TSTP Solution File: SCT005-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SCT005-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n023.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 : Mon Jul 18 21:00:28 EDT 2022
% Result : Timeout 300.10s 300.60s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SCT005-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.11 % Command : bliksem %s
% 0.11/0.30 % Computer : n023.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % DateTime : Sat Jul 2 02:35:28 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.89/1.31 *** allocated 10000 integers for termspace/termends
% 0.89/1.31 *** allocated 10000 integers for clauses
% 0.89/1.31 *** allocated 10000 integers for justifications
% 0.89/1.31 *** allocated 15000 integers for termspace/termends
% 0.89/1.31 *** allocated 22500 integers for termspace/termends
% 0.89/1.31 Bliksem 1.12
% 0.89/1.31
% 0.89/1.31
% 0.89/1.31 Automatic Strategy Selection
% 0.89/1.31
% 0.89/1.31 Clauses:
% 0.89/1.31 [
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( X ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_lessequals'( 'c_Set_Oimage'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_OImage'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 0.89/1.31 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 0.89/1.31 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_ODomain'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_ODomain'( X, Z
% 0.89/1.31 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 0.89/1.31 , 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'(
% 0.89/1.31 Y, Z ) ), ~( 'c_Relation_Osym'( X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ODomain'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 0.89/1.31 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( X, 'c_Relation_ODomain'( U
% 0.89/1.31 , Z, T ), Z ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 0.89/1.31 X, T ), Y ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 0.89/1.31 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.89/1.31 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 0.89/1.31 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y, Z, X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( Z, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X
% 0.89/1.31 , X ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.89/1.31 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( X, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ), T, Y, Z ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( T, Z ), 'tc_bool' )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( X, Y ), 'tc_bool' ) ), Z, X, Y, T ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, T ), 'tc_bool' )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 0.89/1.31 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 0.89/1.31 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ) ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OInf__class_OInf'( 'c_Set_Oinsert'( Y, Z, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Complete__Lattice_OInf__class_OInf'( Z, X ), X ) ) ],
% 0.89/1.31 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.89/1.31 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Y, Y ), 'tc_bool' ) ), Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'(
% 0.89/1.31 'c_List_Osko__Equiv__Relations__XquotientE__1__1'( Z, X, Y, T ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T, T ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( X, 'c_Equiv__Relations_Oquotient'( Z, Y, T ),
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ ~( =( hAPP( 'c_snd'( X, Y ), Z ), hAPP( 'c_snd'( X, Y ), T ) ) ), ~(
% 0.89/1.31 =( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_fst'( X, Y ), T ) ) ), =( Z, T )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( =( hAPP( 'c_snd'( X, Y ), Z ), hAPP( 'c_snd'( X, Y ), T ) ) ), ~(
% 0.89/1.31 =( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_fst'( X, Y ), T ) ) ), =( Z, T )
% 0.89/1.31 ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, Z, T ) ) ) ),
% 0.89/1.31 ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Relation_ORange'( X,
% 0.89/1.31 Y, Z ), 'c_Relation_ORange'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Relation_ORange'( 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Z ), 'tc_bool' ) ), Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Product__Type_OSigma'( X, 'c_COMBK'( Y, 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ), T ), T, Z ), 'c_Product__Type_OSigma'( U, 'c_COMBK'( Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ), 'tc_fun'( 'tc_prod'( T, Z ),
% 0.89/1.31 'tc_bool' ) ), ~( 'c_lessequals'( X, U, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( W, Y, Z ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Product__Type_OSigma'( X, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.89/1.31 , Z, U ), 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U,
% 0.89/1.31 'tc_bool' ), Z ), Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( W, T, U ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ), ~( hBOOL( 'c_in'( Y, X, T ) ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ), ~( hBOOL( 'c_in'( Y, X, T ) ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( 'c_in'( Y, X,
% 0.89/1.31 Z ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y, T, Z ), 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_Set_Oinsert'( X
% 0.89/1.31 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( U, T, Z ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Transitive__Closure_Otrancl'( X, Y ), Z, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Relation_Orel__comp'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ), X, Y, Y, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 0.89/1.31 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 0.89/1.31 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.89/1.31 ) ) ), =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 0.89/1.31 , X ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Relation_ODomain'( X
% 0.89/1.31 , Y, Z ), 'c_Relation_ODomain'( T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ),
% 0.89/1.31 'c_Relation_ODomain'( 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Z ), 'tc_bool' ) ), Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_OId__on'( X, Y ), 'c_Product__Type_OSigma'(
% 0.89/1.31 X, 'c_COMBK'( X, 'tc_fun'( Y, 'tc_bool' ), Y ), Y, Y ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ), Z ), Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ),
% 0.89/1.31 ~( 'c_Relation_Orefl__on'( Y, X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 0.89/1.31 'c_Relation_Orel__comp'( W, V0, Z, T, U ), 'tc_fun'( 'tc_prod'( Z, U ),
% 0.89/1.31 'tc_bool' ) ), ~( 'c_lessequals'( Y, V0, 'tc_fun'( 'tc_prod'( T, U ),
% 0.89/1.31 'tc_bool' ) ) ), ~( 'c_lessequals'( X, W, 'tc_fun'( 'tc_prod'( Z, T ),
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), U, Z, T ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OImage'( X, U,
% 0.89/1.31 Z, T ), 'c_Relation_OImage'( Y, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Relation_OImage'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 0.89/1.31 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, Z, T ) ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ODomain'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( X, Y ), 'tc_bool' ) ), X, Y ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 0.89/1.31 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 0.89/1.31 [ =( X, 'c_Pair'( hAPP( 'c_fst'( Y, Z ), X ), hAPP( 'c_snd'( Y, Z ), X )
% 0.89/1.31 , Y, Z ) ) ],
% 0.89/1.31 [ =( 'c_Pair'( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_snd'( X, Y ), Z ), X
% 0.89/1.31 , Y ), Z ) ],
% 0.89/1.31 [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.89/1.31 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Product__Type_OSigma'( W,
% 0.89/1.31 'c_COMBK'( U, 'tc_fun'( T, 'tc_bool' ), Z ), Z, T ), 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, T ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.89/1.31 , T, X ) ) ), =( Y, Z ) ],
% 0.89/1.31 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.89/1.31 , T, X ) ) ), =( Z, T ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X, Y, Z
% 0.89/1.31 , T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 0.89/1.31 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 0.89/1.31 'c_lessequals'( Y, Z, X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 0.89/1.31 'c_lessequals'( Z, Y, X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X
% 0.89/1.31 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 0.89/1.31 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.89/1.31 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.89/1.31 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.89/1.31 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X,
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ) ), ~( 'c_lessequals'( X,
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.89/1.31 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 0.89/1.31 Y, Z ) ) ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_lessequals'( T, X,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( T, X,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), T, Z, U ), 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 0.89/1.31 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y, 'tc_bool' ) ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 0.89/1.31 'c_Product__Type_OSigma'( W, 'c_COMBK'( V0, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.89/1.31 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 Y, 'c_Product__Type_OSigma'( V1, 'c_COMBK'( V0, 'tc_fun'( U, 'tc_bool' )
% 0.89/1.31 , T ), T, U ), 'tc_fun'( 'tc_prod'( T, U ), 'tc_bool' ) ) ), ~(
% 0.89/1.31 'c_lessequals'( X, 'c_Product__Type_OSigma'( W, 'c_COMBK'( V1, 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ), Z ), Z, T ), 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ), X, 'tc_fun'( 'tc_prod'( Z, Z )
% 0.89/1.31 , 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( X, Z ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), Y ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Relation_ODomain'( X, Y, Y ), 'c_Relation_ORange'( Z, Y, Y ), 'tc_fun'(
% 0.89/1.31 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 0.89/1.31 ) ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ), ~( 'c_Wellfounded_Owf'( X, Y
% 0.89/1.31 ) ), 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Product__Type_OSigma'( X
% 0.89/1.31 , 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.89/1.31 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.89/1.31 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ), ~(
% 0.89/1.31 'c_Relation_Orefl__on'( X, T, Z ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 0.89/1.31 X, 'tc_bool' ) ), Y ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'( 'c_Set_Oinsert'( X, Y, Z ), 'c_COMBK'(
% 0.89/1.31 'c_Set_Oinsert'( T, U, W ), 'tc_fun'( W, 'tc_bool' ), Z ), Z, W ),
% 0.89/1.31 'c_Set_Oinsert'( 'c_Pair'( X, T, Z, W ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Product__Type_OSigma'( Y
% 0.89/1.31 , 'c_COMBK'( 'c_Set_Oinsert'( T, U, W ), 'tc_fun'( W, 'tc_bool' ), Z ), Z
% 0.89/1.31 , W ), 'c_Product__Type_OSigma'( 'c_Set_Oinsert'( X, Y, Z ), 'c_COMBK'( U
% 0.89/1.31 , 'tc_fun'( W, 'tc_bool' ), Z ), Z, W ), 'tc_fun'( 'tc_prod'( Z, W ),
% 0.89/1.31 'tc_bool' ) ), 'tc_prod'( Z, W ) ) ) ],
% 0.89/1.31 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 0.89/1.31 ~( 'c_lessequals'( X, 'c_Relation_OImage'( Z, X, Y, Y ), 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ],
% 0.89/1.31 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.89/1.31 ) ), Y ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_Set_Oinsert'( X
% 0.89/1.31 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), =( T
% 0.89/1.31 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( Z, 'tc_bool'
% 0.89/1.31 ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ), ~(
% 0.89/1.31 =( 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.89/1.31 'c_Relation_Otrans'( Y, Z ) ), ~( 'c_Relation_Otrans'( X, Z ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.89/1.31 ) ) ), ~( =( 'c_Relation_Orel__comp'( T, Y, Z, Z, Z ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.89/1.31 ) ) ), =( 'c_Relation_Orel__comp'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, Z ), 'tc_bool' ) ), Y, Z, Z, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.89/1.31 ) ) ), ~( =( 'c_Relation_Orel__comp'( X, T, Z, Z, Z ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.89/1.31 ) ) ), =( 'c_Relation_Orel__comp'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, Z ), 'tc_bool' ) ), Z, Z, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, Z, T ) ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.89/1.31 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 0.89/1.31 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 0.89/1.31 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.89/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.89/1.31 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_split'( X, Y, Z, T ), U ), hAPP( hAPP( X, hAPP( 'c_fst'( Y
