%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV856-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:59:27 AM UTC 2026
% Result : Unsatisfiable 99.18s 16.89s
% Output : CNFRefutation 16.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 615
% Syntax : Number of formulae : 5548 (3711 unt; 0 typ; 0 def)
% Number of atoms : 27892 (10362 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 101818 (6299 ~;8048 |; 0 &;87471 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 81 usr; 8 con; 0-9 aty)
% Number of variables : 22752 ( 0 ^;22752 !; 0 ?;22752 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2,type,
c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1,type,
c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1,type,
c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2,type,
c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xequals0I__1__1,type,
c_ATP__Linkup_Osko__Set__Xequals0I__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1,type,
c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1: $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_Collect,type,
c_Collect: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(tp_c_Finite__Set_Ofold,type,
c_Finite__Set_Ofold: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofold__graph,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Finite__Set_Ofold__image,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Olinorder__class_OMax,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(tp_c_Finite__Set_Olinorder__class_OMin,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Ofcomp,type,
c_Fun_Ofcomp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Oid,type,
c_Fun_Oid: $i > $i ).
thf(tp_c_Fun_Oinj__on,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(tp_c_Fun_Ooverride__on,type,
c_Fun_Ooverride__on: $i > $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Ohoare__valids,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Otriple__valid,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(tp_c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(tp_c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(tp_c_Map_Orestrict__map,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(tp_c_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Option_Ooption_ONone,type,
c_Option_Ooption_ONone: $i > $i ).
thf(tp_c_OrderedGroup_Oab__semigroup__mult,type,
c_OrderedGroup_Oab__semigroup__mult: $i > $i > $o ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tp_c_Relation_OImage,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(tp_c_Relation_Ototal__on,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tp_c_Set_Ovimage,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Wellfounded_Omax__extp,type,
c_Wellfounded_Omax__extp: $i > $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Finite__Set_Ofinite_Ofinite,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(tp_class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
thf(tp_class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
thf(tp_class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(tp_class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tp_tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_Ga,type,
v_Ga: $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__valids__def__1,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__1: $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__valids__def__2,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__2: $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1,type,
v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1: $i > $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_xa,type,
v_xa: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
! [T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
thf(4,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(5,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(6,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(7,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(8,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(9,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(10,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(11,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(12,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(13,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(14,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(15,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(16,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(17,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(18,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(19,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(20,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(21,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(22,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(23,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(24,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(25,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(26,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(27,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(28,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ominus @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(29,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(30,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Otop @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(31,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(32,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(33,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(34,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(35,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(36,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(37,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(38,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(39,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(40,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(41,axiom,
! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(42,axiom,
! [T_a: $i,V_x: $i,V_S: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(43,axiom,
! [T_b: $i] :
( ~ ( class_Orderings_Obot @ T_b )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(44,axiom,
! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(45,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(46,axiom,
! [T_a: $i,V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(47,axiom,
! [T_a: $i,V_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(48,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(49,axiom,
! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(50,axiom,
! [V_n: $i,V_x: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_x @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_x ) @ V_ts ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ V_n @ V_ts ) ) @ V_ts ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_0) ).
thf(51,axiom,
! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(52,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_xa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(53,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(54,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xequals0I__1__1 @ V_A @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equals0I_0) ).
thf(55,axiom,
! [V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(56,axiom,
! [T_a: $i,V_A: $i,V_B: $i,T_b: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(57,axiom,
! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(58,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1 @ V_A @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_all__not__in__conv_0) ).
thf(59,axiom,
! [T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1 @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_1) ).
thf(60,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(61,axiom,
! [V_n: $i,V_nb: $i,V_ts: $i,V_G: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_nb @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_nb ) @ V_ts ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ V_G @ V_n ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_1) ).
thf(62,axiom,
! [V_G: $i,V_ts: $i,V_x: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ V_G @ V_ts ) @ V_x @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_x ) @ V_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_2) ).
thf(63,axiom,
! [V_n: $i,V_xa: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_xa @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_xa ) @ V_ts ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ V_n @ V_ts ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_1) ).
thf(64,axiom,
! [V_n: $i,V_na: $i,V_ts: $i,V_G: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_na @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_na ) @ V_ts ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ V_G @ V_n ) ) @ V_G ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_0) ).
thf(65,axiom,
! [V_n: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_t @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ V_t @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(66,axiom,
! [V_G: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
thf(67,axiom,
! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ V_f @ V_g @ t_a @ T_c @ T_b ) @ v_x )
= ( hAPP @ V_g @ ( hAPP @ V_f @ v_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
thf(68,axiom,
( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(69,axiom,
! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ t_a ) @ v_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ v_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(70,axiom,
! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ T_b ) @ v_x )
= ( c_Option_Ooption_ONone @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).
thf(71,axiom,
! [V_R: $i,V_S: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_R ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_S ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ V_R ) @ V_S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(72,axiom,
! [V_R: $i,V_S: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_R ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_S ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ V_R ) @ V_S ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).
thf(73,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ooverride__on @ V_f @ V_g @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= V_f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__emptyset_0) ).
thf(74,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(75,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(76,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(77,axiom,
! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(78,axiom,
! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(79,axiom,
! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(80,axiom,
! [V_f: $i,T_a: $i,T_b: $i] : ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(81,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(82,axiom,
! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(83,axiom,
! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(84,axiom,
! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(85,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(86,axiom,
! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(87,axiom,
! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(88,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(89,axiom,
! [V_x: $i,V_z: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( V_x = V_z )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(90,axiom,
! [T_a: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(91,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(92,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(93,axiom,
! [V_A: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(94,axiom,
! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(95,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(96,axiom,
! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(97,axiom,
! [T_a: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(98,axiom,
! [V_f: $i,T_a: $i,V_x: $i] :
~ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
thf(99,axiom,
! [V_R: $i,V_a1: $i] :
~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__extp_Ocases_2) ).
thf(100,axiom,
! [V_P: $i,T_a: $i,V_x: $i] :
( ( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(101,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(102,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(103,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(104,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(105,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(106,axiom,
! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(107,axiom,
! [V_f: $i,V_z: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofold @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= V_z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).
thf(108,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(109,axiom,
! [V_f: $i,V_g: $i,V_z: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofold__image @ V_f @ V_g @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= V_z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__image__empty_0) ).
thf(110,axiom,
! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(111,axiom,
! [T_a: $i,V_P: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(112,axiom,
! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(113,axiom,
! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(114,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(115,axiom,
! [T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(116,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(117,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(118,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(119,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(120,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ T_a ) )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(121,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(122,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ T_a ) )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(123,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(124,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ V_A @ V_B @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_1) ).
thf(125,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ V_A @ V_B @ T_a ) ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_2) ).
thf(126,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(127,axiom,
! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ V_A @ V_B @ T_b @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_1) ).
thf(128,axiom,
! [V_x: $i,V_xa: $i,T_b: $i,V_times: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_xa ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ononempty__iff_2) ).
thf(129,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ V_A @ T_a ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ V_A @ T_a ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_1) ).
thf(130,axiom,
! [T_aa: $i,V_a: $i,V_f: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_aa @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(131,axiom,
! [T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ V_A @ V_B @ T_b @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_1) ).
thf(132,axiom,
! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
thf(133,axiom,
! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_a )
= V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(134,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= V_A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(135,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(136,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(137,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(138,axiom,
! [T_a: $i,V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(139,axiom,
! [T_b: $i,V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(140,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(141,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(142,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(143,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(144,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(145,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_d: $i,T_c: $i,V_h: $i,T_b: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ V_f @ V_g @ T_a @ T_d @ T_c ) @ V_h @ T_a @ T_c @ T_b )
= ( c_Fun_Ofcomp @ V_f @ ( c_Fun_Ofcomp @ V_g @ V_h @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
thf(146,axiom,
! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(147,axiom,
! [T_a: $i,V_A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_A ) @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
thf(148,axiom,
! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(149,axiom,
! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(150,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(151,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(152,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(153,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(154,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(155,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(156,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(157,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( V_A = V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(158,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(159,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(160,axiom,
! [V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_b @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(161,axiom,
! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(162,axiom,
! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ T_a ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(163,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(164,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(165,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(166,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(167,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(168,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(169,axiom,
! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(170,axiom,
! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
thf(171,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(172,axiom,
! [V_times: $i,V_g: $i,V_z: $i,V_a: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ ( c_Set_Oinsert @ V_a @ V_A @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ V_times @ ( hAPP @ V_g @ V_a ) ) @ ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ V_A @ T_a @ T_b ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__image__insert_0) ).
thf(173,axiom,
! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(174,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(175,axiom,
! [V_A: $i,V_f: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(176,axiom,
! [T_b: $i,V_A: $i,V_B: $i,V_M: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_B @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(177,axiom,
! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(178,axiom,
! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(179,axiom,
! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(180,axiom,
! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(181,axiom,
! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(182,axiom,
! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(183,axiom,
! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(184,axiom,
! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(185,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_C @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(186,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(187,axiom,
! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(188,axiom,
! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(189,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(190,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(191,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(192,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(193,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(194,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(195,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(196,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(197,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(198,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(199,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(200,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(201,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(202,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(203,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(204,axiom,
! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(205,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(206,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(207,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(208,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(209,axiom,
! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ T_b ) ) @ V_f ) @ V_g ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_b ) @ ( hAPP @ V_f @ v_x ) ) @ ( hAPP @ V_g @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(210,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(211,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(212,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(213,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(214,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(215,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(216,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(217,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(218,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(219,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(220,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_B ) @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Sup__fold__sup_0) ).
thf(221,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(222,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(223,axiom,
! [T_a: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(224,axiom,
! [V_f: $i,V_g: $i,T_c: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_a @ T_b ) @ V_r @ T_b @ T_a )
= ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_r @ T_b @ T_c ) @ T_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(225,axiom,
! [T_a: $i,V_g: $i,T_b: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ T_a ) @ V_g @ T_a @ T_a @ T_b )
= V_g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
thf(226,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Fun_Ofcomp @ V_f @ ( c_Fun_Oid @ T_b ) @ T_a @ T_b @ T_b )
= V_f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
thf(227,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(228,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(229,axiom,
! [V_Inf: $i,V_A: $i,V_inf: $i,V_top: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ V_A )
= ( c_Finite__Set_Ofold @ V_inf @ V_top @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__fold__inf_0) ).
thf(230,axiom,
! [V_Sup: $i,V_A: $i,V_sup: $i,V_bot: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ V_A )
= ( c_Finite__Set_Ofold @ V_sup @ V_bot @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__fold__sup_0) ).
thf(231,axiom,
! [V_inf: $i,V_B: $i,V_Inf: $i,V_A: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ ( hAPP @ V_inf @ V_B ) @ ( hAPP @ V_Inf @ V_A ) )
= ( c_Finite__Set_Ofold @ V_inf @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Oinf__Inf__fold__inf_0) ).
thf(232,axiom,
! [V_sup: $i,V_B: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ ( hAPP @ V_sup @ V_B ) @ ( hAPP @ V_Sup @ V_A ) )
= ( c_Finite__Set_Ofold @ V_sup @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Osup__Sup__fold__sup_0) ).
thf(233,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(234,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(235,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(236,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(237,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(238,axiom,
! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(239,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(240,axiom,
! [T_aa: $i,V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(241,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(242,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(243,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(244,axiom,
! [V_less__eq: $i,V_x: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(245,axiom,
! [V_less__eq: $i,V_Inf: $i,V_A: $i,V_x: $i,T_a: $i,V_Sup: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(246,axiom,
! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(247,axiom,
! [T_b: $i,V_f: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(248,axiom,
! [T_b: $i,V_a: $i,V_f: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(249,axiom,
! [T_b: $i,V_a: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i,V_f: $i,V_B: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(251,axiom,
! [T_b: $i,V_b: $i,V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_b ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_b ) @ ( hAPP @ V_B @ V_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(252,axiom,
! [T_a: $i,V_b: $i,V_A: $i,V_B: $i,T_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(253,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(254,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(255,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(256,axiom,
! [V_P: $i,V_a: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(257,axiom,
! [T_a: $i,V_a: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(258,axiom,
! [T_a: $i,V_R: $i,V_S: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R )
!= ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) )
| ( V_R = V_S ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(259,axiom,
! [V_f: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(260,axiom,
! [V_f: $i,V_x: $i,V_xa: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_xa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(261,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(262,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( V_x = V_y )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(263,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(264,axiom,
! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(265,axiom,
! [T_a: $i,V_x: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(266,axiom,
! [T_a: $i,V_a: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(267,axiom,
! [T_a: $i,V_x: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(268,axiom,
! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(269,axiom,
! [V_f: $i,V_g: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ V_f @ V_g @ V_A @ T_a @ T_b ) @ V_a )
= ( hAPP @ V_f @ V_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__notin_0) ).
thf(270,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(271,axiom,
! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(272,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(273,axiom,
! [V_f: $i,V_g: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ V_f @ V_g @ V_A @ T_a @ T_b ) @ V_a )
= ( hAPP @ V_g @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_override__on__apply__in_0) ).
thf(274,axiom,
! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(275,axiom,
! [T_a: $i,V_a: $i,V_A: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(276,axiom,
! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_m @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__in_0) ).
thf(277,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(278,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(279,axiom,
! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(280,axiom,
! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(281,axiom,
! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(282,axiom,
! [T_a: $i,V_t: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(283,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(284,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(285,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(286,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(287,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(288,axiom,
! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(289,axiom,
! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(290,axiom,
! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(291,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(292,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(293,axiom,
! [V_a1: $i,V_R: $i,V_a2: $i] :
( ( c_Finite__Set_Ofinite @ V_a1 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ V_a2 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__extp_Ocases_0) ).
thf(294,axiom,
! [V_a2: $i,V_R: $i,V_a1: $i] :
( ( c_Finite__Set_Ofinite @ V_a2 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ V_a2 @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__extp_Ocases_1) ).
thf(295,axiom,
! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(296,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(297,axiom,
! [T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(298,axiom,
! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(299,axiom,
! [V_f: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(300,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(301,axiom,
! [V_f: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(302,axiom,
! [V_f: $i,V_A: $i,T_a: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(303,axiom,
! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(304,axiom,
! [V_B: $i,V_x: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(305,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(306,axiom,
! [V_f: $i,V_z: $i,V_A: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ V_A @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(307,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(308,axiom,
! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(309,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(310,axiom,
! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(311,axiom,
! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(312,axiom,
! [V_f: $i,V_z: $i,V_x: $i,V_A: $i,T_a: $i,V_y: $i,T_b: $i] :
( ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_y @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(313,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(314,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(315,axiom,
! [V_g: $i,V_f: $i,T_b: $i,T_c: $i,T_a: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ V_g @ V_f @ T_b @ T_c @ T_a ) @ V_A @ T_a @ T_c )
| ~ ( c_Fun_Oinj__on @ V_g @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b @ T_c )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
thf(316,axiom,
! [V_times: $i,V_a: $i,V_b: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofold__graph @ V_times @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x @ T_a @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_times @ V_b @ V_A @ V_x @ T_a @ T_a )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__permute__diff_0) ).
thf(317,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(318,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(319,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(320,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(321,axiom,
! [T_a: $i,V_Y: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ T_a ) @ V_Y @ T_a @ T_a )
= V_Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(322,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(323,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(324,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(325,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(326,axiom,
! [V_a: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_B @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a ) ) @ V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(327,axiom,
! [V_g: $i,V_f: $i,T_c: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ V_g @ V_f @ T_c @ T_b @ T_a ) @ V_x @ T_a @ T_b )
= ( c_Set_Ovimage @ V_f @ ( c_Set_Ovimage @ V_g @ V_x @ T_c @ T_b ) @ T_a @ T_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__compose_0) ).
thf(328,axiom,
! [T_a: $i,V_b: $i,V_A: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ V_A @ T_a @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__le__inf_0) ).
thf(329,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(330,axiom,
! [T_a: $i,V_A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ T_a ) @ V_A @ T_a @ T_a )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__id_0) ).
thf(331,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(332,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(333,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(334,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(335,axiom,
! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(336,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(337,axiom,
! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(338,axiom,
! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(339,axiom,
! [T_b: $i,V_A: $i,V_B: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ V_A @ v_x ) @ ( hAPP @ V_B @ v_x ) @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(340,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(341,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_z ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(342,axiom,
! [V_a: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(343,axiom,
! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(344,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Otop @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Otop__class_Otop @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(345,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(346,axiom,
! [V_C: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(347,axiom,
! [V_C: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(348,axiom,
! [T_a: $i,V_A: $i,V_B: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(349,axiom,
! [T_a: $i,V_A: $i,V_B: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(350,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(351,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(352,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(353,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(354,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(355,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(356,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(357,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(358,axiom,
! [V_f: $i,V_g: $i,T_b: $i,T_c: $i,T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ V_f @ V_g @ T_b @ T_c @ T_a ) @ V_x )
= ( hAPP @ V_g @ ( hAPP @ V_f @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
thf(359,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(360,axiom,
! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(361,axiom,
! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(362,axiom,
! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(363,axiom,
! [V_G: $i,V_ts: $i,T_a: $i,V_G_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
thf(364,axiom,
! [V_f: $i,V_x: $i,T_a: $i] : ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(365,axiom,
! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(366,axiom,
! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(367,axiom,
! [V_a: $i,V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ V_a @ V_A @ T_b ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ V_B @ V_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(368,axiom,
! [T_a: $i,V_N: $i,V_M: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ V_N @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_M @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_M @ V_N @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(369,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(370,axiom,
! [V_h: $i,V_F: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_h @ V_F @ T_a @ T_b ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(371,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(372,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(373,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(374,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(375,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(376,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(377,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(378,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(379,axiom,
! [T_b: $i,V_f: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(380,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(381,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(382,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(383,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(384,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(385,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(386,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(387,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(388,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(389,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(390,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(391,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(392,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(393,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(394,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(395,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ V_A @ T_a @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__sup__insert_0) ).
thf(396,axiom,
! [T_a: $i,V_R: $i,V_S: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R ) @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(397,axiom,
! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_lessequals @ V_R @ V_S @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R ) @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(398,axiom,
! [T_b: $i] :
( ~ ( class_Orderings_Otop @ T_b )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(399,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(400,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(401,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(402,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(403,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(404,axiom,
! [T_b: $i,V_f: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) )
| ( c_lessequals @ V_g @ V_f @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(405,axiom,
! [V_x: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(406,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(407,axiom,
! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(408,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(409,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(410,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(411,axiom,
! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(412,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( c_Orderings_Otop__class_Otop @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(413,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ T_a ) )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(414,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(415,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ V_A @ T_a @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__inf__insert_0) ).
