ), Z, Y, Y ), X ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 678, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Oid'( X ), Y, X, X, Z ), Y ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 679, [ =( 'c_Set_Oimage'( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W, U, T
% 1.11/1.48 ), 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, W, U, Z ), Z, T ) ) ] )
% 1.11/1.48 , clause( 680, [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.11/1.48 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X,
% 1.11/1.48 U, W, V0, V1, Z, V2, Y ) ) ] )
% 1.11/1.48 , clause( 681, [ =( hAPP( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.11/1.48 'tc_bool' ) ) ), Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T,
% 1.11/1.48 U, W, V0, V1, V2, Z, Y ) ) ] )
% 1.11/1.48 , clause( 682, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 1.11/1.48 , clause( 683, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 1.11/1.48 , clause( 684, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ] )
% 1.11/1.48 , clause( 685, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X,
% 1.11/1.48 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 1.11/1.48 , clause( 686, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 1.11/1.48 , clause( 687, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 1.11/1.48 , clause( 688, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 1.11/1.48 , clause( 689, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 1.11/1.48 ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 1.11/1.48 , clause( 690, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 1.11/1.48 , clause( 691, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.11/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 1.11/1.48 , clause( 692, [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( 't_a', X )
% 1.11/1.48 ), 'v_x' ), 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( Y, 'v_x'
% 1.11/1.48 ), hAPP( Z, 'v_x' ), X ) ) ] )
% 1.11/1.48 , clause( 693, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 1.11/1.48 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 1.11/1.48 , clause( 694, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 695, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.11/1.48 , clause( 696, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y
% 1.11/1.48 , 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 697, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 1.11/1.48 , clause( 698, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y,
% 1.11/1.48 X ) ] )
% 1.11/1.48 , clause( 699, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 Y, X ) ] )
% 1.11/1.48 , clause( 700, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 701, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OBODY'( V2 ), V3 ), hAPP( V0, V2 ) ) ] )
% 1.11/1.48 , clause( 702, [ =( hAPP( X, 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ),
% 1.11/1.48 ~( 'c_Complete__Lattice_Ocomplete__lattice'( T, X, U, W, V0, V1, V2, V3,
% 1.11/1.48 Z ) ) ] )
% 1.11/1.48 , clause( 703, [ =( hAPP( X, 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), Y ),
% 1.11/1.48 ~( 'c_Complete__Lattice_Ocomplete__lattice'( X, T, U, W, V0, V1, V2, V3,
% 1.11/1.48 Z ) ) ] )
% 1.11/1.48 , clause( 704, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ] )
% 1.11/1.48 , clause( 705, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OCond'( V2, V3, V4 ), V5 ), hAPP( hAPP( hAPP( U, V2 ), V3 ),
% 1.11/1.48 V4 ) ) ] )
% 1.11/1.48 , clause( 706, [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0
% 1.11/1.48 , V1, T, U ) ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 707, [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) )
% 1.11/1.48 , =( hAPP( 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T
% 1.11/1.48 , U, V3, V1, V4 ), W ) ) ] )
% 1.11/1.48 , clause( 708, [ =( 'c_Set_Ovimage'( X, 'c_Set_Oinsert'( Y, Z, T ), U, T )
% 1.11/1.48 , 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Ovimage'( X,
% 1.11/1.48 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), T ), U, T ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U,