% 0.89/1.31 , Z ), U ) ), hAPP( 'c_snd'( Y, Z ), U ) ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.89/1.31 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 0.89/1.31 'c_lessequals'( Z, Y, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 0.89/1.31 'c_lessequals'( Y, Z, X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 0.89/1.31 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 0.89/1.31 ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ), ~(
% 0.89/1.31 'c_Relation_Orefl__on'( X, T, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( X, Y ), 'tc_bool' ) ), X, Y ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.89/1.31 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.89/1.31 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.89/1.31 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.89/1.31 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 0.89/1.31 'c_Product__Type_OSigma'( Z, 'c_COMBK'( Z, 'tc_fun'( Y, 'tc_bool' ), Y )
% 0.89/1.31 , Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 X, 'c_Product__Type_OSigma'( Z, 'c_COMBK'( Z, 'tc_fun'( Y, 'tc_bool' ), Y
% 0.89/1.31 ), Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Transitive__Closure_Ortrancl'( Z
% 0.89/1.31 , Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 0.89/1.31 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.89/1.31 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.89/1.31 'tc_fun'( X, 'tc_bool' ) ) ],
% 0.89/1.31 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.89/1.31 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.89/1.31 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X
% 0.89/1.31 ), 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 0.89/1.31 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 0.89/1.31 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T ) ), ~( hBOOL( 'c_in'( Y, X, T ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 0.89/1.31 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 0.89/1.31 [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.89/1.31 'tc_bool' ) ), Y, X ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Oconverse'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Oconverse'( X,
% 0.89/1.31 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 0.89/1.31 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 0.89/1.31 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Product__Type_OSigma'( X
% 0.89/1.31 , 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.89/1.31 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.89/1.31 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( X, Y ), ~(
% 0.89/1.31 'c_Order__Relation_Ostrict__linear__order__on'( Z, X, Y ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 0.89/1.31 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( X, T, Z ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ),
% 0.89/1.31 Z, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Product__Type_OSigma'( X,
% 0.89/1.31 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.89/1.31 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.89/1.31 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ORange'( X, Z,
% 0.89/1.31 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( X, Z ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( Y, Z ) ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.89/1.31 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OId__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.89/1.31 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'(
% 0.89/1.31 X, X ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, Y ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( 'c_in'( X, Y, Z ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( 'c_Set_Oinsert'( X, T,
% 0.89/1.31 Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 0.89/1.31 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL(
% 0.89/1.31 'c_in'( Y, X, T ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), hBOOL( 'c_in'( T, X
% 0.89/1.31 , Z ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), hBOOL(
% 0.89/1.31 'c_in'( Y, X, T ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), hBOOL( 'c_in'(
% 0.89/1.31 T, X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Oconverse'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_Oconverse'( X,
% 0.89/1.31 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 0.89/1.31 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ) ), hBOOL( 'c_in'( Y, X, T ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 0.89/1.31 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ), hBOOL( 'c_in'( X, T, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~(
% 0.89/1.31 'c_Order__Relation_Ostrict__linear__order__on'( X, Y, Z ) ) ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.89/1.31 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.89/1.31 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, T ), 'tc_bool' ) ), U, Z, T, W ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.89/1.31 , U, Z, T, W ), 'c_Relation_Orel__comp'( Y, U, Z, T, W ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Z, W ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 T, U ), 'tc_bool' ) ), W, T, U ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.89/1.31 , Y, W, T, U ), 'c_Relation_Orel__comp'( X, Z, W, T, U ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( W, U ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 Z, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 T, Z, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 0.89/1.31 'c_lessequals'( Z, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 Z, T, X ), X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 T, Z, X ), X ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ODomain'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ODomain'( X, Z
% 0.89/1.31 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 X, 'tc_bool' ) ), Y, X, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( X, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Wellfounded_Oacc'( X, Y ), 'c_Wellfounded_Oacc'( Z
% 0.89/1.31 , Y ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_ODomain'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.89/1.31 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 0.89/1.31 ) ), Z, X ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OInf__class_OInf'( 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.89/1.31 'tc_bool' ) ), X ), X ), X ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_ORange'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_ORange'( X, Z,
% 0.89/1.31 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, Z, T ) ) )
% 0.89/1.31 ), ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.89/1.31 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( X, 'tc_fun'( Y, 'tc_bool' ) ), Z
% 0.89/1.31 , 'tc_fun'( Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.89/1.31 , 'tc_bool' ) ) ) ), =( 'c_Lattices_Olower__semilattice__class_Oinf'( T,
% 0.89/1.31 Z, 'tc_fun'( Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 Y, 'tc_bool' ) ) ), ~( hBOOL( 'c_in'( T, X, 'tc_fun'( Y, 'tc_bool' ) ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 0.89/1.31 hBOOL( 'c_in'( X, T, Z ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 0.89/1.31 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), Y ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), Y ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 0.89/1.31 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( Y, 'c_Relation_ORange'( U,
% 0.89/1.31 Z, T ), T ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y
% 0.89/1.31 , 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'(
% 0.89/1.31 Y, Z ) ), ~( 'c_Relation_Osym'( X, Z ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ),
% 0.89/1.31 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), hBOOL( 'c_in'( X, Y
% 0.89/1.31 , Z ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z
% 0.89/1.31 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( =( hAPP( X, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U,
% 0.89/1.31 W ) ), hAPP( Y, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U, W
% 0.89/1.31 ) ) ) ), =( 'c_Recdef_Ocut'( X, Z, T, U, W ), 'c_Recdef_Ocut'( Y, Z, T,
% 0.89/1.31 U, W ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 0.89/1.31 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OInf__class_OInf'( 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.89/1.31 'tc_bool' ) ), X ), X ), X ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 0.89/1.31 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), T ) ), ~( hBOOL( 'c_in'( X, Z, T ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( X, Y, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), T ) ), ~( hBOOL( 'c_in'( X, Z, T ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( X, Y, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 X, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 X, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ), ~(
% 0.89/1.31 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( 'c_lessequals'( T, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ), ~(
% 0.89/1.31 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ), ~(
% 0.89/1.31 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), T ) ), ~( hBOOL( 'c_in'( X, Y, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ), T ) ), ~( hBOOL( 'c_in'( X, Z, T ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), Y ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), Y ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), =( X, T ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Set_Oinsert'( T, Y, Z ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), hBOOL( 'c_in'( X, T, Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), Z ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T ) ), hBOOL( 'c_in'( X, Z, T ) ), ~( hBOOL( 'c_in'( X, Y
% 0.89/1.31 , T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T ) ), hBOOL( 'c_in'( X, Z, T ) ), ~( hBOOL( 'c_in'( X, Y
% 0.89/1.31 , T ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 0.89/1.31 hBOOL( 'c_in'( X, T, Z ) ), hBOOL( 'c_in'( X, Y, Z ) ), =( Y, T ) ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( 'c_in'( X, Y, Z ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( hAPP( 'c_fst'( X, Y ), 'c_Pair'( Z, T, X, Y ) ), Z ) ],
% 0.89/1.31 [ =( X, hAPP( 'c_fst'( Y, Z ), 'c_Pair'( X, T, Y, Z ) ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_snd'( X, Y ), 'c_Pair'( Z, T, X, Y ) ), T ) ],
% 0.89/1.31 [ =( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, X, Y, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, hAPP( 'c_fst'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ),
% 0.89/1.31 ~( hBOOL( hAPP( W, U ) ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ),
% 0.89/1.31 ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( W, T ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.89/1.31 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( hBOOL(
% 0.89/1.31 'c_in'( X, Y, Z ) ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 0.89/1.31 Y, X ), Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 T, X ), Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 0.89/1.31 'c_lessequals'( Y, Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 0.89/1.31 Y, X ), Z, X ) ) ],
% 0.89/1.31 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.89/1.31 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.89/1.31 T, X ), Z, X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.89/1.31 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 0.89/1.31 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 0.89/1.31 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'( Z, Y ) ), ~(
% 0.89/1.31 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 0.89/1.31 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Oacyclic'( Z, Y ) )
% 0.89/1.31 ],
% 0.89/1.31 [ 'c_Relation_Osingle__valued'( X, Y, Z ), ~(
% 0.89/1.31 'c_Relation_Osingle__valued'( T, Y, Z ) ), ~( 'c_lessequals'( X, T,
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.89/1.31 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), =(
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ), X ), Y )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.89/1.31 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.89/1.31 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_ODomain'( X, Y, Z ), 'c_Relation_ODomain'(
% 0.89/1.31 T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ),
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.89/1.31 T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Product__Type_OSigma'( X, 'c_COMBK'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ), Z ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.89/1.31 'tc_prod'( Z, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 0.89/1.31 hAPP( X, T ) ) ) ],
% 0.89/1.31 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.89/1.31 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), Z ), ~(
% 0.89/1.31 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 0.89/1.31 , X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.89/1.31 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.89/1.31 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 0.89/1.31 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_lessequals'(
