TSTP Solution File: SCT100-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SCT100-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 21:01:14 EDT 2022
% Result : Unsatisfiable 2.74s 3.12s
% Output : Refutation 2.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SCT100-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : bliksem %s
% 0.15/0.35 % Computer : n021.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % DateTime : Fri Jul 1 22:00:29 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.94/1.33 *** allocated 10000 integers for termspace/termends
% 0.94/1.33 *** allocated 10000 integers for clauses
% 0.94/1.33 *** allocated 10000 integers for justifications
% 0.94/1.33 *** allocated 15000 integers for termspace/termends
% 0.94/1.33 *** allocated 22500 integers for termspace/termends
% 0.94/1.33 Bliksem 1.12
% 0.94/1.33
% 0.94/1.33
% 0.94/1.33 Automatic Strategy Selection
% 0.94/1.33
% 0.94/1.33 Clauses:
% 0.94/1.33 [
% 0.94/1.33 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 0.94/1.33 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.33 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 0.94/1.33 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 0.94/1.33 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.94/1.33 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y, Z, T ),
% 0.94/1.33 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.33 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X
% 0.94/1.33 , X ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.94/1.33 ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ],
% 0.94/1.33 [ =( 'c_Relation_Orel__comp'( X, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.33 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ), T, Y, Z ),
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( T, Z ), 'tc_bool' )
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ =( 'c_Relation_Orel__comp'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.33 'tc_prod'( X, Y ), 'tc_bool' ) ), Z, X, Y, T ),
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, T ), 'tc_bool' )
% 0.94/1.33 ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 0.94/1.33 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), T ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 0.94/1.33 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), Z ) ) ],
% 0.94/1.33 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.94/1.33 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.33 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.33 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.33 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.33 Y, Y ), 'tc_bool' ) ), Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( =( hAPP( 'c_snd'( X, Y ), Z ), hAPP( 'c_snd'( X, Y ), T ) ) ), ~(
% 0.94/1.33 =( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_fst'( X, Y ), T ) ) ), =( Z, T )
% 0.94/1.33 ],
% 0.94/1.33 [ ~( =( hAPP( 'c_snd'( X, Y ), Z ), hAPP( 'c_snd'( X, Y ), T ) ) ), ~(
% 0.94/1.33 =( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_fst'( X, Y ), T ) ) ), =( Z, T )
% 0.94/1.33 ],
% 0.94/1.33 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.33 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, Z, T ) ) ) ),
% 0.94/1.33 ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Relation_ORange'( X,
% 0.94/1.33 Y, Z ), 'c_Relation_ORange'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.33 'c_Relation_ORange'( 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'(
% 0.94/1.33 'tc_prod'( Y, Z ), 'tc_bool' ) ), Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.94/1.33 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'(
% 0.94/1.33 Z, 'tc_bool' ) ) ), ~( 'c_in'( X, T, Z ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Product__Type_OSigma'( X, 'c_COMBK'( Y, 'tc_fun'( Z
% 0.94/1.33 , 'tc_bool' ), T ), T, Z ), 'c_Product__Type_OSigma'( U, 'c_COMBK'( Y,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ), 'tc_fun'( 'tc_prod'( T, Z ),
% 0.94/1.33 'tc_bool' ) ), ~( 'c_lessequals'( X, U, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 0.94/1.33 'c_in'( W, Y, Z ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_Product__Type_OSigma'( X, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.94/1.33 , Z, U ), 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U,
% 0.94/1.33 'tc_bool' ), Z ), Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ),
% 0.94/1.33 ~( 'c_in'( W, T, U ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.94/1.33 ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.94/1.33 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.94/1.33 ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.94/1.33 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 0.94/1.33 Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_in'( Y, X, Z ) ),
% 0.94/1.33 ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y, T, Z ), 'tc_fun'( Z, 'tc_bool'
% 0.94/1.33 ) ) ) ],
% 0.94/1.33 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_Set_Oinsert'( X
% 0.94/1.33 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), ~(
% 0.94/1.33 'c_in'( U, T, Z ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Transitive__Closure_Otrancl'( X, Y ), Z, 'tc_fun'(
% 0.94/1.33 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.33 'c_Relation_Orel__comp'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.33 'c_Transitive__Closure_Otrancl'( X, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.33 'tc_bool' ) ), X, Y, Y, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 0.94/1.33 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) )
% 0.94/1.33 ) ],
% 0.94/1.33 [ =( 'c_Product__Type_OSigma'(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.33 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 0.94/1.33 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( X, Y ), ~( 'c_in'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z
% 0.94/1.33 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.94/1.33 ) ) ), =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 0.94/1.33 , X ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Relation_ODomain'( X
% 0.94/1.33 , Y, Z ), 'c_Relation_ODomain'( T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ),
% 0.94/1.33 'c_Relation_ODomain'( 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'(
% 0.94/1.33 'tc_prod'( Y, Z ), 'tc_bool' ) ), Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 0.94/1.33 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Relation_OId__on'( X, Y ), 'c_Product__Type_OSigma'(
% 0.94/1.33 X, 'c_COMBK'( X, 'tc_fun'( Y, 'tc_bool' ), Y ), Y, Y ), 'tc_fun'(
% 0.94/1.33 'tc_prod'( Y, Y ), 'tc_bool' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'(
% 0.94/1.33 Z, 'tc_bool' ), Z ), Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ),
% 0.94/1.33 ~( 'c_Relation_Orefl__on'( Y, X, Z ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 0.94/1.33 'tc_bool' ) ), X ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 0.94/1.33 'c_Relation_Orel__comp'( W, V0, Z, T, U ), 'tc_fun'( 'tc_prod'( Z, U ),
% 0.94/1.33 'tc_bool' ) ), ~( 'c_lessequals'( Y, V0, 'tc_fun'( 'tc_prod'( T, U ),
% 0.94/1.33 'tc_bool' ) ) ), ~( 'c_lessequals'( X, W, 'tc_fun'( 'tc_prod'( Z, T ),
% 0.94/1.33 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_Relation_OImage'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), U, Z, T ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OImage'( X, U,
% 0.94/1.33 Z, T ), 'c_Relation_OImage'( Y, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 0.94/1.33 ,
% 0.94/1.33 [ =( 'c_Relation_OImage'( X,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 0.94/1.33 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.33 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, Z, T ) ) ) ), ~(
% 0.94/1.33 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.94/1.33 [ =( 'c_Relation_ODomain'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.33 'tc_prod'( X, Y ), 'tc_bool' ) ), X, Y ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.33 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 0.94/1.33 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 0.94/1.33 [ =( X, 'c_Pair'( hAPP( 'c_fst'( Y, Z ), X ), hAPP( 'c_snd'( Y, Z ), X )
% 0.94/1.33 , Y, Z ) ) ],
% 0.94/1.33 [ =( 'c_Pair'( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_snd'( X, Y ), Z ), X
% 0.94/1.33 , Y ), Z ) ],
% 0.94/1.33 [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ],
% 0.94/1.33 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.33 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.94/1.33 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), U, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Product__Type_OSigma'( W,
% 0.94/1.33 'c_COMBK'( U, 'tc_fun'( T, 'tc_bool' ), Z ), Z, T ), 'tc_fun'( 'tc_prod'(
% 0.94/1.33 Z, T ), 'tc_bool' ) ) ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.33 , T, X ) ) ), =( Y, Z ) ],
% 0.94/1.33 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.94/1.33 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.94/1.33 , T, X ) ) ), =( Z, T ) ],
% 0.94/1.33 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.94/1.33 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oimage'( X, Y, Z
% 0.94/1.33 , T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.33 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 0.94/1.33 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.94/1.33 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.94/1.33 ],
% 0.94/1.33 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.33 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.94/1.33 ],
% 0.94/1.33 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 0.94/1.33 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 0.94/1.33 'c_lessequals'( Y, Z, X ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.33 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 0.94/1.33 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.94/1.33 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.94/1.33 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X
% 0.94/1.33 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 0.94/1.33 , 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.33 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.94/1.33 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.94/1.33 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.94/1.33 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.33 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.94/1.33 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.33 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.94/1.34 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 0.94/1.34 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X,
% 0.94/1.34 'tc_prod'( Z, Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.94/1.34 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 0.94/1.34 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 0.94/1.34 X, T ), Y ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ODomain'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 0.94/1.34 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( X, 'c_Relation_ODomain'( U
% 0.94/1.34 , Z, T ), Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 0.94/1.34 , 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'(
% 0.94/1.34 Y, Z ) ), ~( 'c_Relation_Osym'( X, Z ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_ODomain'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_ODomain'( X, Z
% 0.94/1.34 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 0.94/1.34 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.94/1.34 ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'( Z, 'tc_bool'
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Set_Oimage'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_OImage'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 0.94/1.34 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ],
% 0.94/1.34 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_lessequals'( T, X,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( T, X,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), T, Z, U ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 0.94/1.34 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y, 'tc_bool' ) ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 0.94/1.34 'c_Product__Type_OSigma'( W, 'c_COMBK'( V0, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.94/1.34 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.34 Y, 'c_Product__Type_OSigma'( V1, 'c_COMBK'( V0, 'tc_fun'( U, 'tc_bool' )
% 0.94/1.34 , T ), T, U ), 'tc_fun'( 'tc_prod'( T, U ), 'tc_bool' ) ) ), ~(
% 0.94/1.34 'c_lessequals'( X, 'c_Product__Type_OSigma'( W, 'c_COMBK'( V1, 'tc_fun'(
% 0.94/1.34 T, 'tc_bool' ), Z ), Z, T ), 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_lessequals'(
% 0.94/1.34 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ), X, 'tc_fun'( 'tc_prod'( Z, Z )
% 0.94/1.34 , 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( X, Z ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), Y ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Relation_ODomain'( X, Y, Y ), 'c_Relation_ORange'( Z, Y, Y ), 'tc_fun'(
% 0.94/1.34 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 0.94/1.34 ) ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ), ~( 'c_Wellfounded_Owf'( X, Y
% 0.94/1.34 ) ), 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Product__Type_OSigma'( X
% 0.94/1.34 , 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.94/1.34 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.94/1.34 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ), ~(
% 0.94/1.34 'c_Relation_Orefl__on'( X, T, Z ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 0.94/1.34 X, 'tc_bool' ) ), Y ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'( 'c_Set_Oinsert'( X, Y, Z ), 'c_COMBK'(
% 0.94/1.34 'c_Set_Oinsert'( T, U, W ), 'tc_fun'( W, 'tc_bool' ), Z ), Z, W ),
% 0.94/1.34 'c_Set_Oinsert'( 'c_Pair'( X, T, Z, W ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Product__Type_OSigma'( Y
% 0.94/1.34 , 'c_COMBK'( 'c_Set_Oinsert'( T, U, W ), 'tc_fun'( W, 'tc_bool' ), Z ), Z
% 0.94/1.34 , W ), 'c_Product__Type_OSigma'( 'c_Set_Oinsert'( X, Y, Z ), 'c_COMBK'( U
% 0.94/1.34 , 'tc_fun'( W, 'tc_bool' ), Z ), Z, W ), 'tc_fun'( 'tc_prod'( Z, W ),
% 0.94/1.34 'tc_bool' ) ), 'tc_prod'( Z, W ) ) ) ],
% 0.94/1.34 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 0.94/1.34 ~( 'c_lessequals'( X, 'c_Relation_OImage'( Z, X, Y, Y ), 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ],
% 0.94/1.34 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.94/1.34 ) ), Y ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_Set_Oinsert'( X
% 0.94/1.34 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), =( T
% 0.94/1.34 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'( Z, 'tc_bool'
% 0.94/1.34 ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( X, T, Z ) ), ~( =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.94/1.34 'c_Relation_Otrans'( Y, Z ) ), ~( 'c_Relation_Otrans'( X, Z ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.94/1.34 ) ) ), ~( =( 'c_Relation_Orel__comp'( T, Y, Z, Z, Z ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.94/1.34 ) ) ), =( 'c_Relation_Orel__comp'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, Z ), 'tc_bool' ) ), Y, Z, Z, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.94/1.34 ) ) ), ~( =( 'c_Relation_Orel__comp'( X, T, Z, Z, Z ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 0.94/1.34 ) ) ), =( 'c_Relation_Orel__comp'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, Z ), 'tc_bool' ) ), Z, Z, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, Z, T ) ) ) ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.94/1.34 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 0.94/1.34 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ), ~(
% 0.94/1.34 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.94/1.34 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.94/1.34 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ =( hAPP( 'c_split'( X, Y, Z, T ), U ), hAPP( hAPP( X, hAPP( 'c_fst'( Y
% 0.94/1.34 , Z ), U ) ), hAPP( 'c_snd'( Y, Z ), U ) ) ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.94/1.34 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 0.94/1.34 'c_lessequals'( Z, Y, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 0.94/1.34 'c_lessequals'( Y, Z, X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 0.94/1.34 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.94/1.34 ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ) )
% 0.94/1.34 ],
% 0.94/1.34 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.94/1.34 , 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ), ~(
% 0.94/1.34 'c_Relation_Orefl__on'( X, T, Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.34 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.34 'tc_prod'( X, Y ), 'tc_bool' ) ), X, Y ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.94/1.34 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.94/1.34 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.94/1.34 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 0.94/1.34 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 0.94/1.34 'c_Product__Type_OSigma'( Z, 'c_COMBK'( Z, 'tc_fun'( Y, 'tc_bool' ), Y )
% 0.94/1.34 , Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.34 X, 'c_Product__Type_OSigma'( Z, 'c_COMBK'( Z, 'tc_fun'( Y, 'tc_bool' ), Y
% 0.94/1.34 ), Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Transitive__Closure_Ortrancl'( Z
% 0.94/1.34 , Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ),
% 0.94/1.34 ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 0.94/1.34 ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.94/1.34 'tc_fun'( X, 'tc_bool' ) ) ],
% 0.94/1.34 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.94/1.34 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.94/1.34 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X
% 0.94/1.34 ), 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 0.94/1.34 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ) ), ~( 'c_in'( X, T, Z ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 0.94/1.34 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), T ) ), ~( 'c_in'( Y, X, T ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 0.94/1.34 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 0.94/1.34 [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.94/1.34 'tc_bool' ) ), Y, X ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.94/1.34 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Oconverse'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Oconverse'( X,
% 0.94/1.34 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.94/1.34 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.94/1.34 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 0.94/1.34 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 0.94/1.34 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.94/1.34 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z
% 0.94/1.34 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.94/1.34 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , Y, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Product__Type_OSigma'( X
% 0.94/1.34 , 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.94/1.34 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.94/1.34 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, Y ) ), ~( 'c_lessequals'( X,
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.34 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 0.94/1.34 Y, Z ) ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 0.94/1.34 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OId__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 0.94/1.34 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'(
% 0.94/1.34 X, X ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, Y ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_in'( X, Y, Z ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.34 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_lessequals'( 'c_Set_Oinsert'( X, T, Z ), Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 0.94/1.34 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.94/1.34 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), 'c_in'( Y, X
% 0.94/1.34 , T ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_in'( T, X, Z ),
% 0.94/1.34 ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool'
% 0.94/1.34 ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.94/1.34 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), 'c_in'( Y, X
% 0.94/1.34 , T ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_in'( T, X
% 0.94/1.34 , Z ) ],
% 0.94/1.34 [ =( 'c_Relation_Oconverse'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_Oconverse'( X,
% 0.94/1.34 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 0.94/1.34 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ) ), 'c_in'( Y, X, T ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 0.94/1.34 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ), 'c_in'( X, T, Z ) ],
% 0.94/1.34 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~(
% 0.94/1.34 'c_Order__Relation_Ostrict__linear__order__on'( X, Y, Z ) ) ],
% 0.94/1.34 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.94/1.34 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.94/1.34 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 0.94/1.34 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 0.94/1.34 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, T ), 'tc_bool' ) ), U, Z, T, W ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.94/1.34 , U, Z, T, W ), 'c_Relation_Orel__comp'( Y, U, Z, T, W ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Z, W ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 T, U ), 'tc_bool' ) ), W, T, U ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.94/1.34 , Y, W, T, U ), 'c_Relation_Orel__comp'( X, Z, W, T, U ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( W, U ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 Z, T, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 T, Z, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 0.94/1.34 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 0.94/1.34 'c_lessequals'( Z, T, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 Z, T, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 T, Z, X ), X ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ODomain'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ODomain'( X, Z
% 0.94/1.34 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.34 X, 'tc_bool' ) ), Y, X, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.34 'tc_prod'( X, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Wellfounded_Oacc'( X, Y ), 'c_Wellfounded_Oacc'( Z
% 0.94/1.34 , Y ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_ODomain'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.94/1.34 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 0.94/1.34 ) ), Z, X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 0.94/1.34 ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_ORange'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Z, T ), 'tc_bool' ) ), Z, T ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_ORange'( X, Z,
% 0.94/1.34 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 T, 'tc_bool' ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, Z, T ) ) )
% 0.94/1.34 ), ~( 'c_Wellfounded_Owf'( Z, T ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ), T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 0.94/1.34 'c_in'( X, T, Z ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool'
% 0.94/1.34 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ), ~(
% 0.94/1.34 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 0.94/1.34 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), Y ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), Y ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, T ), U,
% 0.94/1.34 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( Y, 'c_Relation_ORange'( U,
% 0.94/1.34 Z, T ), T ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y
% 0.94/1.34 , 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'(
% 0.94/1.34 Y, Z ) ), ~( 'c_Relation_Osym'( X, Z ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y, Z ),
% 0.94/1.34 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), 'c_in'( X, Y, Z ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z
% 0.94/1.34 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 0.94/1.34 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( =( hAPP( X, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U,
% 0.94/1.34 W ) ), hAPP( Y, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, Y, Z, T, U, W
% 0.94/1.34 ) ) ) ), =( 'c_Recdef_Ocut'( X, Z, T, U, W ), 'c_Recdef_Ocut'( Y, Z, T,
% 0.94/1.34 U, W ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Oacyclic'(
% 0.94/1.34 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z ), hAPP( T, Z )
% 0.94/1.34 , X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ), ~( 'c_in'( X, Y
% 0.94/1.34 , T ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z,
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ), ~( 'c_in'( X, Y
% 0.94/1.34 , T ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), ~( 'c_in'( X, Z, T ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), ~( 'c_in'( X, Z, T ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_lessequals'( T, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) )
% 0.94/1.34 ), ~( 'c_in'( X, T, Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_lessequals'( T, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_lessequals'( T, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z,
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Y, T ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z,
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' )
% 0.94/1.34 ), Y ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( 'c_in'( Y, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' )
% 0.94/1.34 ), Y ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' )
% 0.94/1.34 ), Y ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), =( X, T ), ~( 'c_in'( X, 'c_Set_Oinsert'( T, Y, Z )
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), 'c_in'( X, T, Z ), ~( 'c_in'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.34 , Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool'
% 0.94/1.34 ) ), T ), 'c_in'( X, Z, T ), ~( 'c_in'( X, Y, T ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool'
% 0.94/1.34 ) ), T ), 'c_in'( X, Z, T ), ~( 'c_in'( X, Y, T ) ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 0.94/1.34 'c_in'( X, T, Z ), 'c_in'( X, Y, Z ), =( Y, T ) ],
% 0.94/1.34 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( 'c_in'( X, Y, Z ) ) ],
% 0.94/1.34 [ =( hAPP( 'c_fst'( X, Y ), 'c_Pair'( Z, T, X, Y ) ), Z ) ],
% 0.94/1.34 [ =( X, hAPP( 'c_fst'( Y, Z ), 'c_Pair'( X, T, Y, Z ) ) ) ],
% 0.94/1.34 [ =( hAPP( 'c_snd'( X, Y ), 'c_Pair'( Z, T, X, Y ) ), T ) ],
% 0.94/1.34 [ =( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, X, Y, Z ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, hAPP( 'c_fst'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ),
% 0.94/1.34 ~( hBOOL( hAPP( W, U ) ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ),
% 0.94/1.34 ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( W, T ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( X, Y ), ~(
% 0.94/1.34 'c_Order__Relation_Ostrict__linear__order__on'( Z, X, Y ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool'
% 0.94/1.34 ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_in'( X
% 0.94/1.34 , T, Z ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ),
% 0.94/1.34 Z, U ), 'c_HOL_Ominus__class_Ominus'( 'c_Product__Type_OSigma'( X,
% 0.94/1.34 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 0.94/1.34 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 0.94/1.34 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 X, Y, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ), Z, T ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ORange'( X, Z,
% 0.94/1.34 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( X, Z ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( Y, Z ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.34 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( 'c_in'( X, Y
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 0.94/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ) ), X ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 0.94/1.34 Y, X ), Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 T, X ), Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 0.94/1.34 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 0.94/1.34 'c_lessequals'( Y, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 0.94/1.34 Y, X ), Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 0.94/1.34 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 0.94/1.34 T, X ), Z, X ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.34 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.94/1.34 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( T