% 1.11/1.48 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 709, [ =( 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.11/1.48 'tc_bool' ) ), T, Z, 'tc_fun'( U, 'tc_bool' ) ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, T, Z, 'tc_fun'(
% 1.11/1.48 U, 'tc_bool' ) ), 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'(
% 1.11/1.48 Y, T, Z, 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 710, [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP(
% 1.11/1.48 'c_Set_Ovimage'( Y, X, T, U ), Z ) ) ) ] )
% 1.11/1.48 , clause( 711, [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~(
% 1.11/1.48 hBOOL( hAPP( Y, hAPP( X, U ) ) ) ) ] )
% 1.11/1.48 , clause( 712, [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~(
% 1.11/1.48 hBOOL( hAPP( X, T ) ) ) ] )
% 1.11/1.48 , clause( 713, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.11/1.48 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 714, [ =( 'c_Set_Oimage'( X,
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.11/1.48 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 1.11/1.48 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 715, [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Y, 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'(
% 1.11/1.48 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 1.11/1.48 , clause( 716, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OCall'(
% 1.11/1.48 T, U, W ) ) ) ] )
% 1.11/1.48 , clause( 717, [ 'c_Natural_Oevalc'( X, Y, Z ), 'c_Natural_Oevalc'( T, Y, Z
% 1.11/1.48 ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( U, T, X ), Y, Z ) ) ] )
% 1.11/1.48 , clause( 718, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.11/1.48 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 719, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 1.11/1.48 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 1.11/1.48 , clause( 720, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, Z
% 1.11/1.48 , X ) ) ) ] )
% 1.11/1.48 , clause( 721, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OCond'( Y, X
% 1.11/1.48 , Z ) ) ) ] )
% 1.11/1.48 , clause( 722, [ =( 'c_Fun_Ofcomp'( 'c_Fun_Ofcomp'( X, Y, Z, T, U ), W, Z,
% 1.11/1.48 U, V0 ), 'c_Fun_Ofcomp'( X, 'c_Fun_Ofcomp'( Y, W, T, U, V0 ), Z, T, V0 )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 723, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.11/1.48 'tc_nat' ) ] )
% 1.11/1.48 , clause( 724, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.11/1.48 Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 1.11/1.48 , clause( 725, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 726, [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( U ), T ), Z ) ) ), ~(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice'( Y, W, X, V0, V1, V2, V3, V4, U
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 727, [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ), ~(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice'( W, Z, X, V0, V1, V2, V3, V4, U
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 728, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), Y ), 'c_SetInterval_Oord_OatLeastAtMost'( X, U, Z, T ) ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 729, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), Z ), 'c_SetInterval_Oord_OatLeastAtMost'( X, Y, U, T ) ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 730, [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'(
% 1.11/1.48 Y, Z, X, T ) ) ), ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), U ), Z ) ) ) ] )
% 1.11/1.48 , clause( 731, [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Set__Xbex__Un__1__3'(
% 1.11/1.48 Y, Z, X, T ) ) ), ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), U ), Y ) ) ) ] )
% 1.11/1.48 , clause( 732, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.48 'c_ATP__Linkup_Osko__Set__XbexE__1__1'( Y, Z, X ) ), Y ) ), ~( hBOOL(
% 1.11/1.48 hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ) ] )
% 1.11/1.48 , clause( 733, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( Z ), X ), Y ) ) ) ] )
% 1.11/1.48 , clause( 734, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.11/1.48 'c_SetInterval_Oord_OlessThan'( Z, T, X ) ) ), ~( hBOOL( hAPP( hAPP( Z, Y
% 1.11/1.48 ), T ) ) ) ] )
% 1.11/1.48 , clause( 735, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), Y ), 'c_SetInterval_Oord_OlessThan'( X, Z, T ) ) ) ) ] )