% 0.89/1.31 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 0.89/1.31 'tc_bool' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 0.89/1.31 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 0.89/1.31 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 0.89/1.31 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 0.89/1.31 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( hAPP( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, U, Y, Z ) )
% 0.89/1.31 ), hAPP( 'c_fst'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ), ~( hBOOL( hAPP(
% 0.89/1.31 hAPP( X, U ), T ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_ORange'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), 'c_Relation_OImage'(
% 0.89/1.31 U, W, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, W,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, U, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ), Z ), Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ),
% 0.89/1.31 ~( 'c_Equiv__Relations_Oequiv'( Y, X, Z ) ) ],
% 0.89/1.31 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.89/1.31 'c_lessequals'( Z, Y, X ) ],
% 0.89/1.31 [ 'c_Relation_Oirrefl'( X, Y ), ~(
% 0.89/1.31 'c_Order__Relation_Ostrict__linear__order__on'( Z, X, Y ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 0.89/1.31 'tc_prod'( Z, Z ) ), Z ), hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Oacyclic'( T, Z ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Y, X, Z, Z ), T,
% 0.89/1.31 'tc_prod'( Z, Z ) ), Z ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 0.89/1.31 X, Z, T, U ),
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 0.89/1.31 X, Z, T, U ), U, U ), T, 'tc_prod'( U, U ) ) ), ~( hBOOL( hAPP( X, Z ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z, U, U ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 0.89/1.31 T, U ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'(
% 0.89/1.31 X, Z, T, U ), U, U ), T, 'tc_prod'( U, U ) ) ), ~( hBOOL( hAPP( X, Z ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, Y, U, U ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ) ],
% 0.89/1.31 [ =( 'c_Fun_Ooverride__on'( X, Y, 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), X ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 Z ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( T
% 0.89/1.31 , Y, Z ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), ~( hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( Y, 'c_COMBK'( U,
% 0.89/1.31 'tc_fun'( T, 'tc_bool' ), Z ), Z, T ), 'tc_fun'( Z, T ) ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.89/1.31 ), =( X, Y ), ~( hBOOL( 'c_in'( Y, 'c_Equiv__Relations_Oquotient'( T, U
% 0.89/1.31 , Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Equiv__Relations_Oquotient'( T, U, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) )
% 0.89/1.31 , ~( 'c_Equiv__Relations_Oequiv'( T, U, Z ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Z, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.89/1.31 'c_Relation_Orel__comp'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y )
% 0.89/1.31 , 'tc_bool' ) ), X, Y, Y, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 0.89/1.31 ) ) ), ~( 'c_lessequals'( 'c_Relation_OId'( Y ), Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( U, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Relation_OImage'( T, 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( W, T
% 0.89/1.31 , Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( Y, U, Z ) ) ), ~( 'c_lessequals'( 'c_Relation_OImage'( T,
% 0.89/1.31 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ), Z ), Z, Z ), 'c_Relation_OImage'( T, 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, T, Z ) )
% 0.89/1.31 ],
% 0.89/1.31 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 0.89/1.31 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( 'c_in'( Y, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( hAPP( X, Y ), Z, T ) ), ~( hBOOL( 'c_in'( Y, U, W ) ) )
% 0.89/1.31 , ~( 'c_lessequals'( 'c_Set_Oimage'( X, U, W, T ), Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( Y, 'c_Relation_OImage'( U, 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, T ),
% 0.89/1.31 T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'( Z,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T, U ),
% 0.89/1.31 U ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, X, T, U ), Y, 'tc_prod'( T, U ) ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 Y, 'c_Complete__Lattice_OSup__class_OSup'( Z, X ), X ), ~( hBOOL( 'c_in'(
% 0.89/1.31 Y, Z, X ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1'( X, Y, Z ), Z ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( X, 'c_Complete__Lattice_OSup__class_OSup'( Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Product__Type_OSigma'( X, 'c_COMBK'( Y, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ), T ), T, Z ), 'c_Product__Type_OSigma'( U, 'c_COMBK'( Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ) ) ), ~( hBOOL( 'c_in'( W, Y, Z ) )
% 0.89/1.31 ), =( X, U ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'( 'c_Set_Oinsert'(
% 0.89/1.31 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 T, T ), 'tc_bool' ) ), T ), 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 T, T ), 'tc_bool' ) ), T ), 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Transitive__Closure_Otrancl'( Y, Z ), 'tc_prod'(
% 0.89/1.31 Z, Z ) ) ), ~( 'c_lessequals'( T, Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 0.89/1.31 'tc_bool' ) ) ), ~( hBOOL( 'c_in'( X, 'c_Transitive__Closure_Otrancl'( T
% 0.89/1.31 , Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Complete__Lattice_OSup__class_OSup'( Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( 'c_in'( X, Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ) ),
% 0.89/1.31 ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ) ),
% 0.89/1.31 ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.89/1.31 [ ~( 'class_Complete__Lattice_Ocomplete__lattice'( X ) ), 'c_lessequals'(
% 0.89/1.31 'c_Complete__Lattice_OInf__class_OInf'( Y, X ), Z, X ), ~( hBOOL( 'c_in'(
% 0.89/1.31 Z, Y, X ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Equiv__Relations_Oquotient'( T, X, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( Y, T, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Complete__Lattice_OInf__class_OInf'( Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), Z ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1'( X, Y, Z ), Z ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.89/1.31 , X, Y, Y, Y ), 'c_Relation_Orel__comp'( Z, X, Y, Y, Y ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.89/1.31 'tc_bool' ) ), Y ), ~( 'c_Wellfounded_Owf'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 0.89/1.31 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.89/1.31 , X, Z, Z, Z ), 'c_Relation_Orel__comp'( Y, X, Z, Z, Z ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Z, Z ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 0.89/1.31 'tc_bool' ) ), Z ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 0.89/1.31 ) ) ), 'c_Wellfounded_Owf'( X, Y ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Orel__comp'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, Y ), X, Y, Y, Y ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( hBOOL( 'c_in'( X
% 0.89/1.31 , 'c_Set_OPow'( Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_OPow'( Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ),
% 0.89/1.31 ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.89/1.31 ) ), 'c_Set_OPow'( Y, X ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Complete__Lattice_OInf__class_OInf'( X, 'tc_fun'( Y
% 0.89/1.31 , 'tc_bool' ) ), Z, 'tc_fun'( Y, 'tc_bool' ) ), ~( hBOOL( 'c_in'( Z, X,
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Orderings_Obot__class_Obot'(
% 0.89/1.31 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ), 'c_Relation_OId'( X ) )
% 0.89/1.31 ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.89/1.31 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 0.89/1.31 ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), X, 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_Relation_Otrans'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 0.89/1.31 ) ), Y ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 0.89/1.31 ) ), Y ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.89/1.31 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.89/1.31 ~( 'c_Relation_Otrans'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z, Y, Y ),
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y,
% 0.89/1.31 'tc_bool' ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 0.89/1.31 , 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y )
% 0.89/1.31 , ~( 'c_Relation_Oantisym'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~( 'c_Relation_Ototal__on'( X,
% 0.89/1.31 'c_HOL_Ominus__class_Ominus'( Y, 'c_Relation_OId'( Z ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Ototal__on'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.89/1.31 'c_Relation_OId'( Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ),
% 0.89/1.31 ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 T, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Transitive__Closure_Otrancl'( Y, Z ), 'tc_prod'(
% 0.89/1.31 Z, Z ) ) ), ~( hBOOL( 'c_in'( X, Y, 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ 'c_lessequals'( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y
% 0.89/1.31 , Y ), X, Y, Y, Y ), X, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~(
% 0.89/1.31 'c_Relation_Otrans'( X, Y ) ), ~( 'c_Relation_Osym'( X, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Y, X, Z, T )
% 0.89/1.31 , T, T ), 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T ) ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( 'c_Pair'( X, Z, T, T ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( X, Y, Z, T ),
% 0.89/1.31 Z, T, T ), 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'( T, T ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( Y, X, Z, Z ), T,
% 0.89/1.31 'tc_prod'( Z, Z ) ), Z ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 0.89/1.31 'tc_prod'( Z, Z ) ), Z ), hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( T, Z ) ) ],
% 0.89/1.31 [ 'c_Order__Relation_Ostrict__linear__order__on'( X, Y, Z ), ~(
% 0.89/1.31 'c_Relation_Ototal__on'( X, Y, Z ) ), ~( 'c_Relation_Oirrefl'( Y, Z ) ),
% 0.89/1.31 ~( 'c_Relation_Otrans'( Y, Z ) ) ],
% 0.89/1.31 [ 'c_Nitpick_Orefl_H'( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ),
% 0.89/1.31 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ), Y, Y ), X,
% 0.89/1.31 'tc_prod'( Y, Y ) ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Relation_OId'(
% 0.89/1.31 Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ), ~(
% 0.89/1.31 'c_Relation_Oantisym'( X, Y ) ), ~( 'c_Relation_Otrans'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( X,
% 0.89/1.31 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 0.89/1.31 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Relation_Osingle__valued'(
% 0.89/1.31 'c_Relation_Oconverse'( X, T, U ), U, T ) ) ],
% 0.89/1.31 [ 'c_Relation_Oirrefl'( X, Y ), hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ),
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ), Y, Y ), X,
% 0.89/1.31 'tc_prod'( Y, Y ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'v_r', 't_a', 't_b' ), 'c_Relation_ODomain'(
% 0.89/1.31 'c_Relation_Oconverse'( 'v_r', 't_a', 't_b' ), 't_b', 't_a' ) ) ],
% 0.89/1.31 [ 'c_lessequals'( X, 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X
% 0.89/1.31 , Y, Y ), X, Y, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~(
% 0.89/1.31 'c_Relation_Orefl__on'( Z, X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OId'( Y ),
% 0.89/1.31 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 0.89/1.31 Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 0.89/1.31 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 0.89/1.31 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U )
% 0.89/1.31 ), hBOOL( 'c_in'( 'c_Pair'( 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, W
% 0.89/1.31 , Y, Z, T, U ), Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ],
% 0.89/1.31 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X,
% 0.89/1.31 Z ), 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ), Z, Z ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( X, 'c_Relation_OId__on'( Y, Z ), 'tc_prod'( Z, Z ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( X, Y, Z
% 0.89/1.31 ), X, Z ) ), ~( hBOOL( 'c_in'( Y, 'c_Relation_OId__on'( X, Z ),
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1'( X, Y ),
% 0.89/1.31 'c_Wellfounded_Oacc'( X, Y ), Y ) ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( X, Y ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1'( X, Y ),
% 0.89/1.31 'c_Wellfounded_Oacc'( X, Y ), Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Complete__Lattice_OInf__class_OInf'( Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), Z ) ), hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1'( X, Y, Z ), Y,
% 0.89/1.31 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.89/1.31 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ),