% 0.94/1.34 , Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~( 'c_lessequals'(
% 0.94/1.34 Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'( Z, Y ) ), ~(
% 0.94/1.34 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool'
% 0.94/1.34 ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_lessequals'( X, Z, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Oacyclic'( Z, Y ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_Relation_Osingle__valued'( X, Y, Z ), ~(
% 0.94/1.34 'c_Relation_Osingle__valued'( T, Y, Z ) ), ~( 'c_lessequals'( X, T,
% 0.94/1.34 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 T, U, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 0.94/1.34 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 0.94/1.34 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'(
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_ODomain'( X, Y, Z ), 'c_Relation_ODomain'(
% 0.94/1.34 T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ), ~( 'c_lessequals'( X, T, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 0.94/1.34 , 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 0.94/1.34 , 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ),
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 0.94/1.34 T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Product__Type_OSigma'( X, 'c_COMBK'(
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ), Z ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 0.94/1.34 'tc_prod'( Z, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 0.94/1.34 hAPP( X, T ) ) ) ],
% 0.94/1.34 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 0.94/1.34 , 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), Z ), ~(
% 0.94/1.34 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( Z
% 0.94/1.34 , X, 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.34 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.94/1.34 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z
% 0.94/1.34 , T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, U, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_lessequals'(
% 0.94/1.34 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U ), 'tc_fun'( U,
% 0.94/1.34 'tc_bool' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z )
% 0.94/1.34 , 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 0.94/1.34 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 0.94/1.34 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 0.94/1.34 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' )
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( hAPP( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, U, Y, Z ) )
% 0.94/1.34 ), hAPP( 'c_fst'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ), ~( hBOOL( hAPP(
% 0.94/1.34 hAPP( X, U ), T ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_ORange'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), 'c_Relation_OImage'(
% 0.94/1.34 U, W, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( Y, W,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, U, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'(
% 0.94/1.34 Z, 'tc_bool' ), Z ), Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ),
% 0.94/1.34 ~( 'c_Equiv__Relations_Oequiv'( Y, X, Z ) ) ],
% 0.94/1.34 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.94/1.34 'c_lessequals'( Z, Y, X ) ],
% 0.94/1.34 [ 'c_Relation_Oirrefl'( X, Y ), ~(
% 0.94/1.34 'c_Order__Relation_Ostrict__linear__order__on'( Z, X, Y ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 0.94/1.34 'tc_prod'( Z, Z ) ), Z ), 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~(
% 0.94/1.34 'c_Wellfounded_Oacyclic'( T, Z ) ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T
% 0.94/1.34 , Z ), 'tc_prod'( Z, Z ) ) ), ~( 'c_Wellfounded_Oacyclic'(
% 0.94/1.34 'c_Set_Oinsert'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ), Z ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 0.94/1.34 X, Z, T, U ),
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 0.94/1.34 X, Z, T, U ), U, U ), T, 'tc_prod'( U, U ) ), ~( hBOOL( hAPP( X, Z ) ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Y, Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T
% 0.94/1.34 , U ), 'tc_prod'( U, U ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 0.94/1.34 T, U ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'(
% 0.94/1.34 X, Z, T, U ), U, U ), T, 'tc_prod'( U, U ) ), ~( hBOOL( hAPP( X, Z ) ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Z, Y, U, U ), 'c_Transitive__Closure_Ortrancl'( T
% 0.94/1.34 , U ), 'tc_prod'( U, U ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'( X,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_Equiv__Relations_Oequiv'( T, Y, Z ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Z, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 0.94/1.34 'c_Relation_Orel__comp'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y )
% 0.94/1.34 , 'tc_bool' ) ), X, Y, Y, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 0.94/1.34 ) ) ), ~( 'c_lessequals'( 'c_Relation_OId'( Y ), Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), ~( 'c_in'( U,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_OImage'( T,
% 0.94/1.34 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ) ), Z ), Z, Z ), 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), ~( 'c_Equiv__Relations_Oequiv'( W, T,
% 0.94/1.34 Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), ~( 'c_in'( Y,
% 0.94/1.34 U, Z ) ), ~( 'c_lessequals'( 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( T, 'c_Set_Oinsert'( X,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, T, Z ) )
% 0.94/1.34 ],
% 0.94/1.34 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 0.94/1.34 'c_Set_Oimage'( X, Z, T, U ) ), ~( 'c_in'( Y, Z, T ) ) ],
% 0.94/1.34 [ 'c_in'( hAPP( X, Y ), Z, T ), ~( 'c_in'( Y, U, W ) ), ~(
% 0.94/1.34 'c_lessequals'( 'c_Set_Oimage'( X, U, W, T ), Z, 'tc_fun'( T, 'tc_bool' )
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Relation_OImage'( U, 'c_Set_Oinsert'( X,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, T ),
% 0.94/1.34 T ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'( Z,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T, U ),
% 0.94/1.34 U ), ~( 'c_in'( 'c_Pair'( Z, X, T, U ), Y, 'tc_prod'( T, U ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Product__Type_OSigma'( X, 'c_COMBK'( Y, 'tc_fun'( Z,
% 0.94/1.34 'tc_bool' ), T ), T, Z ), 'c_Product__Type_OSigma'( U, 'c_COMBK'( Y,
% 0.94/1.34 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ) ) ), ~( 'c_in'( W, Y, Z ) ), =( X,
% 0.94/1.34 U ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'( 'c_Set_Oinsert'(
% 0.94/1.34 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 T, T ), 'tc_bool' ) ), T ), 'tc_prod'( T, T ) ), ~( 'c_in'( X,
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 T, T ), 'tc_bool' ) ), T ), 'tc_prod'( T, T ) ), ~( 'c_in'( X,
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Transitive__Closure_Otrancl'( Y, Z ), 'tc_prod'( Z, Z )
% 0.94/1.34 ), ~( 'c_lessequals'( T, Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) )
% 0.94/1.34 , ~( 'c_in'( X, 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z
% 0.94/1.34 ) ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.94/1.34 , X, Y, Y, Y ), 'c_Relation_Orel__comp'( Z, X, Y, Y, Y ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 0.94/1.34 'tc_bool' ) ), Y ), ~( 'c_Wellfounded_Owf'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 0.94/1.34 Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 Y, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 0.94/1.34 , X, Z, Z, Z ), 'c_Relation_Orel__comp'( Y, X, Z, Z, Z ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Z, Z ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 0.94/1.34 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 0.94/1.34 ) ) ), 'c_Wellfounded_Owf'( X, Y ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Orel__comp'(
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( X, Y ), X, Y, Y, Y ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 0.94/1.34 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Orderings_Obot__class_Obot'(
% 0.94/1.34 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ), 'c_Relation_OId'( X ) )
% 0.94/1.34 ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.94/1.34 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 0.94/1.34 ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), X, 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_Relation_Otrans'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 0.94/1.34 ) ), Y ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 0.94/1.34 ) ), Y ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 0.94/1.34 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.94/1.34 ~( 'c_Relation_Otrans'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z, Y, Y ),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y,
% 0.94/1.34 'tc_bool' ) ) ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 0.94/1.34 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 0.94/1.34 , 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y )
% 0.94/1.34 , ~( 'c_Relation_Oantisym'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~( 'c_Relation_Ototal__on'( X,
% 0.94/1.34 'c_HOL_Ominus__class_Ominus'( Y, 'c_Relation_OId'( Z ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Ototal__on'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 0.94/1.34 'c_Relation_OId'( Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ),
% 0.94/1.34 ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ],
% 0.94/1.34 [ 'c_lessequals'( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y
% 0.94/1.34 , Y ), X, Y, Y, Y ), X, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~(
% 0.94/1.34 'c_Relation_Otrans'( X, Y ) ), ~( 'c_Relation_Osym'( X, Y ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Y, X, Z, T )
% 0.94/1.34 , T, T ), 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T ) ),
% 0.94/1.34 ~( 'c_in'( 'c_Pair'( X, Z, T, T ), 'c_Transitive__Closure_Otrancl'( Y, T
% 0.94/1.34 ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( X, Y, Z, T ),
% 0.94/1.34 Z, T, T ), 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'( T, T ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Y, Z, T, T ), 'c_Transitive__Closure_Otrancl'( X,
% 0.94/1.34 T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T
% 0.94/1.34 , Z ), 'tc_prod'( Z, Z ) ) ), ~( 'c_Wellfounded_Owf'( 'c_Set_Oinsert'(
% 0.94/1.34 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ), Z ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z, Z ), T,
% 0.94/1.34 'tc_prod'( Z, Z ) ), Z ), 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( T, Z ) ) ],
% 0.94/1.34 [ 'c_Order__Relation_Ostrict__linear__order__on'( X, Y, Z ), ~(
% 0.94/1.34 'c_Relation_Ototal__on'( X, Y, Z ) ), ~( 'c_Relation_Oirrefl'( Y, Z ) ),
% 0.94/1.34 ~( 'c_Relation_Otrans'( Y, Z ) ) ],
% 0.94/1.34 [ 'c_Nitpick_Orefl_H'( X, Y ), ~( 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ),
% 0.94/1.34 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ), Y, Y ), X,
% 0.94/1.34 'tc_prod'( Y, Y ) ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Relation_OId'(
% 0.94/1.34 Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ), ~(
% 0.94/1.34 'c_Relation_Oantisym'( X, Y ) ), ~( 'c_Relation_Otrans'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( X,
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 0.94/1.34 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 0.94/1.34 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Relation_Osingle__valued'(
% 0.94/1.34 'c_Relation_Oconverse'( X, T, U ), U, T ) ) ],
% 0.94/1.34 [ 'c_Relation_Oirrefl'( X, Y ), 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ),
% 0.94/1.34 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ), Y, Y ), X,
% 0.94/1.34 'tc_prod'( Y, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'v_r', 't_a', 't_b' ), 'c_Relation_ODomain'(
% 0.94/1.34 'c_Relation_Oconverse'( 'v_r', 't_a', 't_b' ), 't_b', 't_a' ) ) ],
% 0.94/1.34 [ 'c_lessequals'( X, 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X
% 0.94/1.34 , Y, Y ), X, Y, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~(
% 0.94/1.34 'c_Relation_Orefl__on'( Z, X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OId'( Y ),
% 0.94/1.34 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 0.94/1.34 Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'(
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 0.94/1.34 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup'(
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 0.94/1.34 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ],
% 0.94/1.34 [ =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U )
% 0.94/1.34 ), 'c_in'( 'c_Pair'( 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, W, Y, Z
% 0.94/1.34 , T, U ), Z, T, T ), Y, 'tc_prod'( T, T ) ) ],
% 0.94/1.34 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X,
% 0.94/1.34 Z ), 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ), Z, Z ) )
% 0.94/1.34 , ~( 'c_in'( X, 'c_Relation_OId__on'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( X, Y, Z ), X,
% 0.94/1.34 Z ), ~( 'c_in'( Y, 'c_Relation_OId__on'( X, Z ), 'tc_prod'( Z, Z ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_in'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1'( X, Y ),
% 0.94/1.34 'c_Wellfounded_Oacc'( X, Y ), Y ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_in'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1'( X, Y ),
% 0.94/1.34 'c_Wellfounded_Oacc'( X, Y ), Y ) ) ],
% 0.94/1.34 [ =( X, 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ),
% 0.94/1.34 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ), Y, Y ) ), ~( 'c_in'(
% 0.94/1.34 X, 'c_Relation_OId'( Y ), 'tc_prod'( Y, Y ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( X, Y, Z, T, U, W,
% 0.94/1.34 V0 ), Y, V0, W ), T, 'tc_prod'( V0, W ) ), ~( 'c_in'( 'c_Pair'( X, Y, U,
% 0.94/1.34 W ), 'c_Relation_Orel__comp'( Z, T, U, V0, W ), 'tc_prod'( U, W ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( X, Y, Z, T, U, W,
% 0.94/1.34 V0 ), U, V0 ), Z, 'tc_prod'( U, V0 ) ), ~( 'c_in'( 'c_Pair'( X, Y, U, W )
% 0.94/1.34 , 'c_Relation_Orel__comp'( Z, T, U, V0, W ), 'tc_prod'( U, W ) ) ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ), 'c_in'(
% 0.94/1.34 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'( Z,
% 0.94/1.34 Y ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'(
% 0.94/1.34 Z, Y ), Y, Y ), 'c_Transitive__Closure_Otrancl'( Z, Y ), 'tc_prod'( Y, Y
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( X, Y
% 0.94/1.34 , Z, T ), Z, T, T ), 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'(
% 0.94/1.34 T, T ) ), 'c_in'( 'c_Pair'( Y, Z, T, T ), X, 'tc_prod'( T, T ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( Y, Z, T, T ), 'c_Transitive__Closure_Otrancl'( X, T ),
% 0.94/1.34 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Y, X, Z, T ),
% 0.94/1.34 T, T ), Y, 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( X, Z, T, T ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'(
% 0.94/1.34 X, Y, Z ), 't_a', 't_a' ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ),
% 0.94/1.34 'tc_prod'( 't_a', 't_a' ) ), 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ), Z,
% 0.94/1.34 'tc_prod'( 't_a', 't_a' ) ), ~( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Transitive__Closure_Otrancl'( Z
% 0.94/1.34 , Y ), 'tc_prod'( Y, Y ) ) ), ~( 'c_Wellfounded_Oacyclic'( Z, Y ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( X, Y, Z, T ),
% 0.94/1.34 Y, T, T ), Z, 'tc_prod'( T, T ) ), 'c_in'( 'c_Pair'( X, Y, T, T ), Z,
% 0.94/1.34 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( X, Y, T, T ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( X, Y, Z, T ),
% 0.94/1.34 T, T ), 'c_Transitive__Closure_Otrancl'( Z, T ), 'tc_prod'( T, T ) ),
% 0.94/1.34 'c_in'( 'c_Pair'( X, Y, T, T ), Z, 'tc_prod'( T, T ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, Y, T, T ), 'c_Transitive__Closure_Otrancl'( Z, T ),
% 0.94/1.34 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( X, Y, Z, T )
% 0.94/1.34 , Z, T, T ), X, 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Y, X
% 0.94/1.34 , Z, T ), T, T ), Y, 'tc_prod'( T, T ) ), 'c_in'( 'c_Pair'( X, Z, T, T )
% 0.94/1.34 , Y, 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( X, Z, T, T ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X
% 0.94/1.34 , Y, Z ), Y, 't_a', 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ), 'c_in'(
% 0.94/1.34 'c_Pair'( X, Y, 't_a', 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, Y, 't_a', 't_a' ), 'c_Transitive__Closure_Otrancl'( Z, 't_a'
% 0.94/1.34 ), 'tc_prod'( 't_a', 't_a' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, T, U ), U
% 0.94/1.34 , U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, T, U ), U, U ), T,
% 0.94/1.34 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, T, U ), U, U ), T,
% 0.94/1.34 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, T, U ), U, U ),
% 0.94/1.34 T, 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( X, Y, Z, T )
% 0.94/1.34 , Y, T, T ), Z, 'tc_prod'( T, T ) ), =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y
% 0.94/1.34 , T, T ), 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( X,
% 0.94/1.34 Y, Z, T ), Z, T, T ), 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'(
% 0.94/1.34 T, T ) ), =( Y, Z ), ~( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Y,
% 0.94/1.34 X, Z, T ), T, T ), Y, 'tc_prod'( T, T ) ), =( X, Z ), ~( 'c_in'( 'c_Pair'(
% 0.94/1.34 X, Z, T, T ), 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T )
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 0.94/1.34 X, Z, T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Y, Z,
% 0.94/1.34 U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 0.94/1.34 X, Z, T, U ), Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ),
% 0.94/1.34 'tc_prod'( U, U ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Y,
% 0.94/1.34 Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 0.94/1.34 T, U ), U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U
% 0.94/1.34 ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Z, Y, U, U ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'( X, Z,
% 0.94/1.34 T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Z, Y, U, U
% 0.94/1.34 ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'(
% 0.94/1.34 X, Y, Z ), 't_a', 't_a' ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ),
% 0.94/1.34 'tc_prod'( 't_a', 't_a' ) ), =( Y, X ), ~( 'c_in'( 'c_Pair'( X, Y, 't_a'
% 0.94/1.34 , 't_a' ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ), 'tc_prod'( 't_a'
% 0.94/1.34 , 't_a' ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 0.94/1.34 T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Z, Y, U, U )
% 0.94/1.34 , 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X
% 0.94/1.34 , Y, Z ), Y, 't_a', 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ), =( Y, X ),
% 0.94/1.34 ~( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 0.94/1.34 X, Z, T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Y, Z
% 0.94/1.34 , U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( X, Y, Z, T )
% 0.94/1.34 , T, T ), 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ),
% 0.94/1.34 =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, T, T ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1'( X, Y, Z, T
% 0.94/1.34 , U ), X, T ), ~( 'c_in'( Z, 'c_Product__Type_OSigma'( X, Y, T, U ),
% 0.94/1.34 'tc_prod'( T, U ) ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_OwfP'( 'c_FunDef_Oin__rel'( X, Y, Y ), Y ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Oirrefl'( 'c_HOL_Ominus__class_Ominus'( X,
% 0.94/1.34 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.94/1.34 ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ),
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 0.94/1.34 ) ) ), ~( 'c_in'( 'c_Pair'( Z, Z, Y, Y ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( X, Y ), 'tc_prod'( Y, Y ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.94/1.34 ), 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ), ~( 'c_in'( T
% 0.94/1.34 , U, Z ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.94/1.34 ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), 'c_in'( 'c_Pair'( Y, T,
% 0.94/1.34 Z, Z ), X, 'tc_prod'( Z, Z ) ), ~( 'c_in'( T, U, Z ) ), ~( 'c_in'( Y, U,
% 0.94/1.34 Z ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 0.94/1.34 T, U, Z ) ), ~( 'c_in'( Y, U, Z ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 0.94/1.34 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 0.94/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 0.94/1.34 ), ~( 'c_in'( T, U, Z ) ), ~( 'c_in'( Y, U, Z ) ), ~(
% 0.94/1.34 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), 'c_in'( 'c_Pair'( Y, T, Z, Z )
% 0.94/1.34 , X, 'tc_prod'( Z, Z ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oimage'( 'c_snd'( X, Y ), Z, 'tc_prod'( X, Y ), Y ),
% 0.94/1.34 'c_Relation_ORange'( Z, X, Y ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), =( X, T ), ~( 'c_lessequals'( U,
% 0.94/1.34 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), Z )
% 0.94/1.34 , Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( U, Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ =( 'c_Set_Oimage'( 'c_fst'( X, Y ), Z, 'tc_prod'( X, Y ), X ),
% 0.94/1.34 'c_Relation_ODomain'( Z, X, Y ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Transitive__Closure_Ortrancl'( Y, Z ), 'tc_prod'( Z, Z )
% 0.94/1.34 ), ~( 'c_in'( X, Y, 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Transitive__Closure_Otrancl'( Y, Z ), 'tc_prod'( Z, Z )
% 0.94/1.34 ), ~( 'c_in'( X, Y, 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'(
% 0.94/1.34 Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), =( X, Y )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( Y, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, Z, Z ), Z )
% 0.94/1.34 , 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( U, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_Relation_Osingle__valued'( T, Z, Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oconverse'(
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), Z, Z ), 'tc_prod'( Z, Z ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.94/1.34 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 0.94/1.34 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oconverse'(
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), Z, Z ), 'tc_prod'( Z, Z ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ =( hAPP( 'c_split'( X, Y, Z, T ), 'c_Pair'( U, W, Y, Z ) ), hAPP( hAPP(
% 0.94/1.34 X, U ), W ) ) ],
% 0.94/1.34 [ =( hAPP( 'c_split'( X, Y, Z, T ), 'c_Pair'( U, W, Y, Z ) ), hAPP( hAPP(
% 0.94/1.34 X, U ), W ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( hAPP( hAPP( X, Y ), Z ), T ) ), ~( hBOOL( hAPP( hAPP(
% 0.94/1.34 'c_split'( X, U, W, 'tc_fun'( V0, 'tc_bool' ) ), 'c_Pair'( Y, Z, U, W ) )
% 0.94/1.34 , T ) ) ) ],
% 0.94/1.34 [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ), ~( 'c_in'( Y
% 0.94/1.34 , Z, T ) ) ],
% 0.94/1.34 [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ), ~( 'c_in'( Y
% 0.94/1.34 , Z, T ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( hAPP( T, X ), 'c_Set_Oimage'( T, Y, Z
% 0.94/1.34 , U ), U ) ],
% 0.94/1.34 [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( hAPP( T, X ), 'c_Set_Oimage'( T, Y, Z
% 0.94/1.34 , U ), U ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_Wellfounded_Owf'(
% 0.94/1.34 Y, Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId__on'( X, Y ), Y, Y ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( X, Y, Z, T, U )
% 0.94/1.34 , X, T ), ~( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T, U ), U ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 0.94/1.34 'c_Relation_Osym'( X, Y ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ) ) ) ),
% 0.94/1.34 ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z, T ), T ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), X ), ~(
% 0.94/1.34 'c_Relation_Otrans'( X, Y ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, Z ) ) ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Wellfounded_Oacc'( Z, 't_a' ), 't_a' ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ),
% 0.94/1.34 'c_Wellfounded_Oacc'( Z, T ), T ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z
% 0.94/1.34 , T ), T ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Relation_Osym'(
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.94/1.34 'c_Relation_Osym'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 0.94/1.34 ), 'c_Relation_ODomain'( X, Y, Y ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( X, Y, Z, T
% 0.94/1.34 , U ), X, T ), ~( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T, U ), U ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ ~( 'c_in'( 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( X
% 0.94/1.34 , Y, Z ), 'c_Wellfounded_Oacc'( X, Z ), Z ) ), 'c_in'( Y,
% 0.94/1.34 'c_Wellfounded_Oacc'( X, Z ), Z ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Relation_OId'( X ), X ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( 'c_Relation_OId'( X ), Y, X, X, Z ), Y ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( X, 'c_Relation_OId'( Y ), Z, Y, Y ), X ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_Relation_Oantisym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'(
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ), Y ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ) )
% 0.94/1.34 ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z, T ), T ) ) ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Relation_Orefl__on'( X,
% 0.94/1.34 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ), ~(
% 0.94/1.34 'c_Relation_Orefl__on'( X, Y, Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ), ~(
% 0.94/1.34 'c_Relation_Osym'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ),
% 0.94/1.34 ~( 'c_Wellfounded_Owf'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 0.94/1.34 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_OImage'( 'c_Relation_OId'( X ), Y, X, X ), Y ) ],
% 0.94/1.34 [ 'c_Relation_Osingle__valued'( 'c_Relation_OId'( X ), X, X ) ],
% 0.94/1.34 [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ =( 'c_Relation_Oconverse'( X, Y, Y ), X ), ~( 'c_Relation_Osym'( X, Y
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_Oconverse'( X, Y, Y ), X ) ), 'c_Relation_Osym'( X,
% 0.94/1.34 Y ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y
% 0.94/1.34 ), 'c_Relation_ORange'( X, Y, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ =( 'c_Relation_Oconverse'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ), Z
% 0.94/1.34 , U ), 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( Y, T, U ),
% 0.94/1.34 'c_Relation_Oconverse'( X, Z, T ), U, T, Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y ), Y ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( X, Z ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( X, 'c_Transitive__Closure_Ortrancl'( X, Y
% 0.94/1.34 ), Y, Y, Y ), 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 X, Y ), X, Y, Y, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 0.94/1.34 'c_Relation_Osym'( X, Z ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_Relation_Otrans'( X, Y ), ~( 'c_Relation_Otrans'(
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.94/1.34 'c_Relation_Otrans'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId'( X ), X, X ),
% 0.94/1.34 'c_Relation_OId'( X ) ) ],
% 0.94/1.34 [ 'c_Wellfounded_Owf'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Orel__comp'( X, Y, Z, T, U ),
% 0.94/1.34 W, Z, U, V0 ), 'c_Relation_Orel__comp'( X, 'c_Relation_Orel__comp'( Y, W
% 0.94/1.34 , T, U, V0 ), Z, T, V0 ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T,
% 0.94/1.34 T ), 'c_Relation_Oinv__image'( 'c_Relation_Oconverse'( X, Z, Z ), Y, Z, T
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 0.94/1.34 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( X, Y ), Y
% 0.94/1.34 , Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Relation_Oinv__image'( X, Y, Z, T ), T ), ~(
% 0.94/1.34 'c_Relation_Otrans'( X, Z ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Oconverse'( 'c_Relation_OId__on'( X, Y ), Y, Y ),
% 0.94/1.34 'c_Relation_OId__on'( X, Y ) ) ],
% 0.94/1.34 [ ~( =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y
% 0.94/1.34 , Y, Y ), X ) ), 'c_Equiv__Relations_Oequiv'( 'c_Relation_ODomain'( X, Y
% 0.94/1.34 , Y ), X, Y ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( 'c_Relation_OId'( X ), X ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 0.94/1.34 'c_Relation_ODomain'( X, Y, Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( X,
% 0.94/1.34 Y, Z ), X, Z ), ~( 'c_in'( T, X, Z ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) )
% 0.94/1.34 ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_Relation_Osingle__valued'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 0.94/1.34 , Z, U ), ~( 'c_Relation_Osingle__valued'( Y, T, U ) ), ~(
% 0.94/1.34 'c_Relation_Osingle__valued'( X, Z, T ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Oconverse'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 0.94/1.34 X ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( 'c_Relation_OId'( X ), X ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y