% 1.11/1.48 , clause( 736, [ hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.48 T, 'tc_fun'( U, 'tc_bool' ) ) ), W ), V0 ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.11/1.48 Y, V1 ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), V1 ), X ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 737, [ hBOOL( hAPP(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.48 T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ), U ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ] )
% 1.11/1.48 , clause( 738, [ hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.48 T, 'tc_fun'( U, 'tc_bool' ) ) ), W ), V0 ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.11/1.48 Y, V1 ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), V1 ), X ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 739, [ hBOOL( hAPP(
% 1.11/1.48 'c_Complete__Lattice_Ocomplete__lattice__class_OSUPR'( X, Y, Z, 'tc_fun'(
% 1.11/1.48 T, 'tc_bool' ) ), U ) ), ~( hBOOL( hAPP( hAPP( Y, W ), U ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( Z ), W ), X ) ) ) ] )
% 1.11/1.48 , clause( 740, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), Y ), 'c_SetInterval_Oord_OatLeastLessThan'( U, X, W, Z, T )
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 741, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'c_in'( T ), Z ), 'c_SetInterval_Oord_OatLeastLessThan'( X, U, Y, W, T )
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 742, [ hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.11/1.48 'c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1'( Y, Z, X ) ), Y ) ), ~( hBOOL(
% 1.11/1.48 hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), Y ) ) ) ] )
% 1.11/1.48 , clause( 743, [ hBOOL( hAPP( X,
% 1.11/1.48 'c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1'( Y, X, Z ) ) ), ~( hBOOL(
% 1.11/1.48 hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), Y ) ) ) ] )
% 1.11/1.48 , clause( 744, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 745, [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL(
% 1.11/1.48 hAPP( hAPP( 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 746, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.11/1.48 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 1.11/1.48 , T ) ) ) ] )
% 1.11/1.48 , clause( 747, [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ),
% 1.11/1.48 'c_Set_Oimage'( Y, T, U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z )
% 1.11/1.48 , T ) ) ) ] )
% 1.11/1.48 , clause( 748, [ =( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.11/1.48 hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 1.11/1.48 'tc_bool' ), X ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'(
% 1.11/1.48 't_a', 'tc_bool' ), 'tc_bool' ), Y ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.11/1.48 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.11/1.48 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 't_a',
% 1.11/1.48 'tc_bool' ) ) ) ) ] )
% 1.11/1.48 , clause( 749, [ =( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.11/1.48 hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 1.11/1.48 'tc_bool' ), X ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'(
% 1.11/1.48 't_a', 'tc_bool' ), 'tc_bool' ), Y ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.11/1.48 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.11/1.48 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 't_a',
% 1.11/1.48 'tc_bool' ) ) ) ) ] )
% 1.11/1.48 , clause( 750, [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, 't_a' ), 'v_x' ), hAPP(
% 1.11/1.48 X, hAPP( Y, 'v_x' ) ) ) ] )
% 1.11/1.48 , clause( 751, [ =( hAPP( 'c_Fun_Oid'( 't_a' ), 'v_x' ), 'v_x' ) ] )
% 1.11/1.48 , clause( 752, [ =( hAPP( 'c_Fun_Ofcomp'( X, Y, 't_a', Z, T ), 'v_x' ),
% 1.11/1.48 hAPP( Y, hAPP( X, 'v_x' ) ) ) ] )
% 1.11/1.48 , clause( 753, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 754, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 755, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ] )