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ), Y, Y ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( X, 'c_Relation_OId'( Y ), 'tc_prod'( Y, Y ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( Y, Z, T, U ), 'tc_fun'( T, U ) ) )
% 0.89/1.31 , hBOOL( 'c_in'( 'c_FuncSet_Osko__FuncSet__XPi__I__1__1'( Y, Z, X, T, U )
% 0.89/1.31 , Y, T ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( Y, Z, T, U ), 'tc_fun'( T, U ) ) )
% 0.89/1.31 , hBOOL( 'c_in'( 'c_FuncSet_Osko__FuncSet__XPi__I_H__1__1'( Y, Z, X, T, U
% 0.89/1.31 ), Y, T ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( Y, Z, T, U ), 'tc_fun'( T, U ) ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( hAPP( X, 'c_FuncSet_Osko__FuncSet__XPi__I__1__1'( Y,
% 0.89/1.31 Z, X, T, U ) ), hAPP( Z, 'c_FuncSet_Osko__FuncSet__XPi__I__1__1'( Y, Z, X
% 0.89/1.31 , T, U ) ), U ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( hAPP( X, Y ), Z, T ) ), ~( hBOOL( 'c_in'( Y, U, W ) ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( U, 'c_COMBK'( Z, 'tc_fun'( T,
% 0.89/1.31 'tc_bool' ), W ), W, T ), 'tc_fun'( W, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( Y, Z, T, U ), 'tc_fun'( T, U ) ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( hAPP( X, 'c_FuncSet_Osko__FuncSet__XPi__I_H__1__1'( Y
% 0.89/1.31 , Z, X, T, U ) ), hAPP( Z, 'c_FuncSet_Osko__FuncSet__XPi__I_H__1__1'( Y,
% 0.89/1.31 Z, X, T, U ) ), U ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_List_Osko__Equiv__Relations__XquotientE__1__1'( X, Y
% 0.89/1.31 , Z, T ), X, T ) ), ~( hBOOL( 'c_in'( Y, 'c_Equiv__Relations_Oquotient'(
% 0.89/1.31 X, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( X, Y, Z, T, U, W,
% 0.89/1.31 V0 ), Y, V0, W ), T, 'tc_prod'( V0, W ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 X, Y, U, W ), 'c_Relation_Orel__comp'( Z, T, U, V0, W ), 'tc_prod'( U, W
% 0.89/1.31 ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( X, Y, Z, T, U, W,
% 0.89/1.31 V0 ), U, V0 ), Z, 'tc_prod'( U, V0 ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 Y, U, W ), 'c_Relation_Orel__comp'( Z, T, U, V0, W ), 'tc_prod'( U, W ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ) ),
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'( Z,
% 0.89/1.31 Y ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'(
% 0.89/1.31 Z, Y ), Y, Y ), 'c_Transitive__Closure_Otrancl'( Z, Y ), 'tc_prod'( Y, Y
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( X, Y
% 0.89/1.31 , Z, T ), Z, T, T ), 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'(
% 0.89/1.31 T, T ) ) ), hBOOL( 'c_in'( 'c_Pair'( Y, Z, T, T ), X, 'tc_prod'( T, T ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Y, X, Z, T ),
% 0.89/1.31 T, T ), Y, 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Z, T, T
% 0.89/1.31 ), 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), 't_a', 't_a'
% 0.89/1.31 ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a'
% 0.89/1.31 ) ) ), hBOOL( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ), Z, 'tc_prod'(
% 0.89/1.31 't_a', 't_a' ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a' ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( Z, Y ), 'tc_prod'( Y, Y ) ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Oacyclic'( Z, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( X, Y, Z, T ),
% 0.89/1.31 Y, T, T ), Z, 'tc_prod'( T, T ) ) ), hBOOL( 'c_in'( 'c_Pair'( X, Y, T, T
% 0.89/1.31 ), Z, 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, T, T ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( X, Y, Z, T ),
% 0.89/1.31 T, T ), 'c_Transitive__Closure_Otrancl'( Z, T ), 'tc_prod'( T, T ) ) ),
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, Y, T, T ), Z, 'tc_prod'( T, T ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, Y, T, T ), 'c_Transitive__Closure_Otrancl'( Z, T ),
% 0.89/1.31 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( X, Y, Z, T )
% 0.89/1.31 , Z, T, T ), X, 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z,
% 0.89/1.31 T, T ), 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'( T, T ) ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Y, X
% 0.89/1.31 , Z, T ), T, T ), Y, 'tc_prod'( T, T ) ) ), hBOOL( 'c_in'( 'c_Pair'( X, Z
% 0.89/1.31 , T, T ), Y, 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Z, T,
% 0.89/1.31 T ), 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 0.89/1.31 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ) ), hBOOL( 'c_in'( 'c_Pair'( X, Y
% 0.89/1.31 , 't_a', 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( X, Y, 't_a', 't_a' ), 'c_Transitive__Closure_Otrancl'( Z, 't_a'
% 0.89/1.31 ), 'tc_prod'( 't_a', 't_a' ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1'(
% 0.89/1.31 X, Y, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Complete__Lattice_OSup__class_OSup'( Y, 'tc_fun'( Z, 'tc_bool' ) ), Z
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'(
% 0.89/1.31 X, T, U ), U, U ), T, 'tc_prod'( U, U ) ) ) ), ~( 'c_Wellfounded_Owf'( T
% 0.89/1.31 , U ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, T, U )
% 0.89/1.31 , U, U ), T, 'tc_prod'( U, U ) ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, T, U ), U
% 0.89/1.31 , U ), T, 'tc_prod'( U, U ) ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, T,
% 0.89/1.31 U ), U, U ), T, 'tc_prod'( U, U ) ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) )
% 0.89/1.31 ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( X, Y, Z, T )
% 0.89/1.31 , Y, T, T ), Z, 'tc_prod'( T, T ) ) ), =( X, Y ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( X, Y, T, T ), 'c_Transitive__Closure_Ortrancl'( Z, T ),
% 0.89/1.31 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( X,
% 0.89/1.31 Y, Z, T ), Z, T, T ), 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'(
% 0.89/1.31 T, T ) ) ), =( Y, Z ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Y,
% 0.89/1.31 X, Z, T ), T, T ), Y, 'tc_prod'( T, T ) ) ), =( X, Z ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( X, Z, T, T ), 'c_Transitive__Closure_Ortrancl'( Y, T ),
% 0.89/1.31 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 0.89/1.31 X, Z, T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 Y, Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U )
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 0.89/1.31 X, Z, T, U ), Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ),
% 0.89/1.31 'tc_prod'( U, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Y, Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ),
% 0.89/1.31 'tc_prod'( U, U ) ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'( 'c_Pair'( Z,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 0.89/1.31 T, U ), U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U
% 0.89/1.31 ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, Y, U,
% 0.89/1.31 U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'( X, Z,
% 0.89/1.31 T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z,
% 0.89/1.31 Y, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), 't_a',
% 0.89/1.31 't_a' ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ), 'tc_prod'( 't_a',
% 0.89/1.31 't_a' ) ) ), =( Y, X ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' )
% 0.89/1.31 , 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a' )
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 0.89/1.31 T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, Y
% 0.89/1.31 , U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 0.89/1.31 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ) ), =( Y, X ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( X, Y, 't_a', 't_a' ), 'c_Transitive__Closure_Ortrancl'( Z,
% 0.89/1.31 't_a' ), 'tc_prod'( 't_a', 't_a' ) ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 0.89/1.31 X, Z, T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Y, Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ),
% 0.89/1.31 'tc_prod'( U, U ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( X, Y, Z, T )
% 0.89/1.31 , T, T ), 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) )
% 0.89/1.31 , =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, T, T ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1'( X,
% 0.89/1.31 Y, Z, T, U ), X, T ) ), ~( hBOOL( 'c_in'( Z, 'c_Product__Type_OSigma'( X
% 0.89/1.31 , Y, T, U ), 'tc_prod'( T, U ) ) ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_OwfP'( 'c_FunDef_Oin__rel'( X, Y, Y ), Y ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Oirrefl'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.89/1.31 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.89/1.31 ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ),
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 0.89/1.31 ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, Z, Y, Y ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, Y ), 'tc_prod'( Y, Y ) ) ) ) ],
% 0.89/1.31 [ =( 'c_Equiv__Relations_Oquotient'( 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Z, Y ),
% 0.89/1.31 'c_Equiv__Relations_Oquotient'( 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Z, Y ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( 'c_Pair'( X, T, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( T, U, Y ) ) ), ~( hBOOL( 'c_in'( X, U, Y ) ) ), ~(
% 0.89/1.31 'c_Equiv__Relations_Oequiv'( U, Z, Y ) ) ],
% 0.89/1.31 [ ~( =( 'c_Equiv__Relations_Oquotient'( 'c_Set_Oinsert'( X,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Z, Y ),
% 0.89/1.31 'c_Equiv__Relations_Oquotient'( 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Z, Y ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( T, U, Y ) ) ), ~( hBOOL( 'c_in'( X, U, Y ) ) ), ~(
% 0.89/1.31 'c_Equiv__Relations_Oequiv'( U, Z, Y ) ), hBOOL( 'c_in'( 'c_Pair'( X, T,
% 0.89/1.31 Y, Y ), Z, 'tc_prod'( Y, Y ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.89/1.31 ), hBOOL( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( T, U, Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) )
% 0.89/1.31 ],
% 0.89/1.31 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.89/1.31 ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( T, U, Z ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( Y, U, Z ) ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.89/1.31 , ~( hBOOL( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( T, U, Z ) ) ), ~( hBOOL( 'c_in'( Y, U, Z ) ) ), ~(
% 0.89/1.31 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.89/1.31 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.89/1.31 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( T, U, Z ) ) ), ~( hBOOL( 'c_in'( Y, U, Z ) ) ), ~(
% 0.89/1.31 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), hBOOL( 'c_in'( 'c_Pair'( Y, T,
% 0.89/1.31 Z, Z ), X, 'tc_prod'( Z, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), =( X, T ), ~( 'c_lessequals'( U,
% 0.89/1.31 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), Z )
% 0.89/1.31 , Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( X, T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( U, Z ),
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( 'c_snd'( X, Y ), Z, 'tc_prod'( X, Y ), Y ),
% 0.89/1.31 'c_Relation_ORange'( Z, X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Set_Oimage'( 'c_fst'( X, Y ), Z, 'tc_prod'( X, Y ), X ),
% 0.89/1.31 'c_Relation_ODomain'( Z, X, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ), =( X, Y ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, Z, Z ), Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( Y, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( Y, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, X, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~( 'c_Relation_Osingle__valued'( T, Z, Z
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Otrancl'( T
% 0.89/1.31 , Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oconverse'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( T, Z ), Z, Z ), 'tc_prod'( Z, Z ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oconverse'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( T, Z ), Z, Z ), 'tc_prod'( Z, Z ) ) ) )
% 0.89/1.31 ],
% 0.89/1.31 [ =( hAPP( 'c_split'( X, Y, Z, T ), 'c_Pair'( U, W, Y, Z ) ), hAPP( hAPP(
% 0.89/1.31 X, U ), W ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_split'( X, Y, Z, T ), 'c_Pair'( U, W, Y, Z ) ), hAPP( hAPP(
% 0.89/1.31 X, U ), W ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( hAPP( hAPP( X, Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 0.89/1.31 'c_split'( X, U, W, 'tc_fun'( V0, 'tc_bool' ) ), 'c_Pair'( Y, Z, U, W ) )
% 0.89/1.31 , T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( Y, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( Y, Z, T ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), hBOOL( 'c_in'( hAPP( T, X ),
% 0.89/1.31 'c_Set_Oimage'( T, Y, Z, U ), U ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), hBOOL( 'c_in'( hAPP( T, X ),
% 0.89/1.31 'c_Set_Oimage'( T, Y, Z, U ), U ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, T, U ), W ), hAPP( X, W ) ),
% 0.89/1.31 hBOOL( 'c_in'( W, Z, T ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, T, U ), W ), hAPP( Y, W ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( W, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( Y, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId__on'( X, Y ), Y, Y ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( X, Y, Z