thf(416,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(417,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(418,axiom,
! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(419,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(420,axiom,
! [T_a: $i,V_C: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(421,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(422,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(423,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Otop__class_Otop @ T_a ) )
| ( V_A
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(424,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Otop__class_Otop @ T_a ) )
| ( V_B
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(425,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b )
!= ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(426,axiom,
! [T_a: $i,V_A: $i,T_b: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(427,axiom,
! [T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(428,axiom,
! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_B @ T_a @ T_b )
= ( c_Map_Orestrict__map @ V_m @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__restrict_0) ).
thf(429,axiom,
! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(430,axiom,
! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(431,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(432,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(433,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(434,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(435,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(436,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(437,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(438,axiom,
! [V_B: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ V_A @ V_B @ T_b @ T_a ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_2) ).
thf(439,axiom,
! [V_f: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a )
= V_A )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(440,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(441,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(442,axiom,
! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ T_b ) @ V_c @ T_b @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ V_v ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(443,axiom,
! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(444,axiom,
! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(445,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(446,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(447,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(448,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(449,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(450,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(451,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(452,axiom,
! [T_b: $i,V_A: $i,V_M: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(453,axiom,
! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(454,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(455,axiom,
! [V_times: $i,V_z: $i,V_b: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_Finite__Set_Ofold__graph @ V_times @ V_z @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ ( hAPP @ ( hAPP @ V_times @ V_z ) @ V_y ) @ T_a @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_times @ V_b @ V_A @ V_y @ T_a @ T_a )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__graph__insert__swap_0) ).
thf(456,axiom,
! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(457,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(458,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(459,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(460,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(461,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(462,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(463,axiom,
! [V_Sup: $i,V_Inf: $i,V_less__eq: $i,T_a: $i,V_less: $i,V_sup: $i,V_inf: $i,V_top: $i,V_bot: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ V_Sup @ V_Inf @ ( c_COMBC @ V_less__eq @ T_a @ T_a @ tc_bool ) @ ( c_COMBC @ V_less @ T_a @ T_a @ tc_bool ) @ V_sup @ V_inf @ V_top @ V_bot @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(464,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(465,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(466,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(467,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(468,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(469,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(470,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(471,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(472,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(473,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(474,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(475,axiom,
! [V_A: $i,T_a: $i,V_B: $i] : ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(476,axiom,
! [V_B: $i,T_a: $i,V_A: $i] : ( c_lessequals @ V_B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(477,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(478,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(479,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(480,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(481,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(482,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(483,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(484,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(485,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(486,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(487,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(488,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(489,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(490,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(491,axiom,
! [T_a: $i,V_M: $i,V_N: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ V_M @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_N @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_M @ V_N @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(492,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(493,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(494,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__fold__sup_0) ).
thf(495,axiom,
! [T_a: $i,V_f: $i,V_x: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(496,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(497,axiom,
! [T_b: $i,V_g: $i,V_f: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ~ ( c_lessequals @ V_g @ V_f @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(498,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(499,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(500,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(501,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(502,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(503,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(504,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(505,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(506,axiom,
! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(507,axiom,
! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(508,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(509,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(510,axiom,
! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(511,axiom,
! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(512,axiom,
! [T_a: $i,V_A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ T_a ) @ V_A @ T_a @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(513,axiom,
! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(514,axiom,
! [V_R: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(515,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(516,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(517,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(518,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(519,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(520,axiom,
! [V_h: $i,V_F: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ V_h @ V_F @ T_b @ T_a ) @ T_b )
| ~ ( c_Fun_Oinj__on @ V_h @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
thf(521,axiom,
! [T_b: $i,V_g: $i,T_a: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ T_b ) @ V_g @ T_b @ T_b @ T_a )
= V_g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(522,axiom,
! [V_f: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Oid @ T_a ) @ T_a @ T_b @ T_a )
= V_f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(523,axiom,
! [V_P: $i,V_x: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(524,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_z ) @ V_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(525,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(526,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(527,axiom,
! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(528,axiom,
! [V_g: $i,V_f: $i,V_A: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_g @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_c ) @ T_c @ T_b )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ V_g @ V_f @ T_c @ T_b @ T_a ) @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
thf(529,axiom,
! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ T_b ) ) @ V_f ) @ V_g ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_b ) @ ( hAPP @ V_f @ v_x ) ) @ ( hAPP @ V_g @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(530,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(531,axiom,
! [V_A: $i,T_a: $i,V_f: $i,V_z: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
thf(532,axiom,
! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(533,axiom,
! [T_a: $i,V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(534,axiom,
! [V_B: $i,T_b: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(535,axiom,
! [V_f: $i,T_a: $i,V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_C @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(536,axiom,
! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(537,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(538,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(539,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_f: $i,T_b: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(540,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(541,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(542,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(543,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(544,axiom,
! [V_times: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_a ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__commute_0) ).
thf(545,axiom,
! [V_times: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ V_a ) @ ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ V_times @ V_b ) @ ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__left__commute_0) ).
thf(546,axiom,
! [V_times: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_times @ V_a ) @ ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Omult__ac_I1_J_0) ).
thf(547,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(548,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(549,axiom,
! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(550,axiom,
! [T_a: $i,V_a: $i,V_A: $i,T_b: $i,V_f: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(551,axiom,
! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(552,axiom,
! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(553,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ V_A @ V_B @ T_a )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ V_A @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_3) ).
thf(554,axiom,
! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_x )
= ( c_Option_Ooption_ONone @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_restrict__out_0) ).
thf(555,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(556,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(557,axiom,
! [V_R: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(558,axiom,
! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(559,axiom,
! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(560,axiom,
! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(561,axiom,
! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(562,axiom,
! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(563,axiom,
! [V_f: $i,T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(564,axiom,
! [V_f: $i,V_z: $i,V_A: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(565,axiom,
! [V_B: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ V_A @ V_B @ T_b @ T_a ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_2) ).
thf(566,axiom,
! [T_b: $i,V_A: $i,V_k: $i,V_I: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ ( hAPP @ V_A @ V_k ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_k ) @ V_I ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(567,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(568,axiom,
! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(569,axiom,
! [V_c: $i,T_b: $i,T_c: $i,V_f: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ V_c @ T_b @ T_c ) @ V_f @ T_c @ T_b @ t_a ) @ v_x )
= V_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(570,axiom,
! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(571,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i,T_b: $i,V_I: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_I ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(572,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ V_A @ T_a ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ V_A @ T_a ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_0) ).
thf(573,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b )
!= ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(574,axiom,
! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(575,axiom,
! [V_B: $i,V_x: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(576,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(577,axiom,
! [T_a: $i,V_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(578,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(579,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(580,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(581,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(582,axiom,
! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(583,axiom,
! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(584,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Otop__class_Otop @ T_a ) ) @ V_x )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(585,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ T_a ) )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(586,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(587,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(588,axiom,
! [V_a: $i,V_b: $i,V_f: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(589,axiom,
! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(590,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Ovimage @ V_f @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_a @ T_b )
= V_A )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(591,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(592,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(593,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(594,axiom,
! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(595,axiom,
! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(596,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(597,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ V_A @ T_a @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__le__fold__sup_0) ).
thf(598,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(599,axiom,
! [V_times: $i,V_g: $i,V_z: $i,V_h: $i,V_A: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ ( c_Set_Oimage @ V_h @ V_A @ T_b @ T_c ) @ T_a @ T_c )
= ( c_Finite__Set_Ofold__image @ V_times @ ( c_Fun_Ocomp @ V_g @ V_h @ T_c @ T_a @ T_b ) @ V_z @ V_A @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_h @ V_A @ T_b @ T_c )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult_Ofold__image__reindex_0) ).
thf(600,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(601,axiom,
! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(602,axiom,
! [V_Inf: $i,T_a: $i,V_bot: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
thf(603,axiom,
! [V_Sup: $i,T_a: $i,V_top: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
thf(604,axiom,
! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_a @ V_A @ V_x @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).
thf(605,axiom,
! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(606,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(607,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(608,axiom,
! [V_B: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(609,axiom,
! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(610,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(611,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(612,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(613,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[612]) ).
thf(614,negated_conjecture,
! [V_xb: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ V_xb @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_xb ) @ v_Ga ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(615,negated_conjecture,
~ ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ v_xa @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(616,negated_conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(617,plain,
$false = $false,
inference(unfold_def,[status(thm)],[613]) ).
thf(618,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(619,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(620,plain,
( ( ! [T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(621,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(622,plain,
( ( class_HOL_Ominus @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(623,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(624,plain,
( ( class_Orderings_Otop @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(625,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(626,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(627,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(628,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(629,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(630,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(631,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(632,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(633,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(634,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(635,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(636,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(637,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(638,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(639,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(640,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(641,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(642,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(643,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(644,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(645,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ominus @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(646,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(647,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Otop @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(648,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(649,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(650,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(651,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(652,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(653,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(654,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(655,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(656,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(657,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(658,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(659,plain,
( ( ! [T_a: $i,V_x: $i,V_S: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(660,plain,
( ( ! [T_b: $i] :
( ~ ( class_Orderings_Obot @ T_b )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(661,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(662,plain,
( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(663,plain,
( ( ! [T_a: $i,V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(664,plain,
( ( ! [T_a: $i,V_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(665,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(666,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(667,plain,
( ( ! [V_n: $i,V_x: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_x @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_x ) @ V_ts ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ V_n @ V_ts ) ) @ V_ts ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(668,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(669,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_xa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(670,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(671,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xequals0I__1__1 @ V_A @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(672,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(673,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,T_b: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(674,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(675,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1 @ V_A @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(676,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1 @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(677,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(678,plain,
( ( ! [V_n: $i,V_nb: $i,V_ts: $i,V_G: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_nb @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_nb ) @ V_ts ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ V_G @ V_n ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(679,plain,
( ( ! [V_G: $i,V_ts: $i,V_x: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ V_G @ V_ts ) @ V_x @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_x ) @ V_G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(680,plain,
( ( ! [V_n: $i,V_xa: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_xa @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_xa ) @ V_ts ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ V_n @ V_ts ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(681,plain,
( ( ! [V_n: $i,V_na: $i,V_ts: $i,V_G: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_na @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_na ) @ V_ts ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ V_G @ V_n ) ) @ V_G ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(682,plain,
( ( ! [V_n: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_t @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ V_t @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(683,plain,
( ( ! [V_G: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(684,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ V_f @ V_g @ t_a @ T_c @ T_b ) @ v_x )
= ( hAPP @ V_g @ ( hAPP @ V_f @ v_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(685,plain,
( ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(686,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ t_a ) @ v_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ v_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(687,plain,
( ( ! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ T_b ) @ v_x )
= ( c_Option_Ooption_ONone @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(688,plain,
( ( ! [V_R: $i,V_S: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_R ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_S ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ V_R ) @ V_S ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(689,plain,
( ( ! [V_R: $i,V_S: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_R ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_S ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ V_R ) @ V_S ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(690,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ooverride__on @ V_f @ V_g @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= V_f ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(691,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(692,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(693,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(694,plain,
( ( ! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(695,plain,
( ( ! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(696,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(697,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i] : ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(698,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(699,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(700,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(701,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(702,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(703,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(704,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(705,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(706,plain,
( ( ! [V_x: $i,V_z: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( V_x = V_z )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(707,plain,
( ( ! [T_a: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(708,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(709,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(710,plain,
( ( ! [V_A: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(711,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(712,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(713,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(714,plain,
( ( ! [T_a: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(715,plain,
( ( ! [V_f: $i,T_a: $i,V_x: $i] :
~ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(716,plain,
( ( ! [V_R: $i,V_a1: $i] :
~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(717,plain,
( ( ! [V_P: $i,T_a: $i,V_x: $i] :
( ( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(718,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(719,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(720,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(721,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(722,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(723,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(724,plain,
( ( ! [V_f: $i,V_z: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofold @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= V_z ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(725,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(726,plain,
( ( ! [V_f: $i,V_g: $i,V_z: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofold__image @ V_f @ V_g @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= V_z ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(727,plain,
( ( ! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(728,plain,
( ( ! [T_a: $i,V_P: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(729,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(730,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(731,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(732,plain,
( ( ! [T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(733,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(734,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(735,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(736,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(737,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ T_a ) )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(738,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(739,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ T_a ) )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(740,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(741,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ V_A @ V_B @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(742,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ V_A @ V_B @ T_a ) ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(743,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(744,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ V_A @ V_B @ T_b @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(745,plain,
( ( ! [V_x: $i,V_xa: $i,T_b: $i,V_times: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_xa ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(746,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ V_A @ T_a ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ V_A @ T_a ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(747,plain,
( ( ! [T_aa: $i,V_a: $i,V_f: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_aa @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(748,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ V_A @ V_B @ T_b @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(749,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(750,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_a )
= V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(751,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= V_A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(752,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(753,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(754,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(755,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(756,plain,
( ( ! [T_b: $i,V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(757,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(758,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(759,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(760,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(761,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(762,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_d: $i,T_c: $i,V_h: $i,T_b: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ V_f @ V_g @ T_a @ T_d @ T_c ) @ V_h @ T_a @ T_c @ T_b )
= ( c_Fun_Ofcomp @ V_f @ ( c_Fun_Ofcomp @ V_g @ V_h @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(763,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(764,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_A ) @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(765,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(766,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(767,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(768,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(769,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(770,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(771,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(772,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(773,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(774,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( V_A = V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(775,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(776,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(777,plain,
( ( ! [V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_b @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(778,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(779,plain,
( ( ! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ T_a ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(780,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(781,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(782,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(783,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(784,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(785,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(786,plain,
( ( ! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(787,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(788,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(789,plain,
( ( ! [V_times: $i,V_g: $i,V_z: $i,V_a: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ ( c_Set_Oinsert @ V_a @ V_A @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ V_times @ ( hAPP @ V_g @ V_a ) ) @ ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ V_A @ T_a @ T_b ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(790,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(791,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(792,plain,
( ( ! [V_A: $i,V_f: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(793,plain,
( ( ! [T_b: $i,V_A: $i,V_B: $i,V_M: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_B @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(794,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(795,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(796,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(797,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(798,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(799,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(800,plain,
( ( ! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(801,plain,
( ( ! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(802,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_C @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(803,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(804,plain,
( ( ! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(805,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(806,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(807,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(808,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(809,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(810,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(811,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(812,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(813,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(814,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(815,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(816,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(817,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(818,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(819,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(820,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(821,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(822,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(823,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(824,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(825,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(826,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ T_b ) ) @ V_f ) @ V_g ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_b ) @ ( hAPP @ V_f @ v_x ) ) @ ( hAPP @ V_g @ v_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(827,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(828,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(829,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(830,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(831,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(832,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(833,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(834,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(835,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(836,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(837,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_B ) @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(838,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(839,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(840,plain,
( ( ! [T_a: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(841,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_a @ T_b ) @ V_r @ T_b @ T_a )
= ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_r @ T_b @ T_c ) @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(842,plain,
( ( ! [T_a: $i,V_g: $i,T_b: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ T_a ) @ V_g @ T_a @ T_a @ T_b )
= V_g ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(843,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Fun_Ofcomp @ V_f @ ( c_Fun_Oid @ T_b ) @ T_a @ T_b @ T_b )
= V_f ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(844,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(845,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(846,plain,
( ( ! [V_Inf: $i,V_A: $i,V_inf: $i,V_top: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ V_A )
= ( c_Finite__Set_Ofold @ V_inf @ V_top @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(847,plain,
( ( ! [V_Sup: $i,V_A: $i,V_sup: $i,V_bot: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ V_A )
= ( c_Finite__Set_Ofold @ V_sup @ V_bot @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(848,plain,
( ( ! [V_inf: $i,V_B: $i,V_Inf: $i,V_A: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ ( hAPP @ V_inf @ V_B ) @ ( hAPP @ V_Inf @ V_A ) )
= ( c_Finite__Set_Ofold @ V_inf @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(849,plain,
( ( ! [V_sup: $i,V_B: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ ( hAPP @ V_sup @ V_B ) @ ( hAPP @ V_Sup @ V_A ) )
= ( c_Finite__Set_Ofold @ V_sup @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(850,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(851,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(852,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(853,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(854,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(855,plain,
( ( ! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(856,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(857,plain,
( ( ! [T_aa: $i,V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(858,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(859,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(860,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(861,plain,
( ( ! [V_less__eq: $i,V_x: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(862,plain,
( ( ! [V_less__eq: $i,V_Inf: $i,V_A: $i,V_x: $i,T_a: $i,V_Sup: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(863,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(864,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(865,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(866,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(867,plain,
( ( ! [T_a: $i,V_a: $i,V_f: $i,V_B: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(868,plain,
( ( ! [T_b: $i,V_b: $i,V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_b ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_b ) @ ( hAPP @ V_B @ V_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(869,plain,
( ( ! [T_a: $i,V_b: $i,V_A: $i,V_B: $i,T_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(870,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(871,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(872,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(873,plain,
( ( ! [V_P: $i,V_a: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(874,plain,
( ( ! [T_a: $i,V_a: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(875,plain,
( ( ! [T_a: $i,V_R: $i,V_S: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R )
!= ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) )
| ( V_R = V_S ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(876,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(877,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(878,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(879,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( V_x = V_y )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(880,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(881,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(882,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(883,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(884,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(885,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(886,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ V_f @ V_g @ V_A @ T_a @ T_b ) @ V_a )
= ( hAPP @ V_f @ V_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(887,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(888,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(889,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(890,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ V_f @ V_g @ V_A @ T_a @ T_b ) @ V_a )
= ( hAPP @ V_g @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(891,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(892,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(893,plain,
( ( ! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_m @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(894,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(895,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(896,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(897,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(898,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(899,plain,
( ( ! [T_a: $i,V_t: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(900,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(901,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(902,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(903,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(904,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(905,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(906,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(907,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(908,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(909,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(910,plain,
( ( ! [V_a1: $i,V_R: $i,V_a2: $i] :
( ( c_Finite__Set_Ofinite @ V_a1 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ V_a2 @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(911,plain,
( ( ! [V_a2: $i,V_R: $i,V_a1: $i] :