% 0.94/1.34 , Y ), X ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Oantisym'( 'c_Relation_Oconverse'( X, Y, Y ), Y ), ~(
% 0.94/1.34 'c_Relation_Oantisym'( X, Y ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 0.94/1.34 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, Z ) ) ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Wellfounded_Oacc'( Z, 't_a' ), 't_a' ) ) ],
% 0.94/1.34 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Equiv__Relations_Oequiv'( X,
% 0.94/1.34 Y, Z ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( X, Y, Y )
% 0.94/1.34 , Y ), 'c_Relation_Oconverse'( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 0.94/1.34 Y, Y ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( X, Y, Z )
% 0.94/1.34 , X, Z ), ~( 'c_in'( T, X, Z ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Osym'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Y, X, Z ),
% 0.94/1.34 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_Equiv__Relations_Ocongruent'( X, hAPP( Y, Z ), T, U ), ~( 'c_in'( Z
% 0.94/1.34 , W, V0 ) ), ~( 'c_Equiv__Relations_Ocongruent2'( V1, X, Y, V0, T, U ) )
% 0.94/1.34 , ~( 'c_Equiv__Relations_Oequiv'( W, V1, V0 ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ODomain'( 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ),
% 0.94/1.34 'c_Relation_ORange'( X, Y, Z ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'(
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y, Y, Y ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_Orel__comp'( X
% 0.94/1.34 , 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ) ) ],
% 0.94/1.34 [ =( 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ODomain'(
% 0.94/1.34 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ) ) ],
% 0.94/1.34 [ 'c_Relation_Ototal__on'( X, Y, Z ), ~( 'c_Relation_Ototal__on'( X,
% 0.94/1.34 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ),
% 0.94/1.34 ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ],
% 0.94/1.34 [ 'c_Relation_Otrans'( X, Y ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y )
% 0.94/1.34 ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ),
% 0.94/1.34 'c_Wellfounded_Oacc'( Z, T ), T ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z
% 0.94/1.34 , T ), T ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Otrancl'(
% 0.94/1.34 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ =( 'c_Transitive__Closure_Ortrancl'( 'c_Transitive__Closure_Ortrancl'(
% 0.94/1.34 X, Y ), Y ), 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ],
% 0.94/1.34 [ 'c_Arrow__Order__Mirabelle_OIIA'( 'v_F' ) ],
% 0.94/1.34 [ 'c_Arrow__Order__Mirabelle_Ounanimity'( 'v_F' ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( X, Y
% 0.94/1.34 , Z, T, U ), Y, T, U ), Z, 'tc_prod'( T, U ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Relation_OImage'( Z, X, T, U ), U ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( X, Y, Z ), Y, Z
% 0.94/1.34 , Z ), X, 'tc_prod'( Z, Z ) ), 'c_in'( Y, 'c_Wellfounded_Oacc'( X, Z ), Z
% 0.94/1.34 ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, T, U ), U
% 0.94/1.34 , U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( T, U
% 0.94/1.34 ), U ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ), T,
% 0.94/1.34 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( T,
% 0.94/1.34 't_a' ), 't_a' ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Y, T, Z ), Z, Z ), T
% 0.94/1.34 , 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( U, Y, Z ) ), ~( 'c_Wellfounded_Owf'(
% 0.94/1.34 T, Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1'( X, Y
% 0.94/1.34 , Z, T ), X, T, Z ), Y, 'tc_prod'( T, Z ) ), ~( 'c_in'( X,
% 0.94/1.34 'c_Relation_ORange'( Y, T, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), 'c_in'( 'c_Pair'(
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Y, X, Z ), X, Z,
% 0.94/1.34 Z ), Y, 'tc_prod'( Z, Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'( T,
% 0.94/1.34 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'( 'c_Pair'( X,
% 0.94/1.34 T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z ), 'tc_prod'( Z, Z ) )
% 0.94/1.34 ), ~( 'c_in'( T, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'( Z, 'c_Wellfounded_Oacc'( T, 't_a' ),
% 0.94/1.34 't_a' ), ~( 'c_in'( 'c_Pair'( Z, 'v_sko__Wellfounded__Xacc__Xinducts__1'(
% 0.94/1.34 X, T ), 't_a', 't_a' ), T, 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_ODomain'( Y, Z, Z ), Z ), 'c_in'( 'c_Pair'( X,
% 0.94/1.34 X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z ), 'tc_prod'( Z, Z ) )
% 0.94/1.34 ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ), T,
% 0.94/1.34 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( T,
% 0.94/1.34 't_a' ), 't_a' ) ) ],
% 0.94/1.34 [ 'c_in'( hAPP( hAPP( X, Y ), Z ), 'c_Set_Oimage'( 'c_split'( X, T, U, W
% 0.94/1.34 ), V0, 'tc_prod'( T, U ), W ), W ), ~( 'c_in'( 'c_Pair'( Y, Z, T, U ),
% 0.94/1.34 V0, 'tc_prod'( T, U ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1'( X
% 0.94/1.34 , Y, Z, T ), Z, T ), Y, 'tc_prod'( Z, T ) ), ~( 'c_in'( X,
% 0.94/1.34 'c_Relation_ODomain'( Y, Z, T ), Z ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), 'c_in'( Z, 'c_Wellfounded_Oacc'( T, 't_a' ),
% 0.94/1.34 't_a' ), ~( 'c_in'( 'c_Pair'( Z, 'v_sko__Wellfounded__Xacc__Xinduct__1'(
% 0.94/1.34 X, T ), 't_a', 't_a' ), T, 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Z,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, T, U ), U, U )
% 0.94/1.34 , T, 'tc_prod'( U, U ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( T, U ), U
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Y, T, Z ), Z,
% 0.94/1.34 Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( U, Y, Z ) ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( T, Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X,
% 0.94/1.34 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1'( X, Y, Z, T ), Z, T )
% 0.94/1.34 , Y, 'tc_prod'( Z, T ) ), ~( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ),
% 0.94/1.34 Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( X
% 0.94/1.34 , Y, Z, T, U ), Y, T, U ), Z, 'tc_prod'( T, U ) ), ~( 'c_in'( Y,
% 0.94/1.34 'c_Relation_OImage'( Z, X, T, U ), U ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), 'c_in'(
% 0.94/1.34 X, 'c_Relation_ODomain'( T, Z, Z ), Z ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1'( X
% 0.94/1.34 , Y, Z, T ), X, T, Z ), Y, 'tc_prod'( T, Z ) ), ~( 'c_in'( X,
% 0.94/1.34 'c_Relation_ORange'( Y, T, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, hAPP( 'c_split'( Y, Z, T, 'tc_fun'( U, 'tc_bool' ) ),
% 0.94/1.34 'c_Pair'( W, V0, Z, T ) ), U ), ~( 'c_in'( X, hAPP( hAPP( Y, W ), V0 ), U
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( Z, U, W, W ), V0, 'tc_prod'( W, W ) ) ), ~( 'c_in'( 'c_Pair'( Y
% 0.94/1.34 , T, V1, V1 ), V2, 'tc_prod'( V1, V1 ) ) ), ~(
% 0.94/1.34 'c_Equiv__Relations_Ocongruent2'( V2, V0, X, V1, W, V3 ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_in'( 'c_Pair'( Z, Y, T, U ), W, 'tc_prod'( T, U ) ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( Z, X, T, U ), W, 'tc_prod'( T, U ) ) ), ~(
% 0.94/1.34 'c_Relation_Osingle__valued'( W, T, U ) ) ],
% 0.94/1.34 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( W, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X, W ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( W, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ hBOOL( hAPP( hAPP( 'c_FunDef_Oin__rel'( X, Y, Z ), T ), U ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( T, U, Y, Z ), X, 'tc_prod'( Y, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ), ~( hBOOL( hAPP(
% 0.94/1.34 hAPP( 'c_FunDef_Oin__rel'( U, Z, T ), X ), Y ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X
% 0.94/1.34 , U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Otrans'( T, Z ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X
% 0.94/1.34 , U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Otrans'( T, Z ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Oconverse'( U, T, Z ),
% 0.94/1.34 'tc_prod'( Z, T ) ), ~( 'c_in'( 'c_Pair'( Y, X, T, Z ), U, 'tc_prod'( T,
% 0.94/1.34 Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Oconverse'( U, T, Z ),
% 0.94/1.34 'tc_prod'( Z, T ) ), ~( 'c_in'( 'c_Pair'( Y, X, T, Z ), U, 'tc_prod'( T,
% 0.94/1.34 Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( Y, X, T, Z ), 'c_Relation_Oconverse'( U, Z, T ), 'tc_prod'( T,
% 0.94/1.34 Z ) ) ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ), ~(
% 0.94/1.34 'c_Relation_Oirrefl'( Z, Y ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'(
% 0.94/1.34 Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'(
% 0.94/1.34 Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'(
% 0.94/1.34 Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_in'( 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 0.94/1.34 , 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Transitive__Closure_Ortrancl'( Z, Y
% 0.94/1.34 ), 'tc_prod'( Y, Y ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Transitive__Closure_Ortrancl'( Z, Y
% 0.94/1.34 ), 'tc_prod'( Y, Y ) ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Wellfounded_Owf'(
% 0.94/1.34 T, Z ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_Relation_Oantisym'( T, Z ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 0.94/1.34 'c_Relation_Oantisym'( T, Z ) ) ],
% 0.94/1.34 [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Y, Z, T, T ), U
% 0.94/1.34 , 'tc_prod'( T, T ) ) ), ~( 'c_Equiv__Relations_Ocongruent'( U, X, T, W )
% 0.94/1.34 ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_OId__on'( T
% 0.94/1.34 , Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ ~( =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W, Y, Z, T, U
% 0.94/1.34 ) ) ), =( hAPP( X, V0 ), hAPP( W, V0 ) ), ~( 'c_in'( 'c_Pair'( V0, Z, T
% 0.94/1.34 , T ), Y, 'tc_prod'( T, T ) ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_OId'( Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ), ~(
% 0.94/1.34 'c_Nitpick_Orefl_H'( Z, Y ) ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ) ), ~(
% 0.94/1.34 'c_Wellfounded_Owf'( Z, Y ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oinv__image'( T, U, W, Z )
% 0.94/1.34 , 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( hAPP( U, X ), hAPP( U, Y ), W
% 0.94/1.34 , W ), T, 'tc_prod'( W, W ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( hAPP( X, Y ), hAPP( X, Z ), T, T ), U, 'tc_prod'( T
% 0.94/1.34 , T ) ), ~( 'c_in'( 'c_Pair'( Y, Z, W, W ), 'c_Relation_Oinv__image'( U,
% 0.94/1.34 X, T, W ), 'tc_prod'( W, W ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Osym'( T
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Osym'( T
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Orel__comp'( U, W, Z, V0,
% 0.94/1.34 T ), 'tc_prod'( Z, T ) ), ~( 'c_in'( 'c_Pair'( V1, Y, V0, T ), W,
% 0.94/1.34 'tc_prod'( V0, T ) ) ), ~( 'c_in'( 'c_Pair'( X, V1, Z, V0 ), U, 'tc_prod'(
% 0.94/1.34 Z, V0 ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'(
% 0.94/1.34 Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z
% 0.94/1.34 ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ),
% 0.94/1.34 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 0.94/1.34 'c_Pair'( X, U, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 0.94/1.34 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId'( Y ), 'tc_prod'( Y, Y
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId'( Y ), 'tc_prod'( Y, Y
% 0.94/1.34 ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ), =( X, Y ), =( X, T ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ), =( Y, T ), =( X, T ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omktop', Y ), X ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omktop', Z ), X ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , =( Y, T ), ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt'
% 0.94/1.34 , 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ =( X, Y ), =( Y, X ), 'c_in'( 'c_Pair'( X, Y,
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), X ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omkbot', Y ), X ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omkbot', Z ), Y ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ), =( X, Y ), =( Y, T ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ), =( X, T ), =( Y, T ) ],
% 0.94/1.34 [ =( X, Y ), =( X, Y ), 'c_in'( 'c_Pair'( X, Y,
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), Y ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , =( X, T ), ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt'
% 0.94/1.34 , 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( hAPP(
% 0.94/1.34 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 , =( X, Y ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Product__Type_OSigma'( U, W, Z, T )
% 0.94/1.34 , 'tc_prod'( Z, T ) ), ~( 'c_in'( Y, hAPP( W, X ), T ) ), ~( 'c_in'( X, U
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Product__Type_OSigma'( U, W, Z, T )
% 0.94/1.34 , 'tc_prod'( Z, T ) ), ~( 'c_in'( Y, hAPP( W, X ), T ) ), ~( 'c_in'( X, U
% 0.94/1.34 , Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'( 'c_Pair'( X,
% 0.94/1.34 T, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( T, 'c_Wellfounded_Oacc'(
% 0.94/1.34 Y, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'( 'c_Pair'( X,
% 0.94/1.34 T, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( T, 'c_Wellfounded_Oacc'(
% 0.94/1.34 Y, Z ), Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_OImage'( Y, Z, T, U ), U ), ~( 'c_in'( 'c_Pair'(
% 0.94/1.34 W, X, T, U ), Y, 'tc_prod'( T, U ) ) ), ~( 'c_in'( W, Z, T ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_OImage'( Y, Z, T, U ), U ), ~( 'c_in'( 'c_Pair'(
% 0.94/1.34 W, X, T, U ), Y, 'tc_prod'( T, U ) ) ), ~( 'c_in'( W, Z, T ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z ),
% 0.94/1.34 'c_Relation_OId__on'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId__on'( Z, Y ),
% 0.94/1.34 'tc_prod'( Y, Y ) ), ~( 'c_in'( X, Z, Y ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( T, X, Z, Z ), U, 'tc_prod'( Z
% 0.94/1.34 , Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, U, Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z ), U, 'tc_prod'( Z
% 0.94/1.34 , Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, U, Z ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_ORange'( Y, Z, T ), T ), ~( 'c_in'( 'c_Pair'( U
% 0.94/1.34 , X, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_ORange'( Y, Z, T ), T ), ~( 'c_in'( 'c_Pair'( U
% 0.94/1.34 , X, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ), ~( 'c_in'( 'c_Pair'(
% 0.94/1.34 X, U, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ), ~( 'c_in'( 'c_Pair'(
% 0.94/1.34 X, U, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, hAPP( Y, Z ), T ), ~( 'c_in'( 'c_Pair'( Z, X, U, T ),
% 0.94/1.34 'c_Product__Type_OSigma'( W, Y, U, T ), 'tc_prod'( U, T ) ) ) ],
% 0.94/1.34 [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, U ),
% 0.94/1.34 'c_Product__Type_OSigma'( Y, W, Z, U ), 'tc_prod'( Z, U ) ) ) ],
% 0.94/1.34 [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), 'c_in'(
% 0.94/1.34 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ), =( Y, X ), ~( 'c_in'( X,
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% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 0.94/1.34 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 0.94/1.34 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 0.94/1.34 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 0.94/1.34 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 0.94/1.34 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 0.94/1.34 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 0.94/1.34 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 0.94/1.34 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 0.94/1.34 ],
% 0.94/1.34 [ ~( 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 0.94/1.34 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 0.94/1.34 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ],
% 0.94/1.34 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Lattices_Olattice'( Y ) ) ],
% 0.94/1.34 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Lattices_Olattice'( Y ) ) ],
% 0.94/1.34 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 0.94/1.34 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 0.94/1.34 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Orderings_Opreorder'( Y ) ) ],
% 0.94/1.34 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Lattices_Olattice'( Y ) ) ],
% 0.94/1.34 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.94/1.34 'class_Orderings_Oorder'( Y ) ) ],
% 0.94/1.34 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 0.94/1.34 Y ) ) ],
% 0.94/1.34 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 0.94/1.34 ,
% 0.94/1.34 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 0.94/1.34 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 0.94/1.34 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 0.94/1.34 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 0.94/1.34 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 0.94/1.34 ] .
% 0.94/1.34
% 0.94/1.34
% 0.94/1.34 percentage equality = 0.233571, percentage horn = 0.885434
% 0.94/1.34 This is a problem with some equality
% 0.94/1.34
% 0.94/1.34
% 0.94/1.34
% 0.94/1.34 Options Used:
% 0.94/1.34
% 0.94/1.34 useres = 1
% 0.94/1.34 useparamod = 1
% 0.94/1.34 useeqrefl = 1
% 0.94/1.34 useeqfact = 1
% 0.94/1.34 usefactor = 1
% 0.94/1.34 usesimpsplitting = 0
% 0.94/1.34 usesimpdemod = 5
% 0.94/1.34 usesimpres = 3
% 0.94/1.34
% 0.94/1.34 resimpinuse = 1000
% 0.94/1.34 resimpclauses = 20000
% 0.94/1.34 substype = eqrewr
% 0.94/1.34 backwardsubs = 1
% 0.94/1.34 selectoldest = 5
% 0.94/1.34
% 0.94/1.34 litorderings [0] = split
% 0.94/1.34 litorderings [1] = extend the termordering, first sorting on arguments
% 0.94/1.34
% 0.94/1.34 termordering = kbo
% 0.94/1.34
% 0.94/1.34 litapriori = 0
% 0.94/1.34 termapriori = 1
% 0.94/1.34 litaposteriori = 0
% 0.94/1.34 termaposteriori = 0
% 0.94/1.34 demodaposteriori = 0
% 0.94/1.34 ordereqreflfact = 0
% 0.94/1.34
% 0.94/1.34 litselect = negord
% 0.94/1.34
% 0.94/1.34 maxweight = 15
% 0.94/1.34 maxdepth = 30000
% 0.94/1.34 maxlength = 115
% 0.94/1.34 maxnrvars = 195
% 0.94/1.34 excuselevel = 1
% 0.94/1.34 increasemaxweight = 1
% 0.94/1.34
% 0.94/1.34 maxselected = 10000000
% 0.94/1.34 maxnrclauses = 10000000
% 0.94/1.34
% 0.94/1.34 showgenerated = 0
% 0.94/1.34 showkept = 0
% 0.94/1.34 showselected = 0
% 0.94/1.34 showdeleted = 0
% 0.94/1.34 showresimp = 1
% 0.94/1.34 showstatus = 2000
% 0.94/1.34
% 0.94/1.34 prologoutput = 1
% 0.94/1.34 nrgoals = 5000000
% 0.94/1.34 totalproof = 1
% 0.94/1.34
% 0.94/1.34 Symbols occurring in the translation:
% 0.94/1.34
% 0.94/1.34 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.94/1.34 . [1, 2] (w:1, o:108, a:1, s:1, b:0),
% 0.94/1.34 ! [4, 1] (w:0, o:83, a:1, s:1, b:0),
% 0.94/1.34 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.34 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.94/1.34 'c_Set_Oinsert' [42, 3] (w:1, o:165, a:1, s:1, b:0),
% 0.94/1.34 'tc_bool' [44, 0] (w:1, o:14, a:1, s:1, b:0),
% 0.94/1.34 'tc_fun' [45, 2] (w:1, o:133, a:1, s:1, b:0),
% 0.94/1.34 'c_Lattices_Olower__semilattice__class_Oinf' [46, 3] (w:1, o:166, a:1
% 0.94/1.34 , s:1, b:0),
% 0.94/1.34 'c_Orderings_Obot__class_Obot' [47, 1] (w:1, o:88, a:1, s:1, b:0),
% 0.94/1.34 'c_HOL_Ominus__class_Ominus' [48, 3] (w:1, o:167, a:1, s:1, b:0),
% 0.94/1.34 'class_Orderings_Obot' [49, 1] (w:1, o:89, a:1, s:1, b:0),
% 0.94/1.34 'c_lessequals' [51, 3] (w:1, o:168, a:1, s:1, b:0),
% 0.94/1.34 'tc_prod' [52, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.94/1.34 'c_Relation_Orel__comp' [56, 5] (w:1, o:209, a:1, s:1, b:0),
% 0.94/1.34 'c_Lattices_Oupper__semilattice__class_Osup' [57, 3] (w:1, o:169, a:1
% 0.94/1.34 , s:1, b:0),
% 0.94/1.34 'c_Set_Oimage' [60, 4] (w:1, o:190, a:1, s:1, b:0),
% 0.94/1.34 'c_Transitive__Closure_Ortrancl' [61, 2] (w:1, o:135, a:1, s:1, b:0)
% 0.94/1.34 ,
% 0.94/1.34 'c_snd' [63, 2] (w:1, o:136, a:1, s:1, b:0),
% 0.94/1.34 hAPP [65, 2] (w:1, o:137, a:1, s:1, b:0),
% 0.94/1.34 'c_fst' [67, 2] (w:1, o:138, a:1, s:1, b:0),
% 0.94/1.34 hBOOL [71, 1] (w:1, o:90, a:1, s:1, b:0),
% 0.94/1.34 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1' [73, 3] (w:1, o:
% 0.94/1.34 170, a:1, s:1, b:0),
% 0.94/1.34 'c_Wellfounded_Owf' [74, 2] (w:1, o:139, a:1, s:1, b:0),
% 0.94/1.34 'c_Relation_ORange' [75, 3] (w:1, o:159, a:1, s:1, b:0),
% 0.94/1.34 'c_in' [77, 3] (w:1, o:171, a:1, s:1, b:0),
% 0.94/1.34 'c_COMBK' [78, 3] (w:1, o:172, a:1, s:1, b:0),
% 0.94/1.34 'c_Product__Type_OSigma' [79, 4] (w:1, o:191, a:1, s:1, b:0),
% 0.94/1.34 'c_Transitive__Closure_Otrancl' [81, 2] (w:1, o:140, a:1, s:1, b:0),
% 0.94/1.34
% 0.94/1.34 'c_Relation_ODomain' [84, 3] (w:1, o:160, a:1, s:1, b:0),
% 0.94/1.34 'class_Lattices_Odistrib__lattice' [85, 1] (w:1, o:91, a:1, s:1, b:0)
% 0.94/1.34 ,
% 0.94/1.34 'c_Relation_OId__on' [88, 2] (w:1, o:141, a:1, s:1, b:0),
% 0.94/1.34 'c_Relation_Orefl__on' [89, 3] (w:1, o:161, a:1, s:1, b:0),
% 0.98/1.50 'class_Lattices_Oupper__semilattice' [90, 1] (w:1, o:92, a:1, s:1, b:
% 0.98/1.50 0),
% 0.98/1.50 'c_Relation_OImage' [93, 4] (w:1, o:188, a:1, s:1, b:0),
% 0.98/1.50 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1' [95, 3] (w:1, o:173, a:
% 0.98/1.50 1, s:1, b:0),
% 0.98/1.50 'c_Pair' [96, 4] (w:1, o:192, a:1, s:1, b:0),
% 0.98/1.50 'class_OrderedGroup_Oab__group__add' [99, 1] (w:1, o:93, a:1, s:1, b:
% 0.98/1.50 0),
% 0.98/1.50 'class_Lattices_Olattice' [102, 1] (w:1, o:94, a:1, s:1, b:0),
% 0.98/1.50 'class_Lattices_Olower__semilattice' [103, 1] (w:1, o:95, a:1, s:1
% 0.98/1.50 , b:0),
% 0.98/1.50 'c_Wellfounded_Oacyclic' [104, 2] (w:1, o:142, a:1, s:1, b:0),
% 0.98/1.50 'c_Equiv__Relations_Oequiv' [105, 3] (w:1, o:174, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_Osym' [106, 2] (w:1, o:143, a:1, s:1, b:0),
% 0.98/1.50 'class_Lattices_Obounded__lattice' [107, 1] (w:1, o:96, a:1, s:1, b:0
% 0.98/1.50 ),
% 0.98/1.50 'c_Relation_Otrans' [109, 2] (w:1, o:144, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1' [111, 3] (w:1, o:
% 0.98/1.50 175, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_Oconverse' [112, 3] (w:1, o:162, a:1, s:1, b:0),
% 0.98/1.50 'class_Orderings_Oorder' [113, 1] (w:1, o:97, a:1, s:1, b:0),
% 0.98/1.50 'c_split' [114, 4] (w:1, o:193, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_Oantisym' [115, 2] (w:1, o:145, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_Ototal__on' [117, 3] (w:1, o:164, a:1, s:1, b:0),
% 0.98/1.50 'c_Order__Relation_Ostrict__linear__order__on' [118, 3] (w:1, o:176
% 0.98/1.50 , a:1, s:1, b:0),
% 0.98/1.50 'c_Wellfounded_Oacc' [121, 2] (w:1, o:146, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1' [123, 3]
% 0.98/1.50 (w:1, o:177, a:1, s:1, b:0),
% 0.98/1.50 'c_List_Osko__Recdef__Xcuts__eq__1__1' [125, 6] (w:1, o:217, a:1, s:1
% 0.98/1.50 , b:0),
% 0.98/1.50 'c_Recdef_Ocut' [126, 5] (w:1, o:210, a:1, s:1, b:0),
% 0.98/1.50 'class_HOL_Oord' [127, 1] (w:1, o:98, a:1, s:1, b:0),
% 0.98/1.50 'class_Orderings_Opreorder' [128, 1] (w:1, o:99, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_Osingle__valued' [129, 3] (w:1, o:163, a:1, s:1, b:0),
% 0.98/1.50 'class_OrderedGroup_Opordered__ab__group__add' [130, 1] (w:1, o:100
% 0.98/1.50 , a:1, s:1, b:0),
% 0.98/1.50 'class_Orderings_Olinorder' [132, 1] (w:1, o:101, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_Oirrefl' [133, 2] (w:1, o:147, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'
% 0.98/1.50 [134, 4] (w:1, o:194, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'
% 0.98/1.50 [135, 4] (w:1, o:195, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1' [136, 4
% 0.98/1.50 ] (w:1, o:196, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2' [137, 4
% 0.98/1.50 ] (w:1, o:197, a:1, s:1, b:0),
% 0.98/1.50 'c_Relation_OId' [138, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1' [139, 4]
% 0.98/1.50 (w:1, o:198, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1' [140, 4]
% 0.98/1.50 (w:1, o:199, a:1, s:1, b:0),
% 0.98/1.50 'c_Nitpick_Orefl_H' [141, 2] (w:1, o:148, a:1, s:1, b:0),
% 0.98/1.50 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1' [142, 2] (w:1, o:149
% 0.98/1.50 , a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1' [143, 2] (w:1, o:
% 0.98/1.50 150, a:1, s:1, b:0),
% 0.98/1.50 'v_r' [144, 0] (w:1, o:59, a:1, s:1, b:0),
% 0.98/1.50 't_a' [145, 0] (w:1, o:60, a:1, s:1, b:0),
% 0.98/1.50 't_b' [146, 0] (w:1, o:61, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1' [147, 3] (w:1, o:178
% 0.98/1.50 , a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1' [148, 2] (w:1
% 0.98/1.50 , o:151, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1' [149, 2] (w:1, o:
% 0.98/1.50 152, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Relation__XIdE__1__1' [150, 2] (w:1, o:153, a:1
% 0.98/1.50 , s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1' [151, 7] (w:1
% 0.98/1.50 , o:219, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1' [152
% 0.98/1.50 , 2] (w:1, o:154, a:1, s:1, b:0),
% 0.98/1.50 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1' [153,
% 0.98/1.50 4] (w:1, o:200, a:1, s:1, b:0),
% 2.74/3.12 'v_sko__Transitive__Closure__Xtrancl__Xcases__1' [156, 3] (w:1, o:179
% 2.74/3.12 , a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1' [157, 4]
% 2.74/3.12 (w:1, o:201, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1' [159, 4]
% 2.74/3.12 (w:1, o:202, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1' [160
% 2.74/3.12 , 4] (w:1, o:203, a:1, s:1, b:0),
% 2.74/3.12 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1' [161, 3] (w:1, o:
% 2.74/3.12 180, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1' [162, 5] (w:1, o:
% 2.74/3.12 211, a:1, s:1, b:0),
% 2.74/3.12 'c_FunDef_Oin__rel' [163, 3] (w:1, o:181, a:1, s:1, b:0),
% 2.74/3.12 'c_Wellfounded_OwfP' [164, 2] (w:1, o:155, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Relation__XImageE__1__1' [166, 5] (w:1, o:212
% 2.74/3.12 , a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1' [167, 3] (w:1
% 2.74/3.12 , o:182, a:1, s:1, b:0),
% 2.74/3.12 'v_sko__Wellfounded__Xacc__Xinducts__1' [168, 2] (w:1, o:156, a:1, s:
% 2.74/3.12 1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1' [169, 3]
% 2.74/3.12 (w:1, o:183, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1' [170, 5] (w:1, o:
% 2.74/3.12 213, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1' [171, 3] (w:
% 2.74/3.12 1, o:184, a:1, s:1, b:0),
% 2.74/3.12 'c_Relation_Oinv__image' [172, 4] (w:1, o:189, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1' [174, 3]
% 2.74/3.12 (w:1, o:185, a:1, s:1, b:0),
% 2.74/3.12 'v_sko__Wellfounded__Xacc__Xinduct__1' [175, 2] (w:1, o:157, a:1, s:1
% 2.74/3.12 , b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1' [176, 3] (w:1, o:
% 2.74/3.12 186, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1' [177, 3] (w:1
% 2.74/3.12 , o:187, a:1, s:1, b:0),
% 2.74/3.12 'c_Equiv__Relations_Ocongruent' [179, 4] (w:1, o:204, a:1, s:1, b:0)
% 2.74/3.12 ,
% 2.74/3.12 'c_Equiv__Relations_Ocongruent2' [181, 6] (w:1, o:218, a:1, s:1, b:0)
% 2.74/3.12 ,
% 2.74/3.12 'v_F' [182, 0] (w:1, o:63, a:1, s:1, b:0),
% 2.74/3.12 'c_Arrow__Order__Mirabelle_OIIA' [183, 1] (w:1, o:103, a:1, s:1, b:0)
% 2.74/3.12 ,
% 2.74/3.12 'c_Arrow__Order__Mirabelle_Ounanimity' [184, 1] (w:1, o:104, a:1, s:1
% 2.74/3.12 , b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1' [185, 4] (w:1, o:205
% 2.74/3.12 , a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1' [187, 4] (w:1, o:206
% 2.74/3.12 , a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1' [188, 4] (w:1, o:
% 2.74/3.12 207, a:1, s:1, b:0),
% 2.74/3.12 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1' [189, 4] (w:1, o:
% 2.74/3.12 208, a:1, s:1, b:0),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' [194, 0] (w:1, o:66, a:1, s:1, b:0)
% 2.74/3.12 ,
% 2.74/3.12 'c_Arrow__Order__Mirabelle_Omktop' [195, 0] (w:1, o:67, a:1, s:1, b:0
% 2.74/3.12 ),
% 2.74/3.12 'c_Arrow__Order__Mirabelle_Omkbot' [197, 0] (w:1, o:69, a:1, s:1, b:0
% 2.74/3.12 ),
% 2.74/3.12 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1' [198, 2] (w:1, o:
% 2.74/3.12 158, a:1, s:1, b:0),
% 2.74/3.12 'v_c____' [201, 0] (w:1, o:70, a:1, s:1, b:0),
% 2.74/3.12 'v_d____' [202, 0] (w:1, o:71, a:1, s:1, b:0),
% 2.74/3.12 'v_P____' [203, 0] (w:1, o:72, a:1, s:1, b:0),
% 2.74/3.12 'c_HOL_OIf' [204, 1] (w:1, o:105, a:1, s:1, b:0),
% 2.74/3.12 'tc_nat' [205, 0] (w:1, o:73, a:1, s:1, b:0),
% 2.74/3.12 'c_HOL_Oord__class_Oless' [206, 1] (w:1, o:106, a:1, s:1, b:0),
% 2.74/3.12 'v_h____' [207, 0] (w:1, o:74, a:1, s:1, b:0),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi' [208, 0] (w:1, o:75, a:1, s:1, b:0
% 2.74/3.12 ),
% 2.74/3.12 'c_COMBB' [209, 5] (w:1, o:214, a:1, s:1, b:0),
% 2.74/3.12 'v_n____' [210, 0] (w:1, o:76, a:1, s:1, b:0),
% 2.74/3.12 'c_COMBC' [211, 5] (w:1, o:215, a:1, s:1, b:0),
% 2.74/3.12 'v_e____' [212, 0] (w:1, o:77, a:1, s:1, b:0),
% 2.74/3.12 'c_COMBS' [213, 5] (w:1, o:216, a:1, s:1, b:0),
% 2.74/3.12 'c_fequal' [214, 1] (w:1, o:107, a:1, s:1, b:0),
% 2.74/3.12 'c_Arrow__Order__Mirabelle_Oabove' [215, 0] (w:1, o:78, a:1, s:1, b:0
% 2.74/3.12 ).