% 0.89/1.31 , T, U ), X, T ) ), ~( hBOOL( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T, U
% 0.89/1.31 ), U ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 0.89/1.31 'c_Relation_Osym'( X, Y ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ) ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z, T ), T ) ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), X ), ~(
% 0.89/1.31 'c_Relation_Otrans'( X, Y ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, Z ) ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 Y, 'c_Wellfounded_Oacc'( Z, 't_a' ), 't_a' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ),
% 0.89/1.31 'c_Wellfounded_Oacc'( Z, T ), T ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( Z, T ), T ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Relation_Osym'(
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.89/1.31 'c_Relation_Osym'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 0.89/1.31 ), 'c_Relation_ODomain'( X, Y, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( X, Y
% 0.89/1.31 , Z, T, U ), X, T ) ), ~( hBOOL( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T
% 0.89/1.31 , U ), U ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( X, Y, Z ),
% 0.89/1.31 'c_Wellfounded_Oacc'( X, Z ), Z ) ) ), hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( X, Z ), Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Relation_OId'( X ), X ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( 'c_Relation_OId'( X ), Y, X, X, Z ), Y ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( X, 'c_Relation_OId'( Y ), Z, Y, Y ), X ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_Relation_Oantisym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'(
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ), Y ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ) )
% 0.89/1.31 ) ), ~( hBOOL( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z, T ), T ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Relation_Orefl__on'( X,
% 0.89/1.31 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ), ~(
% 0.89/1.31 'c_Relation_Orefl__on'( X, Y, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ), ~(
% 0.89/1.31 'c_Relation_Osym'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ),
% 0.89/1.31 ~( 'c_Wellfounded_Owf'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 0.89/1.31 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_OImage'( 'c_Relation_OId'( X ), Y, X, X ), Y ) ],
% 0.89/1.31 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId'( X ), X, X ) ],
% 0.89/1.31 [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Relation_Oconverse'( X, Y, Y ), X ), ~( 'c_Relation_Osym'( X, Y
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_Oconverse'( X, Y, Y ), X ) ), 'c_Relation_Osym'( X,
% 0.89/1.31 Y ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 0.89/1.31 ), 'c_Relation_ORange'( X, Y, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( 'c_Relation_Oconverse'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ), Z
% 0.89/1.31 , U ), 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( Y, T, U ),
% 0.89/1.31 'c_Relation_Oconverse'( X, Z, T ), U, T, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( X, 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.89/1.31 ), Y, Y, Y ), 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 X, Y ), X, Y, Y, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 0.89/1.31 'c_Relation_Osym'( X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_Relation_Otrans'( X, Y ), ~( 'c_Relation_Otrans'(
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.89/1.31 'c_Relation_Otrans'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId'( X ), X, X ),
% 0.89/1.31 'c_Relation_OId'( X ) ) ],
% 0.89/1.31 [ 'c_Wellfounded_Owf'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 0.89/1.31 W, Z, U, V0 ), 'c_Relation_Orel__comp'( X, 'c_Relation_Orel__comp'( Y, W
% 0.89/1.31 , T, U, V0 ), Z, T, V0 ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T,
% 0.89/1.31 T ), 'c_Relation_Oinv__image'( 'c_Relation_Oconverse'( X, Z, Z ), Y, Z, T
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 0.89/1.31 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y
% 0.89/1.31 , Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 0.89/1.31 'c_Relation_Otrans'( X, Z ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId__on'( X, Y ), Y, Y ),
% 0.89/1.31 'c_Relation_OId__on'( X, Y ) ) ],
% 0.89/1.31 [ ~( =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y
% 0.89/1.31 , Y, Y ), X ) ), 'c_Equiv__Relations_Oequiv'( 'c_Relation_ODomain'( X, Y
% 0.89/1.31 , Y ), X, Y ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( 'c_Relation_OId'( X ), X ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 0.89/1.31 'c_Relation_ODomain'( X, Y, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( X, Y, Z ), X,
% 0.89/1.31 Z ) ), ~( hBOOL( 'c_in'( T, X, Z ) ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) )
% 0.89/1.31 ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ 'c_Relation_Osingle__valued'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 0.89/1.31 , Z, U ), ~( 'c_Relation_Osingle__valued'( Y, T, U ) ), ~(
% 0.89/1.31 'c_Relation_Osingle__valued'( X, Z, T ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 0.89/1.31 X ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( 'c_Relation_OId'( X ), X ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y
% 0.89/1.31 , Y ), X ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.89/1.31 [ 'c_Relation_Oantisym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.89/1.31 'c_Relation_Oantisym'( X, Y ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.89/1.31 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, Z ) ) ) ), ~( hBOOL( 'c_in'( Y
% 0.89/1.31 , 'c_Wellfounded_Oacc'( Z, 't_a' ), 't_a' ) ) ) ],
% 0.89/1.31 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Equiv__Relations_Oequiv'( X,
% 0.89/1.31 Y, Z ) ) ],
% 0.89/1.31 [ =( 'c_Complete__Lattice_OSup__class_OSup'(
% 0.89/1.31 'c_Equiv__Relations_Oquotient'( X, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ), X
% 0.89/1.31 ), ~( 'c_Equiv__Relations_Oequiv'( X, Y, Z ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 0.89/1.31 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.89/1.31 Y, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( X,
% 0.89/1.31 Y, Z ), X, Z ) ), ~( hBOOL( 'c_in'( T, X, Z ) ) ), ~( 'c_Wellfounded_Owf'(
% 0.89/1.31 Y, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) )
% 0.89/1.31 ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Y, X, Z )
% 0.89/1.31 , 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ) ],
% 0.89/1.31 [ 'c_Equiv__Relations_Ocongruent'( X, hAPP( Y, Z ), T, U ), ~( hBOOL(
% 0.89/1.31 'c_in'( Z, W, V0 ) ) ), ~( 'c_Equiv__Relations_Ocongruent2'( V1, X, Y, V0
% 0.89/1.31 , T, U ) ), ~( 'c_Equiv__Relations_Oequiv'( W, V1, V0 ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ODomain'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 0.89/1.31 'c_Relation_ORange'( X, Y, Z ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'(
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y, Y, Y ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'( X
% 0.89/1.31 , 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ) ) ],
% 0.89/1.31 [ =( 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ODomain'(
% 0.89/1.31 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ) ) ],
% 0.89/1.31 [ =( 'c_Complete__Lattice_OSup__class_OSup'( 'c_Set_OPow'( X, Y ),
% 0.89/1.31 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 0.89/1.31 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~( 'c_Relation_Ototal__on'( X,
% 0.89/1.31 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ),
% 0.89/1.31 ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ],
% 0.89/1.31 [ 'c_Relation_Otrans'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y )
% 0.89/1.31 ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ),
% 0.89/1.31 'c_Wellfounded_Oacc'( Z, T ), T ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( Z, T ), T ) ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Ortrancl'(
% 0.89/1.31 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Transitive__Closure_Ortrancl'( Y, Z ), 'tc_prod'(
% 0.89/1.31 Z, Z ) ) ), ~( hBOOL( 'c_in'( X, Y, 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Set_OPow'( X, Y ), 'tc_fun'( Y, 'tc_bool' ) ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ =( hAPP( 'c_Fun_Ooverride__on'( X, Y, Z, 't_a', T ), 'v_a' ),
% 0.89/1.31 'c_HOL_OIf'( 'c_in'( 'v_a', Z, 't_a' ), hAPP( Y, 'v_a' ), hAPP( X, 'v_a'
% 0.89/1.31 ), T ) ) ],
% 0.89/1.31 [ =( 'c_Orderings_Oord_Omin'( X, 'v_a', 'v_b', 't_a' ), 'c_HOL_OIf'(
% 0.89/1.31 hAPP( hAPP( X, 'v_a' ), 'v_b' ), 'v_a', 'v_b', 't_a' ) ) ],
% 0.89/1.31 [ =( 'c_Orderings_Oord_Omax'( X, 'v_a', 'v_b', 't_a' ), 'c_HOL_OIf'(
% 0.89/1.31 hAPP( hAPP( X, 'v_a' ), 'v_b' ), 'v_b', 'v_a', 't_a' ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'(
% 0.89/1.31 X, Y, Z, T, U ), Y, T, U ), Z, 'tc_prod'( T, U ) ) ), ~( hBOOL( 'c_in'( Y
% 0.89/1.31 , 'c_Relation_OImage'( Z, X, T, U ), U ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( X, Y, Z ), Y, Z
% 0.89/1.31 , Z ), X, 'tc_prod'( Z, Z ) ) ), hBOOL( 'c_in'( Y, 'c_Wellfounded_Oacc'(
% 0.89/1.31 X, Z ), Z ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'(
% 0.89/1.31 X, T, U ), U, U ), T, 'tc_prod'( U, U ) ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( T, U ), U ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a'
% 0.89/1.31 ), T, 'tc_prod'( 't_a', 't_a' ) ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Y, T, Z ), Z, Z ), T
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( U, Y, Z ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1'(
% 0.89/1.31 X, Y, Z, T ), X, T, Z ), Y, 'tc_prod'( T, Z ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Relation_ORange'( Y, T, Z ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Y, X, Z
% 0.89/1.31 ), X, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( T, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( X, T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z ),
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( T, 'c_Wellfounded_Oacc'( Y,
% 0.89/1.31 Z ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'( Z, 'c_Wellfounded_Oacc'( T,
% 0.89/1.31 't_a' ), 't_a' ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z,
% 0.89/1.31 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ), T,
% 0.89/1.31 'tc_prod'( 't_a', 't_a' ) ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, Z ), Z ) ), hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a',
% 0.89/1.31 't_a' ), T, 'tc_prod'( 't_a', 't_a' ) ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( hAPP( hAPP( X, Y ), Z ), 'c_Set_Oimage'( 'c_split'( X,
% 0.89/1.31 T, U, W ), V0, 'tc_prod'( T, U ), W ), W ) ), ~( hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 Y, Z, T, U ), V0, 'tc_prod'( T, U ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1'( X, Y, Z, T ), Z, T ), Y,
% 0.89/1.31 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T
% 0.89/1.31 ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( 'c_in'( Z, 'c_Wellfounded_Oacc'( T,
% 0.89/1.31 't_a' ), 't_a' ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z,
% 0.89/1.31 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ), T,
% 0.89/1.31 'tc_prod'( 't_a', 't_a' ) ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( 'c_in'(
% 0.89/1.31 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, T
% 0.89/1.31 , U ), U, U ), T, 'tc_prod'( U, U ) ) ) ), ~( hBOOL( 'c_in'( Y,
% 0.89/1.31 'c_Wellfounded_Oacc'( T, U ), U ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Y, T, Z ), Z,
% 0.89/1.31 Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( U, Y, Z ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X,
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1'( X, Y, Z, T ), Z, T )
% 0.89/1.31 , Y, 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( X, 'c_Relation_ODomain'( Y
% 0.89/1.31 , Z, T ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( X, Y, Z, T, U ), Y, T
% 0.89/1.31 , U ), Z, 'tc_prod'( T, U ) ) ), ~( hBOOL( 'c_in'( Y, 'c_Relation_OImage'(
% 0.89/1.31 Z, X, T, U ), U ) ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), hBOOL(
% 0.89/1.31 'c_in'( X, 'c_Relation_ODomain'( T, Z, Z ), Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'(
% 0.89/1.31 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1'( X, Y, Z, T ), X, T, Z
% 0.89/1.31 ), Y, 'tc_prod'( T, Z ) ) ), ~( hBOOL( 'c_in'( X, 'c_Relation_ORange'( Y
% 0.89/1.31 , T, Z ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, hAPP( 'c_split'( Y, Z, T, 'tc_fun'( U, 'tc_bool' ) )
% 0.89/1.31 , 'c_Pair'( W, V0, Z, T ) ), U ) ), ~( hBOOL( 'c_in'( X, hAPP( hAPP( Y, W
% 0.89/1.31 ), V0 ), U ) ) ) ],
% 0.89/1.31 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( Z, U, W, W ), V0, 'tc_prod'( W, W ) ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( Y, T, V1, V1 ), V2, 'tc_prod'( V1, V1 ) ) ) ), ~(
% 0.89/1.31 'c_Equiv__Relations_Ocongruent2'( V2, V0, X, V1, W, V3 ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, Y, T, U ), W, 'tc_prod'( T,