( ( c_Finite__Set_Ofinite @ V_a2 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ V_a2 @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(912,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(913,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(914,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(915,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(916,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(917,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(918,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(919,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(920,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(921,plain,
( ( ! [V_B: $i,V_x: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(922,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(923,plain,
( ( ! [V_f: $i,V_z: $i,V_A: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ V_A @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(924,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(925,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(926,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(927,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(928,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(929,plain,
( ( ! [V_f: $i,V_z: $i,V_x: $i,V_A: $i,T_a: $i,V_y: $i,T_b: $i] :
( ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_y @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(930,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(931,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(932,plain,
( ( ! [V_g: $i,V_f: $i,T_b: $i,T_c: $i,T_a: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ V_g @ V_f @ T_b @ T_c @ T_a ) @ V_A @ T_a @ T_c )
| ~ ( c_Fun_Oinj__on @ V_g @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b @ T_c )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(933,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofold__graph @ V_times @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x @ T_a @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_times @ V_b @ V_A @ V_x @ T_a @ T_a )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(934,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(935,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(936,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(937,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) @ V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(938,plain,
( ( ! [T_a: $i,V_Y: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ T_a ) @ V_Y @ T_a @ T_a )
= V_Y ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(939,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(940,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(941,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(942,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(943,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_B @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a ) ) @ V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(944,plain,
( ( ! [V_g: $i,V_f: $i,T_c: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ V_g @ V_f @ T_c @ T_b @ T_a ) @ V_x @ T_a @ T_b )
= ( c_Set_Ovimage @ V_f @ ( c_Set_Ovimage @ V_g @ V_x @ T_c @ T_b ) @ T_a @ T_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(945,plain,
( ( ! [T_a: $i,V_b: $i,V_A: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ V_A @ T_a @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(946,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(947,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ T_a ) @ V_A @ T_a @ T_a )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(948,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(949,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(950,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(951,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(952,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(953,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(954,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(955,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(956,plain,
( ( ! [T_b: $i,V_A: $i,V_B: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ V_A @ v_x ) @ ( hAPP @ V_B @ v_x ) @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(957,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(958,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_z ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(959,plain,
( ( ! [V_a: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(960,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(961,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Otop @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Otop__class_Otop @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(962,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(963,plain,
( ( ! [V_C: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(964,plain,
( ( ! [V_C: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(965,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(966,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(967,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(968,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(969,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(970,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(971,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(972,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(973,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(974,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(975,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_c: $i,T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ V_f @ V_g @ T_b @ T_c @ T_a ) @ V_x )
= ( hAPP @ V_g @ ( hAPP @ V_f @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(976,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(977,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(978,plain,
( ( ! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(979,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(980,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i,V_G_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(981,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i] : ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(982,plain,
( ( ! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(983,plain,
( ( ! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(984,plain,
( ( ! [V_a: $i,V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ V_a @ V_A @ T_b ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ V_B @ V_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(985,plain,
( ( ! [T_a: $i,V_N: $i,V_M: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ V_N @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_M @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_M @ V_N @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(986,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(987,plain,
( ( ! [V_h: $i,V_F: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_h @ V_F @ T_a @ T_b ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(988,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(989,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(990,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(991,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(992,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(993,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(994,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(995,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(996,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(997,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(998,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(999,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(1000,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1001,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(1003,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1004,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1005,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1007,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1008,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1009,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1010,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1011,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ V_A @ T_a @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1013,plain,
( ( ! [T_a: $i,V_R: $i,V_S: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R ) @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1014,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_lessequals @ V_R @ V_S @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R ) @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1015,plain,
( ( ! [T_b: $i] :
( ~ ( class_Orderings_Otop @ T_b )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1016,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1017,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1020,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1021,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) )
| ( c_lessequals @ V_g @ V_f @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1022,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(1026,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1027,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1028,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1029,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( c_Orderings_Otop__class_Otop @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1030,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ T_a ) )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1031,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1032,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ V_A @ T_a @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1033,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1034,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1035,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1036,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1037,plain,
( ( ! [T_a: $i,V_C: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1038,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1039,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1040,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Otop__class_Otop @ T_a ) )
| ( V_A
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1041,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Otop__class_Otop @ T_a ) )
| ( V_B
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1042,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b )
!= ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1043,plain,
( ( ! [T_a: $i,V_A: $i,T_b: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1044,plain,
( ( ! [T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1045,plain,
( ( ! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_B @ T_a @ T_b )
= ( c_Map_Orestrict__map @ V_m @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1046,plain,
( ( ! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1047,plain,
( ( ! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1049,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(1050,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(1051,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(1052,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1053,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1055,plain,
( ( ! [V_B: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ V_A @ V_B @ T_b @ T_a ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1056,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a )
= V_A )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1057,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1058,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1059,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ T_b ) @ V_c @ T_b @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1060,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1061,plain,
( ( ! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1062,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1063,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1064,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1065,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1066,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1067,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1068,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1069,plain,
( ( ! [T_b: $i,V_A: $i,V_M: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1071,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1072,plain,
( ( ! [V_times: $i,V_z: $i,V_b: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_Finite__Set_Ofold__graph @ V_times @ V_z @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ ( hAPP @ ( hAPP @ V_times @ V_z ) @ V_y ) @ T_a @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_times @ V_b @ V_A @ V_y @ T_a @ T_a )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1073,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1074,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1075,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1076,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1077,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1078,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1080,plain,
( ( ! [V_Sup: $i,V_Inf: $i,V_less__eq: $i,T_a: $i,V_less: $i,V_sup: $i,V_inf: $i,V_top: $i,V_bot: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ V_Sup @ V_Inf @ ( c_COMBC @ V_less__eq @ T_a @ T_a @ tc_bool ) @ ( c_COMBC @ V_less @ T_a @ T_a @ tc_bool ) @ V_sup @ V_inf @ V_top @ V_bot @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1081,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1082,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1085,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1086,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1087,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1088,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1089,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1090,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1091,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1092,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] : ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1093,plain,
( ( ! [V_B: $i,T_a: $i,V_A: $i] : ( c_lessequals @ V_B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1097,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1098,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1099,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1100,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1101,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1102,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1104,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1105,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1106,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1107,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1108,plain,
( ( ! [T_a: $i,V_M: $i,V_N: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ V_M @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_N @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_M @ V_N @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1110,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1111,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1113,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1114,plain,
( ( ! [T_b: $i,V_g: $i,V_f: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ~ ( c_lessequals @ V_g @ V_f @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1116,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1117,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1118,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1119,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1122,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1123,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1124,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1125,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1126,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1127,plain,
( ( ! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1128,plain,
( ( ! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ T_a ) @ V_A @ T_a @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1130,plain,
( ( ! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1131,plain,
( ( ! [V_R: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1133,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1134,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1137,plain,
( ( ! [V_h: $i,V_F: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ V_h @ V_F @ T_b @ T_a ) @ T_b )
| ~ ( c_Fun_Oinj__on @ V_h @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1138,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ T_b ) @ V_g @ T_b @ T_b @ T_a )
= V_g ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1139,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Oid @ T_a ) @ T_a @ T_b @ T_a )
= V_f ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1140,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_z ) @ V_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1142,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1144,plain,
( ( ! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1145,plain,
( ( ! [V_g: $i,V_f: $i,V_A: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_g @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_c ) @ T_c @ T_b )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ V_g @ V_f @ T_c @ T_b @ T_a ) @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1146,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ T_b ) ) @ V_f ) @ V_g ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_b ) @ ( hAPP @ V_f @ v_x ) ) @ ( hAPP @ V_g @ v_x ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1147,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1148,plain,
( ( ! [V_A: $i,T_a: $i,V_f: $i,V_z: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1149,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1150,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1151,plain,
( ( ! [V_B: $i,T_b: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1152,plain,
( ( ! [V_f: $i,T_a: $i,V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_C @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1153,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1154,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1155,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1156,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_f: $i,T_b: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1159,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1160,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1161,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_a ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1162,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ V_a ) @ ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ V_times @ V_b ) @ ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1163,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_times @ V_a ) @ ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1164,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1165,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1166,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1167,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i,T_b: $i,V_f: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1168,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1169,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1170,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ V_A @ V_B @ T_a )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ V_A @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1171,plain,
( ( ! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_x )
= ( c_Option_Ooption_ONone @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1172,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1174,plain,
( ( ! [V_R: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1175,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1176,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1177,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1178,plain,
( ( ! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1179,plain,
( ( ! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1180,plain,
( ( ! [V_f: $i,T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(1181,plain,
( ( ! [V_f: $i,V_z: $i,V_A: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1182,plain,
( ( ! [V_B: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ V_A @ V_B @ T_b @ T_a ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1183,plain,
( ( ! [T_b: $i,V_A: $i,V_k: $i,V_I: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ ( hAPP @ V_A @ V_k ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_k ) @ V_I ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1184,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1185,plain,
( ( ! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1186,plain,
( ( ! [V_c: $i,T_b: $i,T_c: $i,V_f: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ V_c @ T_b @ T_c ) @ V_f @ T_c @ T_b @ t_a ) @ v_x )
= V_c ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1187,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1188,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i,T_b: $i,V_I: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_I ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1189,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ V_A @ T_a ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ V_A @ T_a ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1190,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b )
!= ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1191,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1192,plain,
( ( ! [V_B: $i,V_x: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1193,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1195,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1196,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1197,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1198,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1199,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1200,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1201,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Otop__class_Otop @ T_a ) ) @ V_x )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1202,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ T_a ) )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1203,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1204,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1205,plain,
( ( ! [V_a: $i,V_b: $i,V_f: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1206,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1207,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Ovimage @ V_f @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_a @ T_b )
= V_A )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1208,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1209,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1210,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1211,plain,
( ( ! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1212,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1213,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1214,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ V_A @ T_a @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1215,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1216,plain,
( ( ! [V_times: $i,V_g: $i,V_z: $i,V_h: $i,V_A: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ ( c_Set_Oimage @ V_h @ V_A @ T_b @ T_c ) @ T_a @ T_c )
= ( c_Finite__Set_Ofold__image @ V_times @ ( c_Fun_Ocomp @ V_g @ V_h @ T_c @ T_a @ T_b ) @ V_z @ V_A @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_h @ V_A @ T_b @ T_c )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1217,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1218,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1219,plain,
( ( ! [V_Inf: $i,T_a: $i,V_bot: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1220,plain,
( ( ! [V_Sup: $i,T_a: $i,V_top: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1221,plain,
( ( ! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_a @ V_A @ V_x @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(1222,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(1223,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1224,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1225,plain,
( ( ! [V_B: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1226,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1227,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1228,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1229,plain,
( ( ! [V_xb: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ V_xb @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_xb ) @ v_Ga ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1230,plain,
( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ v_xa @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1231,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1232,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[617]) ).
thf(1233,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ v_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(1234,plain,
( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ v_xa @ t_a ) )
= $true ),
inference(copy,[status(thm)],[1230]) ).
thf(1235,plain,
( ( ! [V_xb: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ V_xb @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_xb ) @ v_Ga ) ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1236,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1228]) ).
thf(1237,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1238,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1226]) ).
thf(1239,plain,
( ( ! [V_B: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(1240,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(1241,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(1242,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1243,plain,
( ( ! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_a @ V_A @ V_x @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1244,plain,
( ( ! [V_Sup: $i,T_a: $i,V_top: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(1245,plain,
( ( ! [V_Inf: $i,T_a: $i,V_bot: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1219]) ).
thf(1246,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(1247,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1217]) ).
thf(1248,plain,
( ( ! [V_times: $i,V_g: $i,V_z: $i,V_h: $i,V_A: $i,T_b: $i,T_c: $i,T_a: $i] :
( ( ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ ( c_Set_Oimage @ V_h @ V_A @ T_b @ T_c ) @ T_a @ T_c )
= ( c_Finite__Set_Ofold__image @ V_times @ ( c_Fun_Ocomp @ V_g @ V_h @ T_c @ T_a @ T_b ) @ V_z @ V_A @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_h @ V_A @ T_b @ T_c )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1249,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1250,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ V_A @ T_a @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1251,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1252,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1253,plain,
( ( ! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1254,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1255,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1256,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1257,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Ovimage @ V_f @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_a @ T_b )
= V_A )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1258,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1259,plain,
( ( ! [V_a: $i,V_b: $i,V_f: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1260,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1261,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1262,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ T_a ) )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1263,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Otop__class_Otop @ T_a ) ) @ V_x )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1264,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(1265,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1266,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(1267,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1268,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1269,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1270,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1271,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1272,plain,
( ( ! [V_B: $i,V_x: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1273,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1274,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b )
!= ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1275,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ V_A @ T_a ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ V_A @ T_a ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1276,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i,T_b: $i,V_I: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_I ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1277,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1278,plain,
( ( ! [V_c: $i,T_b: $i,T_c: $i,V_f: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ V_c @ T_b @ T_c ) @ V_f @ T_c @ T_b @ t_a ) @ v_x )
= V_c ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1279,plain,
( ( ! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1185]) ).
thf(1280,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1184]) ).
thf(1281,plain,
( ( ! [T_b: $i,V_A: $i,V_k: $i,V_I: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ ( hAPP @ V_A @ V_k ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_k ) @ V_I ) ) ) )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(1282,plain,
( ( ! [V_B: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ V_A @ V_B @ T_b @ T_a ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(1283,plain,
( ( ! [V_f: $i,V_z: $i,V_A: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(1284,plain,
( ( ! [V_f: $i,T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(1285,plain,
( ( ! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(1286,plain,
( ( ! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1287,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(1288,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1289,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1290,plain,
( ( ! [V_R: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Relation_OImage @ V_R @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1291,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1292,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1293,plain,
( ( ! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_x )
= ( c_Option_Ooption_ONone @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1294,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ V_A @ V_B @ T_a )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ V_A @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1295,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1296,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1297,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i,T_b: $i,V_f: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1298,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(1299,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(1300,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1301,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_times @ V_a ) @ ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(1302,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ V_a ) @ ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ V_times @ V_b ) @ ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1303,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_times @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_times @ V_b ) @ V_a ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1304,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1305,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(1306,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1307,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(1308,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_f: $i,T_b: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1309,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1310,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1311,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(1312,plain,
( ( ! [V_f: $i,T_a: $i,V_A: $i,V_B: $i,T_b: $i,V_C: $i] :
( ( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_C @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(1313,plain,
( ( ! [V_B: $i,T_b: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(1314,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_B: $i,T_b: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(1315,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(1316,plain,
( ( ! [V_A: $i,T_a: $i,V_f: $i,V_z: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1317,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1318,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ T_b ) ) @ V_f ) @ V_g ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_b ) @ ( hAPP @ V_f @ v_x ) ) @ ( hAPP @ V_g @ v_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1319,plain,
( ( ! [V_g: $i,V_f: $i,V_A: $i,T_a: $i,T_c: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_g @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_c ) @ T_c @ T_b )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ V_g @ V_f @ T_c @ T_b @ T_a ) @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(1320,plain,
( ( ! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(1321,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(1322,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(1323,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_z ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(1324,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(1325,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Oid @ T_a ) @ T_a @ T_b @ T_a )
= V_f ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(1326,plain,
( ( ! [T_b: $i,V_g: $i,T_a: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ T_b ) @ V_g @ T_b @ T_b @ T_a )
= V_g ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(1327,plain,
( ( ! [V_h: $i,V_F: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ V_h @ V_F @ T_b @ T_a ) @ T_b )
| ~ ( c_Fun_Oinj__on @ V_h @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(1328,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(1329,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(1330,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1134]) ).
thf(1331,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(1332,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(1333,plain,
( ( ! [V_R: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Relation_OImage @ V_R @ V_A @ T_b @ T_a ) ) @ ( c_Relation_OImage @ V_R @ V_B @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(1334,plain,
( ( ! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(1335,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ T_a ) @ V_A @ T_a @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(1336,plain,
( ( ! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1128]) ).
thf(1337,plain,
( ( ! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(1338,plain,
( ( ! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(1339,plain,
( ( ! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(1340,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1341,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(1342,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(1343,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(1344,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(1345,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1119]) ).
thf(1346,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1118]) ).
thf(1347,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1117]) ).
thf(1348,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(1349,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(1350,plain,
( ( ! [T_b: $i,V_g: $i,V_f: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ~ ( c_lessequals @ V_g @ V_f @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1114]) ).
thf(1351,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(1352,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(1353,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1354,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(1355,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(1356,plain,
( ( ! [T_a: $i,V_M: $i,V_N: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ V_M @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_N @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_M @ V_N @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(1357,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(1358,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(1359,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(1360,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(1361,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(1362,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1363,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1101]) ).
thf(1364,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1365,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(1366,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1367,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1368,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(1369,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(1370,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(1371,plain,
( ( ! [V_B: $i,T_a: $i,V_A: $i] : ( c_lessequals @ V_B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(1372,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] : ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(1373,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(1374,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(1375,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(1376,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(1377,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(1378,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(1379,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1085]) ).
thf(1380,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(1381,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1382,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1383,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(1384,plain,
( ( ! [V_Sup: $i,V_Inf: $i,V_less__eq: $i,T_a: $i,V_less: $i,V_sup: $i,V_inf: $i,V_top: $i,V_bot: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ V_Sup @ V_Inf @ ( c_COMBC @ V_less__eq @ T_a @ T_a @ tc_bool ) @ ( c_COMBC @ V_less @ T_a @ T_a @ tc_bool ) @ V_sup @ V_inf @ V_top @ V_bot @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1385,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(1386,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_z ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(1387,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(1388,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(1389,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1075]) ).
thf(1390,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(1391,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(1392,plain,
( ( ! [V_times: $i,V_z: $i,V_b: $i,V_A: $i,T_a: $i,V_y: $i] :
( ( c_Finite__Set_Ofold__graph @ V_times @ V_z @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ ( hAPP @ ( hAPP @ V_times @ V_z ) @ V_y ) @ T_a @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_times @ V_b @ V_A @ V_y @ T_a @ T_a )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1072]) ).
thf(1393,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(1394,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(1395,plain,
( ( ! [T_b: $i,V_A: $i,V_M: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(1396,plain,
( ( ! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(1397,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1398,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1399,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1065]) ).
thf(1400,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1064]) ).
thf(1401,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1402,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(1403,plain,
( ( ! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(1404,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(1405,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ T_b ) @ V_c @ T_b @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(1406,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(1407,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(1408,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a )
= V_A )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(1409,plain,
( ( ! [V_B: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_B @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ V_A @ V_B @ T_b @ T_a ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(1410,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(1411,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(1412,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(1413,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) @ V_z )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1414,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ V_C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(1415,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(1416,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1417,plain,
( ( ! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(1418,plain,
( ( ! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(1419,plain,
( ( ! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_B @ T_a @ T_b )
= ( c_Map_Orestrict__map @ V_m @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(1420,plain,
( ( ! [T_a: $i,T_b: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[1044]) ).