% 1.11/1.48 , clause( 756, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OSKIP' )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 757, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCall'( X, Y, Z ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 758, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 759, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OAss'( X, Y ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 760, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OSKIP' )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 761, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ] )
% 1.11/1.48 , clause( 762, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OLocal'( X, Y, Z ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 763, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OSKIP', V2 ), X ) ] )
% 1.11/1.48 , clause( 764, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OSKIP', V2 ), X ) ] )
% 1.11/1.48 , clause( 765, [ 'c_Com_OWT'( 'c_Com_Ocom_OSKIP' ) ] )
% 1.11/1.48 , clause( 766, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z ) )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 767, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP' )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 768, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ] )
% 1.11/1.48 , clause( 769, [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y, X
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 770, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OBODY'( Z )
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 771, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevalc'(
% 1.11/1.48 'c_Com_Ocom_OWhile'( X, T ), Y, Z ) ) ] )
% 1.11/1.48 , clause( 772, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'( Z,
% 1.11/1.48 T ) ) ) ] )
% 1.11/1.48 , clause( 773, [ =( 'c_Com_Ocom_Ocom__case'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( W, V2 ), V3 ) ) ] )
% 1.11/1.48 , clause( 774, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OAss'( Z, T
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 775, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCall'( Z,
% 1.11/1.48 T, U ) ) ) ] )
% 1.11/1.48 , clause( 776, [ ~( =( 'c_Com_Ocom_OLocal'( X, Y, Z ), 'c_Com_Ocom_OWhile'(
% 1.11/1.48 T, U ) ) ) ] )
% 1.11/1.48 , clause( 777, [ ~( =( 'c_Com_Ocom_OAss'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T
% 1.11/1.48 ) ) ) ] )
% 1.11/1.48 , clause( 778, [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OWhile'(
% 1.11/1.48 T, U ) ) ) ] )
% 1.11/1.48 , clause( 779, [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'( Z,
% 1.11/1.48 T ) ) ) ] )
% 1.11/1.48 , clause( 780, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, Z ),
% 1.11/1.48 hBOOL( hAPP( X, Z ) ) ] )
% 1.11/1.48 , clause( 781, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OLocal'( Z
% 1.11/1.48 , T, U ) ) ) ] )
% 1.11/1.48 , clause( 782, [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OWhile'( Y, Z )
% 1.11/1.48 ) ) ] )
% 1.11/1.48 , clause( 783, [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T ),
% 1.11/1.48 ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), U, T ) ), ~(
% 1.11/1.48 'c_Natural_Oevalc'( Y, Z, U ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 1.11/1.48 , clause( 784, [ ~( =( 'c_Com_Ocom_OCall'( X, Y, Z ), 'c_Com_Ocom_OWhile'(
% 1.11/1.48 T, U ) ) ) ] )
% 1.11/1.48 , clause( 785, [ 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( X, Y ) ), ~( 'c_Com_OWT'(
% 1.11/1.48 Y ) ) ] )
% 1.11/1.48 , clause( 786, [ 'c_Com_OWT'( X ), ~( 'c_Com_OWT'( 'c_Com_Ocom_OWhile'( Y,
% 1.11/1.48 X ) ) ) ] )
% 1.11/1.48 , clause( 787, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'( Z,
% 1.11/1.48 T, U ) ) ) ] )
% 1.11/1.48 , clause( 788, [ =( 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1,
% 1.11/1.48 'c_Com_Ocom_OWhile'( V2, V3 ), V4 ), hAPP( hAPP( hAPP( W, V2 ), V3 ),
% 1.11/1.48 'c_Com_Ocom_Ocom__rec'( X, Y, Z, T, U, W, V0, V1, V3, V4 ) ) ) ] )
% 1.11/1.48 , clause( 789, [ 'c_Natural_Oevaln'( X, Y, Z, T ), 'c_Natural_Oevaln'( U, Y
% 1.11/1.48 , Z, T ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( W, U, X ), Y, Z, T )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 790, [ 'c_Natural_Oevaln'( X, Y, Z, T ), ~( 'c_lessequals'( U, Z
% 1.11/1.48 , 'tc_nat' ) ), ~( 'c_Natural_Oevaln'( X, Y, U, T ) ) ] )
% 1.11/1.48 , clause( 791, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W