% 0.89/1.31 U ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, X, T, U ), W, 'tc_prod'( T, U )
% 0.89/1.31 ) ) ), ~( 'c_Relation_Osingle__valued'( W, T, U ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( W, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( W, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( hAPP( hAPP( 'c_FunDef_Oin__rel'( X, Y, Z ), T ), U ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( T, U, Y, Z ), X, 'tc_prod'( Y, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ) ), ~(
% 0.89/1.31 hBOOL( hAPP( hAPP( 'c_FunDef_Oin__rel'( U, Z, T ), X ), Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Relation_Otrans'( T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Relation_Otrans'( T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Oconverse'( U, T, Z
% 0.89/1.31 ), 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, T, Z ), U,
% 0.89/1.31 'tc_prod'( T, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Oconverse'( U, T, Z
% 0.89/1.31 ), 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, T, Z ), U,
% 0.89/1.31 'tc_prod'( T, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( Y, X, T, Z ), 'c_Relation_Oconverse'( U, Z, T )
% 0.89/1.31 , 'tc_prod'( T, Z ) ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ) ),
% 0.89/1.31 ~( 'c_Relation_Oirrefl'( Z, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 T, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), T,
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 T, 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 0.89/1.31 , 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_prod'( Y, Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ),
% 0.89/1.31 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_prod'( Y, Y ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ),
% 0.89/1.31 ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Wellfounded_Owf'( T, Z ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z,
% 0.89/1.31 Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z )
% 0.89/1.31 ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z,
% 0.89/1.31 Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z )
% 0.89/1.31 ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) ) ],
% 0.89/1.31 [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z, T,
% 0.89/1.31 T ), U, 'tc_prod'( T, T ) ) ) ), ~( 'c_Equiv__Relations_Ocongruent'( U, X
% 0.89/1.31 , T, W ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.89/1.31 'c_Relation_OId__on'( T, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ ~( =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U
% 0.89/1.31 ) ) ), =( hAPP( X, V0 ), hAPP( W, V0 ) ), ~( hBOOL( 'c_in'( 'c_Pair'( V0
% 0.89/1.31 , Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_OId'(
% 0.89/1.31 Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ), ~(
% 0.89/1.31 'c_Nitpick_Orefl_H'( Z, Y ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ) ),
% 0.89/1.31 ~( 'c_Wellfounded_Owf'( Z, Y ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oinv__image'( T, U
% 0.89/1.31 , W, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( hAPP( U, X )
% 0.89/1.31 , hAPP( U, Y ), W, W ), T, 'tc_prod'( W, W ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( hAPP( X, Y ), hAPP( X, Z ), T, T ), U,
% 0.89/1.31 'tc_prod'( T, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, Z, W, W ),
% 0.89/1.31 'c_Relation_Oinv__image'( U, X, T, W ), 'tc_prod'( W, W ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Relation_Osym'( T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 'c_Relation_Osym'( T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Orel__comp'( U, W,
% 0.89/1.31 Z, V0, T ), 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( V1, Y, V0
% 0.89/1.31 , T ), W, 'tc_prod'( V0, T ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, V1, Z
% 0.89/1.31 , V0 ), U, 'tc_prod'( Z, V0 ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 T, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), T,
% 0.89/1.31 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.89/1.31 T, Z ), 'tc_prod'( Z, Z ) ) ), ~( hBOOL( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.89/1.31 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Otrancl'( T
% 0.89/1.31 , Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId'( Y ),
% 0.89/1.31 'tc_prod'( Y, Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId'( Y ),
% 0.89/1.31 'tc_prod'( Y, Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( hAPP( X, Y ), hAPP( Z, Y ), T ) ), ~( hBOOL( 'c_in'( Y
% 0.89/1.31 , U, W ) ) ), ~( hBOOL( 'c_in'( X, 'c_FuncSet_OPi'( U, Z, W, T ),
% 0.89/1.31 'tc_fun'( W, T ) ) ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), hBOOL( 'c_in'( hAPP( T, X ), hAPP( U
% 0.89/1.31 , X ), W ) ), ~( hBOOL( 'c_in'( T, 'c_FuncSet_OPi'( Y, U, Z, W ),
% 0.89/1.31 'tc_fun'( Z, W ) ) ) ) ],
% 0.89/1.31 [ =( X, Y ), ~( hBOOL( 'c_in'( 'c_Pair'( Z, T, U, U ), W, 'tc_prod'( U,
% 0.89/1.31 U ) ) ) ), ~( hBOOL( 'c_in'( T, Y, U ) ) ), ~( hBOOL( 'c_in'( Z, X, U ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( Y, 'c_Equiv__Relations_Oquotient'( V0, W, U ),
% 0.89/1.31 'tc_fun'( U, 'tc_bool' ) ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Equiv__Relations_Oquotient'( V0, W, U ), 'tc_fun'( U, 'tc_bool' ) ) )
% 0.89/1.31 ), ~( 'c_Equiv__Relations_Oequiv'( V0, W, U ) ) ],
% 0.89/1.31 [ ~( hBOOL( 'c_in'( X, Y, Z ) ) ), ~( hBOOL( 'c_in'( T, Y, Z ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( Y, 'c_Equiv__Relations_Oquotient'( U, W, Z ), 'tc_fun'( Z
% 0.89/1.31 , 'tc_bool' ) ) ) ), ~( hBOOL( 'c_in'( Y, 'c_Equiv__Relations_Oquotient'(
% 0.89/1.31 U, W, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'(
% 0.89/1.31 U, W, Z ) ), hBOOL( 'c_in'( 'c_Pair'( T, X, Z, Z ), W, 'tc_prod'( Z, Z )
% 0.89/1.31 ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( Y, T, 'tc_fun'( Z,
% 0.89/1.31 'tc_bool' ) ) ) ), ~( hBOOL( 'c_in'( X,
% 0.89/1.31 'c_Complete__Lattice_OInf__class_OInf'( T, 'tc_fun'( Z, 'tc_bool' ) ), Z
% 0.89/1.31 ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Complete__Lattice_OSup__class_OSup'( Y, 'tc_fun'(
% 0.89/1.31 Z, 'tc_bool' ) ), Z ) ), ~( hBOOL( 'c_in'( X, T, Z ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Product__Type_OSigma'( U, W
% 0.89/1.31 , Z, T ), 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( Y, hAPP( W, X ), T ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( X, U, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Product__Type_OSigma'( U, W
% 0.89/1.31 , Z, T ), 'tc_prod'( Z, T ) ) ), ~( hBOOL( 'c_in'( Y, hAPP( W, X ), T ) )
% 0.89/1.31 ), ~( hBOOL( 'c_in'( X, U, Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, T, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( T, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, T, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( T, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_OImage'( Y, Z, T, U ), U ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( W, X, T, U ), Y, 'tc_prod'( T, U ) ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( W, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_OImage'( Y, Z, T, U ), U ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( W, X, T, U ), Y, 'tc_prod'( T, U ) ) ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( W, Z, T ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, T, Z, Z ),
% 0.89/1.31 'c_Relation_OId__on'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId__on'( Z, Y ),
% 0.89/1.31 'tc_prod'( Y, Y ) ) ), ~( hBOOL( 'c_in'( X, Z, Y ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( T, X, Z, Z ),
% 0.89/1.31 U, 'tc_prod'( Z, Z ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, U, Z ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, T, Z, Z ),
% 0.89/1.31 U, 'tc_prod'( Z, Z ) ) ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, U, Z ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_ORange'( Y, Z, T ), T ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( U, X, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_ORange'( Y, Z, T ), T ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( U, X, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, U, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ) ), ~( hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( X, U, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, hAPP( Y, Z ), T ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Z,
% 0.89/1.31 X, U, T ), 'c_Product__Type_OSigma'( W, Y, U, T ), 'tc_prod'( U, T ) ) )
% 0.89/1.31 ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, T, Z, U ),
% 0.89/1.31 'c_Product__Type_OSigma'( Y, W, Z, U ), 'tc_prod'( Z, U ) ) ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), hBOOL(
% 0.89/1.31 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), =( Y, X ), ~(
% 0.89/1.31 hBOOL( 'c_in'( X, U, Z ) ) ), ~( hBOOL( 'c_in'( Y, U, Z ) ) ), ~(
% 0.89/1.31 'c_Relation_Ototal__on'( U, T, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ), ~(
% 0.89/1.31 hBOOL( 'c_in'( X, T, Y ) ) ), ~( 'c_Relation_Orefl__on'( T, Z, Y ) ) ]
% 0.89/1.31 ,
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( T, X, Z, Z ),
% 0.89/1.31 U, 'tc_prod'( Z, Z ) ) ) ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( 'c_in'( 'c_Pair'( X, T, Z, Z ),
% 0.89/1.31 U, 'tc_prod'( Z, Z ) ) ) ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ) ],
% 0.89/1.31 [ hBOOL( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ), ~(
% 0.89/1.32 hBOOL( 'c_in'( X, T, Y ) ) ), ~( 'c_Relation_Orefl__on'( T, Z, Y ) ) ]
% 0.89/1.32 ,
% 0.89/1.32 [ hBOOL( 'c_in'( X, 'c_Arrow__Order__Mirabelle_OLin', 'tc_fun'(
% 0.89/1.32 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), ~( hBOOL( 'c_in'(
% 0.89/1.32 'c_Relation_Oconverse'( X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'c_Arrow__Order__Mirabelle_OLin',
% 0.89/1.32 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ],
% 0.89/1.32 [ hBOOL( 'c_in'( 'c_Relation_Oconverse'( X,
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.89/1.32 'c_Arrow__Order__Mirabelle_OLin', 'tc_fun'( 'tc_prod'(
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.89/1.32 'tc_bool' ) ) ), ~( hBOOL( 'c_in'( X, 'c_Arrow__Order__Mirabelle_OLin',
% 0.89/1.32 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ],
% 0.89/1.32 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( Y, W ) ]
% 0.89/1.32 ,
% 0.89/1.32 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( X, U ) ]
% 0.89/1.32 ,
% 0.89/1.32 [ ~( hBOOL( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.89/1.32 ) ), ~( hBOOL( 'c_in'( 'c_Pair'( Y, X, 'tc_Arrow__Order__Mirabelle_Oalt'
% 0.89/1.32 , 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.89/1.32 ) ), =( X, Y ), ~( hBOOL( 'c_in'( Z, 'c_Arrow__Order__Mirabelle_OLin',
% 0.89/1.32 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ],
% 0.89/1.32 [ hBOOL( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.89/1.32 ), hBOOL( 'c_in'( 'c_Pair'( Y, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.89/1.32 ), =( Y, X ), ~( hBOOL( 'c_in'( Z, 'c_Arrow__Order__Mirabelle_OLin',
% 0.89/1.32 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ],
% 0.89/1.32 [ hBOOL( 'c_in'( X, Y, Z ) ), ~( hBOOL( hAPP( Y, X ) ) ) ],
% 0.89/1.32 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_in'( Y, X, Z ) ) ) ],
% 0.89/1.32 [ hBOOL( 'c_in'( 'v_L', 'c_Arrow__Order__Mirabelle_OLin', 'tc_fun'(
% 0.89/1.32 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ],
% 0.89/1.32 [ hBOOL( 'c_in'( 'c_Pair'( 'v_a', 'v_b',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.89/1.32 'v_L', 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ],
% 0.89/1.32 [ hBOOL( 'c_in'( 'c_Pair'( 'v_b', 'v_a',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.89/1.32 'v_L', 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.89/1.32 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ],
% 0.89/1.32 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Complete__Lattice_Ocomplete__lattice'( Y ) ) ],
% 0.89/1.32 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Lattices_Olattice'( Y ) ) ],
% 0.89/1.32 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Lattices_Olattice'( Y ) ) ],
% 0.89/1.32 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 0.89/1.32 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 0.89/1.32 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Orderings_Opreorder'( Y ) ) ],
% 0.89/1.32 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Lattices_Olattice'( Y ) ) ],
% 0.89/1.32 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.89/1.32 'class_Orderings_Oorder'( Y ) ) ],
% 0.89/1.32 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 0.89/1.32 Y ) ) ],
% 0.89/1.32 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 0.89/1.32 ,
% 0.89/1.32 [ 'class_Complete__Lattice_Ocomplete__lattice'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 0.89/1.32 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 0.89/1.32 [ 'c_fequal'( X, X, Y ) ],
% 0.89/1.32 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 0.89/1.32 ] .
% 0.89/1.32
% 0.89/1.32
% 0.89/1.32 percentage equality = 0.227952, percentage horn = 0.894819
% 0.89/1.32 This is a problem with some equality
% 0.89/1.32
% 0.89/1.32
% 0.89/1.32
% 0.89/1.32 Options Used:
% 0.89/1.32
% 0.89/1.32 useres = 1
% 0.89/1.32 useparamod = 1