thf(1421,plain,
( ( ! [T_a: $i,V_A: $i,T_b: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1043]) ).
thf(1422,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b )
!= ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(1423,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Otop__class_Otop @ T_a ) )
| ( V_B
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1424,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Otop__class_Otop @ T_a ) )
| ( V_A
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(1425,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(1426,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(1427,plain,
( ( ! [T_a: $i,V_C: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(1428,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(1429,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1430,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1431,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1432,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ V_A @ T_a @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1433,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1434,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ T_a ) )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1435,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( c_Orderings_Otop__class_Otop @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1436,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1437,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1438,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oimage @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(1439,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1440,plain,
( ( ! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1441,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1442,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1443,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) )
| ( c_lessequals @ V_g @ V_f @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1444,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1445,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1446,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1447,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1448,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1449,plain,
( ( ! [T_b: $i] :
( ~ ( class_Orderings_Otop @ T_b )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(1450,plain,
( ( ! [V_R: $i,V_S: $i,T_a: $i] :
( ( c_lessequals @ V_R @ V_S @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R ) @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(1451,plain,
( ( ! [T_a: $i,V_R: $i,V_S: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R ) @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_R @ V_S @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(1452,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_b @ V_A @ T_a @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1453,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(1454,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1455,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1456,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(1457,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(1458,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1459,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1460,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1461,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(1462,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1463,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1464,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1465,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1466,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1467,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(1468,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(1469,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(1470,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(1471,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1472,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(1473,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(1474,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(1475,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[989]) ).
thf(1476,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(1477,plain,
( ( ! [V_h: $i,V_F: $i,T_a: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_h @ V_F @ T_a @ T_b ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(1478,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(1479,plain,
( ( ! [T_a: $i,V_N: $i,V_M: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ V_N @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_M @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_M @ V_N @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(1480,plain,
( ( ! [V_a: $i,V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ V_a @ V_A @ T_b ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ V_B @ V_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(1481,plain,
( ( ! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(1482,plain,
( ( ! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1483,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i] : ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1484,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i,V_G_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(1485,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i,V_C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) @ V_C )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(1486,plain,
( ( ! [T_a: $i,V_A: $i,V_a: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) )
= ( c_Set_Oinsert @ V_a @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(1487,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(1488,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(1489,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_c: $i,T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ V_f @ V_g @ T_b @ T_c @ T_a ) @ V_x )
= ( hAPP @ V_g @ ( hAPP @ V_f @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(1490,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(1491,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(1492,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(1493,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(1494,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(1495,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1496,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1497,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(1498,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(1499,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(1500,plain,
( ( ! [V_C: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(1501,plain,
( ( ! [V_C: $i,T_a: $i,V_A: $i,V_B: $i] :
( ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1502,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(1503,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Otop @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Otop__class_Otop @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(1504,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(1505,plain,
( ( ! [V_a: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(1506,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_z ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(1507,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(1508,plain,
( ( ! [T_b: $i,V_A: $i,V_B: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ V_A @ v_x ) @ ( hAPP @ V_B @ v_x ) @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(1509,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(1510,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(1511,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1512,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1513,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(1514,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(1515,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1516,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1517,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ T_a ) @ V_A @ T_a @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1518,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1519,plain,
( ( ! [T_a: $i,V_b: $i,V_A: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_b @ V_A @ T_a @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1520,plain,
( ( ! [V_g: $i,V_f: $i,T_c: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ V_g @ V_f @ T_c @ T_b @ T_a ) @ V_x @ T_a @ T_b )
= ( c_Set_Ovimage @ V_f @ ( c_Set_Ovimage @ V_g @ V_x @ T_c @ T_b ) @ T_a @ T_c ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1521,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_B @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a ) ) @ V_B ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1522,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(1523,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1524,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1525,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(1526,plain,
( ( ! [T_a: $i,V_Y: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ T_a ) @ V_Y @ T_a @ T_a )
= V_Y ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1527,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) @ V_A ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(1528,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(1529,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1530,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(1531,plain,
( ( ! [V_times: $i,V_a: $i,V_b: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( c_Finite__Set_Ofold__graph @ V_times @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x @ T_a @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_times @ V_b @ V_A @ V_x @ T_a @ T_a )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(1532,plain,
( ( ! [V_g: $i,V_f: $i,T_b: $i,T_c: $i,T_a: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ V_g @ V_f @ T_b @ T_c @ T_a ) @ V_A @ T_a @ T_c )
| ~ ( c_Fun_Oinj__on @ V_g @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b @ T_c )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1533,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1534,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1535,plain,
( ( ! [V_f: $i,V_z: $i,V_x: $i,V_A: $i,T_a: $i,V_y: $i,T_b: $i] :
( ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_y @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1536,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(1537,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1538,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(1539,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(1540,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(1541,plain,
( ( ! [V_f: $i,V_z: $i,V_A: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ V_A @ ( hAPP @ ( hAPP @ V_f @ V_x ) @ V_y ) @ T_a @ T_b )
| ~ ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(1542,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(1543,plain,
( ( ! [V_B: $i,V_x: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(1544,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1545,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_a )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1546,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(1547,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(1548,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1549,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Otop__class_Otop @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1550,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Oid @ T_a ) @ V_x )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1551,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1552,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_lessequals @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1553,plain,
( ( ! [V_a2: $i,V_R: $i,V_a1: $i] :
( ( c_Finite__Set_Ofinite @ V_a2 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ V_a2 @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1554,plain,
( ( ! [V_a1: $i,V_R: $i,V_a2: $i] :
( ( c_Finite__Set_Ofinite @ V_a1 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ V_a2 @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1555,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(1556,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1557,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1558,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1559,plain,
( ( ! [T_a: $i,V_F: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_F ) @ V_G ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1560,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1561,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1562,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1563,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1564,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1565,plain,
( ( ! [T_a: $i,V_t: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(1566,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1567,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1568,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(1569,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1570,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1571,plain,
( ( ! [V_m: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ V_A @ T_a @ T_b ) @ V_x )
= ( hAPP @ V_m @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1572,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(1573,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(1574,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ V_f @ V_g @ V_A @ T_a @ T_b ) @ V_a )
= ( hAPP @ V_g @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1575,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1576,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1577,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1578,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ V_f @ V_g @ V_A @ T_a @ T_b ) @ V_a )
= ( hAPP @ V_f @ V_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1579,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1580,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(1581,plain,
( ( ! [T_a: $i,V_a: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1582,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(1583,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1584,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(1585,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( V_x = V_y )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(1586,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1587,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_xa ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1588,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1589,plain,
( ( ! [T_a: $i,V_R: $i,V_S: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_R )
!= ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_S ) )
| ( V_R = V_S ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1590,plain,
( ( ! [T_a: $i,V_a: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(1591,plain,
( ( ! [V_P: $i,V_a: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(1592,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1593,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1594,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_A @ T_a )
!= ( c_Set_Oinsert @ V_x @ V_B @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1595,plain,
( ( ! [T_a: $i,V_b: $i,V_A: $i,V_B: $i,T_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1596,plain,
( ( ! [T_b: $i,V_b: $i,V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_b ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_b ) @ ( hAPP @ V_B @ V_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_a: $i,V_f: $i,V_B: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1598,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1599,plain,
( ( ! [T_b: $i,V_a: $i,V_f: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1600,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(1601,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1602,plain,
( ( ! [V_less__eq: $i,V_Inf: $i,V_A: $i,V_x: $i,T_a: $i,V_Sup: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1603,plain,
( ( ! [V_less__eq: $i,V_x: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1604,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(1605,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1606,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1607,plain,
( ( ! [T_aa: $i,V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1608,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1609,plain,
( ( ! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) ) @ V_A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1610,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1611,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1612,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1613,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1614,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1615,plain,
( ( ! [V_sup: $i,V_B: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ ( hAPP @ V_sup @ V_B ) @ ( hAPP @ V_Sup @ V_A ) )
= ( c_Finite__Set_Ofold @ V_sup @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1616,plain,
( ( ! [V_inf: $i,V_B: $i,V_Inf: $i,V_A: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ ( hAPP @ V_inf @ V_B ) @ ( hAPP @ V_Inf @ V_A ) )
= ( c_Finite__Set_Ofold @ V_inf @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1617,plain,
( ( ! [V_Sup: $i,V_A: $i,V_sup: $i,V_bot: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ V_A )
= ( c_Finite__Set_Ofold @ V_sup @ V_bot @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1618,plain,
( ( ! [V_Inf: $i,V_A: $i,V_inf: $i,V_top: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ V_A )
= ( c_Finite__Set_Ofold @ V_inf @ V_top @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1619,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1620,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1621,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Fun_Ofcomp @ V_f @ ( c_Fun_Oid @ T_b ) @ T_a @ T_b @ T_b )
= V_f ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1622,plain,
( ( ! [T_a: $i,V_g: $i,T_b: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ T_a ) @ V_g @ T_a @ T_a @ T_b )
= V_g ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1623,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_a @ T_b ) @ V_r @ T_b @ T_a )
= ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_r @ T_b @ T_c ) @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1624,plain,
( ( ! [T_a: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1625,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1626,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(1627,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_B ) @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_B @ V_A @ T_a @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1628,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1629,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1630,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1631,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ V_y ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1632,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1633,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1634,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(1635,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_a ) @ V_b ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(1636,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1637,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1638,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ T_b ) ) @ V_f ) @ V_g ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_b ) @ ( hAPP @ V_f @ v_x ) ) @ ( hAPP @ V_g @ v_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1639,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1640,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1641,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1642,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1643,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1644,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1645,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1646,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(1647,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1648,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1649,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1650,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1651,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1652,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1653,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1654,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1655,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1656,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1657,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1658,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1659,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1660,plain,
( ( ! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(1661,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1662,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_C: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_C @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1663,plain,
( ( ! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1664,plain,
( ( ! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1665,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Collect @ V_P @ T_a ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1666,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1667,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1668,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1669,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_a @ T_b ) ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1670,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1671,plain,
( ( ! [T_b: $i,V_A: $i,V_B: $i,V_M: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_B @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1672,plain,
( ( ! [V_A: $i,V_f: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1673,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1674,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1675,plain,
( ( ! [V_times: $i,V_g: $i,V_z: $i,V_a: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ ( c_Set_Oinsert @ V_a @ V_A @ T_b ) @ T_a @ T_b )
= ( hAPP @ ( hAPP @ V_times @ ( hAPP @ V_g @ V_a ) ) @ ( c_Finite__Set_Ofold__image @ V_times @ V_g @ V_z @ V_A @ T_a @ T_b ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1676,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1677,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1678,plain,
( ( ! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1679,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1680,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1681,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1682,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(1683,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1684,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1685,plain,
( ( ! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ T_a ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1686,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1687,plain,
( ( ! [V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_b @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1688,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(1689,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1690,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( V_A = V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1691,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1692,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1693,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1694,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1695,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1696,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1697,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1698,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1699,plain,
( ( ! [V_f: $i,T_b: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_b @ tc_bool ) ) @ V_A ) @ V_B ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1700,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ T_a ) @ T_a @ ( tc_fun @ T_a @ tc_bool ) @ tc_bool ) @ V_A ) @ T_a )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1701,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1702,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_d: $i,T_c: $i,V_h: $i,T_b: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ V_f @ V_g @ T_a @ T_d @ T_c ) @ V_h @ T_a @ T_c @ T_b )
= ( c_Fun_Ofcomp @ V_f @ ( c_Fun_Ofcomp @ V_g @ V_h @ T_d @ T_c @ T_b ) @ T_a @ T_d @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1703,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1704,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1705,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1706,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1707,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1708,plain,
( ( ! [T_b: $i,V_x: $i,V_A: $i,T_a: $i,V_f: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1709,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(1710,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_x ) ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1711,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1712,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1713,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= V_A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1714,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_a )
= V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1715,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1716,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ V_A @ V_B @ T_b @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(1717,plain,
( ( ! [T_aa: $i,V_a: $i,V_f: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_aa @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(1718,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ V_A @ T_a ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ V_A @ T_a ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1719,plain,
( ( ! [V_x: $i,V_xa: $i,T_b: $i,V_times: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_b )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_xa ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ V_times @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(1720,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ V_A @ V_B @ T_b @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1721,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1722,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ V_A @ V_B @ T_a ) ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1723,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ V_A @ V_B @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1724,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1725,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ T_a ) )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1726,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1727,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ T_a ) )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(1728,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(1729,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1730,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ T_a ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(1731,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1732,plain,
( ( ! [T_a: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(1733,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1734,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1735,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1736,plain,
( ( ! [T_a: $i,V_P: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1737,plain,
( ( ! [T_a: $i,V_r: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_r @ T_a ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1738,plain,
( ( ! [V_f: $i,V_g: $i,V_z: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofold__image @ V_f @ V_g @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= V_z ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1739,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1740,plain,
( ( ! [V_f: $i,V_z: $i,T_b: $i,T_a: $i] :
( ( c_Finite__Set_Ofold @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= V_z ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1741,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1742,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1743,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1744,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1745,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1746,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1747,plain,
( ( ! [V_P: $i,T_a: $i,V_x: $i] :
( ( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1748,plain,
( ( ! [V_R: $i,V_a1: $i] :
~ ( c_Wellfounded_Omax__extp @ V_R @ V_a1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1749,plain,
( ( ! [V_f: $i,T_a: $i,V_x: $i] :
~ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1750,plain,
( ( ! [T_a: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1751,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1752,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1753,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(1754,plain,
( ( ! [V_A: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1755,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(1756,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1757,plain,
( ( ! [T_a: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1758,plain,
( ( ! [V_x: $i,V_z: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( V_x = V_z )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(1759,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1760,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(1761,plain,
( ( ! [V_R: $i,T_b: $i,T_a: $i] :
( ( c_Relation_OImage @ V_R @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(1762,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1763,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(1764,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1765,plain,
( ( ! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1766,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(1767,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i] : ( c_Fun_Oinj__on @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(1768,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(1769,plain,
( ( ! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(1770,plain,
( ( ! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(1771,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1772,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(1773,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(1774,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ooverride__on @ V_f @ V_g @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= V_f ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(1775,plain,
( ( ! [V_R: $i,V_S: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_R ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_S ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ V_R ) @ V_S ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1776,plain,
( ( ! [V_R: $i,V_S: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_R ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ V_S ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ V_R ) @ V_S ) ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1777,plain,
( ( ! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ V_m @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ T_b ) @ v_x )
= ( c_Option_Ooption_ONone @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1778,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ t_a ) @ v_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ v_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(1779,plain,
( ( ( hAPP @ ( c_Fun_Oid @ t_a ) @ v_x )
= v_x )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1780,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ V_f @ V_g @ t_a @ T_c @ T_b ) @ v_x )
= ( hAPP @ V_g @ ( hAPP @ V_f @ v_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1781,plain,
( ( ! [V_G: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1782,plain,
( ( ! [V_n: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_t @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ V_t @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1783,plain,
( ( ! [V_n: $i,V_na: $i,V_ts: $i,V_G: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_na @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_na ) @ V_ts ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ V_G @ V_n ) ) @ V_G ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1784,plain,
( ( ! [V_n: $i,V_xa: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_xa @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_xa ) @ V_ts ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ V_n @ V_ts ) @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1785,plain,
( ( ! [V_G: $i,V_ts: $i,V_x: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ V_G @ V_ts ) @ V_x @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_x ) @ V_G ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1786,plain,
( ( ! [V_n: $i,V_nb: $i,V_ts: $i,V_G: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_nb @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_nb ) @ V_ts ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ V_G @ V_n ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ V_G @ V_ts @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1787,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1788,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1 @ V_A @ T_a ) ) @ V_A ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1789,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1 @ V_A @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1790,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1791,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,T_b: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1792,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1793,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xequals0I__1__1 @ V_A @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(1794,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_b ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1795,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_x @ V_xa @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_xa ) ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(1796,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(1797,plain,
( ( ! [V_n: $i,V_x: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_x @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ V_x ) @ V_ts ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ V_n @ V_ts ) ) @ V_ts ) ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(1798,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(1799,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(1800,plain,
( ( ! [T_a: $i,V_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1801,plain,
( ( ! [T_a: $i,V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1802,plain,
( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(1803,plain,
( ( ! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(1804,plain,
( ( ! [T_b: $i] :
( ~ ( class_Orderings_Obot @ T_b )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(1805,plain,
( ( ! [T_a: $i,V_x: $i,V_S: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1806,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1807,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1808,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1809,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(1810,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(1811,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Odistrib__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(1812,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(1813,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(1814,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(1815,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(1816,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(1817,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Otop @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(1818,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(1819,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ominus @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1820,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(1821,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(1822,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(1823,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1824,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(1825,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(1826,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1827,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(1828,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1829,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(1830,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1831,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(1832,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(1833,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(1834,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1835,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1836,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(1837,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(1838,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(1839,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(1840,plain,
( ( class_Orderings_Otop @ tc_bool )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(1841,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(1842,plain,
( ( class_HOL_Ominus @ tc_bool )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(1843,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(1844,plain,
( ( ! [T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(1845,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(1846,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1847,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1848,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1681]) ).
thf(1849,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX4 )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1746]) ).
thf(1850,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX3 )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1743]) ).
thf(1851,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ SX0 @ SX1 )
!= ( hAPP @ SX0 @ SX2 ) )
| ~ ( c_Fun_Oinj__on @ SX0 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SX3 @ tc_bool ) ) @ SX3 @ SX4 )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1304]) ).
thf(1852,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX4 )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1744]) ).
thf(1853,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SX0 @ SX1 @ SX2 @ ( tc_fun @ SX3 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ( ( hAPP @ SX1 @ SX4 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX2 ) @ SX4 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1792]) ).
thf(1854,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX3 )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1745]) ).
thf(1855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1355]) ).
thf(1856,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Set_Oinsert @ SX0 @ SX3 @ SX2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX2 ) @ SX0 ) @ SX3 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX2 ) @ SX0 ) @ SX1 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1594]) ).
thf(1857,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ SX0 ) )
| ( SX2
= ( c_Orderings_Obot__class_Obot @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1730]) ).
thf(1858,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX0 ) @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX0 ) @ SX1 ) @ SX3 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX3 ) @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1790]) ).