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Starting Search:
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 6105
% 2.74/3.12 Kept: 2061
% 2.74/3.12 Inuse: 190
% 2.74/3.12 Deleted: 2
% 2.74/3.12 Deletedinuse: 1
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 15138
% 2.74/3.12 Kept: 4069
% 2.74/3.12 Inuse: 358
% 2.74/3.12 Deleted: 7
% 2.74/3.12 Deletedinuse: 4
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 24189
% 2.74/3.12 Kept: 6590
% 2.74/3.12 Inuse: 423
% 2.74/3.12 Deleted: 11
% 2.74/3.12 Deletedinuse: 6
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 37759
% 2.74/3.12 Kept: 9118
% 2.74/3.12 Inuse: 554
% 2.74/3.12 Deleted: 13
% 2.74/3.12 Deletedinuse: 6
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 59672
% 2.74/3.12 Kept: 11575
% 2.74/3.12 Inuse: 617
% 2.74/3.12 Deleted: 16
% 2.74/3.12 Deletedinuse: 7
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 89976
% 2.74/3.12 Kept: 15416
% 2.74/3.12 Inuse: 676
% 2.74/3.12 Deleted: 26
% 2.74/3.12 Deletedinuse: 11
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 108614
% 2.74/3.12 Kept: 17810
% 2.74/3.12 Inuse: 679
% 2.74/3.12 Deleted: 29
% 2.74/3.12 Deletedinuse: 12
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 Intermediate Status:
% 2.74/3.12 Generated: 126534
% 2.74/3.12 Kept: 20757
% 2.74/3.12 Inuse: 723
% 2.74/3.12 Deleted: 33
% 2.74/3.12 Deletedinuse: 14
% 2.74/3.12
% 2.74/3.12 Resimplifying inuse:
% 2.74/3.12 Done
% 2.74/3.12
% 2.74/3.12 Resimplifying clauses:
% 2.74/3.12
% 2.74/3.12 Bliksems!, er is een bewijs:
% 2.74/3.12 % SZS status Unsatisfiable
% 2.74/3.12 % SZS output start Refutation
% 2.74/3.12
% 2.74/3.12 clause( 555, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ) ), ~( 'c_in'( 'c_Pair'( 'v_c____',
% 2.74/3.12 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'(
% 2.74/3.12 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 2.74/3.12 ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.12 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.12 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.12 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.12 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.12 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.12 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.12 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.12 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.12 ) ] )
% 2.74/3.12 .
% 2.74/3.12 clause( 557, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 2.74/3.12 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 2.74/3.12 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.12 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.12 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.12 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.12 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.12 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.12 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.12 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.12 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.12 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.12 ] )
% 2.74/3.12 .
% 2.74/3.12 clause( 558, [ ~( 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.12 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.12 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ] )
% 2.74/3.12 .
% 2.74/3.12 clause( 20770, [] )
% 2.74/3.12 .
% 2.74/3.12
% 2.74/3.12
% 2.74/3.12 % SZS output end Refutation
% 2.74/3.12 found a proof!
% 2.74/3.12
% 2.74/3.12 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.74/3.12
% 2.74/3.12 initialclauses(
% 2.74/3.12 [ clause( 20772, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.12 , clause( 20773, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ] )
% 2.74/3.12 , clause( 20774, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20775, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.12 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), T ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20776, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 2.74/3.12 , clause( 20777, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( X, X ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( X, X ),
% 2.74/3.12 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20778, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.12 X, 'tc_bool' ) ), Y, 'tc_fun'( X, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20779, [ =( 'c_Relation_Orel__comp'( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' )
% 2.74/3.12 ), T, Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( T, Z
% 2.74/3.12 ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20780, [ =( 'c_Relation_Orel__comp'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' )
% 2.74/3.12 ), Z, X, Y, T ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X
% 2.74/3.12 , T ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20781, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 2.74/3.12 Y, 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), T ) ) ] )
% 2.74/3.12 , clause( 20782, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Set_Oinsert'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.12 , clause( 20783, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 2.74/3.12 'tc_bool' ) ), 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20784, [ 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 2.74/3.12 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Y, Y ), 'tc_bool' ) ), Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20785, [ ~( =( hAPP( 'c_snd'( X, Y ), Z ), hAPP( 'c_snd'( X, Y )
% 2.74/3.12 , T ) ) ), ~( =( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_fst'( X, Y ), T ) )
% 2.74/3.12 ), =( Z, T ) ] )
% 2.74/3.12 , clause( 20786, [ ~( =( hAPP( 'c_snd'( X, Y ), Z ), hAPP( 'c_snd'( X, Y )
% 2.74/3.12 , T ) ) ), ~( =( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_fst'( X, Y ), T ) )
% 2.74/3.12 ), =( Z, T ) ] )
% 2.74/3.12 , clause( 20787, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, Z, T ) ) ) ),
% 2.74/3.12 ~( 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 2.74/3.12 , clause( 20788, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ORange'( T, Y, Z ), 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ), 'c_Relation_ORange'( 'c_HOL_Ominus__class_Ominus'( X, T
% 2.74/3.12 , 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ), Y, Z ), 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20789, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20790, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.12 'c_lessequals'( 'c_Set_Oinsert'( T, X, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) )
% 2.74/3.12 ) ] )
% 2.74/3.12 , clause( 20791, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y,
% 2.74/3.12 Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_in'( X, T, Z ) ) ] )
% 2.74/3.12 , clause( 20792, [ 'c_lessequals'( 'c_Product__Type_OSigma'( X, 'c_COMBK'(
% 2.74/3.12 Y, 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ), 'c_Product__Type_OSigma'( U,
% 2.74/3.12 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ), 'tc_fun'( 'tc_prod'(
% 2.74/3.12 T, Z ), 'tc_bool' ) ), ~( 'c_lessequals'( X, U, 'tc_fun'( T, 'tc_bool' )
% 2.74/3.12 ) ), ~( 'c_in'( W, Y, Z ) ) ] )
% 2.74/3.12 , clause( 20793, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.12 'c_lessequals'( 'c_Product__Type_OSigma'( X, 'c_COMBK'( T, 'tc_fun'( U,
% 2.74/3.12 'tc_bool' ), Z ), Z, U ), 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T,
% 2.74/3.12 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ), 'tc_fun'( 'tc_prod'( Z, U ),
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_in'( W, T, U ) ) ] )
% 2.74/3.12 , clause( 20794, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_lessequals'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20795, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), ~( 'c_in'( Y, X, T ) ), ~( 'c_lessequals'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20796, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.12 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool'
% 2.74/3.12 ) ), ~( 'c_in'( Y, X, Z ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y, T
% 2.74/3.12 , Z ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20797, [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 2.74/3.12 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ), Y ) ), ~( 'c_in'( U, T, Z ) ) ] )
% 2.74/3.12 , clause( 20798, [ 'c_lessequals'( 'c_Transitive__Closure_Otrancl'( X, Y )
% 2.74/3.12 , Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.12 'c_Relation_Orel__comp'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Transitive__Closure_Otrancl'( X, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ), X, Y, Y, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 2.74/3.12 ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) )
% 2.74/3.12 ) ] )
% 2.74/3.12 , clause( 20799, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 2.74/3.12 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20800, [ =( X, Y ), ~( 'c_in'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20801, [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y
% 2.74/3.12 , 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 2.74/3.12 , 'tc_bool' ) ) ) ), =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20802, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Relation_ODomain'( X, Y, Z ), 'c_Relation_ODomain'( T, Y, Z ),
% 2.74/3.12 'tc_fun'( Y, 'tc_bool' ) ), 'c_Relation_ODomain'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( 'tc_prod'( Y, Z ),
% 2.74/3.12 'tc_bool' ) ), Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20803, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20804, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 2.74/3.12 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20805, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20806, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20807, [ 'c_lessequals'( 'c_Relation_OId__on'( X, Y ),
% 2.74/3.12 'c_Product__Type_OSigma'( X, 'c_COMBK'( X, 'tc_fun'( Y, 'tc_bool' ), Y )
% 2.74/3.12 , Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20808, [ 'c_lessequals'( X, 'c_Product__Type_OSigma'( Y,
% 2.74/3.12 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), Z ), Z, Z ), 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), ~( 'c_Relation_Orefl__on'( Y, X, Z ) ) ] )
% 2.74/3.12 , clause( 20809, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X,
% 2.74/3.12 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20810, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ] )
% 2.74/3.12 , clause( 20811, [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 2.74/3.12 , 'c_Relation_Orel__comp'( W, V0, Z, T, U ), 'tc_fun'( 'tc_prod'( Z, U )
% 2.74/3.12 , 'tc_bool' ) ), ~( 'c_lessequals'( Y, V0, 'tc_fun'( 'tc_prod'( T, U ),
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_lessequals'( X, W, 'tc_fun'( 'tc_prod'( Z, T ),
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20812, [ =( 'c_Relation_OImage'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), U, Z, T ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OImage'( X, U,
% 2.74/3.12 Z, T ), 'c_Relation_OImage'( Y, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20813, [ =( 'c_Relation_OImage'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 2.74/3.12 'tc_fun'( U, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20814, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.12 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, Z, T ) ) ) ), ~(
% 2.74/3.12 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 2.74/3.12 , clause( 20815, [ =( 'c_Relation_ODomain'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ) ), X, Y ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20816, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 2.74/3.12 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ] )
% 2.74/3.12 , clause( 20817, [ =( X, 'c_Pair'( hAPP( 'c_fst'( Y, Z ), X ), hAPP(
% 2.74/3.12 'c_snd'( Y, Z ), X ), Y, Z ) ) ] )
% 2.74/3.12 , clause( 20818, [ =( 'c_Pair'( hAPP( 'c_fst'( X, Y ), Z ), hAPP( 'c_snd'(
% 2.74/3.12 X, Y ), Z ), X, Y ), Z ) ] )
% 2.74/3.12 , clause( 20819, [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ] )
% 2.74/3.12 , clause( 20820, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20821, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 2.74/3.12 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ] )
% 2.74/3.12 , clause( 20822, [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ), U,
% 2.74/3.12 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X,
% 2.74/3.12 'c_Product__Type_OSigma'( W, 'c_COMBK'( U, 'tc_fun'( T, 'tc_bool' ), Z )
% 2.74/3.12 , Z, T ), 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20823, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 2.74/3.12 , T, X ) ) ), =( Y, Z ) ] )
% 2.74/3.12 , clause( 20824, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.74/3.12 , T, X ) ) ), =( Z, T ) ] )
% 2.74/3.12 , clause( 20825, [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20826, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'c_Set_Oimage'( X, 'c_HOL_Ominus__class_Ominus'( Y, U,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20827, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20828, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20829, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20830, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20831, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20832, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20833, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), X ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20834, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20835, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 2.74/3.12 'c_lessequals'( Y, Z, X ) ) ] )
% 2.74/3.12 , clause( 20836, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 2.74/3.12 'c_lessequals'( Y, Z, X ) ] )
% 2.74/3.12 , clause( 20837, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 2.74/3.12 'c_lessequals'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20838, [ 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20839, [ 'c_lessequals'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20840, [ 'c_lessequals'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20841, [ 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20842, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20843, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X
% 2.74/3.12 ), X ) ] )
% 2.74/3.12 , clause( 20844, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X
% 2.74/3.12 ), X ) ] )
% 2.74/3.12 , clause( 20845, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20846, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 T, X ), ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20847, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ] )
% 2.74/3.12 , clause( 20848, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ] )
% 2.74/3.12 , clause( 20849, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20850, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20851, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20852, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 2.74/3.12 X, Y ) ) ] )
% 2.74/3.12 , clause( 20853, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' )
% 2.74/3.12 ) ) ] )
% 2.74/3.12 , clause( 20854, [ 'c_lessequals'( 'c_Relation_OImage'( X, 'c_Set_Oinsert'(
% 2.74/3.12 Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z
% 2.74/3.12 ), 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X,
% 2.74/3.12 'tc_prod'( Z, Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 2.74/3.12 , clause( 20855, [ =( 'c_Relation_OImage'( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20856, [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 2.74/3.12 'c_Set_Oinsert'( X, Y, Z ) ) ] )
% 2.74/3.12 , clause( 20857, [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 2.74/3.12 'c_Set_Oinsert'( Z, X, T ), Y ) ) ) ] )
% 2.74/3.12 , clause( 20858, [ =( 'c_Relation_ODomain'( 'c_Set_Oinsert'( 'c_Pair'( X, Y
% 2.74/3.12 , Z, T ), U, 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( X,
% 2.74/3.12 'c_Relation_ODomain'( U, Z, T ), Z ) ) ] )
% 2.74/3.12 , clause( 20859, [ 'c_Relation_Osym'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'( Y, Z ) ), ~(
% 2.74/3.12 'c_Relation_Osym'( X, Z ) ) ] )
% 2.74/3.12 , clause( 20860, [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y )
% 2.74/3.12 , 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20861, [ 'c_lessequals'( 'c_Relation_ODomain'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), Z, T ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_ODomain'( X, Z
% 2.74/3.12 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20862, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 X ) ) ] )
% 2.74/3.12 , clause( 20863, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 2.74/3.12 , clause( 20864, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 2.74/3.12 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 2.74/3.12 ) ) ) ] )
% 2.74/3.12 , clause( 20865, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 2.74/3.12 ) ] )
% 2.74/3.12 , clause( 20866, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, X, Z ), 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20867, [ 'c_lessequals'( 'c_Set_Oimage'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20868, [ 'c_lessequals'( 'c_Relation_OImage'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 2.74/3.12 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20869, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_lessequals'( T, X,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20870, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( T, X,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20871, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T, Z, U )
% 2.74/3.12 , 'c_HOL_Ominus__class_Ominus'( 'c_Product__Type_OSigma'( X, T, Z, U ),
% 2.74/3.12 'c_Product__Type_OSigma'( Y, T, Z, U ), 'tc_fun'( 'tc_prod'( Z, U ),
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20872, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20873, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 2.74/3.12 ) ] )
% 2.74/3.12 , clause( 20874, [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, Y, Z, T, U )
% 2.74/3.12 , 'c_Product__Type_OSigma'( W, 'c_COMBK'( V0, 'tc_fun'( U, 'tc_bool' ), Z
% 2.74/3.12 ), Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.12 Y, 'c_Product__Type_OSigma'( V1, 'c_COMBK'( V0, 'tc_fun'( U, 'tc_bool' )
% 2.74/3.12 , T ), T, U ), 'tc_fun'( 'tc_prod'( T, U ), 'tc_bool' ) ) ), ~(
% 2.74/3.12 'c_lessequals'( X, 'c_Product__Type_OSigma'( W, 'c_COMBK'( V1, 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ), Z ), Z, T ), 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ) )
% 2.74/3.12 ] )
% 2.74/3.12 , clause( 20875, [ 'c_Wellfounded_Owf'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_lessequals'( 'c_Relation_Orel__comp'( X
% 2.74/3.12 , Y, Z, Z, Z ), X, 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ), ~(
% 2.74/3.12 'c_Wellfounded_Owf'( Y, Z ) ), ~( 'c_Wellfounded_Owf'( X, Z ) ) ] )
% 2.74/3.12 , clause( 20876, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL(
% 2.74/3.12 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), Y ) ) ) ] )
% 2.74/3.12 , clause( 20877, [ hBOOL( hAPP(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ] )
% 2.74/3.12 , clause( 20878, [ hBOOL( hAPP(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 2.74/3.12 , clause( 20879, [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Relation_ODomain'( X, Y, Y ), 'c_Relation_ORange'( Z, Y, Y ), 'tc_fun'(
% 2.74/3.12 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 2.74/3.12 ) ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ), ~( 'c_Wellfounded_Owf'( X, Y
% 2.74/3.12 ) ), 'c_Wellfounded_Owf'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ] )
% 2.74/3.12 , clause( 20880, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Product__Type_OSigma'( X
% 2.74/3.12 , 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 2.74/3.12 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 2.74/3.12 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20881, [ 'c_Relation_Orefl__on'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U,
% 2.74/3.12 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 2.74/3.12 'c_Relation_Orefl__on'( Y, U, Z ) ), ~( 'c_Relation_Orefl__on'( X, T, Z )
% 2.74/3.12 ) ] )
% 2.74/3.12 , clause( 20882, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20883, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20884, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20885, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20886, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20887, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20888, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ] )
% 2.74/3.12 , clause( 20889, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ] )
% 2.74/3.12 , clause( 20890, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 2.74/3.12 X, 'tc_bool' ) ), Y ) ] )
% 2.74/3.12 , clause( 20891, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20892, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 2.74/3.12 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 2.74/3.12 ) ) ) ] )
% 2.74/3.12 , clause( 20893, [ =( 'c_Product__Type_OSigma'( 'c_Set_Oinsert'( X, Y, Z )
% 2.74/3.12 , 'c_COMBK'( 'c_Set_Oinsert'( T, U, W ), 'tc_fun'( W, 'tc_bool' ), Z ), Z
% 2.74/3.12 , W ), 'c_Set_Oinsert'( 'c_Pair'( X, T, Z, W ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Product__Type_OSigma'( Y
% 2.74/3.12 , 'c_COMBK'( 'c_Set_Oinsert'( T, U, W ), 'tc_fun'( W, 'tc_bool' ), Z ), Z
% 2.74/3.12 , W ), 'c_Product__Type_OSigma'( 'c_Set_Oinsert'( X, Y, Z ), 'c_COMBK'( U
% 2.74/3.12 , 'tc_fun'( W, 'tc_bool' ), Z ), Z, W ), 'tc_fun'( 'tc_prod'( Z, W ),
% 2.74/3.12 'tc_bool' ) ), 'tc_prod'( Z, W ) ) ) ] )
% 2.74/3.12 , clause( 20894, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Relation_OImage'( Z, X, Y, Y )
% 2.74/3.12 , 'tc_fun'( Y, 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ] )
% 2.74/3.12 , clause( 20895, [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.12 X, 'tc_bool' ) ), Y ) ) ) ] )
% 2.74/3.12 , clause( 20896, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 2.74/3.12 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20897, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20898, [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ), T, Z, Y ),
% 2.74/3.12 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ), Y ) ), =( T, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20899, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'c_HOL_Ominus__class_Ominus'( T, U, 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'( U, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20900, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( X, T, Z ) ), ~( =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 2.74/3.12 ) ) ] )
% 2.74/3.12 , clause( 20901, [ 'c_Relation_Otrans'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Otrans'( Y, Z ) ), ~(
% 2.74/3.12 'c_Relation_Otrans'( X, Z ) ) ] )
% 2.74/3.12 , clause( 20902, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ] )
% 2.74/3.12 , clause( 20903, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20904, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ] )
% 2.74/3.12 , clause( 20905, [ ~( =( 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 2.74/3.12 ) ) ), ~( =( 'c_Relation_Orel__comp'( T, Y, Z, Z, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 2.74/3.12 ) ) ), =( 'c_Relation_Orel__comp'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), Y, Z, Z, Z ), 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20906, [ ~( =( 'c_Relation_Orel__comp'( X, Y, Z, Z, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 2.74/3.12 ) ) ), ~( =( 'c_Relation_Orel__comp'( X, T, Z, Z, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' )
% 2.74/3.12 ) ) ), =( 'c_Relation_Orel__comp'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), Z, Z, Z ), 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20907, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, Z, T ) ) ) ), ~(