% 0.89/1.32 useeqrefl = 1
% 0.89/1.32 useeqfact = 1
% 0.89/1.32 usefactor = 1
% 0.89/1.32 usesimpsplitting = 0
% 0.89/1.32 usesimpdemod = 5
% 0.89/1.32 usesimpres = 3
% 0.89/1.32
% 0.89/1.32 resimpinuse = 1000
% 0.89/1.32 resimpclauses = 20000
% 0.89/1.32 substype = eqrewr
% 0.89/1.32 backwardsubs = 1
% 0.89/1.32 selectoldest = 5
% 0.89/1.32
% 0.89/1.32 litorderings [0] = split
% 0.89/1.32 litorderings [1] = extend the termordering, first sorting on arguments
% 0.89/1.32
% 0.89/1.32 termordering = kbo
% 0.89/1.32
% 0.89/1.32 litapriori = 0
% 0.89/1.32 termapriori = 1
% 0.89/1.32 litaposteriori = 0
% 0.89/1.32 termaposteriori = 0
% 0.89/1.32 demodaposteriori = 0
% 0.89/1.32 ordereqreflfact = 0
% 0.89/1.32
% 0.89/1.32 litselect = negord
% 0.89/1.32
% 0.89/1.32 maxweight = 15
% 0.89/1.32 maxdepth = 30000
% 0.89/1.32 maxlength = 115
% 0.89/1.32 maxnrvars = 195
% 0.89/1.32 excuselevel = 1
% 0.89/1.32 increasemaxweight = 1
% 0.89/1.32
% 0.89/1.32 maxselected = 10000000
% 0.89/1.32 maxnrclauses = 10000000
% 0.89/1.32
% 0.89/1.32 showgenerated = 0
% 0.89/1.32 showkept = 0
% 0.89/1.32 showselected = 0
% 0.89/1.32 showdeleted = 0
% 0.89/1.32 showresimp = 1
% 0.89/1.32 showstatus = 2000
% 0.89/1.32
% 0.89/1.32 prologoutput = 1
% 0.89/1.32 nrgoals = 5000000
% 0.89/1.32 totalproof = 1
% 0.89/1.32
% 0.89/1.32 Symbols occurring in the translation:
% 0.89/1.32
% 0.89/1.32 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.89/1.32 . [1, 2] (w:1, o:97, a:1, s:1, b:0),
% 0.89/1.32 ! [4, 1] (w:0, o:76, a:1, s:1, b:0),
% 0.89/1.32 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.32 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.32 'tc_bool' [41, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.89/1.32 'tc_fun' [42, 2] (w:1, o:122, a:1, s:1, b:0),
% 0.89/1.32 'c_Orderings_Obot__class_Obot' [43, 1] (w:1, o:81, a:1, s:1, b:0),
% 0.89/1.32 'c_Lattices_Olower__semilattice__class_Oinf' [44, 3] (w:1, o:150, a:1
% 0.89/1.32 , s:1, b:0),
% 0.89/1.32 'c_Set_Oinsert' [47, 3] (w:1, o:157, a:1, s:1, b:0),
% 0.89/1.32 'c_lessequals' [48, 3] (w:1, o:158, a:1, s:1, b:0),
% 0.89/1.32 'class_Complete__Lattice_Ocomplete__lattice' [49, 1] (w:1, o:82, a:1
% 0.89/1.32 , s:1, b:0),
% 0.89/1.32 'c_Complete__Lattice_OSup__class_OSup' [50, 2] (w:1, o:123, a:1, s:1
% 0.89/1.32 , b:0),
% 0.89/1.32 'c_Set_Oimage' [53, 4] (w:1, o:185, a:1, s:1, b:0),
% 0.89/1.32 'c_Relation_OImage' [55, 4] (w:1, o:183, a:1, s:1, b:0),
% 0.89/1.32 'class_Lattices_Obounded__lattice' [56, 1] (w:1, o:83, a:1, s:1, b:0)
% 0.89/1.32 ,
% 0.89/1.32 'tc_prod' [58, 2] (w:1, o:124, a:1, s:1, b:0),
% 0.89/1.32 'c_Relation_ODomain' [59, 3] (w:1, o:151, a:1, s:1, b:0),
% 0.89/1.32 'c_Transitive__Closure_Ortrancl' [61, 2] (w:1, o:126, a:1, s:1, b:0)
% 0.89/1.32 ,
% 0.89/1.32 'c_Lattices_Oupper__semilattice__class_Osup' [63, 3] (w:1, o:159, a:1
% 0.89/1.32 , s:1, b:0),
% 0.89/1.32 'c_Relation_Osym' [64, 2] (w:1, o:127, a:1, s:1, b:0),
% 0.89/1.32 'c_Pair' [66, 4] (w:1, o:188, a:1, s:1, b:0),
% 0.89/1.32 hAPP [67, 2] (w:1, o:128, a:1, s:1, b:0),
% 0.89/1.32 hBOOL [68, 1] (w:1, o:84, a:1, s:1, b:0),
% 0.89/1.32 'c_HOL_Ominus__class_Ominus' [70, 3] (w:1, o:160, a:1, s:1, b:0),
% 0.89/1.32 'class_Orderings_Obot' [71, 1] (w:1, o:85, a:1, s:1, b:0),
% 0.89/1.32 'c_Relation_Orel__comp' [73, 5] (w:1, o:209, a:1, s:1, b:0),
% 0.89/1.32 'c_Complete__Lattice_OInf__class_OInf' [75, 2] (w:1, o:129, a:1, s:1
% 0.89/1.32 , b:0),
% 0.89/1.32 'c_List_Osko__Equiv__Relations__XquotientE__1__1' [78, 4] (w:1, o:189
% 0.89/1.32 , a:1, s:1, b:0),
% 0.89/1.32 'c_Equiv__Relations_Oquotient' [79, 3] (w:1, o:161, a:1, s:1, b:0),
% 0.89/1.32 'c_in' [80, 3] (w:1, o:162, a:1, s:1, b:0),
% 0.89/1.32 'c_snd' [81, 2] (w:1, o:130, a:1, s:1, b:0),
% 0.89/1.32 'c_fst' [83, 2] (w:1, o:131, a:1, s:1, b:0),
% 0.89/1.32 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1' [87, 3] (w:1, o:
% 0.89/1.32 163, a:1, s:1, b:0),
% 0.89/1.32 'c_Wellfounded_Owf' [88, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.89/1.32 'c_Relation_ORange' [89, 3] (w:1, o:152, a:1, s:1, b:0),
% 0.89/1.32 'c_COMBK' [90, 3] (w:1, o:164, a:1, s:1, b:0),
% 0.93/1.53 'c_Product__Type_OSigma' [91, 4] (w:1, o:190, a:1, s:1, b:0),
% 0.93/1.53 'c_Transitive__Closure_Otrancl' [93, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.93/1.53
% 0.93/1.53 'class_Lattices_Odistrib__lattice' [96, 1] (w:1, o:86, a:1, s:1, b:0)
% 0.93/1.53 ,
% 0.93/1.53 'c_Relation_OId__on' [98, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Orefl__on' [99, 3] (w:1, o:153, a:1, s:1, b:0),
% 0.93/1.53 'class_Lattices_Oupper__semilattice' [100, 1] (w:1, o:87, a:1, s:1
% 0.93/1.53 , b:0),
% 0.93/1.53 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1' [104, 3] (w:1, o:165
% 0.93/1.53 , a:1, s:1, b:0),
% 0.93/1.53 'class_OrderedGroup_Oab__group__add' [107, 1] (w:1, o:88, a:1, s:1
% 0.93/1.53 , b:0),
% 0.93/1.53 'class_Lattices_Olattice' [110, 1] (w:1, o:89, a:1, s:1, b:0),
% 0.93/1.53 'class_Lattices_Olower__semilattice' [111, 1] (w:1, o:90, a:1, s:1
% 0.93/1.53 , b:0),
% 0.93/1.53 'c_Wellfounded_Oacyclic' [112, 2] (w:1, o:135, a:1, s:1, b:0),
% 0.93/1.53 'c_Equiv__Relations_Oequiv' [113, 3] (w:1, o:166, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Otrans' [115, 2] (w:1, o:136, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1' [117, 3] (w:1, o:
% 0.93/1.53 167, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Oconverse' [118, 3] (w:1, o:154, a:1, s:1, b:0),
% 0.93/1.53 'class_Orderings_Oorder' [119, 1] (w:1, o:91, a:1, s:1, b:0),
% 0.93/1.53 'c_split' [120, 4] (w:1, o:191, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Oantisym' [121, 2] (w:1, o:137, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Ototal__on' [123, 3] (w:1, o:156, a:1, s:1, b:0),
% 0.93/1.53 'c_Order__Relation_Ostrict__linear__order__on' [124, 3] (w:1, o:168
% 0.93/1.53 , a:1, s:1, b:0),
% 0.93/1.53 'c_Wellfounded_Oacc' [127, 2] (w:1, o:138, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1' [129, 3]
% 0.93/1.53 (w:1, o:169, a:1, s:1, b:0),
% 0.93/1.53 'c_List_Osko__Recdef__Xcuts__eq__1__1' [131, 6] (w:1, o:217, a:1, s:1
% 0.93/1.53 , b:0),
% 0.93/1.53 'c_Recdef_Ocut' [132, 5] (w:1, o:210, a:1, s:1, b:0),
% 0.93/1.53 'class_HOL_Oord' [133, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.93/1.53 'class_Orderings_Opreorder' [134, 1] (w:1, o:93, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Osingle__valued' [135, 3] (w:1, o:155, a:1, s:1, b:0),
% 0.93/1.53 'class_OrderedGroup_Opordered__ab__group__add' [136, 1] (w:1, o:94
% 0.93/1.53 , a:1, s:1, b:0),
% 0.93/1.53 'class_Orderings_Olinorder' [138, 1] (w:1, o:95, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_Oirrefl' [139, 2] (w:1, o:139, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'
% 0.93/1.53 [140, 4] (w:1, o:192, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'
% 0.93/1.53 [141, 4] (w:1, o:193, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1' [142, 4
% 0.93/1.53 ] (w:1, o:194, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2' [143, 4
% 0.93/1.53 ] (w:1, o:195, a:1, s:1, b:0),
% 0.93/1.53 'c_Fun_Ooverride__on' [144, 5] (w:1, o:211, a:1, s:1, b:0),
% 0.93/1.53 'c_FuncSet_OPi' [145, 4] (w:1, o:197, a:1, s:1, b:0),
% 0.93/1.53 'c_Relation_OId' [147, 1] (w:1, o:96, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1' [148, 3] (w:1
% 0.93/1.53 , o:170, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1' [149, 3] (w:1
% 0.93/1.53 , o:171, a:1, s:1, b:0),
% 0.93/1.53 'c_Set_OPow' [150, 2] (w:1, o:125, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1' [151, 4]
% 0.93/1.53 (w:1, o:198, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1' [152, 4]
% 0.93/1.53 (w:1, o:199, a:1, s:1, b:0),
% 0.93/1.53 'c_Nitpick_Orefl_H' [153, 2] (w:1, o:140, a:1, s:1, b:0),
% 0.93/1.53 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1' [154, 2] (w:1, o:141
% 0.93/1.53 , a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1' [155, 2] (w:1, o:
% 0.93/1.53 142, a:1, s:1, b:0),
% 0.93/1.53 'v_r' [156, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.93/1.53 't_a' [157, 0] (w:1, o:62, a:1, s:1, b:0),
% 0.93/1.53 't_b' [158, 0] (w:1, o:63, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1' [159, 3] (w:1, o:172
% 0.93/1.53 , a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1' [160, 2] (w:1
% 0.93/1.53 , o:143, a:1, s:1, b:0),
% 0.93/1.53 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1' [161, 2] (w:1, o:
% 8.33/8.78 144, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XIdE__1__1' [162, 2] (w:1, o:145, a:1
% 8.33/8.78 , s:1, b:0),
% 8.33/8.78 'c_FuncSet_Osko__FuncSet__XPi__I__1__1' [163, 5] (w:1, o:212, a:1, s:
% 8.33/8.78 1, b:0),
% 8.33/8.78 'c_FuncSet_Osko__FuncSet__XPi__I_H__1__1' [164, 5] (w:1, o:213, a:1
% 8.33/8.78 , s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1' [165, 7] (w:1
% 8.33/8.78 , o:219, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1' [166
% 8.33/8.78 , 2] (w:1, o:146, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1' [167,
% 8.33/8.78 4] (w:1, o:200, a:1, s:1, b:0),
% 8.33/8.78 'v_sko__Transitive__Closure__Xtrancl__Xcases__1' [170, 3] (w:1, o:173
% 8.33/8.78 , a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1' [171, 4]
% 8.33/8.78 (w:1, o:201, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1' [173, 4]
% 8.33/8.78 (w:1, o:202, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1' [174
% 8.33/8.78 , 4] (w:1, o:203, a:1, s:1, b:0),
% 8.33/8.78 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1' [175, 3] (w:1, o:
% 8.33/8.78 174, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1' [176, 5] (w:1, o:
% 8.33/8.78 214, a:1, s:1, b:0),
% 8.33/8.78 'c_FunDef_Oin__rel' [177, 3] (w:1, o:175, a:1, s:1, b:0),
% 8.33/8.78 'c_Wellfounded_OwfP' [178, 2] (w:1, o:147, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XImageE__1__1' [180, 5] (w:1, o:215
% 8.33/8.78 , a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1' [181, 3] (w:1
% 8.33/8.78 , o:176, a:1, s:1, b:0),
% 8.33/8.78 'v_sko__Wellfounded__Xacc__Xinducts__1' [182, 2] (w:1, o:148, a:1, s:
% 8.33/8.78 1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1' [183, 3]
% 8.33/8.78 (w:1, o:177, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1' [184, 5] (w:1, o:
% 8.33/8.78 216, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1' [185, 3] (w:
% 8.33/8.78 1, o:178, a:1, s:1, b:0),
% 8.33/8.78 'c_Relation_Oinv__image' [186, 4] (w:1, o:184, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1' [188, 3]
% 8.33/8.78 (w:1, o:179, a:1, s:1, b:0),
% 8.33/8.78 'v_sko__Wellfounded__Xacc__Xinduct__1' [189, 2] (w:1, o:149, a:1, s:1
% 8.33/8.78 , b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1' [190, 3] (w:1, o:
% 8.33/8.78 180, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1' [191, 3] (w:1
% 8.33/8.78 , o:181, a:1, s:1, b:0),
% 8.33/8.78 'c_Equiv__Relations_Ocongruent' [193, 4] (w:1, o:196, a:1, s:1, b:0)
% 8.33/8.78 ,
% 8.33/8.78 'c_Equiv__Relations_Ocongruent2' [195, 6] (w:1, o:218, a:1, s:1, b:0)
% 8.33/8.78 ,
% 8.33/8.78 'v_a' [196, 0] (w:1, o:65, a:1, s:1, b:0),
% 8.33/8.78 'c_HOL_OIf' [197, 4] (w:1, o:204, a:1, s:1, b:0),
% 8.33/8.78 'v_b' [199, 0] (w:1, o:67, a:1, s:1, b:0),
% 8.33/8.78 'c_Orderings_Oord_Omin' [200, 4] (w:1, o:186, a:1, s:1, b:0),
% 8.33/8.78 'c_Orderings_Oord_Omax' [201, 4] (w:1, o:187, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1' [202, 4] (w:1, o:205
% 8.33/8.78 , a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1' [204, 4] (w:1, o:206
% 8.33/8.78 , a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1' [205, 4] (w:1, o:
% 8.33/8.78 207, a:1, s:1, b:0),
% 8.33/8.78 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1' [206, 4] (w:1, o:
% 8.33/8.78 208, a:1, s:1, b:0),
% 8.33/8.78 'c_Arrow__Order__Mirabelle_OLin' [212, 0] (w:1, o:71, a:1, s:1, b:0)
% 8.33/8.78 ,
% 8.33/8.78 'tc_Arrow__Order__Mirabelle_Oalt' [213, 0] (w:1, o:72, a:1, s:1, b:0)
% 8.33/8.78 ,
% 8.33/8.78 'v_L' [216, 0] (w:1, o:73, a:1, s:1, b:0),
% 8.33/8.78 'c_fequal' [219, 3] (w:1, o:182, a:1, s:1, b:0).
% 8.33/8.78
% 8.33/8.78
% 8.33/8.78 Starting Search:
% 8.33/8.78
% 8.33/8.78 Resimplifying inuse:
% 8.33/8.78 Done
% 8.33/8.78
% 8.33/8.78
% 8.33/8.78 Intermediate Status:
% 8.33/8.78 Generated: 4145
% 8.33/8.78 Kept: 2017
% 8.33/8.78 Inuse: 155
% 8.33/8.78 Deleted: 1
% 8.33/8.78 Deletedinuse: 0
% 8.33/8.78
% 8.33/8.78 Resimplifying inuse:
% 8.33/8.78 Done
% 8.33/8.78
% 8.33/8.78 Resimplifying inuse:
% 8.33/8.78 Done
% 8.33/8.78
% 8.33/8.78
% 8.33/8.78 Intermediate Status:
% 8.33/8.78 Generated: 11171
% 8.33/8.78 Kept: 4033
% 8.33/8.78 Inuse: 265
% 8.33/8.78 Deleted: 2
% 8.33/8.78 Deletedinuse: 1
% 8.33/8.78
% 8.33/8.78 Resimplifying inuse:
% 8.33/8.78 Done
% 8.33/8.78
% 8.33/8.78 Resimplifying inuse:
% 8.33/8.78 Done
% 8.33/8.78
% 8.33/8.78
% 8.33/8.78 Intermediate Status:
% 8.33/8.78 Generated: 18440
% 8.33/8.78 Kept: 6033
% 8.33/8.78 Inuse: 359
% 8.33/8.78 Deleted: 5
% 8.33/8.78 Deletedinuse: 2
% 8.33/8.78
% 8.33/8.78 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 26569
% 31.45/31.87 Kept: 8123
% 31.45/31.87 Inuse: 446
% 31.45/31.87 Deleted: 10
% 31.45/31.87 Deletedinuse: 5
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 35318
% 31.45/31.87 Kept: 10131
% 31.45/31.87 Inuse: 530
% 31.45/31.87 Deleted: 11
% 31.45/31.87 Deletedinuse: 6
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 43442