thf(1859,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1772]) ).
thf(1860,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX0 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX1 ) @ SX2 ) ) @ SX3 )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX2 ) @ SX3 ) ) )
| ( c_lessequals @ SX3 @ SX1 @ ( tc_fun @ SX0 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1291]) ).
thf(1861,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ SX0 ) @ SX0 @ ( tc_fun @ SX0 @ tc_bool ) @ tc_bool ) @ SX1 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SX0 ) @ SX0 @ ( tc_fun @ SX0 @ tc_bool ) @ tc_bool ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1589]) ).
thf(1862,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oimage @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Set_Oimage @ SX0 @ SX4 @ SX2 @ SX3 ) )
| ~ ( c_Fun_Oinj__on @ SX0 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 @ SX3 )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1422]) ).
thf(1863,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1682]) ).
thf(1864,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Otop__class_Otop @ SX0 ) )
| ( SX1
= ( c_Orderings_Otop__class_Otop @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1424]) ).
thf(1865,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_bool ) ) @ SX1 )
!= ( c_Set_Oinsert @ SX2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_bool ) ) @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1768]) ).
thf(1866,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX1 ) @ SX2 )
!= SX2 )
| ( c_lessequals @ SX1 @ SX2 @ ( tc_fun @ SX0 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1476]) ).
thf(1867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i,SX9: $i,SX10: $i] :
( ( ( hAPP @ SX0 @ ( hAPP @ SX1 @ SX2 ) )
!= ( hAPP @ SX3 @ ( hAPP @ SX4 @ SX5 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SX0 @ SX1 @ SX6 @ SX7 @ SX8 ) @ SX2 )
= ( hAPP @ ( c_Fun_Ocomp @ SX3 @ SX4 @ SX9 @ SX7 @ SX10 ) @ SX5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1667]) ).
thf(1868,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SX0 @ tc_bool ) ) @ ( c_Set_Oimage @ SX1 @ ( c_HOL_Ominus__class_Ominus @ SX2 @ SX3 @ ( tc_fun @ SX4 @ tc_bool ) ) @ SX4 @ SX0 ) ) @ ( c_Set_Oimage @ SX1 @ ( c_HOL_Ominus__class_Ominus @ SX3 @ SX2 @ ( tc_fun @ SX4 @ tc_bool ) ) @ SX4 @ SX0 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SX1 @ SX3 @ SX4 @ SX0 )
| ~ ( c_Fun_Oinj__on @ SX1 @ SX2 @ SX4 @ SX0 )
| ( c_Fun_Oinj__on @ SX1 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX4 @ tc_bool ) ) @ SX2 ) @ SX3 ) @ SX4 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1340]) ).
thf(1869,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ ( tc_fun @ SX0 @ tc_bool ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1317]) ).
thf(1870,plain,
( ( ! [SX0: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1750]) ).
thf(1871,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ SX0 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SX1 @ SX0 @ SX2 @ SX3 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SX1 @ SX0 @ SX2 @ ( tc_fun @ SX3 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1409]) ).
thf(1872,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX2 ) @ SX0 ) @ SX1 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1719]) ).
thf(1873,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SX0 ) @ SX1 ) @ SX2 )
!= SX1 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1368]) ).
thf(1874,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ SX0 ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1729]) ).
thf(1875,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX4 @ SX3 @ SX0 )
| ~ ( c_lessequals @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1679]) ).
thf(1876,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ SX1 )
!= ( hAPP @ SX0 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX2 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX1 ) @ SX4 ) )
| ~ ( c_Fun_Oinj__on @ SX0 @ SX4 @ SX3 @ SX5 )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1587]) ).
thf(1877,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX3 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1354]) ).
thf(1878,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ SX1 )
!= ( hAPP @ SX0 @ SX2 ) )
| ~ ( c_Fun_Oinj__on @ SX0 @ SX3 @ SX4 @ SX5 )
| ( SX1 = SX2 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX4 ) @ SX2 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX4 ) @ SX1 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1588]) ).
thf(1879,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 ) @ SX1 ) @ SX2 )
!= SX2 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1472]) ).
thf(1880,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oimage @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Set_Oimage @ SX0 @ SX4 @ SX2 @ SX3 ) )
| ~ ( c_Fun_Oinj__on @ SX0 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX1 ) @ SX4 ) @ SX2 @ SX3 )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1274]) ).
thf(1881,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1300]) ).
thf(1882,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Set_Oinsert @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1739]) ).
thf(1883,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Collect @ SX1 @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1736]) ).
thf(1884,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SX0 @ tc_bool ) ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ( SX2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1771]) ).
thf(1885,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i,SX7: $i,SX8: $i] :
( ( ( c_Fun_Ocomp @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
!= ( c_Fun_Ocomp @ SX5 @ SX6 @ SX7 @ SX3 @ SX4 ) )
| ( ( hAPP @ SX0 @ ( hAPP @ SX1 @ SX8 ) )
= ( hAPP @ SX5 @ ( hAPP @ SX6 @ SX8 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1666]) ).
thf(1886,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX2 ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1795]) ).
thf(1887,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1299]) ).
thf(1888,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( c_Fun_Ocomp @ SX0 @ SX1 @ SX2 @ SX3 @ SX4 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SX3 ) @ SX5 @ SX3 @ SX3 @ SX4 ) )
| ( ( hAPP @ SX0 @ ( hAPP @ SX1 @ SX6 ) )
= ( hAPP @ SX5 @ SX6 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1405]) ).
thf(1889,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SX1 @ SX2 @ SX3 @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ( ( hAPP @ SX2 @ SX4 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX4 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1791]) ).
thf(1890,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1625]) ).
thf(1891,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Set_Oimage @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1733]) ).
thf(1892,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1626]) ).
thf(1893,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1762]) ).
thf(1894,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Set_Oimage @ SX1 @ SX2 @ SX3 @ SX0 ) )
| ( SX2
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1764]) ).
thf(1895,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_Orderings_Otop__class_Otop @ SX0 ) )
| ( SX2
= ( c_Orderings_Otop__class_Otop @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1423]) ).
thf(1896,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Collect @ SX0 @ SX1 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1747]) ).
thf(1897,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX2 @ SX1 @ SX0 )
| ~ ( c_lessequals @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1680]) ).
thf(1898,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ SX0 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SX1 @ SX0 @ SX2 @ SX3 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SX1 @ SX0 @ SX2 @ ( tc_fun @ SX3 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1282]) ).
thf(1899,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ SX1 )
!= ( hAPP @ SX0 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX2 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX1 ) @ SX4 ) )
| ~ ( c_Fun_Oinj__on @ SX0 @ SX4 @ SX3 @ SX5 )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1586]) ).
thf(1900,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( hAPP @ SX0 @ SX1 )
!= ( hAPP @ SX0 @ SX2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX2 ) @ SX4 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SX3 ) @ SX1 ) @ SX4 ) )
| ( SX1 = SX2 )
| ~ ( c_Fun_Oinj__on @ SX0 @ SX4 @ SX3 @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1585]) ).
thf(1901,plain,
( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ v_xa @ t_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1902,plain,
! [SV1: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ SV1 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1 ) @ v_Ga ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1903,plain,
! [SV2: $i] :
( ( ! [SY2234: $i,SY2235: $i,SY2236: $i,SY2237: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SY2234 @ SY2235 @ SY2236 ) @ ( c_Set_Oimage @ SV2 @ SY2237 @ SY2235 @ SY2236 ) @ ( tc_fun @ SY2236 @ tc_bool ) )
| ~ ( c_lessequals @ SY2234 @ SY2237 @ ( tc_fun @ SY2235 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2235 @ tc_bool ) ) @ SY2235 @ SY2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1904,plain,
! [SV3: $i] :
( ( ! [SY2238: $i,SY2239: $i,SY2240: $i,SY2241: $i] :
( ( c_Fun_Oinj__on @ SV3 @ SY2238 @ SY2239 @ SY2240 )
| ~ ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SY2241 @ SY2238 @ SY2239 ) @ SY2239 @ SY2240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1905,plain,
! [SV4: $i] :
( ( ! [SY2242: $i,SY2243: $i,SY2244: $i,SY2245: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
| ( c_lessequals @ ( hAPP @ SY2242 @ SY2243 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2244 @ SY2242 @ SY2245 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2245 ) @ SY2243 ) @ SY2244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1906,plain,
! [SV5: $i] :
( ( ! [SY2246: $i,SY2247: $i,SY2248: $i,SY2249: $i] :
( ( c_lessequals @ ( hAPP @ SV5 @ SY2246 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2247 @ SV5 @ SY2248 @ ( tc_fun @ SY2249 @ tc_bool ) ) @ ( tc_fun @ SY2249 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2248 ) @ SY2246 ) @ SY2247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1907,plain,
! [SV6: $i] :
( ( ! [SY2250: $i,SY2251: $i,SY2252: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV6 @ SY2250 @ SY2251 ) @ SY2252 @ ( tc_fun @ SY2251 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SY2250 @ SY2252 @ ( tc_fun @ SY2251 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2251 ) @ SV6 ) @ SY2252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1908,plain,
! [SV7: $i] :
( ( ! [SY2253: $i,SY2254: $i,SY2255: $i] :
( ( c_lessequals @ SV7 @ SY2253 @ ( tc_fun @ SY2254 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY2255 @ SV7 @ SY2254 ) @ SY2253 @ ( tc_fun @ SY2254 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1909,plain,
! [SV8: $i] :
( ( ! [SY2256: $i,SY2257: $i,SY2258: $i] :
( ( c_lessequals @ SV8 @ ( c_Set_Oinsert @ SY2256 @ SY2257 @ SY2258 ) @ ( tc_fun @ SY2258 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SY2257 @ ( tc_fun @ SY2258 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1910,plain,
! [SV9: $i] :
( ( ! [SY2259: $i,SY2260: $i,SY2261: $i,SY2262: $i] :
( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SY2259 @ SY2260 @ SY2261 ) @ SY2262 @ SY2261 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2261 ) @ SY2259 ) @ SY2260 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SY2259 @ SY2260 @ SY2262 @ SY2261 @ SY2261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1911,plain,
! [SV10: $i] :
( ( ! [SY2263: $i,SY2264: $i,SY2265: $i,SY2266: $i,SY2267: $i,SY2268: $i,SY2269: $i,SY2270: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2263 @ tc_bool ) ) )
= SY2264 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2265 @ SV10 @ SY2266 @ SY2267 @ SY2268 @ SY2269 @ SY2270 @ SY2264 @ SY2263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1912,plain,
! [SV11: $i] :
( ( ! [SY2271: $i,SY2272: $i,SY2273: $i,SY2274: $i,SY2275: $i,SY2276: $i,SY2277: $i,SY2278: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2271 @ tc_bool ) ) )
= SY2272 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SY2273 @ SY2274 @ SY2275 @ SY2276 @ SY2277 @ SY2272 @ SY2278 @ SY2271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1913,plain,
! [SV12: $i] :
( ( ! [SY2279: $i,SY2280: $i,SY2281: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SY2279 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2280 @ tc_bool ) ) @ SY2280 ) @ ( tc_fun @ SY2280 @ tc_bool ) ) @ SY2281 @ ( tc_fun @ SY2280 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2280 ) @ SY2279 ) @ SV12 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2280 ) @ SY2279 ) @ SY2281 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SY2279 @ SY2281 @ SY2280 ) @ ( tc_fun @ SY2280 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1914,plain,
! [SV13: $i] :
( ( ! [SY2282: $i,SY2283: $i,SY2284: $i] :
( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SY2282 @ SY2283 @ SY2284 ) @ ( tc_fun @ SY2284 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2284 ) @ SY2282 ) @ SV13 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SY2282 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2284 @ tc_bool ) ) @ SY2284 ) @ ( tc_fun @ SY2284 @ tc_bool ) ) @ SY2283 @ ( tc_fun @ SY2284 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2284 ) @ SY2282 ) @ SY2283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1915,plain,
! [SV14: $i] :
( ( ! [SY2285: $i,SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i,SY2290: $i,SY2291: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SY2285 @ SY2286 @ ( c_Set_Oimage @ SY2287 @ SY2288 @ SY2289 @ SY2290 ) @ SY2291 @ SY2290 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SY2285 @ SY2287 @ SY2290 @ SY2291 @ SY2289 ) @ SY2286 @ SY2288 @ SY2291 @ SY2289 ) )
| ~ ( c_Fun_Oinj__on @ SY2287 @ SY2288 @ SY2289 @ SY2290 )
| ~ ( c_Finite__Set_Ofinite @ SY2288 @ SY2289 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY2291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1916,plain,
! [SV15: $i] :
( ( ! [SY2292: $i,SY2293: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SY2292 @ ( tc_fun @ SY2293 @ tc_bool ) ) @ SY2293 )
| ~ ( c_Finite__Set_Ofinite @ SV15 @ SY2293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1917,plain,
! [SV16: $i] :
( ( ! [SY2294: $i,SY2295: $i,SY2296: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV16 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SY2294 ) @ SY2295 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SY2295 @ SY2296 @ SV16 @ SV16 ) @ SV16 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SY2294 ) @ SY2296 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2296 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1918,plain,
! [SV17: $i] :
( ( ! [SY2297: $i,SY2298: $i,SY2299: $i,SY2300: $i] :
( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SY2297 @ SY2298 @ ( tc_fun @ SY2299 @ tc_bool ) ) @ SY2299 @ SY2300 )
| ~ ( c_Fun_Oinj__on @ SV17 @ SY2297 @ SY2299 @ SY2300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1919,plain,
! [SV18: $i] :
( ( ! [SY2301: $i,SY2302: $i,SY2303: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2301 @ SY2302 @ SV18 ) ) @ SY2303 )
= ( c_Set_Oinsert @ SY2301 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ SY2302 ) @ SY2303 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1920,plain,
! [SV19: $i] :
( ( ! [SY2304: $i,SY2305: $i,SY2306: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SY2304 ) @ ( c_Set_Oinsert @ SY2305 @ SY2306 @ SV19 ) )
= ( c_Set_Oinsert @ SY2305 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SY2304 ) @ SY2306 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1921,plain,
! [SV20: $i] :
( ( ! [SY2307: $i,SY2308: $i,SY2309: $i,SY2310: $i] :
( ( c_Set_Ovimage @ SV20 @ ( c_HOL_Ominus__class_Ominus @ SY2307 @ SY2308 @ ( tc_fun @ SY2309 @ tc_bool ) ) @ SY2310 @ SY2309 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV20 @ SY2307 @ SY2310 @ SY2309 ) @ ( c_Set_Ovimage @ SV20 @ SY2308 @ SY2310 @ SY2309 ) @ ( tc_fun @ SY2310 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1922,plain,
! [SV21: $i] :
( ( ! [SY2311: $i,SY2312: $i,SY2313: $i] :
( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SY2311 @ SY2312 @ SY2313 ) @ ( tc_fun @ SY2313 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2313 ) @ SY2311 ) @ SV21 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SY2311 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2313 @ tc_bool ) ) @ SY2313 ) @ ( tc_fun @ SY2313 @ tc_bool ) ) @ SY2312 @ ( tc_fun @ SY2313 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SY2312 @ ( tc_fun @ SY2313 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1923,plain,
! [SV22: $i] :
( ( ! [SY2314: $i,SY2315: $i,SY2316: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV22 @ ( c_Set_Ovimage @ SV22 @ SY2314 @ SY2315 @ SY2316 ) @ SY2315 @ SY2316 ) @ SY2314 @ ( tc_fun @ SY2316 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1924,plain,
! [SV23: $i] :
( ( ! [SY2317: $i,SY2318: $i,SY2319: $i] :
( ( ( c_Set_Ovimage @ SV23 @ ( c_Set_Oimage @ SV23 @ SY2317 @ SY2318 @ SY2319 ) @ SY2318 @ SY2319 )
= SY2317 )
| ~ ( c_Fun_Oinj__on @ SV23 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2318 @ tc_bool ) ) @ SY2318 @ SY2319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1925,plain,
! [SV24: $i] :
( ( ! [SY2320: $i] :
( ( c_Collect @ SV24 @ SY2320 )
= SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1926,plain,
! [SV25: $i] :
( ( ! [SY2321: $i,SY2322: $i,SY2323: $i] :
( ( SV25 = SY2321 )
| ~ ( c_Finite__Set_Ofold1Set @ SY2322 @ ( c_Set_Oinsert @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2323 @ tc_bool ) ) @ SY2323 ) @ SY2321 @ SY2323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1927,plain,
! [SV26: $i] :
( ( ! [SY2324: $i,SY2325: $i] :
( ( c_Set_Ovimage @ SV26 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2324 @ tc_bool ) ) @ SY2325 @ SY2324 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2325 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1928,plain,
! [SV27: $i] :
( ( ! [SY2326: $i,SY2327: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV27 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2326 @ SY2327 @ SV27 ) @ SV27 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 ) @ SY2326 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SY2327 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1929,plain,
! [SV28: $i] :
( ( ! [SY2328: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV28 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV28 ) @ SY2328 ) @ ( c_Orderings_Otop__class_Otop @ SV28 ) )
= ( c_Orderings_Otop__class_Otop @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1930,plain,
! [SV29: $i] :
( ( ! [SY2329: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV29 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV29 ) @ ( c_Orderings_Otop__class_Otop @ SV29 ) ) @ SY2329 )
= ( c_Orderings_Otop__class_Otop @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1931,plain,
! [SV30: $i] :