% 2.74/3.12 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 2.74/3.12 , clause( 20908, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~(
% 2.74/3.12 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 2.74/3.12 , clause( 20909, [ 'c_Wellfounded_Oacyclic'( 'c_Relation_Oconverse'( X, Y,
% 2.74/3.12 Y ), Y ), ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ] )
% 2.74/3.12 , clause( 20910, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20911, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20912, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.74/3.12 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.74/3.12 , clause( 20913, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.74/3.12 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.74/3.12 , clause( 20914, [ =( hAPP( 'c_split'( X, Y, Z, T ), U ), hAPP( hAPP( X,
% 2.74/3.12 hAPP( 'c_fst'( Y, Z ), U ) ), hAPP( 'c_snd'( Y, Z ), U ) ) ) ] )
% 2.74/3.12 , clause( 20915, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.74/3.12 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20916, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ] )
% 2.74/3.12 , clause( 20917, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20918, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 2.74/3.12 'c_lessequals'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20919, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 2.74/3.12 'c_lessequals'( Y, Z, X ) ] )
% 2.74/3.12 , clause( 20920, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 2.74/3.12 'c_lessequals'( Y, Z, X ) ) ] )
% 2.74/3.12 , clause( 20921, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Y ), ~( 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20922, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), X ), ~( 'c_lessequals'( Y, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20923, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 2.74/3.12 , 'tc_fun'( Z, 'tc_bool' ) ), Y ) ), 'c_lessequals'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20924, [ 'c_Relation_Orefl__on'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, U,
% 2.74/3.12 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ), ~(
% 2.74/3.12 'c_Relation_Orefl__on'( Y, U, Z ) ), ~( 'c_Relation_Orefl__on'( X, T, Z )
% 2.74/3.12 ) ] )
% 2.74/3.12 , clause( 20925, [ 'c_Relation_Oantisym'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20926, [ =( 'c_Relation_ORange'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ) ), X, Y ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20927, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 2.74/3.12 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ] )
% 2.74/3.12 , clause( 20928, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 2.74/3.12 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ] )
% 2.74/3.12 , clause( 20929, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 2.74/3.12 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ] )
% 2.74/3.12 , clause( 20930, [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 2.74/3.12 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ] )
% 2.74/3.12 , clause( 20931, [ 'c_lessequals'( 'c_Transitive__Closure_Otrancl'( X, Y )
% 2.74/3.12 , 'c_Product__Type_OSigma'( Z, 'c_COMBK'( Z, 'tc_fun'( Y, 'tc_bool' ), Y
% 2.74/3.12 ), Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.12 X, 'c_Product__Type_OSigma'( Z, 'c_COMBK'( Z, 'tc_fun'( Y, 'tc_bool' ), Y
% 2.74/3.12 ), Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20932, [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y )
% 2.74/3.12 , 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ), ~( 'c_lessequals'( X, 'c_Transitive__Closure_Ortrancl'( Z
% 2.74/3.12 , Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20933, [ =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20934, [ 'c_lessequals'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.12 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 2.74/3.12 ) ), 'tc_fun'( X, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20935, [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 2.74/3.12 'tc_bool' ) ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ] )
% 2.74/3.12 , clause( 20936, [ 'c_Relation_Orefl__on'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20937, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), ~( 'c_in'( X, T, Z ) ) ] )
% 2.74/3.12 , clause( 20938, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'(
% 2.74/3.12 Y, 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), T ) ), ~( 'c_in'( Y, X, T ) ) ] )
% 2.74/3.12 , clause( 20939, [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U )
% 2.74/3.12 , 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ] )
% 2.74/3.12 , clause( 20940, [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( X, 'tc_bool' ) ), Y, X ) ] )
% 2.74/3.12 , clause( 20941, [ 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( T, U,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.12 Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z
% 2.74/3.12 , 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20942, [ =( 'c_Relation_Oconverse'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), Z, T ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Oconverse'( X,
% 2.74/3.12 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20943, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ] )
% 2.74/3.12 , clause( 20944, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ] )
% 2.74/3.12 , clause( 20945, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 2.74/3.12 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20946, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 2.74/3.12 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20947, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X
% 2.74/3.12 ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 20948, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 Z, X ) ] )
% 2.74/3.12 , clause( 20949, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 Y, X ) ] )
% 2.74/3.12 , clause( 20950, [ 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20951, [ 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20952, [ 'c_lessequals'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z,
% 2.74/3.12 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20953, [ 'c_lessequals'( X,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z,
% 2.74/3.12 'tc_fun'( T, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20954, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Product__Type_OSigma'( X
% 2.74/3.12 , 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ),
% 2.74/3.12 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 2.74/3.12 , Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20955, [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ] )
% 2.74/3.12 , clause( 20956, [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 2.74/3.12 'c_Transitive__Closure_Ortrancl'( Z, Y ) ), ~( 'c_lessequals'( X,
% 2.74/3.12 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20957, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), X, 'tc_fun'( Z, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 20958, [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 2.74/3.12 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 2.74/3.12 Y, Z ) ) ] )
% 2.74/3.12 , clause( 20959, [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Y, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X
% 2.74/3.12 , Z ) ] )
% 2.74/3.12 , clause( 20960, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20961, [ =( 'c_Relation_OId__on'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( X, 'tc_bool' ) ), X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.12 'tc_prod'( X, X ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20962, [ =( 'c_Set_Oimage'( 'c_COMBK'( X, Y, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z, Y ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20963, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), 'c_in'( X
% 2.74/3.12 , Y, Z ) ] )
% 2.74/3.12 , clause( 20964, [ 'c_Wellfounded_Owf'( 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' ) ), X ) ] )
% 2.74/3.12 , clause( 20965, [ 'c_in'( X, Y, Z ), ~( 'c_lessequals'( 'c_Set_Oinsert'( X
% 2.74/3.12 , T, Z ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20966, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, Z, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Product__Type_OSigma'( X, T, Z, U ), 'c_Product__Type_OSigma'( Y, T, Z
% 2.74/3.12 , U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20967, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL(
% 2.74/3.12 hAPP( Y, T ) ) ) ] )
% 2.74/3.12 , clause( 20968, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 2.74/3.12 'c_in'( Y, X, T ) ] )
% 2.74/3.12 , clause( 20969, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_in'(
% 2.74/3.12 T, X, Z ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z
% 2.74/3.12 , 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20970, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 2.74/3.12 'c_in'( Y, X, T ) ] )
% 2.74/3.12 , clause( 20971, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.12 'c_lessequals'( X, 'c_Set_Oinsert'( T, Y, Z ), 'tc_fun'( Z, 'tc_bool' ) )
% 2.74/3.12 ), 'c_in'( T, X, Z ) ] )
% 2.74/3.12 , clause( 20972, [ =( 'c_Relation_Oconverse'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), Z, T ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_Oconverse'( X,
% 2.74/3.12 Z, T ), 'c_Relation_Oconverse'( Y, Z, T ), 'tc_fun'( 'tc_prod'( T, Z ),
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20973, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ) ), 'c_in'( Y, X, T ) ] )
% 2.74/3.12 , clause( 20974, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.12 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ), 'c_in'( X, T, Z ) ] )
% 2.74/3.12 , clause( 20975, [ 'c_Relation_Ototal__on'( X, Y, Z ), ~(
% 2.74/3.12 'c_Order__Relation_Ostrict__linear__order__on'( X, Y, Z ) ) ] )
% 2.74/3.12 , clause( 20976, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 2.74/3.12 , 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 2.74/3.12 , 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20977, [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y
% 2.74/3.12 , 'tc_fun'( Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z
% 2.74/3.12 , 'tc_bool' ) ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20978, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 2.74/3.12 , clause( 20979, [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( X ) ) ] )
% 2.74/3.12 , clause( 20980, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20981, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20982, [ =( 'c_Relation_Orel__comp'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), U, Z, T, W ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 2.74/3.12 , U, Z, T, W ), 'c_Relation_Orel__comp'( Y, U, Z, T, W ), 'tc_fun'(
% 2.74/3.12 'tc_prod'( Z, W ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20983, [ =( 'c_Relation_Orel__comp'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 T, U ), 'tc_bool' ) ), W, T, U ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 2.74/3.12 , Y, W, T, U ), 'c_Relation_Orel__comp'( X, Z, W, T, U ), 'tc_fun'(
% 2.74/3.12 'tc_prod'( W, U ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20984, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.12 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20985, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.12 'c_lessequals'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20986, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20987, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 2.74/3.12 , clause( 20988, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 T, X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.74/3.12 , clause( 20989, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 2.74/3.12 T, X ), ~( 'c_lessequals'( Z, T, X ) ) ] )
% 2.74/3.12 , clause( 20990, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ] )
% 2.74/3.12 , clause( 20991, [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 2.74/3.12 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( Y,
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ), X ) ) ] )
% 2.74/3.12 , clause( 20992, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20993, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 Y, X, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20994, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20995, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ] )
% 2.74/3.12 , clause( 20996, [ =( 'c_Relation_ODomain'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), Z, T ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ODomain'( X, Z
% 2.74/3.12 , T ), 'c_Relation_ODomain'( Y, Z, T ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20997, [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 20998, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, X, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, Z ), 'tc_bool' )
% 2.74/3.12 ) ) ] )
% 2.74/3.12 , clause( 20999, [ 'c_lessequals'( 'c_Wellfounded_Oacc'( X, Y ),
% 2.74/3.12 'c_Wellfounded_Oacc'( Z, Y ), 'tc_fun'( Y, 'tc_bool' ) ), ~(
% 2.74/3.12 'c_lessequals'( Z, X, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 21000, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 21001, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 2.74/3.12 , clause( 21002, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ] )
% 2.74/3.12 , clause( 21003, [ ~( =( 'c_Relation_ODomain'( X, Y, Z ),
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ) ) ), =( X,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' )
% 2.74/3.12 ) ) ] )
% 2.74/3.12 , clause( 21004, [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 2.74/3.12 'tc_bool' ) ), 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.12 'tc_fun'( Z, 'tc_bool' ) ), Z, X ) ) ] )
% 2.74/3.12 , clause( 21005, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.12 Z, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 2.74/3.12 ) ) ) ] )
% 2.74/3.12 , clause( 21006, [ 'c_lessequals'( 'c_Relation_ORange'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, T ), 'tc_bool' ) ), Z, T ),
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Relation_ORange'( X, Z,
% 2.74/3.12 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ) ] )
% 2.74/3.12 , clause( 21007, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.12 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'( X, Z, T ) ) )
% 2.74/3.12 ), ~( 'c_Wellfounded_Owf'( Z, T ) ) ] )
% 2.74/3.12 , clause( 21008, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.12 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 2.74/3.12 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.12 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.12 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Y, Y ), 'tc_bool' ) ), Y ) ) ] )
% 2.74/3.12 , clause( 21009, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y,
% 2.74/3.12 Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 2.74/3.12 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ),
% 2.74/3.12 'c_in'( X, T, Z ) ] )
% 2.74/3.12 , clause( 21010, [ 'c_lessequals'( X, 'c_Set_Oinsert'( Y, Z, T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( T, 'tc_bool' ) ) ),
% 2.74/3.12 ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), 'tc_fun'(
% 2.74/3.12 T, 'tc_bool' ) ), Z, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.12 , clause( 21011, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), Y ) ) ) ] )
% 2.74/3.12 , clause( 21012, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 2.74/3.12 'tc_bool' ) ), Y ) ) ) ] )
% 2.74/3.12 , clause( 21013, [ =( 'c_Relation_ORange'( 'c_Set_Oinsert'( 'c_Pair'( X, Y
% 2.74/3.12 , Z, T ), U, 'tc_prod'( Z, T ) ), Z, T ), 'c_Set_Oinsert'( Y,
% 2.74/3.12 'c_Relation_ORange'( U, Z, T ), T ) ) ] )
% 2.74/3.12 , clause( 21014, [ 'c_Relation_Osym'(
% 2.74/3.12 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.12 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Relation_Osym'( Y, Z ) ), ~(
% 2.74/3.12 'c_Relation_Osym'( X, Z ) ) ] )
% 2.74/3.12 , clause( 21015, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Set_Oinsert'( X, Y,
% 2.74/3.12 Z ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.12 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Y ), 'c_in'( X, Y, Z ) ]
% 2.74/3.12 )
% 2.74/3.12 , clause( 21016, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21017, [ 'c_lessequals'( X,
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ), Z,
% 2.74/3.13 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21018, [ ~( =( hAPP( X, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X
% 2.74/3.13 , Y, Z, T, U, W ) ), hAPP( Y, 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X,
% 2.74/3.13 Y, Z, T, U, W ) ) ) ), =( 'c_Recdef_Ocut'( X, Z, T, U, W ),
% 2.74/3.13 'c_Recdef_Ocut'( Y, Z, T, U, W ) ) ] )
% 2.74/3.13 , clause( 21019, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~(
% 2.74/3.13 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X,
% 2.74/3.13 'tc_prod'( Y, Y ) ), Y ) ) ] )
% 2.74/3.13 , clause( 21020, [ ~( 'class_HOL_Oord'( X ) ), 'c_lessequals'( hAPP( Y, Z )
% 2.74/3.13 , hAPP( T, Z ), X ), ~( 'c_lessequals'( Y, T, 'tc_fun'( U, X ) ) ) ] )
% 2.74/3.13 , clause( 21021, [ 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 Y, Z, 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ), ~( 'c_in'(
% 2.74/3.13 X, Y, T ) ) ] )
% 2.74/3.13 , clause( 21022, [ 'c_in'( X, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 Y, Z, 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ), ~( 'c_in'(
% 2.74/3.13 X, Y, T ) ) ] )
% 2.74/3.13 , clause( 21023, [ 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), ~( 'c_in'( X
% 2.74/3.13 , Z, T ) ) ] )
% 2.74/3.13 , clause( 21024, [ 'c_in'( X, 'c_Set_Oinsert'( Y, Z, T ), T ), ~( 'c_in'( X
% 2.74/3.13 , Z, T ) ) ] )
% 2.74/3.13 , clause( 21025, [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~(
% 2.74/3.13 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21026, [ 'c_in'( X, Y, Z ), ~( 'c_lessequals'( T, Y, 'tc_fun'( Z
% 2.74/3.13 , 'tc_bool' ) ) ), ~( 'c_in'( X, T, Z ) ) ] )
% 2.74/3.13 , clause( 21027, [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~(
% 2.74/3.13 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21028, [ 'c_in'( X, Y, Z ), ~( 'c_in'( X, T, Z ) ), ~(
% 2.74/3.13 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21029, [ 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 Y, Z, 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Y, T ) ) ] )
% 2.74/3.13 , clause( 21030, [ 'c_in'( X, 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 Y, Z, 'tc_fun'( T, 'tc_bool' ) ), T ), ~( 'c_in'( X, Z, T ) ) ] )
% 2.74/3.13 , clause( 21031, [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.13 Y, 'tc_bool' ) ), Y ) ) ] )
% 2.74/3.13 , clause( 21032, [ hBOOL( hAPP( X, Y ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21033, [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.13 Y, 'tc_bool' ) ), Y ) ) ] )
% 2.74/3.13 , clause( 21034, [ ~( 'c_in'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.13 Y, 'tc_bool' ) ), Y ) ) ] )
% 2.74/3.13 , clause( 21035, [ 'c_in'( X, Y, Z ), =( X, T ), ~( 'c_in'( X,
% 2.74/3.13 'c_Set_Oinsert'( T, Y, Z ), Z ) ) ] )
% 2.74/3.13 , clause( 21036, [ 'c_in'( X, Y, Z ), 'c_in'( X, T, Z ), ~( 'c_in'( X,
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21037, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( X,
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21038, [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21039, [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ] )
% 2.74/3.13 , clause( 21040, [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ] )
% 2.74/3.13 , clause( 21041, [ 'c_in'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ) ] )
% 2.74/3.13 , clause( 21042, [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( T, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21043, [ 'c_in'( X, Y, Z ), ~( 'c_in'( X,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21044, [ ~( hBOOL( hAPP( X, Y ) ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21045, [ 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'(
% 2.74/3.13 T, 'tc_bool' ) ), T ), 'c_in'( X, Z, T ), ~( 'c_in'( X, Y, T ) ) ] )
% 2.74/3.13 , clause( 21046, [ 'c_in'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'(
% 2.74/3.13 T, 'tc_bool' ) ), T ), 'c_in'( X, Z, T ), ~( 'c_in'( X, Y, T ) ) ] )
% 2.74/3.13 , clause( 21047, [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T
% 2.74/3.13 , Z ) ) ), 'c_in'( X, T, Z ), 'c_in'( X, Y, Z ), =( Y, T ) ] )
% 2.74/3.13 , clause( 21048, [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( 'c_in'( X, Y, Z )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21049, [ =( hAPP( 'c_fst'( X, Y ), 'c_Pair'( Z, T, X, Y ) ), Z )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21050, [ =( X, hAPP( 'c_fst'( Y, Z ), 'c_Pair'( X, T, Y, Z ) ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21051, [ =( hAPP( 'c_snd'( X, Y ), 'c_Pair'( Z, T, X, Y ) ), T )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21052, [ =( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, X, Y, Z ) ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21053, [ hBOOL( hAPP( X, hAPP( 'c_fst'( Y, Z ), 'c_Pair'( T, U, Y
% 2.74/3.13 , Z ) ) ) ), ~( hBOOL( hAPP( W, U ) ) ), ~( hBOOL( hAPP( X, T ) ) ) ] )
% 2.74/3.13 , clause( 21054, [ hBOOL( hAPP( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T, U, Y
% 2.74/3.13 , Z ) ) ) ), ~( hBOOL( hAPP( X, U ) ) ), ~( hBOOL( hAPP( W, T ) ) ) ] )
% 2.74/3.13 , clause( 21055, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ] )
% 2.74/3.13 , clause( 21056, [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ] )
% 2.74/3.13 , clause( 21057, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 2.74/3.13 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21058, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21059, [ 'c_Relation_Otrans'( X, Y ), ~(
% 2.74/3.13 'c_Order__Relation_Ostrict__linear__order__on'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21060, [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ] )
% 2.74/3.13 , clause( 21061, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ), T, 'tc_fun'(
% 2.74/3.13 Z, 'tc_bool' ) ), ~( 'c_lessequals'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 2.74/3.13 ~( 'c_in'( X, T, Z ) ) ] )
% 2.74/3.13 , clause( 21062, [ =( 'c_Product__Type_OSigma'(
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), 'c_COMBK'(
% 2.74/3.13 T, 'tc_fun'( U, 'tc_bool' ), Z ), Z, U ), 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.13 'c_Product__Type_OSigma'( X, 'c_COMBK'( T, 'tc_fun'( U, 'tc_bool' ), Z )
% 2.74/3.13 , Z, U ), 'c_Product__Type_OSigma'( Y, 'c_COMBK'( T, 'tc_fun'( U,
% 2.74/3.13 'tc_bool' ), Z ), Z, U ), 'tc_fun'( 'tc_prod'( Z, U ), 'tc_bool' ) ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21063, [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 2.74/3.13 , clause( 21064, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ] )
% 2.74/3.13 , clause( 21065, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21066, [ =( 'c_Relation_ORange'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Z, T ), 'tc_bool' ) ), Z, T ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_ORange'( X, Z,
% 2.74/3.13 T ), 'c_Relation_ORange'( Y, Z, T ), 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21067, [ 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Wellfounded_Owf'( X, Z ) ) ] )
% 2.74/3.13 , clause( 21068, [ 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Wellfounded_Owf'( Y, Z ) ) ] )
% 2.74/3.13 , clause( 21069, [ =( 'c_Set_Oinsert'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 2.74/3.13 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), Z ), 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y ), ~( 'c_in'( X, Y
% 2.74/3.13 , Z ) ) ] )
% 2.74/3.13 , clause( 21070, [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ] )
% 2.74/3.13 , clause( 21071, [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X,
% 2.74/3.13 'tc_fun'( Y, 'tc_bool' ) ), X ) ] )