% 1.11/1.48 ), ~( 'c_Natural_Oevaln'( Z, T, U, W ) ), hBOOL( hAPP( X, T ) ) ] )
% 1.11/1.48 , clause( 792, [ 'c_Natural_Oevaln'( X, Y, Z, T ), hBOOL( hAPP( U, Y ) ),
% 1.11/1.48 ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( U, W, X ), Y, Z, T ) ) ] )
% 1.11/1.48 , clause( 793, [ 'c_Natural_Oevaln'( X, Y, 'c_Suc'( Z ), T ), ~(
% 1.11/1.48 'c_Natural_Oevaln'( X, Y, Z, T ) ) ] )
% 1.11/1.48 , clause( 794, [ 'c_Natural_Oevaln'( X, Y,
% 1.11/1.48 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( Z, X, T, Y, U, W ), W ),
% 1.11/1.48 ~( 'c_Natural_Oevaln'( X, Y, V0, W ) ), ~( 'c_Natural_Oevaln'( Z, T, V1,
% 1.11/1.48 U ) ) ] )
% 1.11/1.48 , clause( 795, [ 'c_Natural_Oevaln'( X, Y,
% 1.11/1.48 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( X, Z, Y, T, U, W ), U ),
% 1.11/1.48 ~( 'c_Natural_Oevaln'( Z, T, V0, W ) ), ~( 'c_Natural_Oevaln'( X, Y, V1,
% 1.11/1.48 U ) ) ] )
% 1.11/1.48 , clause( 796, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U, W
% 1.11/1.48 ), ~( 'c_Natural_Oevaln'( Y, T, U, W ) ), ~( hBOOL( hAPP( X, T ) ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 797, [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevaln'( Z, Y, T, U
% 1.11/1.48 ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OCond'( X, Z, W ), Y, T, U ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 798, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T, U )
% 1.11/1.48 , ~( 'c_Natural_Oevaln'( Y, W, T, U ) ), ~( 'c_Natural_Oevaln'( X, Z, T,
% 1.11/1.48 W ) ) ] )
% 1.11/1.48 , clause( 799, [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y
% 1.11/1.48 , T, Z ) ) ] )
% 1.11/1.48 , clause( 800, [ 'c_Natural_Oevalc'( X, Y, Z ), ~( 'c_Natural_Oevaln'( X, Y
% 1.11/1.48 , T, Z ) ) ] )
% 1.11/1.48 , clause( 801, [ =( hAPP( 'c_COMBI'( 't_a' ), 'v_P' ), 'v_P' ) ] )
% 1.11/1.48 , clause( 802, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, Z ), ~(
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ), Y, Z ) ) ] )
% 1.11/1.48 , clause( 803, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.11/1.48 , Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.11/1.48 't_a' ) ), 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ) ), T
% 1.11/1.48 ) ), ~( 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ] )
% 1.11/1.48 , clause( 804, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.11/1.48 , Z ) ) ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( 'c_Suc'( X ),
% 1.11/1.48 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ), 't_a' ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 805, [ 'c_Hoare__Mirabelle_Ohoare__valids'( X, Y, 't_a' ),
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple__valid'(
% 1.11/1.48 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__2'( X, Y ), Z, 't_a' ),
% 1.11/1.48 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Z
% 1.11/1.48 ), X ) ) ) ] )
% 1.11/1.48 , clause( 806, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.11/1.48 , Z ) ) ), ~( 'c_Hoare__Mirabelle_Otriple__valid'( X,
% 1.11/1.48 'v_sko__Hoare__Mirabelle__Xhoare__valids__def__1'( T, X ), 't_a' ) ), ~(
% 1.11/1.48 'c_Hoare__Mirabelle_Ohoare__valids'( T, Z, 't_a' ) ) ] )
% 1.11/1.48 , clause( 807, [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a',
% 1.11/1.48 'tc_bool' ) ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.11/1.48 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ] )
% 1.11/1.48 , clause( 808, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ),
% 1.11/1.48 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( X, Y, Z, T, U ), Z
% 1.11/1.48 , U ), ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_Natural_Oevaln'(
% 1.11/1.48 'c_Com_Ocom_OWhile'( X, Y ), T, Z, U ) ) ] )
% 1.11/1.48 , clause( 809, [ 'c_Natural_Oevaln'( X, Y, Z,
% 1.11/1.48 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( T, X, Z, Y, U ) ),
% 1.11/1.48 =( U, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( T, X ), Y, Z, U )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 810, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ),
% 1.11/1.48 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( X, Y, Z, T, U ), Z
% 1.11/1.48 , U ), =( U, T ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), T,