( ( ! [SY2330: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV30 @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV30 @ tc_bool ) ) ) @ SY2330 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV30 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1932,plain,
! [SV31: $i] :
( ( ! [SY2331: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV31 @ tc_bool ) ) @ SY2331 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV31 @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV31 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1933,plain,
! [SV32: $i] :
( ( ! [SY2332: $i,SY2333: $i,SY2334: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV32 @ ( c_Set_Oinsert @ SY2332 @ SY2333 @ SY2334 ) @ ( tc_fun @ SY2334 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SY2333 @ ( tc_fun @ SY2334 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2332 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2334 @ tc_bool ) ) @ SY2334 ) @ ( tc_fun @ SY2334 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1934,plain,
! [SV33: $i] :
( ( ! [SY2335: $i,SY2336: $i,SY2337: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SY2335 @ SY2336 @ SY2337 ) @ ( tc_fun @ SY2337 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SY2335 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2337 @ tc_bool ) ) @ SY2337 ) @ ( tc_fun @ SY2337 @ tc_bool ) ) @ SY2336 @ ( tc_fun @ SY2337 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1935,plain,
! [SV34: $i] :
( ( ! [SY2338: $i,SY2339: $i] :
( ( c_Finite__Set_Ofinite @ SV34 @ SY2338 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SY2339 @ ( tc_fun @ SY2338 @ tc_bool ) ) @ SY2338 )
| ~ ( c_Finite__Set_Ofinite @ SY2339 @ SY2338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1936,plain,
! [SV35: $i] :
( ( ! [SY2340: $i,SY2341: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SY2340 @ ( tc_fun @ SY2341 @ tc_bool ) ) @ SY2341 )
| ~ ( c_Finite__Set_Ofinite @ SV35 @ SY2341 )
| ~ ( c_Finite__Set_Ofinite @ SY2340 @ SY2341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1937,plain,
! [SV36: $i] :
( ( ! [SY2342: $i,SY2343: $i,SY2344: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2342 @ SY2343 @ SV36 ) ) @ ( c_Set_Oinsert @ SY2342 @ SY2344 @ SV36 ) )
= ( c_Set_Oinsert @ SY2342 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ SY2343 ) @ SY2344 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1938,plain,
! [SV37: $i] :
( ( ! [SY2345: $i,SY2346: $i] :
( ( c_Set_Oinsert @ SV37 @ ( c_Set_Oinsert @ SV37 @ SY2345 @ SY2346 ) @ SY2346 )
= ( c_Set_Oinsert @ SV37 @ SY2345 @ SY2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1939,plain,
! [SV38: $i] :
( ( ! [SY2347: $i,SY2348: $i,SY2349: $i,SY2350: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SY2347 ) @ SY2348 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2349 ) @ SY2347 ) @ SY2350 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2350 @ SV38 @ SY2349 @ ( tc_fun @ SY2348 @ tc_bool ) ) @ SY2348 )
| ~ ( c_Finite__Set_Ofinite @ SY2350 @ SY2349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1940,plain,
! [SV39: $i] :
( ( ! [SY2351: $i,SY2352: $i,SY2353: $i] :
( ( hBOOL @ ( hAPP @ SV39 @ SY2351 ) )
| ( SY2352 = SY2351 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2352 @ SV39 @ SY2353 ) @ SY2351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1941,plain,
! [SV40: $i] :
( ( ! [SY2354: $i] :
( ( SV40
= ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SV40 @ SY2354 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SV40 @ SY2354 ) @ SY2354 ) )
| ( SV40
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2354 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1942,plain,
! [SV41: $i] :
( ( ! [SY2355: $i,SY2356: $i,SY2357: $i,SY2358: $i,SY2359: $i] :
( ( c_lessequals @ ( hAPP @ SV41 @ SY2355 ) @ SY2356 @ ( tc_fun @ SY2357 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2358 ) @ SY2355 ) @ SY2359 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2359 @ SV41 @ SY2358 @ ( tc_fun @ SY2357 @ tc_bool ) ) @ SY2356 @ ( tc_fun @ SY2357 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1943,plain,
! [SV42: $i] :
( ( ! [SY2360: $i,SY2361: $i] : ( c_lessequals @ SV42 @ ( c_Set_Oinsert @ SY2360 @ SV42 @ SY2361 ) @ ( tc_fun @ SY2361 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1944,plain,
! [SV43: $i] :
( ( ! [SY2362: $i,SY2363: $i,SY2364: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV43 @ SY2362 @ SY2363 ) @ SY2364 @ SY2363 @ SY2362 @ t_a ) @ v_x )
= SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1945,plain,
! [SV44: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ( c_Finite__Set_Ofinite @ SV44 @ SY2365 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY2366 @ SV44 @ SY2365 ) @ SY2365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1946,plain,
! [SV45: $i] :
( ( ! [SY2367: $i,SY2368: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV45 @ SY2367 @ SY2368 ) @ SY2368 )
| ~ ( c_Finite__Set_Ofinite @ SY2367 @ SY2368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1947,plain,
! [SV46: $i] :
( ( ! [SY2369: $i,SY2370: $i,SY2371: $i,SY2372: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SY2369 @ SY2370 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2371 @ SY2369 @ SY2372 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2371 @ SY2369 @ SY2372 @ ( tc_fun @ SV46 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2372 ) @ SY2370 ) @ SY2371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1948,plain,
! [SV47: $i] :
( ( ! [SY2373: $i,SY2374: $i,SY2375: $i,SY2376: $i,SY2377: $i,SY2378: $i] :
( ( c_Finite__Set_Ofold__graph @ SV47 @ SY2373 @ SY2374 @ ( hAPP @ ( hAPP @ SV47 @ SY2375 ) @ SY2376 ) @ SY2377 @ SY2378 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2377 ) @ SY2375 ) @ SY2374 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SY2373 @ ( c_HOL_Ominus__class_Ominus @ SY2374 @ ( c_Set_Oinsert @ SY2375 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2377 @ tc_bool ) ) @ SY2377 ) @ ( tc_fun @ SY2377 @ tc_bool ) ) @ SY2376 @ SY2377 @ SY2378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1949,plain,
! [SV48: $i] :
( ( ! [SY2379: $i,SY2380: $i,SY2381: $i,SY2382: $i] :
( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2379 @ tc_bool ) ) @ SY2380 ) @ SY2381 ) @ SY2379 @ SY2382 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2382 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SY2380 @ SY2379 @ SY2382 ) ) @ ( c_Set_Oimage @ SV48 @ SY2381 @ SY2379 @ SY2382 ) ) )
| ~ ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2379 @ tc_bool ) ) @ SY2379 @ SY2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1950,plain,
! [SV49: $i] :
( ( ! [SY2383: $i,SY2384: $i,SY2385: $i,SY2386: $i,SY2387: $i,SY2388: $i,SY2389: $i,SY2390: $i,SY2391: $i,SY2392: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SY2383 @ ( c_Set_Oinsert @ SY2384 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2385 @ tc_bool ) ) @ SY2385 ) @ SY2385 ) )
= ( hAPP @ ( hAPP @ SY2386 @ SY2383 ) @ SY2384 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2387 @ SV49 @ SY2388 @ SY2389 @ SY2390 @ SY2386 @ SY2391 @ SY2392 @ SY2385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1951,plain,
! [SV50: $i] :
( ( ! [SY2393: $i,SY2394: $i,SY2395: $i,SY2396: $i,SY2397: $i,SY2398: $i,SY2399: $i,SY2400: $i,SY2401: $i,SY2402: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SY2393 @ ( c_Set_Oinsert @ SY2394 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2395 @ tc_bool ) ) @ SY2395 ) @ SY2395 ) )
= ( hAPP @ ( hAPP @ SY2396 @ SY2393 ) @ SY2394 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SY2397 @ SY2398 @ SY2399 @ SY2396 @ SY2400 @ SY2401 @ SY2402 @ SY2395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1952,plain,
! [SV51: $i] :
( ( ! [SY2403: $i,SY2404: $i,SY2405: $i,SY2406: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV51 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2403 @ tc_bool ) ) @ SY2404 ) @ SY2405 ) @ SY2403 @ SY2406 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2406 @ tc_bool ) ) @ ( c_Set_Oimage @ SV51 @ SY2404 @ SY2403 @ SY2406 ) ) @ ( c_Set_Oimage @ SV51 @ SY2405 @ SY2403 @ SY2406 ) ) @ ( tc_fun @ SY2406 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1953,plain,
! [SV52: $i] :
( ( ! [SY2407: $i,SY2408: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SY2407 ) @ SY2408 ) @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SY2408 @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SY2407 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1954,plain,
! [SV53: $i] :
( ( ! [SY2409: $i,SY2410: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SY2409 ) @ SY2410 ) @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SY2410 @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SY2409 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1955,plain,
! [SV54: $i] :
( ( ! [SY2411: $i,SY2412: $i,SY2413: $i,SY2414: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV54 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2411 @ tc_bool ) ) @ SY2412 ) @ SY2413 ) @ SY2411 @ SY2414 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2414 @ tc_bool ) ) @ ( c_Relation_OImage @ SV54 @ SY2412 @ SY2411 @ SY2414 ) ) @ ( c_Relation_OImage @ SV54 @ SY2413 @ SY2411 @ SY2414 ) ) @ ( tc_fun @ SY2414 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1956,plain,
! [SV55: $i] :
( ( ! [SY2415: $i,SY2416: $i,SY2417: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SY2415 ) @ SY2416 ) ) @ SY2417 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SY2415 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ SY2416 ) @ SY2417 ) ) )
| ~ ( c_lessequals @ SY2417 @ SY2415 @ ( tc_fun @ SV55 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1957,plain,
! [SV56: $i] :
( ( ! [SY2418: $i,SY2419: $i,SY2420: $i,SY2421: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV56 @ SY2418 @ SY2419 @ SY2420 ) @ SY2421 )
= ( c_Option_Ooption_ONone @ SY2420 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2419 ) @ SY2421 ) @ SY2418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1958,plain,
! [SV57: $i] :
( ( ! [SY2422: $i,SY2423: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV57 @ tc_bool ) ) @ SY2422 ) @ SY2423 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV57 @ tc_bool ) ) )
| ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SY2422 @ SY2423 @ SV57 )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SY2422 @ SY2423 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1959,plain,
! [SV58: $i] :
( ( ! [SY2424: $i,SY2425: $i,SY2426: $i,SY2427: $i,SY2428: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV58 @ SY2424 @ SY2425 @ SY2426 @ SY2427 ) @ SY2428 )
= ( hAPP @ SV58 @ ( hAPP @ SY2424 @ SY2428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1960,plain,
! [SV59: $i] :
( ( ! [SY2429: $i,SY2430: $i,SY2431: $i,SY2432: $i,SY2433: $i] :
( ( hAPP @ SV59 @ ( hAPP @ SY2429 @ SY2430 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV59 @ SY2429 @ SY2431 @ SY2432 @ SY2433 ) @ SY2430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1961,plain,
! [SV60: $i] :
( ( ! [SY2434: $i,SY2435: $i,SY2436: $i,SY2437: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SY2434 ) @ SY2435 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2436 ) @ ( hAPP @ SY2437 @ SY2434 ) ) @ ( c_Set_Oimage @ SY2437 @ SY2435 @ SV60 @ SY2436 ) ) )
| ~ ( c_Fun_Oinj__on @ SY2437 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SY2436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1962,plain,
! [SV61: $i] :
( ( ! [SY2438: $i,SY2439: $i,SY2440: $i,SY2441: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SY2438 @ SY2439 ) ) @ ( c_Set_Oimage @ SY2438 @ SY2440 @ SY2441 @ SV61 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2441 ) @ SY2439 ) @ SY2440 ) )
| ~ ( c_Fun_Oinj__on @ SY2438 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2441 @ tc_bool ) ) @ SY2441 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1963,plain,
! [SV62: $i] :
( ( ! [SY2442: $i,SY2443: $i,SY2444: $i,SY2445: $i] :
( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SY2442 ) @ SY2443 ) ) @ SY2444 )
= ( hAPP @ ( hAPP @ SV62 @ SY2442 ) @ ( hAPP @ ( hAPP @ SV62 @ SY2443 ) @ SY2444 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SY2445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1964,plain,
! [SV63: $i] :
( ( ! [SY2446: $i,SY2447: $i,SY2448: $i,SY2449: $i] :
( ( ( hAPP @ ( hAPP @ SV63 @ SY2446 ) @ ( hAPP @ ( hAPP @ SV63 @ SY2447 ) @ SY2448 ) )
= ( hAPP @ ( hAPP @ SV63 @ SY2447 ) @ ( hAPP @ ( hAPP @ SV63 @ SY2446 ) @ SY2448 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SY2449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1965,plain,
! [SV64: $i] :
( ( ! [SY2450: $i,SY2451: $i,SY2452: $i] :
( ( ( hAPP @ ( hAPP @ SV64 @ SY2450 ) @ SY2451 )
= ( hAPP @ ( hAPP @ SV64 @ SY2451 ) @ SY2450 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV64 @ SY2452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1966,plain,
! [SV65: $i] :
( ( ! [SY2453: $i,SY2454: $i,SY2455: $i] :
( ( hBOOL @ ( hAPP @ SV65 @ SY2453 ) )
| ( hBOOL @ ( hAPP @ SY2454 @ SY2453 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2455 @ tc_bool ) ) @ SY2454 ) @ SV65 ) @ SY2453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1967,plain,
! [SV66: $i] :
( ( ! [SY2456: $i,SY2457: $i,SY2458: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV66 @ tc_bool ) ) @ SY2456 ) @ SY2457 ) @ SY2458 ) )
| ~ ( hBOOL @ ( hAPP @ SY2457 @ SY2458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1968,plain,
! [SV67: $i] :
( ( ! [SY2459: $i,SY2460: $i,SY2461: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV67 @ tc_bool ) ) @ SY2459 ) @ SY2460 ) @ SY2461 ) )
| ~ ( hBOOL @ ( hAPP @ SY2459 @ SY2461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1969,plain,
! [SV68: $i] :
( ( ! [SY2462: $i,SY2463: $i,SY2464: $i,SY2465: $i] :
( ( c_lessequals @ SV68 @ SY2462 @ ( tc_fun @ SY2463 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SY2464 @ SV68 @ SY2463 @ SY2465 ) @ ( c_Set_Oimage @ SY2464 @ SY2462 @ SY2463 @ SY2465 ) @ ( tc_fun @ SY2465 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY2464 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2463 @ tc_bool ) ) @ SY2463 @ SY2465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1970,plain,
! [SV69: $i] :
( ( ! [SY2466: $i,SY2467: $i,SY2468: $i] :
( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SY2466 @ SY2467 @ SY2468 ) @ ( tc_fun @ SY2468 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2468 ) @ SY2466 ) @ SV69 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SY2466 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2468 @ tc_bool ) ) @ SY2468 ) @ ( tc_fun @ SY2468 @ tc_bool ) ) @ SY2467 @ ( tc_fun @ SY2468 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1971,plain,
! [SV70: $i] :
( ( ! [SY2469: $i,SY2470: $i,SY2471: $i] :
( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SY2469 @ SY2470 @ SY2471 ) @ ( tc_fun @ SY2471 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2471 ) @ SY2469 ) @ SV70 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SY2469 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2471 @ tc_bool ) ) @ SY2471 ) @ ( tc_fun @ SY2471 @ tc_bool ) ) @ SY2470 @ ( tc_fun @ SY2471 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1972,plain,
! [SV71: $i] :
( ( ! [SY2472: $i,SY2473: $i,SY2474: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SY2472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2473 @ tc_bool ) ) @ SY2473 ) @ ( tc_fun @ SY2473 @ tc_bool ) ) @ SY2474 @ ( tc_fun @ SY2473 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2473 ) @ SY2472 ) @ SV71 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SY2472 @ SY2474 @ SY2473 ) @ ( tc_fun @ SY2473 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1973,plain,
! [SV72: $i] :
( ( ! [SY2475: $i,SY2476: $i,SY2477: $i,SY2478: $i,SY2479: $i] :
( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2475 @ tc_bool ) ) @ SY2476 ) @ SY2477 ) @ SY2475 @ SY2478 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2478 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SY2476 @ SY2475 @ SY2478 ) ) @ ( c_Set_Oimage @ SV72 @ SY2477 @ SY2475 @ SY2478 ) ) )
| ~ ( c_lessequals @ SY2477 @ SY2479 @ ( tc_fun @ SY2475 @ tc_bool ) )
| ~ ( c_lessequals @ SY2476 @ SY2479 @ ( tc_fun @ SY2475 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SY2479 @ SY2475 @ SY2478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1974,plain,
! [SV73: $i] :
( ( ! [SY2480: $i,SY2481: $i,SY2482: $i,SY2483: $i] :
( ( c_Finite__Set_Ofinite @ SV73 @ SY2480 )
| ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SY2481 @ SY2482 @ SY2483 @ SY2480 ) @ ( tc_fun @ SY2480 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY2482 @ SY2483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1975,plain,
! [SV74: $i] :
( ( ! [SY2484: $i,SY2485: $i,SY2486: $i,SY2487: $i,SY2488: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SY2484 @ SY2485 ) ) @ SY2486 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2487 ) @ SY2485 ) @ SY2488 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SY2484 @ SY2488 @ SY2487 @ SV74 ) @ SY2486 @ ( tc_fun @ SV74 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1976,plain,
! [SV75: $i] :
( ( ! [SY2489: $i,SY2490: $i,SY2491: $i,SY2492: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SY2489 @ SY2490 ) @ SY2491 @ SY2490 @ SY2489 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2489 @ tc_bool ) ) @ SY2489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2490 ) @ SY2492 ) @ SY2491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1977,plain,
! [SV76: $i] :
( ( ! [SY2493: $i,SY2494: $i,SY2495: $i,SY2496: $i,SY2497: $i] :
( ( c_Finite__Set_Ofinite @ SV76 @ SY2493 )
| ~ ( c_Finite__Set_Ofold__graph @ SY2494 @ SY2495 @ SV76 @ SY2496 @ SY2493 @ SY2497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1978,plain,
! [SV77: $i] :
( ( ! [SY2498: $i,SY2499: $i] :
( ~ ( class_Lattices_Olattice @ SV77 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ SV77 ) ) @ SY2498 ) @ SY2499 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV77 ) @ ( hAPP @ SY2498 @ v_x ) ) @ ( hAPP @ SY2499 @ v_x ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1979,plain,
! [SV78: $i] :
( ( ! [SY2500: $i,SY2501: $i,SY2502: $i,SY2503: $i,SY2504: $i] :
( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SY2500 @ SY2501 @ SY2502 @ SY2503 ) @ SY2503 @ SY2504 )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SY2500 @ SY2503 @ SY2504 @ SY2502 ) @ SY2501 @ SY2502 @ SY2504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1980,plain,
! [SV79: $i] :
( ( ! [SY2505: $i,SY2506: $i,SY2507: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ SY2505 ) @ SY2506 ) ) @ SY2507 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SY2505 ) @ SY2507 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SY2506 ) @ SY2507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1981,plain,
! [SV80: $i] :
( ( ! [SY2508: $i,SY2509: $i,SY2510: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SY2508 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ SY2509 ) @ SY2510 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SY2508 ) @ SY2509 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SY2508 ) @ SY2510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1982,plain,
! [SV81: $i] :
( ( ! [SY2511: $i,SY2512: $i,SY2513: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SY2511 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ SY2512 ) @ SY2513 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SY2511 ) @ SY2512 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SY2511 ) @ SY2513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1983,plain,