% 2.74/3.13 , clause( 21072, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.13 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 2.74/3.13 , clause( 21073, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.13 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 2.74/3.13 , clause( 21074, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.13 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 2.74/3.13 ), X ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.74/3.13 , clause( 21075, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.13 'c_lessequals'( Y, 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X
% 2.74/3.13 ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.74/3.13 , clause( 21076, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.13 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), Z, X ) ) ] )
% 2.74/3.13 , clause( 21077, [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 2.74/3.13 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), Z, X ) ) ] )
% 2.74/3.13 , clause( 21078, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( X, T,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21079, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T, X,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), Y, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21080, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.74/3.13 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21081, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.74/3.13 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21082, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 2.74/3.13 , clause( 21083, [ 'c_lessequals'( X, X, 'tc_fun'( Y, 'tc_bool' ) ) ] )
% 2.74/3.13 , clause( 21084, [ 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( T, Y, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 2.74/3.13 , T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21085, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( Z, Y ) ) ), ~(
% 2.74/3.13 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21086, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_lessequals'( X, Z,
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~( 'c_Wellfounded_Owf'( Z,
% 2.74/3.13 Y ) ) ] )
% 2.74/3.13 , clause( 21087, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 2.74/3.13 , X ) ] )
% 2.74/3.13 , clause( 21088, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.74/3.13 , Y, X ) ] )
% 2.74/3.13 , clause( 21089, [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 2.74/3.13 Z, Y ) ), ~( 'c_lessequals'( X, Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 2.74/3.13 ) ) ) ] )
% 2.74/3.13 , clause( 21090, [ hBOOL( hAPP( X, Y ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'(
% 2.74/3.13 T, 'tc_bool' ) ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ] )
% 2.74/3.13 , clause( 21091, [ 'c_Wellfounded_Oacyclic'( X, Y ), ~( 'c_lessequals'( X,
% 2.74/3.13 Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ), ~(
% 2.74/3.13 'c_Wellfounded_Oacyclic'( Z, Y ) ) ] )
% 2.74/3.13 , clause( 21092, [ 'c_Relation_Osingle__valued'( X, Y, Z ), ~(
% 2.74/3.13 'c_Relation_Osingle__valued'( T, Y, Z ) ), ~( 'c_lessequals'( X, T,
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21093, [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ),
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21094, [ 'c_lessequals'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, U,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.13 Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, T, 'tc_fun'( Z
% 2.74/3.13 , 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21095, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.13 T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21096, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( Y, T, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.13 Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21097, [ 'c_in'( X, 'c_Set_Oinsert'( X,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ), Y ) ] )
% 2.74/3.13 , clause( 21098, [ 'c_lessequals'( 'c_Relation_ODomain'( X, Y, Z ),
% 2.74/3.13 'c_Relation_ODomain'( T, Y, Z ), 'tc_fun'( Y, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( X, T, 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21099, [ =( X, 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), =( X, 'c_Orderings_Obot__class_Obot'(
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'tc_fun'(
% 2.74/3.13 Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21100, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_fun'( T, 'tc_bool' ) ),
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.13 T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21101, [ =( 'c_Product__Type_OSigma'( X, 'c_COMBK'(
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 2.74/3.13 'tc_bool' ), Z ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( Z, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21102, [ hBOOL( hAPP(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL( hAPP( X, T )
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21103, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'(
% 2.74/3.13 T, 'tc_bool' ) ), Z ), ~( 'c_lessequals'( X, Y, 'tc_fun'( T, 'tc_bool' )
% 2.74/3.13 ) ), ~( 'c_lessequals'( Z, X, 'tc_fun'( T, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21104, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.74/3.13 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 2.74/3.13 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.74/3.13 , clause( 21105, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.74/3.13 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 2.74/3.13 ~( 'c_lessequals'( U, T, X ) ) ] )
% 2.74/3.13 , clause( 21106, [ 'c_lessequals'( 'c_Set_Oimage'( X, Y, Z, T ),
% 2.74/3.13 'c_Set_Oimage'( X, U, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( Y, U, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21107, [ ~( 'c_lessequals'( X, Y, 'tc_fun'( Z, 'tc_bool' ) ) ),
% 2.74/3.13 'c_lessequals'( 'c_Set_Oimage'( T, X, Z, U ), 'c_Set_Oimage'( T, Y, Z, U
% 2.74/3.13 ), 'tc_fun'( U, 'tc_bool' ) ) ] )
% 2.74/3.13 , clause( 21108, [ 'c_lessequals'( 'c_Set_Oinsert'( X, Y, Z ),
% 2.74/3.13 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.13 Y, T, 'tc_fun'( Z, 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21109, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 2.74/3.13 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21110, [ =( 'c_Set_Oimage'( X,
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Set_Oimage'( X, Y, T, U ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U,
% 2.74/3.13 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21111, [ =( 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' )
% 2.74/3.13 ), X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X ),
% 2.74/3.13 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21112, [ hBOOL( hAPP( hAPP( X, hAPP( 'c_snd'( Y, Z ), 'c_Pair'( T
% 2.74/3.13 , U, Y, Z ) ) ), hAPP( 'c_fst'( Y, Z ), 'c_Pair'( T, U, Y, Z ) ) ) ), ~(
% 2.74/3.13 hBOOL( hAPP( hAPP( X, U ), T ) ) ) ] )
% 2.74/3.13 , clause( 21113, [ ~( =( 'c_Relation_ORange'( X, Y, Z ),
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ), =( X,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Z ), 'tc_bool' )
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21114, [ 'c_lessequals'( 'c_Relation_OImage'( X, Y, Z, T ),
% 2.74/3.13 'c_Relation_OImage'( U, W, Z, T ), 'tc_fun'( T, 'tc_bool' ) ), ~(
% 2.74/3.13 'c_lessequals'( Y, W, 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_lessequals'( X
% 2.74/3.13 , U, 'tc_fun'( 'tc_prod'( Z, T ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21115, [ 'c_lessequals'( X, 'c_Product__Type_OSigma'( Y,
% 2.74/3.13 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), Z ), Z, Z ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Z, Z ), 'tc_bool' ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, X, Z ) ) ] )
% 2.74/3.13 , clause( 21116, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.74/3.13 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.74/3.13 , clause( 21117, [ 'c_Relation_Oirrefl'( X, Y ), ~(
% 2.74/3.13 'c_Order__Relation_Ostrict__linear__order__on'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21118, [ 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( X,
% 2.74/3.13 Y, Z, Z ), T, 'tc_prod'( Z, Z ) ), Z ), 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~(
% 2.74/3.13 'c_Wellfounded_Oacyclic'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21119, [ ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Wellfounded_Oacyclic'( 'c_Set_Oinsert'( 'c_Pair'( Y, X, Z, Z ), T,
% 2.74/3.13 'tc_prod'( Z, Z ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21120, [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 2.74/3.13 X, Z, T, U ),
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 2.74/3.13 X, Z, T, U ), U, U ), T, 'tc_prod'( U, U ) ), ~( hBOOL( hAPP( X, Z ) ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( Y, Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T
% 2.74/3.13 , U ), 'tc_prod'( U, U ) ) ) ] )
% 2.74/3.13 , clause( 21121, [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 2.74/3.13 T, U ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'(
% 2.74/3.13 X, Z, T, U ), U, U ), T, 'tc_prod'( U, U ) ), ~( hBOOL( hAPP( X, Z ) ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( Z, Y, U, U ), 'c_Transitive__Closure_Ortrancl'( T
% 2.74/3.13 , U ), 'tc_prod'( U, U ) ) ) ] )
% 2.74/3.13 , clause( 21122, [ 'c_in'( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'( X,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 Z ), ~( 'c_in'( X, T, Z ) ), ~( 'c_Equiv__Relations_Oequiv'( T, Y, Z ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21123, [ 'c_lessequals'( 'c_Transitive__Closure_Ortrancl'( X, Y )
% 2.74/3.13 , Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_lessequals'(
% 2.74/3.13 'c_Relation_Orel__comp'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y )
% 2.74/3.13 , 'tc_bool' ) ), X, Y, Y, Y ), Z, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool'
% 2.74/3.13 ) ) ), ~( 'c_lessequals'( 'c_Relation_OId'( Y ), Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21124, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 ~( 'c_in'( U, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Relation_OImage'( T, 'c_Set_Oinsert'( X,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( T, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ), Z ) ), ~( 'c_Equiv__Relations_Oequiv'( W, T,
% 2.74/3.13 Z ) ) ] )
% 2.74/3.13 , clause( 21125, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 ~( 'c_in'( Y, U, Z ) ), ~( 'c_lessequals'( 'c_Relation_OImage'( T,
% 2.74/3.13 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 2.74/3.13 'tc_bool' ) ), Z ), Z, Z ), 'c_Relation_OImage'( T, 'c_Set_Oinsert'( X,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ) ) ), ~( 'c_Equiv__Relations_Oequiv'( U, T, Z ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21126, [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z,
% 2.74/3.13 T, U ), U ), 'c_Set_Oimage'( X, Z, T, U ) ), ~( 'c_in'( Y, Z, T ) ) ] )
% 2.74/3.13 , clause( 21127, [ 'c_in'( hAPP( X, Y ), Z, T ), ~( 'c_in'( Y, U, W ) ),
% 2.74/3.13 ~( 'c_lessequals'( 'c_Set_Oimage'( X, U, W, T ), Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21128, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ),
% 2.74/3.13 ~( 'c_in'( Y, 'c_Relation_OImage'( U, 'c_Set_Oinsert'( X,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, T ),
% 2.74/3.13 T ) ) ] )
% 2.74/3.13 , clause( 21129, [ 'c_in'( X, 'c_Relation_OImage'( Y, 'c_Set_Oinsert'( Z,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) ), T ), T, U ),
% 2.74/3.13 U ), ~( 'c_in'( 'c_Pair'( Z, X, T, U ), Y, 'tc_prod'( T, U ) ) ) ] )
% 2.74/3.13 , clause( 21130, [ ~( =( 'c_Product__Type_OSigma'( X, 'c_COMBK'( Y,
% 2.74/3.13 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ), 'c_Product__Type_OSigma'( U,
% 2.74/3.13 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), T ), T, Z ) ) ), ~( 'c_in'( W, Y
% 2.74/3.13 , Z ) ), =( X, U ) ] )
% 2.74/3.13 , clause( 21131, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Set_Oinsert'( 'c_Pair'( Z, T, Y, Y ), X, 'tc_prod'( Y, Y ) ), Y ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21132, [ 'c_in'( X, 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 T, T ), 'tc_bool' ) ), T ), 'tc_prod'( T, T ) ), ~( 'c_in'( X,
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21133, [ 'c_in'( X, 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 T, T ), 'tc_bool' ) ), T ), 'tc_prod'( T, T ) ), ~( 'c_in'( X,
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21134, [ 'c_in'( X, 'c_Transitive__Closure_Otrancl'( Y, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ), ~( 'c_lessequals'( T, Y, 'tc_fun'( 'tc_prod'( Z, Z )
% 2.74/3.13 , 'tc_bool' ) ) ), ~( 'c_in'( X, 'c_Transitive__Closure_Otrancl'( T, Z )
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21135, [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 2.74/3.13 , clause( 21136, [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 2.74/3.13 , clause( 21137, [ 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 2.74/3.13 , X, Y, Y, Y ), 'c_Relation_Orel__comp'( Z, X, Y, Y, Y ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Y, Y ), 'tc_bool' ) ), Z, 'tc_fun'( 'tc_prod'( Y, Y ),
% 2.74/3.13 'tc_bool' ) ), Y ), ~( 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Y, Y ), 'tc_bool' ) ), Y ) ) ] )
% 2.74/3.13 , clause( 21138, [ 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Z, Z ), 'tc_bool' ) ), Z ), ~( 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_Orel__comp'( X
% 2.74/3.13 , X, Z, Z, Z ), 'c_Relation_Orel__comp'( Y, X, Z, Z, Z ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Z, Z ), 'tc_bool' ) ), Y, 'tc_fun'( 'tc_prod'( Z, Z ),
% 2.74/3.13 'tc_bool' ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21139, [ ~( =( 'c_Relation_Orel__comp'( X, X, Y, Y, Y ),
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 2.74/3.13 ) ) ), 'c_Wellfounded_Owf'( X, Y ) ] )
% 2.74/3.13 , clause( 21140, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Orel__comp'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), X, Y, Y, Y ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21141, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21142, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21143, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( X, X ), 'tc_bool' )
% 2.74/3.13 ), X ), 'c_Relation_OId'( X ) ) ] )
% 2.74/3.13 , clause( 21144, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_HOL_Ominus__class_Ominus'( X, 'c_Relation_OId'( Y ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ), 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 X, Y ) ) ] )
% 2.74/3.13 , clause( 21145, [ 'c_Relation_Oantisym'( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 X, Y ), Y ), ~( 'c_Wellfounded_Oacyclic'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21146, [ 'c_lessequals'( 'c_Relation_Orel__comp'( X, X, Y, Y, Y )
% 2.74/3.13 , X, 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), ~( 'c_Relation_Otrans'(
% 2.74/3.13 X, Y ) ) ] )
% 2.74/3.13 , clause( 21147, [ 'c_Relation_Osym'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_Oconverse'(
% 2.74/3.13 X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ] )
% 2.74/3.13 , clause( 21148, [ 'c_Relation_Osym'(
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Relation_Oconverse'(
% 2.74/3.13 X, Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ] )
% 2.74/3.13 , clause( 21149, [ 'c_Relation_Otrans'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ), ~( 'c_Relation_Otrans'(
% 2.74/3.13 X, Y ) ) ] )
% 2.74/3.13 , clause( 21150, [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z
% 2.74/3.13 , Y, Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y
% 2.74/3.13 , 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21151, [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ) ] )
% 2.74/3.13 , clause( 21152, [ 'c_Relation_Oantisym'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ), ~( 'c_Relation_Oantisym'(
% 2.74/3.13 X, Y ) ) ] )
% 2.74/3.13 , clause( 21153, [ 'c_Relation_Ototal__on'( X, Y, Z ), ~(
% 2.74/3.13 'c_Relation_Ototal__on'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 2.74/3.13 'c_Relation_OId'( Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21154, [ 'c_Relation_Ototal__on'( X, 'c_HOL_Ominus__class_Ominus'(
% 2.74/3.13 Y, 'c_Relation_OId'( Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ), Z )
% 2.74/3.13 , ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ] )
% 2.74/3.13 , clause( 21155, [ 'c_lessequals'( 'c_Relation_Orel__comp'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y, Y ), X, 'tc_fun'( 'tc_prod'(
% 2.74/3.13 Y, Y ), 'tc_bool' ) ), ~( 'c_Relation_Otrans'( X, Y ) ), ~(
% 2.74/3.13 'c_Relation_Osym'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21156, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( Y, X, Z, T )
% 2.74/3.13 , T, T ), 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( X, Z, T, T ), 'c_Transitive__Closure_Otrancl'( Y, T
% 2.74/3.13 ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21157, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( X, Y, Z, T ),
% 2.74/3.13 Z, T, T ), 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'( T, T ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( Y, Z, T, T ), 'c_Transitive__Closure_Otrancl'( X,
% 2.74/3.13 T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21158, [ ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( Y, X, Z, Z ), T,
% 2.74/3.13 'tc_prod'( Z, Z ) ), Z ) ) ] )
% 2.74/3.13 , clause( 21159, [ 'c_Wellfounded_Owf'( 'c_Set_Oinsert'( 'c_Pair'( X, Y, Z
% 2.74/3.13 , Z ), T, 'tc_prod'( Z, Z ) ), Z ), 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~(
% 2.74/3.13 'c_Wellfounded_Owf'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21160, [ 'c_Order__Relation_Ostrict__linear__order__on'( X, Y, Z
% 2.74/3.13 ), ~( 'c_Relation_Ototal__on'( X, Y, Z ) ), ~( 'c_Relation_Oirrefl'( Y,
% 2.74/3.13 Z ) ), ~( 'c_Relation_Otrans'( Y, Z ) ) ] )
% 2.74/3.13 , clause( 21161, [ 'c_Nitpick_Orefl_H'( X, Y ), ~( 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ),
% 2.74/3.13 'c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1'( X, Y ), Y, Y ), X,
% 2.74/3.13 'tc_prod'( Y, Y ) ) ) ] )
% 2.74/3.13 , clause( 21162, [ 'c_Relation_Otrans'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.13 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 2.74/3.13 ~( 'c_Relation_Oantisym'( X, Y ) ), ~( 'c_Relation_Otrans'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21163, [ =( 'c_Relation_OImage'( X,
% 2.74/3.13 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 2.74/3.13 'tc_bool' ) ), T, U ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 2.74/3.13 'tc_fun'( U, 'tc_bool' ) ) ), ~( 'c_Relation_Osingle__valued'(
% 2.74/3.13 'c_Relation_Oconverse'( X, T, U ), U, T ) ) ] )
% 2.74/3.13 , clause( 21164, [ 'c_Relation_Oirrefl'( X, Y ), 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ),
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1'( X, Y ), Y, Y ), X,
% 2.74/3.13 'tc_prod'( Y, Y ) ) ] )
% 2.74/3.13 , clause( 21165, [ =( 'c_Relation_ORange'( 'v_r', 't_a', 't_b' ),
% 2.74/3.13 'c_Relation_ODomain'( 'c_Relation_Oconverse'( 'v_r', 't_a', 't_b' ),
% 2.74/3.13 't_b', 't_a' ) ) ] )
% 2.74/3.13 , clause( 21166, [ 'c_lessequals'( X, 'c_Relation_Orel__comp'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), X, Y, Y, Y ), 'tc_fun'( 'tc_prod'( Y,
% 2.74/3.13 Y ), 'tc_bool' ) ), ~( 'c_Relation_Orefl__on'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21167, [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Relation_OId'( Y ),
% 2.74/3.13 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 2.74/3.13 Y, Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21168, [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Y, Y ), 'tc_bool' ) ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21169, [ =( 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21170, [ =( 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 2.74/3.13 'c_Lattices_Oupper__semilattice__class_Osup'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), 'c_Relation_OId'( Y ), 'tc_fun'(
% 2.74/3.13 'tc_prod'( Y, Y ), 'tc_bool' ) ) ) ] )
% 2.74/3.13 , clause( 21171, [ =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'( W
% 2.74/3.13 , Y, Z, T, U ) ), 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_List_Osko__Recdef__Xcuts__eq__1__1'( X, W, Y, Z, T, U ), Z, T, T ), Y
% 2.74/3.13 , 'tc_prod'( T, T ) ) ] )
% 2.74/3.13 , clause( 21172, [ =( X, 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ),
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'( Y, X, Z ), Z, Z ) ), ~(
% 2.74/3.13 'c_in'( X, 'c_Relation_OId__on'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21173, [ 'c_in'( 'c_ATP__Linkup_Osko__Relation__XId__onE__1__1'(
% 2.74/3.13 X, Y, Z ), X, Z ), ~( 'c_in'( Y, 'c_Relation_OId__on'( X, Z ), 'tc_prod'(
% 2.74/3.13 Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21174, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1'( X, Y ),
% 2.74/3.13 'c_Wellfounded_Oacc'( X, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21175, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1'( X, Y ),
% 2.74/3.13 'c_Wellfounded_Oacc'( X, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21176, [ =( X, 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ),
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XIdE__1__1'( X, Y ), Y, Y ) ), ~( 'c_in'(
% 2.74/3.13 X, 'c_Relation_OId'( Y ), 'tc_prod'( Y, Y ) ) ) ] )
% 2.74/3.13 , clause( 21177, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( X, Y, Z, T, U, W,
% 2.74/3.13 V0 ), Y, V0, W ), T, 'tc_prod'( V0, W ) ), ~( 'c_in'( 'c_Pair'( X, Y, U,
% 2.74/3.13 W ), 'c_Relation_Orel__comp'( Z, T, U, V0, W ), 'tc_prod'( U, W ) ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21178, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1'( X, Y, Z, T, U, W,
% 2.74/3.13 V0 ), U, V0 ), Z, 'tc_prod'( U, V0 ) ), ~( 'c_in'( 'c_Pair'( X, Y, U, W )
% 2.74/3.13 , 'c_Relation_Orel__comp'( Z, T, U, V0, W ), 'tc_prod'( U, W ) ) ) ] )
% 2.74/3.13 , clause( 21179, [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y )
% 2.74/3.13 ) ), 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'( Z,
% 2.74/3.13 Y ), 'c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1'(
% 2.74/3.13 Z, Y ), Y, Y ), 'c_Transitive__Closure_Otrancl'( Z, Y ), 'tc_prod'( Y, Y
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21180, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( X, Y
% 2.74/3.13 , Z, T ), Z, T, T ), 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'(
% 2.74/3.13 T, T ) ), 'c_in'( 'c_Pair'( Y, Z, T, T ), X, 'tc_prod'( T, T ) ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( Y, Z, T, T ), 'c_Transitive__Closure_Otrancl'( X, T ),
% 2.74/3.13 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21181, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1'( Y, X, Z, T ),
% 2.74/3.13 T, T ), Y, 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( X, Z, T, T ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21182, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), 't_a', 't_a'
% 2.74/3.13 ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a'
% 2.74/3.13 ) ), 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ), Z, 'tc_prod'( 't_a', 't_a'
% 2.74/3.13 ) ), ~( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21183, [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( Z, Y ), 'tc_prod'( Y, Y ) ) ), ~(
% 2.74/3.13 'c_Wellfounded_Oacyclic'( Z, Y ) ) ] )
% 2.74/3.13 , clause( 21184, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( X, Y, Z, T ),
% 2.74/3.13 Y, T, T ), Z, 'tc_prod'( T, T ) ), 'c_in'( 'c_Pair'( X, Y, T, T ), Z,
% 2.74/3.13 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( X, Y, T, T ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21185, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1'( X, Y, Z, T ),
% 2.74/3.13 T, T ), 'c_Transitive__Closure_Otrancl'( Z, T ), 'tc_prod'( T, T ) ),
% 2.74/3.13 'c_in'( 'c_Pair'( X, Y, T, T ), Z, 'tc_prod'( T, T ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, Y, T, T ), 'c_Transitive__Closure_Otrancl'( Z, T ),
% 2.74/3.13 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21186, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1'( X, Y, Z, T )