% 1.11/1.48 Z, U ) ) ] )
% 1.11/1.48 , clause( 811, [ 'c_Natural_Oevaln'( X, Y, Z,
% 1.11/1.48 'c_Natural_Osko__Natural__Xevaln__WHILE__case__1__1'( T, X, Z, Y, U ) ),
% 1.11/1.48 ~( hBOOL( hAPP( T, Y ) ) ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( T
% 1.11/1.48 , X ), Y, Z, U ) ) ] )
% 1.11/1.48 , clause( 812, [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( 'c_Natural_Oevaln'( T
% 1.11/1.48 , U, W, Z ) ), ~( hBOOL( hAPP( hAPP( V0, Y ), U ) ) ), ~(
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple__valid'( W,
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, X, 't_a' ), 't_a' ) ) ] )
% 1.11/1.48 , clause( 813, [ 'c_Hoare__Mirabelle_Otriple__valid'( X, Y, 't_a' ), ~(
% 1.11/1.48 hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), Y )
% 1.11/1.48 , Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'(
% 1.11/1.48 't_a' ) ), 'v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1'( X, Z ) ),
% 1.11/1.48 Z ) ) ] )
% 1.11/1.48 , clause( 814, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevaln'(
% 1.11/1.48 'c_Com_Ocom_OWhile'( X, T ), Y, U, Z ) ) ] )
% 1.11/1.48 , clause( 815, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', X, Y, X ) ] )
% 1.11/1.48 , clause( 816, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 817, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 818, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, Z )
% 1.11/1.48 , hBOOL( hAPP( X, Z ) ) ] )
% 1.11/1.48 , clause( 819, [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.11/1.48 Z, Y ) ) ) ] )
% 1.11/1.48 , clause( 820, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ),
% 1.11/1.48 Y ), X ) ) ) ] )
% 1.11/1.48 , clause( 821, [ 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T, U )
% 1.11/1.48 , ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OWhile'( X, Y ), W, T, U ) ), ~(
% 1.11/1.48 'c_Natural_Oevaln'( Y, Z, T, W ) ), ~( hBOOL( hAPP( X, Z ) ) ) ] )
% 1.11/1.48 , clause( 822, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z
% 1.11/1.48 , T ) ) ), =( X, Z ) ] )
% 1.11/1.48 , clause( 823, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z
% 1.11/1.48 , T ) ) ), =( Y, T ) ] )
% 1.11/1.48 , clause( 824, [ =( X, Y ), ~( 'c_Natural_Oevaln'( 'c_Com_Ocom_OSKIP', Y, Z
% 1.11/1.48 , X ) ) ] )
% 1.11/1.48 , clause( 825, [ =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' )
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 826, [ hBOOL( hAPP( hAPP( 'v_P', 'v_x' ), 'v_sa' ) ) ] )
% 1.11/1.48 , clause( 827, [ 'c_Hoare__Mirabelle_Otriple__valid'( 'v_na', X, 't_a' ),
% 1.11/1.48 ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), X
% 1.11/1.48 ), 'v_G' ) ) ) ] )
% 1.11/1.48 , clause( 828, [ hBOOL( hAPP( 'v_b', 'v_sa' ) ), ~( hBOOL( hAPP( hAPP(
% 1.11/1.48 'v_P', 'v_x' ), 'v_sa' ) ) ) ] )
% 1.11/1.48 , clause( 829, [ hBOOL( hAPP( hAPP( 'v_P', X ), Y ) ), ~(
% 1.11/1.48 'c_Natural_Oevaln'( 'v_c', Z, T, Y ) ), ~( hBOOL( hAPP( 'v_b', Z ) ) ),
% 1.11/1.48 ~( hBOOL( hAPP( hAPP( 'v_P', X ), Z ) ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.11/1.48 'tc_Hoare__Mirabelle_Otriple'( 't_a' ) ), 'v_nb'( T ) ), 'v_G' ) ) ] )
% 1.11/1.48 , clause( 830, [ hBOOL( hAPP( hAPP( 'v_P', X ), Y ) ), ~(
% 1.11/1.48 'c_Natural_Oevaln'( 'v_c', Z, T, Y ) ), ~( hBOOL( hAPP( 'v_b', Z ) ) ),
% 1.11/1.48 ~( hBOOL( hAPP( hAPP( 'v_P', X ), Z ) ) ), ~(
% 1.11/1.48 'c_Hoare__Mirabelle_Otriple__valid'( T, 'v_nb'( T ), 't_a' ) ) ] )
% 1.11/1.48 , clause( 831, [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X
% 1.11/1.48 , Y ) ), ~( 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ] )
% 1.11/1.48 , clause( 832, [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ),
% 1.11/1.48 ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.11/1.48 , clause( 833, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ),
% 1.11/1.48 ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 1.11/1.48 , clause( 834, [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ),
% 1.11/1.48 ~( 'class_Lattices_Odistrib__lattice'( Y ) ) ] )
% 1.11/1.48 , clause( 835, [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ),
% 1.11/1.48 ~( 'class_Lattices_Obounded__lattice'( Y ) ) ] )
% 1.11/1.48 , clause( 836, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.48 'class_Orderings_Opreorder'( Y ) ) ] )