! [SV82: $i] :
( ( ! [SY2514: $i,SY2515: $i,SY2516: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ SY2514 ) @ SY2515 ) ) @ SY2516 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SY2514 ) @ SY2516 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SY2515 ) @ SY2516 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1984,plain,
! [SV83: $i] :
( ( ! [SY2517: $i,SY2518: $i,SY2519: $i] :
( ( hBOOL @ ( hAPP @ SV83 @ SY2517 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2518 ) @ SY2517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2518 @ tc_bool ) ) @ SY2519 ) @ ( c_Collect @ SV83 @ SY2518 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1985,plain,
! [SV84: $i] :
( ( ! [SY2520: $i,SY2521: $i] :
( ( c_Fun_Ocomp @ SV84 @ ( c_Fun_Oid @ SY2520 ) @ SY2520 @ SY2521 @ SY2520 )
= SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1986,plain,
! [SV85: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV85 ) @ SY2522 @ SV85 @ SV85 @ SY2523 )
= SY2522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1987,plain,
! [SV86: $i] :
( ( ! [SY2524: $i,SY2525: $i,SY2526: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SY2524 @ SY2525 @ SY2526 ) @ SY2525 )
| ~ ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2525 @ tc_bool ) ) @ SY2525 @ SY2526 )
| ~ ( c_Finite__Set_Ofinite @ SY2524 @ SY2526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1988,plain,
! [SV87: $i] :
( ( ! [SY2527: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV87 @ tc_bool ) ) @ SY2527 ) @ SY2527 )
= SY2527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1989,plain,
! [SV88: $i] :
( ( ! [SY2528: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV88 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 ) @ SY2528 ) @ SY2528 )
= SY2528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1990,plain,
! [SV89: $i] :
( ( ! [SY2529: $i,SY2530: $i,SY2531: $i] :
( ~ ( class_Orderings_Opreorder @ SV89 )
| ( c_HOL_Oord__class_Oless @ SY2529 @ SY2530 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY2531 @ SY2530 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY2529 @ SY2531 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1991,plain,
! [SV90: $i] :
( ( ! [SY2532: $i,SY2533: $i,SY2534: $i] :
( ( c_HOL_Oord__class_Oless @ SV90 @ SY2532 @ ( tc_fun @ SY2533 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2534 @ SY2532 @ ( tc_fun @ SY2533 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ SY2534 @ ( tc_fun @ SY2533 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1992,plain,
! [SV91: $i] :
( ( ! [SY2535: $i,SY2536: $i,SY2537: $i] :
( ~ ( class_Orderings_Oorder @ SV91 )
| ( c_HOL_Oord__class_Oless @ SY2535 @ SY2536 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY2535 @ SY2537 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY2537 @ SY2536 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1993,plain,
! [SV92: $i] :
( ( ! [SY2538: $i,SY2539: $i,SY2540: $i,SY2541: $i] :
( ( c_Relation_OImage @ SV92 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2538 @ tc_bool ) ) @ SY2539 ) @ SY2540 ) @ SY2538 @ SY2541 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2541 @ tc_bool ) ) @ ( c_Relation_OImage @ SV92 @ SY2539 @ SY2538 @ SY2541 ) ) @ ( c_Relation_OImage @ SV92 @ SY2540 @ SY2538 @ SY2541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1994,plain,
! [SV93: $i] :
( ( ! [SY2542: $i,SY2543: $i,SY2544: $i,SY2545: $i] :
( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SY2542 @ SY2543 @ SY2544 ) @ SY2544 @ SY2545 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2545 ) @ ( hAPP @ SV93 @ SY2542 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SY2543 @ ( c_Set_Oinsert @ SY2542 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2544 @ tc_bool ) ) @ SY2544 ) @ ( tc_fun @ SY2544 @ tc_bool ) ) @ SY2544 @ SY2545 ) ) )
| ~ ( c_Fun_Oinj__on @ SV93 @ SY2543 @ SY2544 @ SY2545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1995,plain,
! [SV94: $i] :
( ( ! [SY2546: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ SV94 ) @ SY2546 @ SV94 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1996,plain,
! [SV95: $i] :
( ( ! [SY2547: $i,SY2548: $i,SY2549: $i] :
( ( c_Set_Oinsert @ SV95 @ ( c_Set_Oinsert @ SY2547 @ SY2548 @ SY2549 ) @ SY2549 )
= ( c_Set_Oinsert @ SY2547 @ ( c_Set_Oinsert @ SV95 @ SY2548 @ SY2549 ) @ SY2549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1997,plain,
! [SV96: $i] :
( ( ! [SY2550: $i,SY2551: $i,SY2552: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV96 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2550 @ tc_bool ) ) @ SY2551 @ SY2550 @ ( tc_fun @ SY2552 @ tc_bool ) ) @ ( tc_fun @ SY2552 @ tc_bool ) )
= SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1998,plain,
! [SV97: $i] :
( ( ! [SY2553: $i,SY2554: $i,SY2555: $i,SY2556: $i,SY2557: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV97 @ SY2553 @ SY2554 @ SY2555 ) @ SY2556 ) @ SY2557 )
= ( hAPP @ ( hAPP @ SV97 @ SY2557 ) @ SY2556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1999,plain,
! [SV98: $i] :
( ( ! [SY2558: $i,SY2559: $i,SY2560: $i] :
( ( hAPP @ ( c_COMBK @ SV98 @ SY2558 @ SY2559 ) @ SY2560 )
= SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(2000,plain,
! [SV99: $i] :
( ( ! [SY2561: $i,SY2562: $i,SY2563: $i,SY2564: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SY2561 @ ( c_HOL_Ominus__class_Ominus @ SY2562 @ SY2563 @ ( tc_fun @ SY2564 @ tc_bool ) ) @ SY2564 @ SV99 ) ) @ ( c_Set_Oimage @ SY2561 @ ( c_HOL_Ominus__class_Ominus @ SY2563 @ SY2562 @ ( tc_fun @ SY2564 @ tc_bool ) ) @ SY2564 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SY2561 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2564 @ tc_bool ) ) @ SY2562 ) @ SY2563 ) @ SY2564 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(2001,plain,
! [SV100: $i] :
( ( ! [SY2565: $i,SY2566: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SY2565 @ ( tc_fun @ SY2566 @ tc_bool ) ) @ SY2565 @ ( tc_fun @ SY2566 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV100 @ SY2565 @ ( tc_fun @ SY2566 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(2002,plain,
! [SV101: $i] :
( ( ! [SY2567: $i,SY2568: $i] :
( ~ ( class_Orderings_Olinorder @ SV101 )
| ( c_HOL_Oord__class_Oless @ SY2567 @ SY2568 @ SV101 )
| ( c_lessequals @ SY2568 @ SY2567 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(2003,plain,
! [SV102: $i] :
( ( ! [SY2569: $i] :
( ~ ( class_Orderings_Olinorder @ SV102 )
| ~ ( c_lessequals @ SY2569 @ SY2569 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SY2569 @ SY2569 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(2004,plain,
! [SV103: $i] :
( ( ! [SY2570: $i] :
( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_HOL_Oord__class_Oless @ SY2570 @ SY2570 @ SV103 )
| ( c_lessequals @ SY2570 @ SY2570 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(2005,plain,
! [SV104: $i] :
( ( ! [SY2571: $i,SY2572: $i] :
( ~ ( class_Orderings_Olinorder @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SY2571 @ SY2572 @ SV104 )
| ~ ( c_lessequals @ SY2572 @ SY2571 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(2006,plain,
! [SV105: $i] :
( ( ! [SY2573: $i,SY2574: $i] :
( ~ ( class_Orderings_Olinorder @ SV105 )
| ( c_lessequals @ SY2573 @ SY2574 @ SV105 )
| ( c_HOL_Oord__class_Oless @ SY2574 @ SY2573 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(2007,plain,
! [SV106: $i] :
( ( ! [SY2575: $i,SY2576: $i] :
( ~ ( class_Orderings_Olinorder @ SV106 )
| ~ ( c_lessequals @ SY2575 @ SY2576 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SY2576 @ SY2575 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(2008,plain,
! [SV107: $i] :
( ( ! [SY2577: $i,SY2578: $i] :
( ~ ( class_Orderings_Olinorder @ SV107 )
| ( c_HOL_Oord__class_Oless @ SY2577 @ SY2578 @ SV107 )
| ( c_lessequals @ SY2578 @ SY2577 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(2009,plain,
! [SV108: $i] :
( ( ! [SY2579: $i,SY2580: $i,SY2581: $i] :
( ~ ( class_HOL_Oord @ SV108 )
| ~ ( c_lessequals @ SY2579 @ SY2580 @ ( tc_fun @ SY2581 @ SV108 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2580 @ SY2579 @ ( tc_fun @ SY2581 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(2010,plain,
! [SV109: $i] :
( ( ! [SY2582: $i,SY2583: $i] :
( ~ ( class_Orderings_Opreorder @ SV109 )
| ~ ( c_lessequals @ SY2582 @ SY2583 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY2583 @ SY2582 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(2011,plain,
! [SV110: $i] :
( ( ! [SY2584: $i,SY2585: $i,SY2586: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV110 ) @ ( hAPP @ SY2584 @ SY2585 ) ) @ ( c_Set_Oimage @ SY2584 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2586 @ tc_bool ) ) @ SY2586 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(2012,plain,
! [SV111: $i] :
( ( ! [SY2587: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV111 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ SY2587 @ SV111 )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 ) @ ( c_Orderings_Obot__class_Obot @ SV111 ) @ SY2587 @ SV111 @ SV111 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2587 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(2013,plain,
! [SV112: $i] :
( ( ! [SY2588: $i,SY2589: $i] :
( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SY2588 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY2589 @ SV112 ) @ SV112 )
| ~ ( c_Finite__Set_Ofinite @ SY2589 @ SV112 )
| ( SY2588
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2588 @ SY2589 @ ( tc_fun @ SV112 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(2014,plain,
! [SV113: $i] :
( ( ! [SY2590: $i] :
( ~ ( class_Orderings_Olinorder @ SV113 )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SY2590 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV113 @ tc_bool ) ) @ SV113 ) @ SV113 )
= SY2590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(2015,plain,
! [SV114: $i] :
( ( ! [SY2591: $i,SY2592: $i,SY2593: $i,SY2594: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV114 @ SY2591 @ SY2592 @ SY2593 ) @ ( c_Set_Oimage @ SV114 @ SY2594 @ SY2592 @ SY2593 ) @ ( tc_fun @ SY2593 @ tc_bool ) ) @ ( c_Set_Oimage @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SY2591 @ SY2594 @ ( tc_fun @ SY2592 @ tc_bool ) ) @ SY2592 @ SY2593 ) @ ( tc_fun @ SY2593 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(2016,plain,
! [SV115: $i] :
( ( ! [SY2595: $i,SY2596: $i,SY2597: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SY2595 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SY2596 ) @ SY2597 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SY2596 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SY2595 ) @ SY2597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(2017,plain,
! [SV116: $i] :
( ( ! [SY2598: $i,SY2599: $i,SY2600: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SY2598 ) @ SY2599 ) ) @ SY2600 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SY2598 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SY2599 ) @ SY2600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(2018,plain,
! [SV117: $i] :
( ( ! [SY2601: $i,SY2602: $i,SY2603: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SY2601 ) @ SY2602 ) ) @ SY2603 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SY2601 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SY2602 ) @ SY2603 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(2019,plain,
! [SV118: $i] :
( ( ! [SY2604: $i,SY2605: $i,SY2606: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SY2604 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SY2605 ) @ SY2606 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SY2605 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SY2604 ) @ SY2606 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(2020,plain,
! [SV119: $i] :
( ( ! [SY2607: $i,SY2608: $i,SY2609: $i] :
( ~ ( class_Lattices_Olattice @ SV119 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SY2607 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SY2608 ) @ SY2609 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SY2608 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SY2607 ) @ SY2609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(2021,plain,
! [SV120: $i] :
( ( ! [SY2610: $i,SY2611: $i,SY2612: $i] :
( ~ ( class_Lattices_Olattice @ SV120 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SY2610 ) @ SY2611 ) ) @ SY2612 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SY2610 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SY2611 ) @ SY2612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(2022,plain,
! [SV121: $i] :
( ( ! [SY2613: $i,SY2614: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV121 @ tc_bool ) ) @ SY2613 ) @ SY2614 )
= SY2613 )
| ~ ( c_lessequals @ SY2613 @ SY2614 @ ( tc_fun @ SV121 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(2023,plain,
! [SV122: $i] :
( ( ! [SY2615: $i,SY2616: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV122 @ tc_bool ) ) @ SY2615 ) @ SY2616 )
= SY2616 )
| ~ ( c_lessequals @ SY2616 @ SY2615 @ ( tc_fun @ SV122 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(2024,plain,
! [SV123: $i] :
( ( ! [SY2617: $i,SY2618: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV123 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SY2617 ) @ SY2618 )
= SY2617 )
| ~ ( c_lessequals @ SY2617 @ SY2618 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(2025,plain,
! [SV124: $i] :
( ( ! [SY2619: $i,SY2620: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV124 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SY2619 ) @ SY2620 )
= SY2620 )
| ~ ( c_lessequals @ SY2620 @ SY2619 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(2026,plain,
! [SV125: $i] :
( ( ! [SY2621: $i,SY2622: $i,SY2623: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SY2621 ) @ SY2622 ) @ SY2623 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SY2622 @ SY2623 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SY2621 @ SY2623 @ ( tc_fun @ SV125 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(2027,plain,
! [SV126: $i] :
( ( ! [SY2624: $i,SY2625: $i] : ( c_lessequals @ SV126 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2624 @ tc_bool ) ) @ SY2625 ) @ SV126 ) @ ( tc_fun @ SY2624 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(2028,plain,
! [SV127: $i] :
( ( ! [SY2626: $i,SY2627: $i] : ( c_lessequals @ SV127 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2626 @ tc_bool ) ) @ SV127 ) @ SY2627 ) @ ( tc_fun @ SY2626 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(2029,plain,
! [SV128: $i] :
( ( ! [SY2628: $i,SY2629: $i,SY2630: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SY2628 ) @ SY2629 ) @ SY2630 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SY2629 @ SY2630 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SY2628 @ SY2630 @ ( tc_fun @ SV128 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(2030,plain,
! [SV129: $i] :
( ( ! [SY2631: $i,SY2632: $i,SY2633: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV129 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SY2631 ) @ SY2632 ) @ SY2633 @ SV129 )
| ~ ( c_lessequals @ SY2632 @ SY2633 @ SV129 )
| ~ ( c_lessequals @ SY2631 @ SY2633 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(2031,plain,
! [SV130: $i] :
( ( ! [SY2634: $i,SY2635: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV130 )
| ( c_lessequals @ SY2634 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 ) @ SY2634 ) @ SY2635 ) @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(2032,plain,
! [SV131: $i] :
( ( ! [SY2636: $i,SY2637: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( c_lessequals @ SY2636 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 ) @ SY2637 ) @ SY2636 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(2033,plain,
! [SV132: $i] :
( ( ! [SY2638: $i,SY2639: $i,SY2640: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SY2638 ) @ SY2639 ) @ SY2640 @ SV132 )
| ~ ( c_lessequals @ SY2639 @ SY2640 @ SV132 )
| ~ ( c_lessequals @ SY2638 @ SY2640 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(2034,plain,
! [SV133: $i] :
( ( ! [SY2641: $i,SY2642: $i,SY2643: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV133 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SY2641 ) @ SY2642 ) @ SY2643 @ SV133 )
| ~ ( c_lessequals @ SY2642 @ SY2643 @ SV133 )
| ~ ( c_lessequals @ SY2641 @ SY2643 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(2035,plain,
! [SV134: $i] :
( ( ! [SY2644: $i,SY2645: $i] :
( ~ ( class_Lattices_Olattice @ SV134 )
| ( c_lessequals @ SY2644 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 ) @ SY2645 ) @ SY2644 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(2036,plain,
! [SV135: $i] :
( ( ! [SY2646: $i,SY2647: $i] :
( ~ ( class_Lattices_Olattice @ SV135 )
| ( c_lessequals @ SY2646 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV135 ) @ SY2646 ) @ SY2647 ) @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(2037,plain,
! [SV136: $i] :
( ( ! [SY2648: $i,SY2649: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV136 @ tc_bool ) ) @ SY2648 ) @ SY2649 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV136 @ tc_bool ) ) @ SY2649 ) @ SY2648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(2038,plain,
! [SV137: $i] :
( ( ! [SY2650: $i,SY2651: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV137 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SY2650 ) @ SY2651 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SY2651 ) @ SY2650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(2039,plain,
! [SV138: $i] :
( ( ! [SY2652: $i,SY2653: $i] :
( ~ ( class_Lattices_Olattice @ SV138 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SY2652 ) @ SY2653 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SY2653 ) @ SY2652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(2040,plain,
! [SV139: $i] :
( ( ! [SY2654: $i,SY2655: $i,SY2656: $i,SY2657: $i,SY2658: $i,SY2659: $i,SY2660: $i,SY2661: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SY2654 @ ( c_COMBC @ SY2655 @ SY2656 @ SY2656 @ tc_bool ) @ ( c_COMBC @ SY2657 @ SY2656 @ SY2656 @ tc_bool ) @ SY2658 @ SY2659 @ SY2660 @ SY2661 @ SY2656 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2654 @ SV139 @ SY2655 @ SY2657 @ SY2659 @ SY2658 @ SY2661 @ SY2660 @ SY2656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(2041,plain,
! [SV140: $i] :
( ( ! [SY2662: $i,SY2663: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV140 @ tc_bool ) ) @ SY2662 ) @ ( c_HOL_Ominus__class_Ominus @ SY2663 @ SY2662 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= SY2663 )
| ~ ( c_lessequals @ SY2662 @ SY2663 @ ( tc_fun @ SV140 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(2042,plain,
! [SV141: $i] :
( ( ! [SY2664: $i,SY2665: $i,SY2666: $i] :
( ~ ( class_Lattices_Olattice @ SV141 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SY2664 ) @ SY2665 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SY2664 ) @ SY2666 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SY2664 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ SY2665 ) @ SY2666 ) ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(2043,plain,
! [SV142: $i] :
( ( ! [SY2667: $i,SY2668: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SY2667 @ ( tc_fun @ SY2668 @ tc_bool ) ) @ SV142 @ ( tc_fun @ SY2668 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(2044,plain,
! [SV143: $i] :
( ( ! [SY2669: $i,SY2670: $i] :
( ( c_Set_Oinsert @ SV143 @ ( c_HOL_Ominus__class_Ominus @ SY2669 @ ( c_Set_Oinsert @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2670 @ tc_bool ) ) @ SY2670 ) @ ( tc_fun @ SY2670 @ tc_bool ) ) @ SY2670 )