% 2.74/3.13 , Z, T, T ), X, 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21187, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1'( Y, X
% 2.74/3.13 , Z, T ), T, T ), Y, 'tc_prod'( T, T ) ), 'c_in'( 'c_Pair'( X, Z, T, T )
% 2.74/3.13 , Y, 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( X, Z, T, T ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( Y, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21188, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'v_sko__Transitive__Closure__Xtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 2.74/3.13 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ), 'c_in'( 'c_Pair'( X, Y, 't_a',
% 2.74/3.13 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ), ~( 'c_in'( 'c_Pair'( X, Y, 't_a'
% 2.74/3.13 , 't_a' ), 'c_Transitive__Closure_Otrancl'( Z, 't_a' ), 'tc_prod'( 't_a'
% 2.74/3.13 , 't_a' ) ) ) ] )
% 2.74/3.13 , clause( 21189, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1'(
% 2.74/3.13 X, T, U ), U, U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21190, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1'( X, T, U )
% 2.74/3.13 , U, U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ] )
% 2.74/3.13 , clause( 21191, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'c_List_Osko__Recdef__Xtfl__wf__induct__1__1'( X, T, U ), U
% 2.74/3.13 , U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ] )
% 2.74/3.13 , clause( 21192, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1'( X, T,
% 2.74/3.13 U ), U, U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_Wellfounded_Owf'( T, U ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21193, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( X, Y, Z, T )
% 2.74/3.13 , Y, T, T ), Z, 'tc_prod'( T, T ) ), =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y
% 2.74/3.13 , T, T ), 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21194, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( X,
% 2.74/3.13 Y, Z, T ), Z, T, T ), 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'(
% 2.74/3.13 T, T ) ), =( Y, Z ), ~( 'c_in'( 'c_Pair'( Y, Z, T, T ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21195, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1'( Y,
% 2.74/3.13 X, Z, T ), T, T ), Y, 'tc_prod'( T, T ) ), =( X, Z ), ~( 'c_in'( 'c_Pair'(
% 2.74/3.13 X, Z, T, T ), 'c_Transitive__Closure_Ortrancl'( Y, T ), 'tc_prod'( T, T )
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21196, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 2.74/3.13 X, Z, T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Y, Z,
% 2.74/3.13 U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21197, [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2'(
% 2.74/3.13 X, Z, T, U ), Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ),
% 2.74/3.13 'tc_prod'( U, U ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Y,
% 2.74/3.13 Z, U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21198, [ hBOOL( hAPP( X, Y ) ), 'c_in'( 'c_Pair'( Z,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 2.74/3.13 T, U ), U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U
% 2.74/3.13 ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Z, Y, U, U ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ] )
% 2.74/3.13 , clause( 21199, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2'( X, Z,
% 2.74/3.13 T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Z, Y, U, U
% 2.74/3.13 ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ] )
% 2.74/3.13 , clause( 21200, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), 't_a',
% 2.74/3.13 't_a' ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ), 'tc_prod'( 't_a',
% 2.74/3.13 't_a' ) ), =( Y, X ), ~( 'c_in'( 'c_Pair'( X, Y, 't_a', 't_a' ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ), 'tc_prod'( 't_a', 't_a' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21201, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1'( X, Z,
% 2.74/3.13 T, U ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Z, Y, U, U )
% 2.74/3.13 , 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) ) ] )
% 2.74/3.13 , clause( 21202, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'v_sko__Transitive__Closure__Xrtrancl__Xcases__1'( X, Y, Z ), Y, 't_a',
% 2.74/3.13 't_a' ), Z, 'tc_prod'( 't_a', 't_a' ) ), =( Y, X ), ~( 'c_in'( 'c_Pair'(
% 2.74/3.13 X, Y, 't_a', 't_a' ), 'c_Transitive__Closure_Ortrancl'( Z, 't_a' ),
% 2.74/3.13 'tc_prod'( 't_a', 't_a' ) ) ) ] )
% 2.74/3.13 , clause( 21203, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1'(
% 2.74/3.13 X, Z, T, U ) ) ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( 'c_in'( 'c_Pair'( Y, Z
% 2.74/3.13 , U, U ), 'c_Transitive__Closure_Ortrancl'( T, U ), 'tc_prod'( U, U ) ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21204, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1'( X, Y, Z, T )
% 2.74/3.13 , T, T ), 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ),
% 2.74/3.13 =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, T, T ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( Z, T ), 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21205, [ 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1'( X, Y, Z, T, U ), X, T
% 2.74/3.13 ), ~( 'c_in'( Z, 'c_Product__Type_OSigma'( X, Y, T, U ), 'tc_prod'( T, U
% 2.74/3.13 ) ) ) ] )
% 2.74/3.13 , clause( 21206, [ 'c_Wellfounded_OwfP'( 'c_FunDef_Oin__rel'( X, Y, Y ), Y
% 2.74/3.13 ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21207, [ 'c_Relation_Oirrefl'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.74/3.13 'c_Relation_OId'( Y ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ), Y ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21208, [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), 'c_Transitive__Closure_Ortrancl'( X, Y
% 2.74/3.13 ), 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' ) ),
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_prod'( Y, Y ), 'tc_bool' )
% 2.74/3.13 ) ) ), ~( 'c_in'( 'c_Pair'( Z, Z, Y, Y ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), 'tc_prod'( Y, Y ) ) ) ] )
% 2.74/3.13 , clause( 21209, [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 2.74/3.13 ), 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ), ~( 'c_in'( T
% 2.74/3.13 , U, Z ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ) ] )
% 2.74/3.13 , clause( 21210, [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 2.74/3.13 ), ~( 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), 'c_in'( 'c_Pair'( Y, T,
% 2.74/3.13 Z, Z ), X, 'tc_prod'( Z, Z ) ), ~( 'c_in'( T, U, Z ) ), ~( 'c_in'( Y, U,
% 2.74/3.13 Z ) ) ] )
% 2.74/3.13 , clause( 21211, [ =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( Y, T, Z, Z ), X, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 2.74/3.13 T, U, Z ) ), ~( 'c_in'( Y, U, Z ) ), ~( 'c_Equiv__Relations_Oequiv'( U, X
% 2.74/3.13 , Z ) ) ] )
% 2.74/3.13 , clause( 21212, [ ~( =( 'c_Relation_OImage'( X, 'c_Set_Oinsert'( Y,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ),
% 2.74/3.13 'c_Relation_OImage'( X, 'c_Set_Oinsert'( T,
% 2.74/3.13 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z, Z ) )
% 2.74/3.13 ), ~( 'c_in'( T, U, Z ) ), ~( 'c_in'( Y, U, Z ) ), ~(
% 2.74/3.13 'c_Equiv__Relations_Oequiv'( U, X, Z ) ), 'c_in'( 'c_Pair'( Y, T, Z, Z )
% 2.74/3.13 , X, 'tc_prod'( Z, Z ) ) ] )
% 2.74/3.13 , clause( 21213, [ =( 'c_Set_Oimage'( 'c_snd'( X, Y ), Z, 'tc_prod'( X, Y )
% 2.74/3.13 , Y ), 'c_Relation_ORange'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21214, [ 'c_in'( X, Y, Z ), =( X, T ), ~( 'c_lessequals'( U,
% 2.74/3.13 'c_Product__Type_OSigma'( Y, 'c_COMBK'( Y, 'tc_fun'( Z, 'tc_bool' ), Z )
% 2.74/3.13 , Z, Z ), 'tc_fun'( 'tc_prod'( Z, Z ), 'tc_bool' ) ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( U, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21215, [ =( 'c_Set_Oimage'( 'c_fst'( X, Y ), Z, 'tc_prod'( X, Y )
% 2.74/3.13 , X ), 'c_Relation_ODomain'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21216, [ 'c_in'( X, 'c_Transitive__Closure_Ortrancl'( Y, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ), ~( 'c_in'( X, Y, 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21217, [ 'c_in'( X, 'c_Transitive__Closure_Otrancl'( Y, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ), ~( 'c_in'( X, Y, 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21218, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z
% 2.74/3.13 , Z ) ) ) ] )
% 2.74/3.13 , clause( 21219, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X
% 2.74/3.13 , U, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z )
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21220, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), =( X, Y ) ] )
% 2.74/3.13 , clause( 21221, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), =( X, Y ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 2.74/3.13 ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21222, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), =( X, Y ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z
% 2.74/3.13 ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21223, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( 'c_Relation_Oconverse'( T, Z, Z ), Z )
% 2.74/3.13 , 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21224, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Y, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21225, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), 'c_in'(
% 2.74/3.13 'c_Pair'( Y, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( U, X, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z )
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Osingle__valued'( T, Z, Z ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21226, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21227, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21228, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21229, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oconverse'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), Z, Z ), 'tc_prod'( Z, Z ) ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 'c_Relation_Oconverse'( T, Z, Z ), Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21230, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( 'c_Relation_Oconverse'( T, Z, Z ), Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Relation_Oconverse'( 'c_Transitive__Closure_Otrancl'( T, Z ), Z, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21231, [ =( hAPP( 'c_split'( X, Y, Z, T ), 'c_Pair'( U, W, Y, Z )
% 2.74/3.13 ), hAPP( hAPP( X, U ), W ) ) ] )
% 2.74/3.13 , clause( 21232, [ =( hAPP( 'c_split'( X, Y, Z, T ), 'c_Pair'( U, W, Y, Z )
% 2.74/3.13 ), hAPP( hAPP( X, U ), W ) ) ] )
% 2.74/3.13 , clause( 21233, [ hBOOL( hAPP( hAPP( hAPP( X, Y ), Z ), T ) ), ~( hBOOL(
% 2.74/3.13 hAPP( hAPP( 'c_split'( X, U, W, 'tc_fun'( V0, 'tc_bool' ) ), 'c_Pair'( Y
% 2.74/3.13 , Z, U, W ) ), T ) ) ) ] )
% 2.74/3.13 , clause( 21234, [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U )
% 2.74/3.13 , ~( 'c_in'( Y, Z, T ) ) ] )
% 2.74/3.13 , clause( 21235, [ 'c_in'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U )
% 2.74/3.13 , ~( 'c_in'( Y, Z, T ) ) ] )
% 2.74/3.13 , clause( 21236, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( hAPP( T, X ),
% 2.74/3.13 'c_Set_Oimage'( T, Y, Z, U ), U ) ] )
% 2.74/3.13 , clause( 21237, [ ~( 'c_in'( X, Y, Z ) ), 'c_in'( hAPP( T, X ),
% 2.74/3.13 'c_Set_Oimage'( T, Y, Z, U ), U ) ] )
% 2.74/3.13 , clause( 21238, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~(
% 2.74/3.13 'c_Wellfounded_Owf'( Y, Z ) ) ] )
% 2.74/3.13 , clause( 21239, [ 'c_Relation_Osingle__valued'( 'c_Relation_OId__on'( X, Y
% 2.74/3.13 ), Y, Y ) ] )
% 2.74/3.13 , clause( 21240, [ 'c_in'( 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( X
% 2.74/3.13 , Y, Z, T, U ), X, T ), ~( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T, U ),
% 2.74/3.13 U ) ) ] )
% 2.74/3.13 , clause( 21241, [ 'c_Relation_Osym'( 'c_Transitive__Closure_Otrancl'( X, Y
% 2.74/3.13 ), Y ), ~( 'c_Relation_Osym'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21242, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ) ) ) ),
% 2.74/3.13 ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z, T ), T ) ) ] )
% 2.74/3.13 , clause( 21243, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ), X ), ~(
% 2.74/3.13 'c_Relation_Otrans'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21244, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.13 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, Z ) ) ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Wellfounded_Oacc'( Z, 't_a' ), 't_a' ) ) ] )
% 2.74/3.13 , clause( 21245, [ hBOOL( hAPP( X, Y ) ), 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ),
% 2.74/3.13 'c_Wellfounded_Oacc'( Z, T ), T ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z
% 2.74/3.13 , T ), T ) ) ] )
% 2.74/3.13 , clause( 21246, [ 'c_Relation_Osym'( X, Y ), ~( 'c_Relation_Osym'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21247, [ 'c_Relation_Osym'( 'c_Relation_Oconverse'( X, Y, Y ), Y
% 2.74/3.13 ), ~( 'c_Relation_Osym'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21248, [ =( 'c_Relation_ODomain'( 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 X, Y ), Y, Y ), 'c_Relation_ODomain'( X, Y, Y ) ) ] )
% 2.74/3.13 , clause( 21249, [ 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( X, Y, Z, T, U ), X, T
% 2.74/3.13 ), ~( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T, U ), U ) ) ] )
% 2.74/3.13 , clause( 21250, [ ~( 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( X, Y, Z ),
% 2.74/3.13 'c_Wellfounded_Oacc'( X, Z ), Z ) ), 'c_in'( Y, 'c_Wellfounded_Oacc'( X,
% 2.74/3.13 Z ), Z ) ] )
% 2.74/3.13 , clause( 21251, [ 'c_Relation_Osym'( 'c_Relation_OId'( X ), X ) ] )
% 2.74/3.13 , clause( 21252, [ 'c_Relation_Otrans'( 'c_Relation_OId__on'( X, Y ), Y ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21253, [ =( 'c_Relation_Orel__comp'( 'c_Relation_OId'( X ), Y, X
% 2.74/3.13 , X, Z ), Y ) ] )
% 2.74/3.13 , clause( 21254, [ =( 'c_Relation_Orel__comp'( X, 'c_Relation_OId'( Y ), Z
% 2.74/3.13 , Y, Y ), X ) ] )
% 2.74/3.13 , clause( 21255, [ 'c_Relation_Oantisym'( 'c_Relation_OId__on'( X, Y ), Y )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21256, [ 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ), Y ), ~(
% 2.74/3.13 'c_Wellfounded_Owf'( 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21257, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'( X, Z, T ) )
% 2.74/3.13 ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z, T ), T ) ) ] )
% 2.74/3.13 , clause( 21258, [ 'c_Relation_Orefl__on'( X, Y, Z ), ~(
% 2.74/3.13 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ] )
% 2.74/3.13 , clause( 21259, [ 'c_Relation_Orefl__on'( X, 'c_Relation_Oconverse'( Y, Z
% 2.74/3.13 , Z ), Z ), ~( 'c_Relation_Orefl__on'( X, Y, Z ) ) ] )
% 2.74/3.13 , clause( 21260, [ 'c_Relation_Osym'( 'c_Transitive__Closure_Ortrancl'( X,
% 2.74/3.13 Y ), Y ), ~( 'c_Relation_Osym'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21261, [ 'c_Wellfounded_Owf'( 'c_Relation_Orel__comp'( X, X, Y, Y
% 2.74/3.13 , Y ), Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21262, [ 'c_Wellfounded_Owf'( X, Y ), ~( 'c_Wellfounded_Owf'(
% 2.74/3.13 'c_Relation_Orel__comp'( X, X, Y, Y, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21263, [ =( 'c_Relation_OImage'( 'c_Relation_OId'( X ), Y, X, X )
% 2.74/3.13 , Y ) ] )
% 2.74/3.13 , clause( 21264, [ 'c_Relation_Osingle__valued'( 'c_Relation_OId'( X ), X,
% 2.74/3.13 X ) ] )
% 2.74/3.13 , clause( 21265, [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y
% 2.74/3.13 , Y ), X ) ] )
% 2.74/3.13 , clause( 21266, [ =( 'c_Relation_Oconverse'( X, Y, Y ), X ), ~(
% 2.74/3.13 'c_Relation_Osym'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21267, [ ~( =( 'c_Relation_Oconverse'( X, Y, Y ), X ) ),
% 2.74/3.13 'c_Relation_Osym'( X, Y ) ] )
% 2.74/3.13 , clause( 21268, [ =( 'c_Relation_ORange'( 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 X, Y ), Y, Y ), 'c_Relation_ORange'( X, Y, Y ) ) ] )
% 2.74/3.13 , clause( 21269, [ 'c_Relation_Otrans'( 'c_Transitive__Closure_Otrancl'( X
% 2.74/3.13 , Y ), Y ) ] )
% 2.74/3.13 , clause( 21270, [ =( 'c_Relation_Oconverse'( 'c_Relation_Orel__comp'( X, Y
% 2.74/3.13 , Z, T, U ), Z, U ), 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( Y,
% 2.74/3.13 T, U ), 'c_Relation_Oconverse'( X, Z, T ), U, T, Z ) ) ] )
% 2.74/3.13 , clause( 21271, [ 'c_Relation_Osym'( 'c_Relation_OId__on'( X, Y ), Y ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21272, [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y )
% 2.74/3.13 , Y ) ] )
% 2.74/3.13 , clause( 21273, [ 'c_Wellfounded_Owf'( 'c_Relation_Oinv__image'( X, Y, Z,
% 2.74/3.13 T ), T ), ~( 'c_Wellfounded_Owf'( X, Z ) ) ] )
% 2.74/3.13 , clause( 21274, [ =( 'c_Relation_Orel__comp'( X,
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 2.74/3.13 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 2.74/3.13 Y, Y ) ) ] )
% 2.74/3.13 , clause( 21275, [ 'c_Relation_Osym'( 'c_Relation_Oinv__image'( X, Y, Z, T
% 2.74/3.13 ), T ), ~( 'c_Relation_Osym'( X, Z ) ) ] )
% 2.74/3.13 , clause( 21276, [ =( 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21277, [ 'c_Relation_Otrans'( 'c_Transitive__Closure_Ortrancl'( X
% 2.74/3.13 , Y ), Y ) ] )
% 2.74/3.13 , clause( 21278, [ 'c_Relation_Otrans'( X, Y ), ~( 'c_Relation_Otrans'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21279, [ 'c_Relation_Otrans'( 'c_Relation_Oconverse'( X, Y, Y ),
% 2.74/3.13 Y ), ~( 'c_Relation_Otrans'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21280, [ =( 'c_Relation_Oconverse'( 'c_Relation_OId'( X ), X, X )
% 2.74/3.13 , 'c_Relation_OId'( X ) ) ] )
% 2.74/3.13 , clause( 21281, [ 'c_Wellfounded_Owf'( 'c_Transitive__Closure_Otrancl'( X
% 2.74/3.13 , Y ), Y ), ~( 'c_Wellfounded_Owf'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21282, [ =( 'c_Relation_Orel__comp'( 'c_Relation_Orel__comp'( X,
% 2.74/3.13 Y, Z, T, U ), W, Z, U, V0 ), 'c_Relation_Orel__comp'( X,
% 2.74/3.13 'c_Relation_Orel__comp'( Y, W, T, U, V0 ), Z, T, V0 ) ) ] )
% 2.74/3.13 , clause( 21283, [ =( 'c_Relation_Oconverse'( 'c_Relation_Oinv__image'( X,
% 2.74/3.13 Y, Z, T ), T, T ), 'c_Relation_Oinv__image'( 'c_Relation_Oconverse'( X, Z
% 2.74/3.13 , Z ), Y, Z, T ) ) ] )
% 2.74/3.13 , clause( 21284, [ =( 'c_Transitive__Closure_Otrancl'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), Y ), 'c_Relation_Oconverse'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), Y, Y ) ) ] )
% 2.74/3.13 , clause( 21285, [ 'c_Relation_Otrans'( 'c_Relation_Oinv__image'( X, Y, Z,
% 2.74/3.13 T ), T ), ~( 'c_Relation_Otrans'( X, Z ) ) ] )
% 2.74/3.13 , clause( 21286, [ =( 'c_Relation_Oconverse'( 'c_Relation_OId__on'( X, Y )
% 2.74/3.13 , Y, Y ), 'c_Relation_OId__on'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21287, [ ~( =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X
% 2.74/3.13 , Y, Y ), X, Y, Y, Y ), X ) ), 'c_Equiv__Relations_Oequiv'(
% 2.74/3.13 'c_Relation_ODomain'( X, Y, Y ), X, Y ) ] )
% 2.74/3.13 , clause( 21288, [ 'c_Relation_Oantisym'( 'c_Relation_OId'( X ), X ) ] )
% 2.74/3.13 , clause( 21289, [ =( 'c_Relation_ORange'( 'c_Relation_Oconverse'( X, Y, Z
% 2.74/3.13 ), Z, Y ), 'c_Relation_ODomain'( X, Y, Z ) ) ] )
% 2.74/3.13 , clause( 21290, [ 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( X, Y, Z ), X,
% 2.74/3.13 Z ), ~( 'c_in'( T, X, Z ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ) ] )
% 2.74/3.13 , clause( 21291, [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y
% 2.74/3.13 , Y ), X ) ] )
% 2.74/3.13 , clause( 21292, [ 'c_Relation_Osingle__valued'( 'c_Relation_Orel__comp'( X
% 2.74/3.13 , Y, Z, T, U ), Z, U ), ~( 'c_Relation_Osingle__valued'( Y, T, U ) ), ~(
% 2.74/3.13 'c_Relation_Osingle__valued'( X, Z, T ) ) ] )
% 2.74/3.13 , clause( 21293, [ =( 'c_Relation_Oconverse'( 'c_Relation_Oconverse'( X, Y
% 2.74/3.13 , Z ), Z, Y ), X ) ] )
% 2.74/3.13 , clause( 21294, [ 'c_Relation_Otrans'( 'c_Relation_OId'( X ), X ) ] )
% 2.74/3.13 , clause( 21295, [ =( 'c_Relation_Orel__comp'( 'c_Relation_Oconverse'( X, Y
% 2.74/3.13 , Y ), X, Y, Y, Y ), X ), ~( 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21296, [ =( 'c_Relation_Orel__comp'(
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y, Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21297, [ 'c_Relation_Oantisym'( X, Y ), ~( 'c_Relation_Oantisym'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21298, [ 'c_Relation_Oantisym'( 'c_Relation_Oconverse'( X, Y, Y )
% 2.74/3.13 , Y ), ~( 'c_Relation_Oantisym'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21299, [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 2.74/3.13 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, Z ) ) ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Wellfounded_Oacc'( Z, 't_a' ), 't_a' ) ) ] )
% 2.74/3.13 , clause( 21300, [ 'c_Relation_Orefl__on'( X, Y, Z ), ~(
% 2.74/3.13 'c_Equiv__Relations_Oequiv'( X, Y, Z ) ) ] )
% 2.74/3.13 , clause( 21301, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Y ), Y ), 'c_Relation_Oconverse'(
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), Y, Y ) ) ] )
% 2.74/3.13 , clause( 21302, [ 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( X, Y, Z ), X, Z ),
% 2.74/3.13 ~( 'c_in'( T, X, Z ) ), ~( 'c_Wellfounded_Owf'( Y, Z ) ) ] )
% 2.74/3.13 , clause( 21303, [ 'c_Relation_Osym'( X, Y ), ~(
% 2.74/3.13 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21304, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Y, X, Z ),
% 2.74/3.13 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ] )
% 2.74/3.13 , clause( 21305, [ 'c_Equiv__Relations_Ocongruent'( X, hAPP( Y, Z ), T, U )
% 2.74/3.13 , ~( 'c_in'( Z, W, V0 ) ), ~( 'c_Equiv__Relations_Ocongruent2'( V1, X, Y
% 2.74/3.13 , V0, T, U ) ), ~( 'c_Equiv__Relations_Oequiv'( W, V1, V0 ) ) ] )
% 2.74/3.13 , clause( 21306, [ =( 'c_Relation_ODomain'( 'c_Relation_Oconverse'( X, Y, Z
% 2.74/3.13 ), Z, Y ), 'c_Relation_ORange'( X, Y, Z ) ) ] )
% 2.74/3.13 , clause( 21307, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 2.74/3.13 'c_Relation_Orel__comp'( 'c_Transitive__Closure_Ortrancl'( X, Y ), X, Y,
% 2.74/3.13 Y, Y ) ) ] )
% 2.74/3.13 , clause( 21308, [ =( 'c_Transitive__Closure_Otrancl'( X, Y ),
% 2.74/3.13 'c_Relation_Orel__comp'( X, 'c_Transitive__Closure_Ortrancl'( X, Y ), Y,
% 2.74/3.13 Y, Y ) ) ] )
% 2.74/3.13 , clause( 21309, [ =( 'c_Relation_ORange'( X, Y, Z ), 'c_Relation_ODomain'(
% 2.74/3.13 'c_Relation_Oconverse'( X, Y, Z ), Z, Y ) ) ] )
% 2.74/3.13 , clause( 21310, [ 'c_Relation_Ototal__on'( X, Y, Z ), ~(
% 2.74/3.13 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z, Z ), Z ) ) ] )
% 2.74/3.13 , clause( 21311, [ 'c_Relation_Ototal__on'( X, 'c_Relation_Oconverse'( Y, Z
% 2.74/3.13 , Z ), Z ), ~( 'c_Relation_Ototal__on'( X, Y, Z ) ) ] )
% 2.74/3.13 , clause( 21312, [ 'c_Relation_Otrans'( X, Y ), ~(
% 2.74/3.13 'c_Equiv__Relations_Oequiv'( Z, X, Y ) ) ] )
% 2.74/3.13 , clause( 21313, [ hBOOL( hAPP( X, Y ) ), 'c_in'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, Z, T ),
% 2.74/3.13 'c_Wellfounded_Oacc'( Z, T ), T ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( Z
% 2.74/3.13 , T ), T ) ) ] )
% 2.74/3.13 , clause( 21314, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( X, Y ), Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21315, [ =( 'c_Transitive__Closure_Ortrancl'(
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ), Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( X, Y ) ) ] )
% 2.74/3.13 , clause( 21316, [ 'c_Arrow__Order__Mirabelle_OIIA'( 'v_F' ) ] )
% 2.74/3.13 , clause( 21317, [ 'c_Arrow__Order__Mirabelle_Ounanimity'( 'v_F' ) ] )
% 2.74/3.13 , clause( 21318, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XImageE__1__1'( X, Y, Z, T, U ), Y, T, U )
% 2.74/3.13 , Z, 'tc_prod'( T, U ) ), ~( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T, U )
% 2.74/3.13 , U ) ) ] )
% 2.74/3.13 , clause( 21319, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1'( X, Y, Z ), Y, Z
% 2.74/3.13 , Z ), X, 'tc_prod'( Z, Z ) ), 'c_in'( Y, 'c_Wellfounded_Oacc'( X, Z ), Z
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21320, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1'(
% 2.74/3.13 X, T, U ), U, U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Wellfounded_Oacc'( T, U ), U ) ) ] )
% 2.74/3.13 , clause( 21321, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a'