% 31.45/31.87 Kept: 12220
% 31.45/31.87 Inuse: 583
% 31.45/31.87 Deleted: 15
% 31.45/31.87 Deletedinuse: 7
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 57269
% 31.45/31.87 Kept: 14425
% 31.45/31.87 Inuse: 638
% 31.45/31.87 Deleted: 17
% 31.45/31.87 Deletedinuse: 9
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 78965
% 31.45/31.87 Kept: 17907
% 31.45/31.87 Inuse: 696
% 31.45/31.87 Deleted: 21
% 31.45/31.87 Deletedinuse: 11
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 97321
% 31.45/31.87 Kept: 20438
% 31.45/31.87 Inuse: 701
% 31.45/31.87 Deleted: 21
% 31.45/31.87 Deletedinuse: 11
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying clauses:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 113906
% 31.45/31.87 Kept: 22804
% 31.45/31.87 Inuse: 732
% 31.45/31.87 Deleted: 321
% 31.45/31.87 Deletedinuse: 11
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 139059
% 31.45/31.87 Kept: 24862
% 31.45/31.87 Inuse: 747
% 31.45/31.87 Deleted: 321
% 31.45/31.87 Deletedinuse: 11
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 160214
% 31.45/31.87 Kept: 27577
% 31.45/31.87 Inuse: 809
% 31.45/31.87 Deleted: 326
% 31.45/31.87 Deletedinuse: 14
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 174277
% 31.45/31.87 Kept: 29899
% 31.45/31.87 Inuse: 852
% 31.45/31.87 Deleted: 330
% 31.45/31.87 Deletedinuse: 16
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 187504
% 31.45/31.87 Kept: 32570
% 31.45/31.87 Inuse: 867
% 31.45/31.87 Deleted: 330
% 31.45/31.87 Deletedinuse: 16
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 206091
% 31.45/31.87 Kept: 34592
% 31.45/31.87 Inuse: 926
% 31.45/31.87 Deleted: 331
% 31.45/31.87 Deletedinuse: 17
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 221297
% 31.45/31.87 Kept: 36698
% 31.45/31.87 Inuse: 957
% 31.45/31.87 Deleted: 331
% 31.45/31.87 Deletedinuse: 17
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 237841
% 31.45/31.87 Kept: 38819
% 31.45/31.87 Inuse: 1002
% 31.45/31.87 Deleted: 331
% 31.45/31.87 Deletedinuse: 17
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying clauses:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 255918
% 31.45/31.87 Kept: 40841
% 31.45/31.87 Inuse: 1052
% 31.45/31.87 Deleted: 796
% 31.45/31.87 Deletedinuse: 18
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 272316
% 31.45/31.87 Kept: 43605
% 31.45/31.87 Inuse: 1077
% 31.45/31.87 Deleted: 798
% 31.45/31.87 Deletedinuse: 20
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 291961
% 31.45/31.87 Kept: 46148
% 31.45/31.87 Inuse: 1112
% 31.45/31.87 Deleted: 803
% 31.45/31.87 Deletedinuse: 25
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 307265
% 31.45/31.87 Kept: 48152
% 31.45/31.87 Inuse: 1159
% 31.45/31.87 Deleted: 806
% 31.45/31.87 Deletedinuse: 28
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 323184
% 31.45/31.87 Kept: 50163
% 31.45/31.87 Inuse: 1205
% 31.45/31.87 Deleted: 811
% 31.45/31.87 Deletedinuse: 32
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 343171
% 31.45/31.87 Kept: 53257
% 31.45/31.87 Inuse: 1221
% 31.45/31.87 Deleted: 811
% 31.45/31.87 Deletedinuse: 32
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 355177
% 31.45/31.87 Kept: 55310
% 31.45/31.87 Inuse: 1261
% 31.45/31.87 Deleted: 811
% 31.45/31.87 Deletedinuse: 32
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 366354
% 31.45/31.87 Kept: 57492
% 31.45/31.87 Inuse: 1281
% 31.45/31.87 Deleted: 812
% 31.45/31.87 Deletedinuse: 33
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 376157
% 31.45/31.87 Kept: 59500
% 31.45/31.87 Inuse: 1309
% 31.45/31.87 Deleted: 814
% 31.45/31.87 Deletedinuse: 33
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 394993
% 31.45/31.87 Kept: 62342
% 31.45/31.87 Inuse: 1319
% 31.45/31.87 Deleted: 814
% 31.45/31.87 Deletedinuse: 33
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying clauses:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87 Resimplifying inuse:
% 31.45/31.87 Done
% 31.45/31.87
% 31.45/31.87
% 31.45/31.87 Intermediate Status:
% 31.45/31.87 Generated: 407819
% 31.45/31.87 Kept: 64344
% 83.90/84.36 Inuse: 1348
% 83.90/84.36 Deleted: 1469
% 83.90/84.36 Deletedinuse: 33
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 427180
% 83.90/84.36 Kept: 67043
% 83.90/84.36 Inuse: 1369
% 83.90/84.36 Deleted: 1469
% 83.90/84.36 Deletedinuse: 33
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 439433
% 83.90/84.36 Kept: 69373
% 83.90/84.36 Inuse: 1404
% 83.90/84.36 Deleted: 1470
% 83.90/84.36 Deletedinuse: 34
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 453383
% 83.90/84.36 Kept: 71373
% 83.90/84.36 Inuse: 1444
% 83.90/84.36 Deleted: 1476
% 83.90/84.36 Deletedinuse: 40
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 465379
% 83.90/84.36 Kept: 73398
% 83.90/84.36 Inuse: 1484
% 83.90/84.36 Deleted: 1480
% 83.90/84.36 Deletedinuse: 44
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 477206
% 83.90/84.36 Kept: 75581
% 83.90/84.36 Inuse: 1517
% 83.90/84.36 Deleted: 1483
% 83.90/84.36 Deletedinuse: 45
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 492398
% 83.90/84.36 Kept: 77604
% 83.90/84.36 Inuse: 1551
% 83.90/84.36 Deleted: 1488
% 83.90/84.36 Deletedinuse: 49
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 503701
% 83.90/84.36 Kept: 79614
% 83.90/84.36 Inuse: 1587
% 83.90/84.36 Deleted: 1491
% 83.90/84.36 Deletedinuse: 50
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 520073
% 83.90/84.36 Kept: 81887
% 83.90/84.36 Inuse: 1628
% 83.90/84.36 Deleted: 1495
% 83.90/84.36 Deletedinuse: 53
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying clauses:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 531908
% 83.90/84.36 Kept: 84053
% 83.90/84.36 Inuse: 1653
% 83.90/84.36 Deleted: 2093
% 83.90/84.36 Deletedinuse: 54
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 544509
% 83.90/84.36 Kept: 86293
% 83.90/84.36 Inuse: 1683
% 83.90/84.36 Deleted: 2093
% 83.90/84.36 Deletedinuse: 54
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36 Resimplifying inuse:
% 83.90/84.36 Done
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 552278
% 83.90/84.36 Kept: 88306
% 83.90/84.36 Inuse: 1708
% 83.90/84.36 Deleted: 2096
% 83.90/84.36 Deletedinuse: 57
% 83.90/84.36
% 83.90/84.36
% 83.90/84.36 Intermediate Status:
% 83.90/84.36 Generated: 568095
% 83.90/84.36 Kept: 91575
% 83.90/84.36 Inuse: 1713
% 83.90/84.37 Deleted: 2096
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 583766
% 83.90/84.37 Kept: 94843
% 83.90/84.37 Inuse: 1718
% 83.90/84.37 Deleted: 2096
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 599787
% 83.90/84.37 Kept: 98167
% 83.90/84.37 Inuse: 1722
% 83.90/84.37 Deleted: 2097
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 608692
% 83.90/84.37 Kept: 100180
% 83.90/84.37 Inuse: 1743
% 83.90/84.37 Deleted: 2098
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 651060
% 83.90/84.37 Kept: 103766
% 83.90/84.37 Inuse: 1746
% 83.90/84.37 Deleted: 2098
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying clauses:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 670092
% 83.90/84.37 Kept: 107818
% 83.90/84.37 Inuse: 1756
% 83.90/84.37 Deleted: 2281
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 727581
% 83.90/84.37 Kept: 112358
% 83.90/84.37 Inuse: 1764
% 83.90/84.37 Deleted: 2283
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 747963
% 83.90/84.37 Kept: 114480
% 83.90/84.37 Inuse: 1784
% 83.90/84.37 Deleted: 2283
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 777328
% 83.90/84.37 Kept: 119961
% 83.90/84.37 Inuse: 1799
% 83.90/84.37 Deleted: 2283
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 798983
% 83.90/84.37 Kept: 123893
% 83.90/84.37 Inuse: 1814
% 83.90/84.37 Deleted: 2283
% 83.90/84.37 Deletedinuse: 57
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying clauses:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 811844
% 83.90/84.37 Kept: 126414
% 83.90/84.37 Inuse: 1837
% 83.90/84.37 Deleted: 2331
% 83.90/84.37 Deletedinuse: 62
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 838836
% 83.90/84.37 Kept: 128457
% 83.90/84.37 Inuse: 1861
% 83.90/84.37 Deleted: 2332
% 83.90/84.37 Deletedinuse: 63
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 83.90/84.37
% 83.90/84.37 Intermediate Status:
% 83.90/84.37 Generated: 850756
% 83.90/84.37 Kept: 130519
% 83.90/84.37 Inuse: 1882
% 83.90/84.37 Deleted: 2332
% 83.90/84.37 Deletedinuse: 63
% 83.90/84.37
% 83.90/84.37 Resimplifying inuse:
% 83.90/84.37 Done
% 83.90/84.37
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 870499
% 222.73/223.22 Kept: 132524
% 222.73/223.22 Inuse: 1919
% 222.73/223.22 Deleted: 2332
% 222.73/223.22 Deletedinuse: 63
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 887638
% 222.73/223.22 Kept: 134533
% 222.73/223.22 Inuse: 1972
% 222.73/223.22 Deleted: 2333
% 222.73/223.22 Deletedinuse: 64
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 910898
% 222.73/223.22 Kept: 136551
% 222.73/223.22 Inuse: 1997
% 222.73/223.22 Deleted: 2333
% 222.73/223.22 Deletedinuse: 64
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 923553
% 222.73/223.22 Kept: 138560
% 222.73/223.22 Inuse: 2040
% 222.73/223.22 Deleted: 2334
% 222.73/223.22 Deletedinuse: 65
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 936886
% 222.73/223.22 Kept: 140934
% 222.73/223.22 Inuse: 2062
% 222.73/223.22 Deleted: 2335
% 222.73/223.22 Deletedinuse: 66
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 951507
% 222.73/223.22 Kept: 143299
% 222.73/223.22 Inuse: 2082
% 222.73/223.22 Deleted: 2335
% 222.73/223.22 Deletedinuse: 66
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying clauses:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 964850
% 222.73/223.22 Kept: 145341
% 222.73/223.22 Inuse: 2097
% 222.73/223.22 Deleted: 3222
% 222.73/223.22 Deletedinuse: 66
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 975018
% 222.73/223.22 Kept: 147604
% 222.73/223.22 Inuse: 2117
% 222.73/223.22 Deleted: 3225
% 222.73/223.22 Deletedinuse: 69
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 997414
% 222.73/223.22 Kept: 152317
% 222.73/223.22 Inuse: 2127
% 222.73/223.22 Deleted: 3225
% 222.73/223.22 Deletedinuse: 69
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1020303
% 222.73/223.22 Kept: 154646
% 222.73/223.22 Inuse: 2137
% 222.73/223.22 Deleted: 3225
% 222.73/223.22 Deletedinuse: 69
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1042561
% 222.73/223.22 Kept: 156916
% 222.73/223.22 Inuse: 2142
% 222.73/223.22 Deleted: 3225
% 222.73/223.22 Deletedinuse: 69
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1051854
% 222.73/223.22 Kept: 159042
% 222.73/223.22 Inuse: 2161
% 222.73/223.22 Deleted: 3226
% 222.73/223.22 Deletedinuse: 69
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1060093
% 222.73/223.22 Kept: 161065
% 222.73/223.22 Inuse: 2181
% 222.73/223.22 Deleted: 3226
% 222.73/223.22 Deletedinuse: 69
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1069859
% 222.73/223.22 Kept: 163462
% 222.73/223.22 Inuse: 2196
% 222.73/223.22 Deleted: 3236
% 222.73/223.22 Deletedinuse: 79
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying clauses:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1099031
% 222.73/223.22 Kept: 167303
% 222.73/223.22 Inuse: 2216
% 222.73/223.22 Deleted: 4235
% 222.73/223.22 Deletedinuse: 80
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1122273
% 222.73/223.22 Kept: 172233
% 222.73/223.22 Inuse: 2226
% 222.73/223.22 Deleted: 4239
% 222.73/223.22 Deletedinuse: 84
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1146005
% 222.73/223.22 Kept: 177020
% 222.73/223.22 Inuse: 2236
% 222.73/223.22 Deleted: 4240
% 222.73/223.22 Deletedinuse: 85
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1154130
% 222.73/223.22 Kept: 179084
% 222.73/223.22 Inuse: 2256
% 222.73/223.22 Deleted: 4243
% 222.73/223.22 Deletedinuse: 88
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1164286
% 222.73/223.22 Kept: 181225
% 222.73/223.22 Inuse: 2271
% 222.73/223.22 Deleted: 4243
% 222.73/223.22 Deletedinuse: 88
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1213228
% 222.73/223.22 Kept: 187460
% 222.73/223.22 Inuse: 2290
% 222.73/223.22 Deleted: 4245
% 222.73/223.22 Deletedinuse: 89
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying clauses:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1226105
% 222.73/223.22 Kept: 189725
% 222.73/223.22 Inuse: 2305
% 222.73/223.22 Deleted: 4718
% 222.73/223.22 Deletedinuse: 89
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1236196
% 222.73/223.22 Kept: 192203
% 222.73/223.22 Inuse: 2325
% 222.73/223.22 Deleted: 4718
% 222.73/223.22 Deletedinuse: 89
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1244026
% 222.73/223.22 Kept: 194231
% 222.73/223.22 Inuse: 2341
% 222.73/223.22 Deleted: 4720
% 222.73/223.22 Deletedinuse: 90
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22 Resimplifying inuse:
% 222.73/223.22 Done
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1250982
% 222.73/223.22 Kept: 196410
% 222.73/223.22 Inuse: 2354
% 222.73/223.22 Deleted: 4726
% 222.73/223.22 Deletedinuse: 91
% 222.73/223.22
% 222.73/223.22
% 222.73/223.22 Intermediate Status:
% 222.73/223.22 Generated: 1280116
% 222.73/223.22 Kept: 199Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------