% 1.11/1.48 , clause( 837, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.48 'class_Lattices_Olattice'( Y ) ) ] )
% 1.11/1.48 , clause( 838, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.48 'class_Orderings_Oorder'( Y ) ) ] )
% 1.11/1.48 , clause( 839, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 1.11/1.48 'class_Orderings_Obot'( Y ) ) ] )
% 1.11/1.48 , clause( 840, [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 841, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 842, [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 843, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 844, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 845, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 846, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 847, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 1.11/1.48 , clause( 848, [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 849, [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 850, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 851, [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 852, [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 853, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 854, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 855, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 856, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 1.11/1.48 , clause( 857, [ 'c_fequal'( X, X, Y ) ] )
% 1.11/1.48 , clause( 858, [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ] )
% 1.11/1.48 ] ).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 eqswap(
% 1.11/1.48 clause( 1190, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 816, [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) ) )
% 1.11/1.48 ] )
% 1.11/1.48 , 0, substitution( 0, [ :=( X, X ), :=( Y, Y )] )).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 subsumption(
% 1.11/1.48 clause( 325, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ]
% 1.11/1.48 )
% 1.11/1.48 , clause( 1190, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) )
% 1.11/1.48 ] )
% 1.11/1.48 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 1.11/1.48 )] ) ).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 eqswap(
% 1.11/1.48 clause( 1527, [ =( 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' ), 'c_Com_Ocom_OSKIP'
% 1.11/1.48 ) ] )
% 1.11/1.48 , clause( 825, [ =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' )
% 1.11/1.48 ) ] )
% 1.11/1.48 , 0, substitution( 0, [] )).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 subsumption(
% 1.11/1.48 clause( 333, [ =( 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' ), 'c_Com_Ocom_OSKIP' )
% 1.11/1.48 ] )
% 1.11/1.48 , clause( 1527, [ =( 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' ),
% 1.11/1.48 'c_Com_Ocom_OSKIP' ) ] )
% 1.11/1.48 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 resolution(
% 1.11/1.48 clause( 1530, [] )
% 1.11/1.48 , clause( 325, [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) )
% 1.11/1.48 ] )
% 1.11/1.48 , 0, clause( 333, [ =( 'c_Com_Ocom_OWhile'( 'v_b', 'v_c' ),
% 1.11/1.48 'c_Com_Ocom_OSKIP' ) ] )
% 1.11/1.48 , 0, substitution( 0, [ :=( X, 'v_b' ), :=( Y, 'v_c' )] ), substitution( 1
% 1.11/1.48 , [] )).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 subsumption(
% 1.11/1.48 clause( 413, [] )
% 1.11/1.48 , clause( 1530, [] )
% 1.11/1.48 , substitution( 0, [] ), permutation( 0, [] ) ).
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 end.
% 1.11/1.48
% 1.11/1.48 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.11/1.48
% 1.11/1.48 Memory use:
% 1.11/1.48
% 1.11/1.48 space for terms: 22486
% 1.11/1.48 space for clauses: 40161
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 clauses generated: 581
% 1.11/1.48 clauses kept: 414
% 1.11/1.48 clauses selected: 35
% 1.11/1.48 clauses deleted: 2
% 1.11/1.48 clauses inuse deleted: 0
% 1.11/1.48
% 1.11/1.48 subsentry: 5693
% 1.11/1.48 literals s-matched: 4100
% 1.11/1.48 literals matched: 4060
% 1.11/1.48 full subsumption: 1821
% 1.11/1.48
% 1.11/1.48 checksum: -1875226274
% 1.11/1.48
% 1.11/1.48
% 1.11/1.48 Bliksem ended
%------------------------------------------------------------------------------