% 2.74/3.13 ), T, 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'(
% 2.74/3.13 T, 't_a' ), 't_a' ) ) ] )
% 2.74/3.13 , clause( 21322, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1'( Y, T, Z ), Z, Z ), T
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( U, Y, Z ) ), ~( 'c_Wellfounded_Owf'(
% 2.74/3.13 T, Z ) ) ] )
% 2.74/3.13 , clause( 21323, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XRangeE__1__1'( X, Y, Z, T ), X, T, Z ), Y
% 2.74/3.13 , 'tc_prod'( T, Z ) ), ~( 'c_in'( X, 'c_Relation_ORange'( Y, T, Z ), Z )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21324, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), 'c_in'(
% 2.74/3.13 'c_Pair'( 'c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1'( Y, X, Z
% 2.74/3.13 ), X, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ] )
% 2.74/3.13 , clause( 21325, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'(
% 2.74/3.13 T, 'c_Wellfounded_Oacc'( Y, Z ), Z ) ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z )
% 2.74/3.13 , 'c_Transitive__Closure_Ortrancl'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21326, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, T, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( T, 'c_Wellfounded_Oacc'( Y, Z ), Z ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21327, [ hBOOL( hAPP( X, Y ) ), 'c_in'( Z, 'c_Wellfounded_Oacc'(
% 2.74/3.13 T, 't_a' ), 't_a' ), ~( 'c_in'( 'c_Pair'( Z,
% 2.74/3.13 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a', 't_a' ), T,
% 2.74/3.13 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( T,
% 2.74/3.13 't_a' ), 't_a' ) ) ] )
% 2.74/3.13 , clause( 21328, [ 'c_in'( X, 'c_Relation_ODomain'( Y, Z, Z ), Z ), 'c_in'(
% 2.74/3.13 'c_Pair'( X, X, Z, Z ), 'c_Transitive__Closure_Ortrancl'( Y, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ] )
% 2.74/3.13 , clause( 21329, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'v_sko__Wellfounded__Xacc__Xinducts__1'( X, T ), 't_a',
% 2.74/3.13 't_a' ), T, 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Wellfounded_Oacc'( T, 't_a' ), 't_a' ) ) ] )
% 2.74/3.13 , clause( 21330, [ 'c_in'( hAPP( hAPP( X, Y ), Z ), 'c_Set_Oimage'(
% 2.74/3.13 'c_split'( X, T, U, W ), V0, 'tc_prod'( T, U ), W ), W ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Y, Z, T, U ), V0, 'tc_prod'( T, U ) ) ) ] )
% 2.74/3.13 , clause( 21331, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XDomainE__1__1'( X, Y, Z, T ), Z, T ), Y,
% 2.74/3.13 'tc_prod'( Z, T ) ), ~( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21332, [ hBOOL( hAPP( X, Y ) ), 'c_in'( Z, 'c_Wellfounded_Oacc'(
% 2.74/3.13 T, 't_a' ), 't_a' ), ~( 'c_in'( 'c_Pair'( Z,
% 2.74/3.13 'v_sko__Wellfounded__Xacc__Xinduct__1'( X, T ), 't_a', 't_a' ), T,
% 2.74/3.13 'tc_prod'( 't_a', 't_a' ) ) ), ~( 'c_in'( Y, 'c_Wellfounded_Oacc'( T,
% 2.74/3.13 't_a' ), 't_a' ) ) ] )
% 2.74/3.13 , clause( 21333, [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Z, 'c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1'( X, T
% 2.74/3.13 , U ), U, U ), T, 'tc_prod'( U, U ) ) ), ~( 'c_in'( Y,
% 2.74/3.13 'c_Wellfounded_Oacc'( T, U ), U ) ) ] )
% 2.74/3.13 , clause( 21334, [ ~( 'c_in'( X, Y, Z ) ), ~( 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1'( Y, T, Z ), Z,
% 2.74/3.13 Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( U, Y, Z ) ), ~(
% 2.74/3.13 'c_Wellfounded_Owf'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21335, [ 'c_in'( 'c_Pair'( X,
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1'( X, Y, Z, T ), Z, T )
% 2.74/3.13 , Y, 'tc_prod'( Z, T ) ), ~( 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ),
% 2.74/3.13 Z ) ) ] )
% 2.74/3.13 , clause( 21336, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XImage__iff__1__1'( X, Y, Z, T, U ), Y, T
% 2.74/3.13 , U ), Z, 'tc_prod'( T, U ) ), ~( 'c_in'( Y, 'c_Relation_OImage'( Z, X, T
% 2.74/3.13 , U ), U ) ) ] )
% 2.74/3.13 , clause( 21337, [ =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ), 'c_in'(
% 2.74/3.13 X, 'c_Relation_ODomain'( T, Z, Z ), Z ) ] )
% 2.74/3.13 , clause( 21338, [ 'c_in'( 'c_Pair'(
% 2.74/3.13 'c_ATP__Linkup_Osko__Relation__XRange__iff__1__1'( X, Y, Z, T ), X, T, Z
% 2.74/3.13 ), Y, 'tc_prod'( T, Z ) ), ~( 'c_in'( X, 'c_Relation_ORange'( Y, T, Z )
% 2.74/3.13 , Z ) ) ] )
% 2.74/3.13 , clause( 21339, [ 'c_in'( X, hAPP( 'c_split'( Y, Z, T, 'tc_fun'( U,
% 2.74/3.13 'tc_bool' ) ), 'c_Pair'( W, V0, Z, T ) ), U ), ~( 'c_in'( X, hAPP( hAPP(
% 2.74/3.13 Y, W ), V0 ), U ) ) ] )
% 2.74/3.13 , clause( 21340, [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, T ), U ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( Z, U, W, W ), V0, 'tc_prod'( W, W ) ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( Y, T, V1, V1 ), V2, 'tc_prod'( V1, V1 ) ) ), ~(
% 2.74/3.13 'c_Equiv__Relations_Ocongruent2'( V2, V0, X, V1, W, V3 ) ) ] )
% 2.74/3.13 , clause( 21341, [ =( X, Y ), ~( 'c_in'( 'c_Pair'( Z, Y, T, U ), W,
% 2.74/3.13 'tc_prod'( T, U ) ) ), ~( 'c_in'( 'c_Pair'( Z, X, T, U ), W, 'tc_prod'( T
% 2.74/3.13 , U ) ) ), ~( 'c_Relation_Osingle__valued'( W, T, U ) ) ] )
% 2.74/3.13 , clause( 21342, [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X
% 2.74/3.13 , W ) ), ~( 'c_in'( 'c_Pair'( W, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21343, [ =( hAPP( 'c_Recdef_Ocut'( X, Y, Z, T, U ), W ), hAPP( X
% 2.74/3.13 , W ) ), ~( 'c_in'( 'c_Pair'( W, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21344, [ hBOOL( hAPP( hAPP( 'c_FunDef_Oin__rel'( X, Y, Z ), T ),
% 2.74/3.13 U ) ), ~( 'c_in'( 'c_Pair'( T, U, Y, Z ), X, 'tc_prod'( Y, Z ) ) ) ] )
% 2.74/3.13 , clause( 21345, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ),
% 2.74/3.13 ~( hBOOL( hAPP( hAPP( 'c_FunDef_Oin__rel'( U, Z, T ), X ), Y ) ) ) ] )
% 2.74/3.13 , clause( 21346, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Otrans'(
% 2.74/3.13 T, Z ) ) ] )
% 2.74/3.13 , clause( 21347, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Otrans'(
% 2.74/3.13 T, Z ) ) ] )
% 2.74/3.13 , clause( 21348, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Oconverse'(
% 2.74/3.13 U, T, Z ), 'tc_prod'( Z, T ) ), ~( 'c_in'( 'c_Pair'( Y, X, T, Z ), U,
% 2.74/3.13 'tc_prod'( T, Z ) ) ) ] )
% 2.74/3.13 , clause( 21349, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Oconverse'(
% 2.74/3.13 U, T, Z ), 'tc_prod'( Z, T ) ), ~( 'c_in'( 'c_Pair'( Y, X, T, Z ), U,
% 2.74/3.13 'tc_prod'( T, Z ) ) ) ] )
% 2.74/3.13 , clause( 21350, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), U, 'tc_prod'( Z, T ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( Y, X, T, Z ), 'c_Relation_Oconverse'( U, Z, T ),
% 2.74/3.13 'tc_prod'( T, Z ) ) ) ] )
% 2.74/3.13 , clause( 21351, [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y )
% 2.74/3.13 ) ), ~( 'c_Relation_Oirrefl'( Z, Y ) ) ] )
% 2.74/3.13 , clause( 21352, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X
% 2.74/3.13 , U, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21353, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z
% 2.74/3.13 , Z ) ) ) ] )
% 2.74/3.13 , clause( 21354, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X
% 2.74/3.13 , U, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z )
% 2.74/3.13 ) ) ] )
% 2.74/3.13 , clause( 21355, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ), T, 'tc_prod'( Z
% 2.74/3.13 , Z ) ) ) ] )
% 2.74/3.13 , clause( 21356, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21357, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Ortrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21358, [ 'c_in'( 'c_Pair'( X, X, Y, Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_prod'( Y, Y ) ) ] )
% 2.74/3.13 , clause( 21359, [ 'c_in'( 'c_Pair'( X, X, Y, Y ),
% 2.74/3.13 'c_Transitive__Closure_Ortrancl'( Z, Y ), 'tc_prod'( Y, Y ) ) ] )
% 2.74/3.13 , clause( 21360, [ ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z )
% 2.74/3.13 ) ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Wellfounded_Owf'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21361, [ =( X, Y ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T,
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z
% 2.74/3.13 , Z ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21362, [ =( X, Y ), ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T,
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z
% 2.74/3.13 , Z ) ) ), ~( 'c_Relation_Oantisym'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21363, [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~( 'c_in'( 'c_Pair'( Y
% 2.74/3.13 , Z, T, T ), U, 'tc_prod'( T, T ) ) ), ~( 'c_Equiv__Relations_Ocongruent'(
% 2.74/3.13 U, X, T, W ) ) ] )
% 2.74/3.13 , clause( 21364, [ =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Relation_OId__on'( T, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21365, [ ~( =( 'c_Recdef_Ocut'( X, Y, Z, T, U ), 'c_Recdef_Ocut'(
% 2.74/3.13 W, Y, Z, T, U ) ) ), =( hAPP( X, V0 ), hAPP( W, V0 ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( V0, Z, T, T ), Y, 'tc_prod'( T, T ) ) ) ] )
% 2.74/3.13 , clause( 21366, [ =( X, Y ), ~( 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Relation_OId'( Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21367, [ 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ),
% 2.74/3.13 ~( 'c_Nitpick_Orefl_H'( Z, Y ) ) ] )
% 2.74/3.13 , clause( 21368, [ ~( 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y )
% 2.74/3.13 ) ), ~( 'c_Wellfounded_Owf'( Z, Y ) ) ] )
% 2.74/3.13 , clause( 21369, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), 'c_Relation_Oinv__image'(
% 2.74/3.13 T, U, W, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'( 'c_Pair'( hAPP( U, X ),
% 2.74/3.13 hAPP( U, Y ), W, W ), T, 'tc_prod'( W, W ) ) ) ] )
% 2.74/3.13 , clause( 21370, [ 'c_in'( 'c_Pair'( hAPP( X, Y ), hAPP( X, Z ), T, T ), U
% 2.74/3.13 , 'tc_prod'( T, T ) ), ~( 'c_in'( 'c_Pair'( Y, Z, W, W ),
% 2.74/3.13 'c_Relation_Oinv__image'( U, X, T, W ), 'tc_prod'( W, W ) ) ) ] )
% 2.74/3.13 , clause( 21371, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Relation_Osym'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21372, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 ~( 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~(
% 2.74/3.13 'c_Relation_Osym'( T, Z ) ) ] )
% 2.74/3.13 , clause( 21373, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Relation_Orel__comp'(
% 2.74/3.13 U, W, Z, V0, T ), 'tc_prod'( Z, T ) ), ~( 'c_in'( 'c_Pair'( V1, Y, V0, T
% 2.74/3.13 ), W, 'tc_prod'( V0, T ) ) ), ~( 'c_in'( 'c_Pair'( X, V1, Z, V0 ), U,
% 2.74/3.13 'tc_prod'( Z, V0 ) ) ) ] )
% 2.74/3.13 , clause( 21374, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X
% 2.74/3.13 , U, Z, Z ), T, 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21375, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( U, Y, Z, Z ), 'c_Transitive__Closure_Otrancl'( T, Z ),
% 2.74/3.13 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( 'c_Pair'( X, U, Z, Z ),
% 2.74/3.13 'c_Transitive__Closure_Otrancl'( T, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21376, [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_prod'( Y, Y ) ) ] )
% 2.74/3.13 , clause( 21377, [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId'( Y ),
% 2.74/3.13 'tc_prod'( Y, Y ) ) ] )
% 2.74/3.13 , clause( 21378, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ), =( X, Y ), =( X, T ) ] )
% 2.74/3.13 , clause( 21379, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ), =( Y, T ), =( X, T ) ] )
% 2.74/3.13 , clause( 21380, [ ~( 'c_in'( 'c_Pair'( X, X,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Y ), X ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21381, [ ~( 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), X ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21382, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ), Z
% 2.74/3.13 , 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ), =( Y, T ), ~( 'c_in'( 'c_Pair'( X
% 2.74/3.13 , Y, 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt'
% 2.74/3.13 ), hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), T ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21383, [ =( X, Y ), =( Y, X ), 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), X ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21384, [ ~( 'c_in'( 'c_Pair'( X, X,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Y ), X ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21385, [ ~( 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), Y ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21386, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ), =( X, Y ), =( Y, T ) ] )
% 2.74/3.13 , clause( 21387, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), Z, 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ), =( X, T ), =( Y, T ) ] )
% 2.74/3.13 , clause( 21388, [ =( X, Y ), =( X, Y ), 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omktop', Z ), Y ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21389, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ), Z
% 2.74/3.13 , 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ), =( X, T ), ~( 'c_in'( 'c_Pair'( X
% 2.74/3.13 , Y, 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt'
% 2.74/3.13 ), hAPP( hAPP( 'c_Arrow__Order__Mirabelle_Omkbot', Z ), T ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21390, [ 'c_in'( 'c_Pair'( X, Y,
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 , =( X, Y ) ] )
% 2.74/3.13 , clause( 21391, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Product__Type_OSigma'(
% 2.74/3.13 U, W, Z, T ), 'tc_prod'( Z, T ) ), ~( 'c_in'( Y, hAPP( W, X ), T ) ), ~(
% 2.74/3.13 'c_in'( X, U, Z ) ) ] )
% 2.74/3.13 , clause( 21392, [ 'c_in'( 'c_Pair'( X, Y, Z, T ), 'c_Product__Type_OSigma'(
% 2.74/3.13 U, W, Z, T ), 'tc_prod'( Z, T ) ), ~( 'c_in'( Y, hAPP( W, X ), T ) ), ~(
% 2.74/3.13 'c_in'( X, U, Z ) ) ] )
% 2.74/3.13 , clause( 21393, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, T, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( T,
% 2.74/3.13 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ] )
% 2.74/3.13 , clause( 21394, [ 'c_in'( X, 'c_Wellfounded_Oacc'( Y, Z ), Z ), ~( 'c_in'(
% 2.74/3.13 'c_Pair'( X, T, Z, Z ), Y, 'tc_prod'( Z, Z ) ) ), ~( 'c_in'( T,
% 2.74/3.13 'c_Wellfounded_Oacc'( Y, Z ), Z ) ) ] )
% 2.74/3.13 , clause( 21395, [ 'c_in'( X, 'c_Relation_OImage'( Y, Z, T, U ), U ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( W, X, T, U ), Y, 'tc_prod'( T, U ) ) ), ~( 'c_in'( W, Z
% 2.74/3.13 , T ) ) ] )
% 2.74/3.13 , clause( 21396, [ 'c_in'( X, 'c_Relation_OImage'( Y, Z, T, U ), U ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( W, X, T, U ), Y, 'tc_prod'( T, U ) ) ), ~( 'c_in'( W, Z
% 2.74/3.13 , T ) ) ] )
% 2.74/3.13 , clause( 21397, [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z ),
% 2.74/3.13 'c_Relation_OId__on'( Y, Z ), 'tc_prod'( Z, Z ) ) ) ] )
% 2.74/3.13 , clause( 21398, [ 'c_in'( 'c_Pair'( X, X, Y, Y ), 'c_Relation_OId__on'( Z
% 2.74/3.13 , Y ), 'tc_prod'( Y, Y ) ), ~( 'c_in'( X, Z, Y ) ) ] )
% 2.74/3.13 , clause( 21399, [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( T, X, Z, Z ), U
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, U, Z ) ) ] )
% 2.74/3.13 , clause( 21400, [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z ), U
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ), ~( 'c_Equiv__Relations_Oequiv'( Y, U, Z ) ) ] )
% 2.74/3.13 , clause( 21401, [ 'c_in'( X, 'c_Relation_ORange'( Y, Z, T ), T ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( U, X, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ] )
% 2.74/3.13 , clause( 21402, [ 'c_in'( X, 'c_Relation_ORange'( Y, Z, T ), T ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( U, X, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ] )
% 2.74/3.13 , clause( 21403, [ 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( X, U, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ] )
% 2.74/3.13 , clause( 21404, [ 'c_in'( X, 'c_Relation_ODomain'( Y, Z, T ), Z ), ~(
% 2.74/3.13 'c_in'( 'c_Pair'( X, U, Z, T ), Y, 'tc_prod'( Z, T ) ) ) ] )
% 2.74/3.13 , clause( 21405, [ 'c_in'( X, hAPP( Y, Z ), T ), ~( 'c_in'( 'c_Pair'( Z, X
% 2.74/3.13 , U, T ), 'c_Product__Type_OSigma'( W, Y, U, T ), 'tc_prod'( U, T ) ) ) ]
% 2.74/3.13 )
% 2.74/3.13 , clause( 21406, [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, U ),
% 2.74/3.13 'c_Product__Type_OSigma'( Y, W, Z, U ), 'tc_prod'( Z, U ) ) ) ] )
% 2.74/3.13 , clause( 21407, [ 'c_in'( 'c_Pair'( X, Y, Z, Z ), T, 'tc_prod'( Z, Z ) ),
% 2.74/3.13 'c_in'( 'c_Pair'( Y, X, Z, Z ), T, 'tc_prod'( Z, Z ) ), =( Y, X ), ~(
% 2.74/3.13 'c_in'( X, U, Z ) ), ~( 'c_in'( Y, U, Z ) ), ~( 'c_Relation_Ototal__on'(
% 2.74/3.13 U, T, Z ) ) ] )
% 2.74/3.13 , clause( 21408, [ 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ),
% 2.74/3.13 ~( 'c_in'( X, T, Y ) ), ~( 'c_Relation_Orefl__on'( T, Z, Y ) ) ] )
% 2.74/3.13 , clause( 21409, [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( T, X, Z, Z ), U
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ) ] )
% 2.74/3.13 , clause( 21410, [ 'c_in'( X, Y, Z ), ~( 'c_in'( 'c_Pair'( X, T, Z, Z ), U
% 2.74/3.13 , 'tc_prod'( Z, Z ) ) ), ~( 'c_Relation_Orefl__on'( Y, U, Z ) ) ] )
% 2.74/3.13 , clause( 21411, [ 'c_in'( 'c_Pair'( X, X, Y, Y ), Z, 'tc_prod'( Y, Y ) ),
% 2.74/3.13 ~( 'c_in'( X, T, Y ) ), ~( 'c_Relation_Orefl__on'( T, Z, Y ) ) ] )
% 2.74/3.13 , clause( 21412, [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) )
% 2.74/3.13 , =( Y, W ) ] )
% 2.74/3.13 , clause( 21413, [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) )
% 2.74/3.13 , =( X, U ) ] )
% 2.74/3.13 , clause( 21414, [ 'c_in'( X, Y, Z ), ~( hBOOL( hAPP( Y, X ) ) ) ] )
% 2.74/3.13 , clause( 21415, [ hBOOL( hAPP( X, Y ) ), ~( 'c_in'( Y, X, Z ) ) ] )
% 2.74/3.13 , clause( 21416, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ), ~( 'c_in'( 'c_Pair'( 'v_c____',
% 2.74/3.13 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'(
% 2.74/3.13 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 2.74/3.13 ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21417, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 2.74/3.13 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 2.74/3.13 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 , ~( 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ] )
% 2.74/3.13 , clause( 21418, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 2.74/3.13 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 2.74/3.13 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21419, [ ~( 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ] )
% 2.74/3.13 , clause( 21420, [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) )
% 2.74/3.13 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 2.74/3.13 , clause( 21421, [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) )
% 2.74/3.13 , ~( 'class_Lattices_Olattice'( Y ) ) ] )
% 2.74/3.13 , clause( 21422, [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ),
% 2.74/3.13 ~( 'class_Lattices_Odistrib__lattice'( Y ) ) ] )
% 2.74/3.13 , clause( 21423, [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ),
% 2.74/3.13 ~( 'class_Lattices_Obounded__lattice'( Y ) ) ] )
% 2.74/3.13 , clause( 21424, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 2.74/3.13 'class_Orderings_Opreorder'( Y ) ) ] )
% 2.74/3.13 , clause( 21425, [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 2.74/3.13 'class_Lattices_Olattice'( Y ) ) ] )
% 2.74/3.13 , clause( 21426, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 2.74/3.13 'class_Orderings_Oorder'( Y ) ) ] )
% 2.74/3.13 , clause( 21427, [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~(
% 2.74/3.13 'class_Orderings_Obot'( Y ) ) ] )
% 2.74/3.13 , clause( 21428, [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~(
% 2.74/3.13 'class_HOL_Oord'( Y ) ) ] )
% 2.74/3.13 , clause( 21429, [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21430, [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21431, [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21432, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21433, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21434, [ 'class_Lattices_Olattice'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21435, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21436, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21437, [ 'class_HOL_Oord'( 'tc_nat' ) ] )
% 2.74/3.13 , clause( 21438, [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21439, [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21440, [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21441, [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21442, [ 'class_Orderings_Opreorder'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21443, [ 'class_Lattices_Olattice'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21444, [ 'class_Orderings_Oorder'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21445, [ 'class_Orderings_Obot'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21446, [ 'class_HOL_Oord'( 'tc_bool' ) ] )
% 2.74/3.13 , clause( 21447, [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ] )
% 2.74/3.13 , clause( 21448, [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y
% 2.74/3.13 ) ) ) ] )
% 2.74/3.13 ] ).
% 2.74/3.13
% 2.74/3.13
% 2.74/3.13
% 2.74/3.13 subsumption(
% 2.74/3.13 clause( 555, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ), ~( 'c_in'( 'c_Pair'( 'v_c____',
% 2.74/3.13 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'(
% 2.74/3.13 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 2.74/3.13 ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , clause( 21416, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ), ~( 'c_in'( 'c_Pair'( 'v_c____',
% 2.74/3.13 'v_d____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'(
% 2.74/3.13 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 2.74/3.13 ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ) ] )
% 2.74/3.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 ), ==>( 1, 1 )] )
% 2.74/3.13 ).
% 2.74/3.13
% 2.74/3.13
% 2.74/3.13 subsumption(
% 2.74/3.13 clause( 557, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 2.74/3.13 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 2.74/3.13 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ] )
% 2.74/3.13 , clause( 21418, [ 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 2.74/3.13 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 2.74/3.13 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omktop', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBS'(
% 2.74/3.13 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_fequal'( 'tc_nat' ), 'v_h____',
% 2.74/3.13 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_n____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 2.74/3.13 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_COMBC'(
% 2.74/3.13 'c_COMBC'( 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Oabove', 'v_P____',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_c____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ) ), 'v_e____', 'tc_Arrow__Order__Mirabelle_Oindi',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'c_COMBC'(
% 2.74/3.13 'c_COMBB'( 'c_Arrow__Order__Mirabelle_Omkbot', 'v_P____', 'tc_fun'(
% 2.74/3.13 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_e____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ),
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'tc_prod'(
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 2.74/3.13 ] )
% 2.74/3.13 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.74/3.13
% 2.74/3.13
% 2.74/3.13 subsumption(
% 2.74/3.13 clause( 558, [ ~( 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.13 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ] )
% 2.74/3.13 , clause( 21419, [ ~( 'c_in'( 'c_Pair'( 'v_c____', 'v_d____',
% 2.74/3.13 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 2.74/3.14 hAPP( 'v_F', 'v_P____' ), 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 2.74/3.14 'tc_Arrow__Order__Mirabelle_Oalt' ) ) ) ] )
% 2.74/3.14 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.74/3.14
% 2.74/3.14
% 2.74/3.14
% 2.74/3.14 ==> clause( 20770, [] )
% 2.74/3.14
% 2.74/3.14
% 2.74/3.14
% 2.74/3.14 !!! Internal Problem: OH, OH, COULD NOT DERIVE GOAL !!!
% 2.74/3.14
% 2.74/3.14 Bliksem ended
%------------------------------------------------------------------------------