= ( c_Set_Oinsert @ SV143 @ SY2669 @ SY2670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(2045,plain,
! [SV144: $i] :
( ( ! [SY2671: $i,SY2672: $i,SY2673: $i] :
( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SY2671 @ SY2672 @ SY2673 ) @ ( tc_fun @ SY2673 @ tc_bool ) )
| ~ ( c_lessequals @ SV144 @ SY2672 @ ( tc_fun @ SY2673 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SY2671 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2673 @ tc_bool ) ) @ SY2673 ) @ ( tc_fun @ SY2673 @ tc_bool ) ) @ SY2672 @ ( tc_fun @ SY2673 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2673 ) @ SY2671 ) @ SY2672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(2046,plain,
! [SV145: $i] :
( ( ! [SY2674: $i,SY2675: $i,SY2676: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY2674 ) @ SY2675 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY2675 ) @ SY2676 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY2676 ) @ SY2674 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY2674 ) @ SY2675 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY2675 ) @ SY2676 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY2676 ) @ SY2674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(2047,plain,
! [SV146: $i] :
( ( ! [SY2677: $i,SY2678: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV146 @ SY2677 @ SY2678 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2678 @ tc_bool ) ) @ SY2678 @ SY2677 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2677 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(2048,plain,
! [SV147: $i] :
( ( ! [SY2679: $i,SY2680: $i,SY2681: $i,SY2682: $i,SY2683: $i] :
( ( c_Finite__Set_Ofold__graph @ SV147 @ SY2679 @ ( c_Set_Oinsert @ SY2680 @ SY2681 @ SY2682 ) @ ( hAPP @ ( hAPP @ SV147 @ SY2679 ) @ SY2683 ) @ SY2682 @ SY2682 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2682 ) @ SY2680 ) @ SY2681 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SY2680 @ SY2681 @ SY2683 @ SY2682 @ SY2682 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SY2682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(2049,plain,
! [SV148: $i] :
( ( ! [SY2684: $i,SY2685: $i,SY2686: $i,SY2687: $i] :
( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SY2684 @ SY2685 @ ( tc_fun @ SY2686 @ tc_bool ) ) @ SY2686 @ SY2687 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SY2684 @ SY2686 @ SY2687 ) @ ( c_Set_Oimage @ SV148 @ SY2685 @ SY2686 @ SY2687 ) @ ( tc_fun @ SY2687 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2686 @ tc_bool ) ) @ SY2686 @ SY2687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(2050,plain,
! [SV149: $i] :
( ( ! [SY2688: $i,SY2689: $i,SY2690: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV149 ) @ SY2688 ) @ SY2689 ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY2688 @ SY2690 @ SV149 ) @ SY2689 @ ( tc_fun @ SV149 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(2051,plain,
! [SV150: $i] :
( ( ! [SY2691: $i,SY2692: $i,SY2693: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV150 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2691 @ ( c_COMBK @ SY2692 @ SV150 @ SY2693 ) @ SY2693 @ SV150 )
= SY2692 )
| ( SY2691
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2693 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(2052,plain,
! [SV151: $i] :
( ( ! [SY2694: $i,SY2695: $i,SY2696: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV151 @ SY2694 @ SY2695 ) @ SY2696 ) )
| ~ ( hBOOL @ ( hAPP @ SY2694 @ SY2696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(2053,plain,
! [SV152: $i] :
( ( ! [SY2697: $i,SY2698: $i,SY2699: $i,SY2700: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SY2697 ) @ ( c_Set_Oimage @ SV152 @ SY2698 @ SY2699 @ SY2700 ) @ SY2700 )
= ( c_Set_Oimage @ SV152 @ SY2698 @ SY2699 @ SY2700 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2699 ) @ SY2697 ) @ SY2698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(2054,plain,
! [SV153: $i] :
( ( ! [SY2701: $i,SY2702: $i,SY2703: $i] :
( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SY2701 @ SY2702 @ SY2703 ) @ ( tc_fun @ SY2703 @ tc_bool ) )
| ~ ( c_lessequals @ SV153 @ SY2702 @ ( tc_fun @ SY2703 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2703 ) @ SY2701 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(2055,plain,
! [SV154: $i] :
( ( ! [SY2704: $i,SY2705: $i,SY2706: $i] :
( ( c_lessequals @ SV154 @ SY2704 @ ( tc_fun @ SY2705 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2705 ) @ SY2706 ) @ SV154 ) )
| ~ ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SY2706 @ SY2704 @ SY2705 ) @ ( tc_fun @ SY2705 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(2056,plain,
! [SV155: $i] :
( ( ! [SY2707: $i,SY2708: $i,SY2709: $i] :
( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SY2707 @ SY2708 @ SY2709 ) @ ( tc_fun @ SY2709 @ tc_bool ) )
| ~ ( c_lessequals @ SV155 @ SY2708 @ ( tc_fun @ SY2709 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2709 ) @ SY2707 ) @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(2057,plain,
! [SV156: $i] :
( ( ! [SY2710: $i,SY2711: $i,SY2712: $i] :
( ( c_lessequals @ SV156 @ SY2710 @ ( tc_fun @ SY2711 @ tc_bool ) )
| ~ ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SY2712 @ SY2710 @ SY2711 ) @ ( tc_fun @ SY2711 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2711 ) @ SY2712 ) @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(2058,plain,
! [SV157: $i] :
( ( ! [SY2713: $i,SY2714: $i,SY2715: $i,SY2716: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SY2713 @ SY2714 @ SY2715 ) @ ( c_Set_Ovimage @ SV157 @ SY2716 @ SY2714 @ SY2715 ) @ ( tc_fun @ SY2714 @ tc_bool ) )
| ~ ( c_lessequals @ SY2713 @ SY2716 @ ( tc_fun @ SY2715 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(2059,plain,
! [SV158: $i] :
( ( ! [SY2717: $i,SY2718: $i,SY2719: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SY2717 ) @ ( c_Set_Oinsert @ SY2718 @ SY2719 @ SV158 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SY2717 ) @ SY2719 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV158 ) @ SY2718 ) @ SY2717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(2060,plain,
! [SV159: $i] :
( ( ! [SY2720: $i,SY2721: $i,SY2722: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2720 @ SY2721 @ SV159 ) ) @ SY2722 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ SY2721 ) @ SY2722 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV159 ) @ SY2720 ) @ SY2722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(2061,plain,
! [SV160: $i] :
( ( ! [SY2723: $i,SY2724: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV160 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2723 @ SY2724 @ ( tc_fun @ SV160 @ tc_bool ) ) ) @ SY2724 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV160 @ tc_bool ) ) @ SY2723 ) @ SY2724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(2062,plain,
! [SV161: $i] :
( ( ! [SY2725: $i,SY2726: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV161 @ tc_bool ) ) @ SY2725 ) @ ( c_HOL_Ominus__class_Ominus @ SY2726 @ SY2725 @ ( tc_fun @ SV161 @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV161 @ tc_bool ) ) @ SY2725 ) @ SY2726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(2063,plain,
! [SV162: $i] :
( ( ! [SY2727: $i,SY2728: $i] :
( ( ( c_Set_Oimage @ SV162 @ SY2727 @ SY2728 @ SY2728 )
= SY2727 )
| ~ ( c_Fun_Oinj__on @ SV162 @ SY2727 @ SY2728 @ SY2728 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SY2727 @ SY2728 @ SY2728 ) @ SY2727 @ ( tc_fun @ SY2728 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY2727 @ SY2728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(2064,plain,
! [SV163: $i] :
( ( ! [SY2729: $i,SY2730: $i,SY2731: $i] :
( ~ ( class_Lattices_Olattice @ SV163 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SY2729 ) @ SY2730 ) ) @ SY2731 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SY2729 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SY2730 ) @ SY2731 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(2065,plain,
! [SV164: $i] :
( ( ! [SY2732: $i,SY2733: $i,SY2734: $i] :
( ~ ( class_Lattices_Olattice @ SV164 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SY2732 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SY2733 ) @ SY2734 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SY2733 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SY2732 ) @ SY2734 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(2066,plain,
! [SV165: $i] :
( ( ! [SY2735: $i,SY2736: $i,SY2737: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV165 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SY2735 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SY2736 ) @ SY2737 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SY2736 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SY2735 ) @ SY2737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(2067,plain,
! [SV166: $i] :
( ( ! [SY2738: $i,SY2739: $i,SY2740: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV166 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SY2738 ) @ SY2739 ) ) @ SY2740 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SY2738 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SY2739 ) @ SY2740 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(2068,plain,
! [SV167: $i] :
( ( ! [SY2741: $i,SY2742: $i,SY2743: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SY2741 ) @ SY2742 ) ) @ SY2743 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SY2741 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SY2742 ) @ SY2743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(2069,plain,
! [SV168: $i] :
( ( ! [SY2744: $i,SY2745: $i,SY2746: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SY2744 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SY2745 ) @ SY2746 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SY2745 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SY2744 ) @ SY2746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(2070,plain,
! [SV169: $i] :
( ( ! [SY2747: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SY2747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV169 @ tc_bool ) ) @ SV169 ) @ SV169 )
= SY2747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(2071,plain,
! [SV170: $i] :
( ( ! [SY2748: $i,SY2749: $i] :
( ( c_Finite__Set_Ofinite @ SV170 @ SY2748 )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2748 @ tc_bool ) ) @ SV170 ) @ SY2749 ) @ SY2748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(2072,plain,
! [SV171: $i] :
( ( ! [SY2750: $i,SY2751: $i] :
( ( c_Finite__Set_Ofinite @ SV171 @ SY2750 )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2750 @ tc_bool ) ) @ SY2751 ) @ SV171 ) @ SY2750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(2073,plain,
! [SV172: $i] :
( ( ! [SY2752: $i,SY2753: $i,SY2754: $i,SY2755: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ SV172 @ SY2752 @ SY2753 @ SY2754 ) @ SY2755 @ SY2753 @ SY2754 )
= ( c_Map_Orestrict__map @ SV172 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2753 @ tc_bool ) ) @ SY2752 ) @ SY2755 ) @ SY2753 @ SY2754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(2074,plain,
! [SV173: $i] :
( ( ! [SY2756: $i,SY2757: $i,SY2758: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV173 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2756 @ tc_bool ) ) @ SY2757 @ SY2756 @ ( tc_fun @ SV173 @ tc_bool ) ) ) @ SY2758 )
= SY2758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(2075,plain,
! [SV174: $i] :
( ( ! [SY2759: $i,SY2760: $i,SY2761: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV174 @ tc_bool ) ) @ SY2759 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2760 @ tc_bool ) ) @ SY2761 @ SY2760 @ ( tc_fun @ SV174 @ tc_bool ) ) )
= SY2759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(2076,plain,
! [SV175: $i] :
( ( ! [SY2762: $i,SY2763: $i,SY2764: $i] :
( ( c_lessequals @ SV175 @ SY2762 @ ( tc_fun @ SY2763 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2763 ) @ SY2764 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2763 ) @ SY2764 ) @ SY2762 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SY2764 @ SY2762 @ SY2763 ) @ ( tc_fun @ SY2763 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(2077,plain,
! [SV176: $i] :
( ( ! [SY2765: $i,SY2766: $i,SY2767: $i] :
( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SY2765 @ SY2766 @ SY2767 ) @ ( tc_fun @ SY2767 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SY2766 @ ( tc_fun @ SY2767 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2767 ) @ SY2765 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2767 ) @ SY2765 ) @ SY2766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(2078,plain,
! [SV177: $i] :
( ( ! [SY2768: $i,SY2769: $i,SY2770: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SY2768 ) @ ( c_HOL_Ominus__class_Ominus @ SY2769 @ SY2770 @ ( tc_fun @ SV177 @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SY2768 ) @ SY2769 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SY2768 ) @ SY2770 ) @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(2079,plain,
! [SV178: $i] :
( ( ! [SY2771: $i,SY2772: $i,SY2773: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2771 @ SY2772 @ ( tc_fun @ SV178 @ tc_bool ) ) ) @ SY2773 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SY2771 ) @ SY2773 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SY2772 ) @ SY2773 ) @ ( tc_fun @ SV178 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(2080,plain,
! [SV179: $i] :
( ( ! [SY2774: $i,SY2775: $i,SY2776: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV179 @ SY2774 @ SY2775 ) @ SY2776 @ SY2775 @ SY2774 )
= ( c_Set_Oinsert @ SV179 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2774 @ tc_bool ) ) @ SY2774 ) )
| ( SY2776
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2775 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(2081,plain,
! [SV180: $i] :
( ( ! [SY2777: $i,SY2778: $i,SY2779: $i] :
( ( c_HOL_Oord__class_Oless @ SV180 @ SY2777 @ ( tc_fun @ SY2778 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2778 ) @ SY2779 ) @ SY2777 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SY2779 @ SY2777 @ SY2778 ) @ ( tc_fun @ SY2778 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(2082,plain,
! [SV181: $i] :
( ( ! [SY2780: $i,SY2781: $i,SY2782: $i] :
( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SY2780 @ SY2781 @ SY2782 ) @ ( tc_fun @ SY2782 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2782 ) @ SY2780 ) @ SY2781 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SY2781 @ ( tc_fun @ SY2782 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(2083,plain,
! [SV182: $i] :
( ( ! [SY2783: $i,SY2784: $i,SY2785: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV182 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SY2783 @ ( c_Set_Oinsert @ SY2784 @ SY2785 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SY2784 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SY2783 @ SY2785 @ SV182 @ SV182 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY2785 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(2084,plain,
! [SV183: $i] :
( ( ! [SY2786: $i,SY2787: $i,SY2788: $i,SY2789: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SY2786 @ ( tc_fun @ SY2787 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2788 @ SY2789 @ ( tc_fun @ SY2787 @ tc_bool ) ) @ ( tc_fun @ SY2787 @ tc_bool ) )
| ~ ( c_lessequals @ SY2789 @ SY2786 @ ( tc_fun @ SY2787 @ tc_bool ) )
| ~ ( c_lessequals @ SV183 @ SY2788 @ ( tc_fun @ SY2787 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(2085,plain,
! [SV184: $i] :
( ( ! [SY2790: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV184 ) @ SY2790 ) @ ( c_Orderings_Otop__class_Otop @ SV184 ) )
= SY2790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(2086,plain,
! [SV185: $i] :
( ( ! [SY2791: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV185 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV185 ) @ ( c_Orderings_Otop__class_Otop @ SV185 ) ) @ SY2791 )
= SY2791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(2087,plain,
! [SV186: $i] :
( ( ! [SY2792: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV186 @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV186 @ tc_bool ) ) ) @ SY2792 )
= SY2792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(2088,plain,
! [SV187: $i] :
( ( ! [SY2793: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV187 @ tc_bool ) ) @ SY2793 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV187 @ tc_bool ) ) )
= SY2793 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(2089,plain,
! [SV188: $i] :
( ( ! [SY2794: $i,SY2795: $i,SY2796: $i] :
( ( c_Set_Oimage @ SV188 @ ( c_Set_Ovimage @ SV188 @ SY2794 @ SY2795 @ SY2796 ) @ SY2795 @ SY2796 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2796 @ tc_bool ) ) @ SY2794 ) @ ( c_Set_Oimage @ SV188 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2795 @ tc_bool ) ) @ SY2795 @ SY2796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(2090,plain,
! [SV189: $i] :
( ( ! [SY2797: $i,SY2798: $i,SY2799: $i] :
( ~ ( class_Lattices_Olattice @ SV189 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SY2797 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ SY2798 ) @ SY2799 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SY2797 ) @ SY2798 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SY2797 ) @ SY2799 ) ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(2091,plain,
! [SV190: $i] :
( ( ! [SY2800: $i,SY2801: $i,SY2802: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SY2800 ) @ SY2801 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SY2802 ) @ SY2801 ) @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SY2800 ) @ SY2801 ) @ SY2802 @ ( tc_fun @ SV190 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(2092,plain,
! [SV191: $i] :
( ( ! [SY2803: $i,SY2804: $i] :
( ~ ( class_Orderings_Opreorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SY2803 @ SY2804 @ SV191 )
| ( c_lessequals @ SY2804 @ SY2803 @ SV191 )
| ~ ( c_lessequals @ SY2803 @ SY2804 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(2093,plain,
! [SV192: $i] :
( ( ! [SY2805: $i] :
~ ( c_HOL_Oord__class_Oless @ SV192 @ SV192 @ ( tc_fun @ SY2805 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(2094,plain,
! [SV193: $i] :
( ( ! [SY2806: $i,SY2807: $i,SY2808: $i] :
( ~ ( class_HOL_Oord @ SV193 )
| ( c_HOL_Oord__class_Oless @ SY2806 @ SY2807 @ ( tc_fun @ SY2808 @ SV193 ) )
| ( c_lessequals @ SY2807 @ SY2806 @ ( tc_fun @ SY2808 @ SV193 ) )
| ~ ( c_lessequals @ SY2806 @ SY2807 @ ( tc_fun @ SY2808 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(2095,plain,
! [SV194: $i] :
( ( ! [SY2809: $i] :
( ~ ( class_Orderings_Oorder @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SY2809 @ SY2809 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(2096,plain,
! [SV195: $i] :
( ( ! [SY2810: $i] :
( ~ ( class_Orderings_Olinorder @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SY2810 @ SY2810 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(2097,plain,
! [SV196: $i] :
( ( ! [SY2811: $i] :
( ~ ( class_Orderings_Opreorder @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ SY2811 @ SY2811 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(2098,plain,
! [SV197: $i] :
( ( ! [SY2812: $i,SY2813: $i] :
( ~ ( class_Lattices_Olattice @ SV197 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 ) @ SY2812 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV197 ) @ SY2812 ) @ SY2813 ) )
= SY2812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(2099,plain,
! [SV198: $i] :
( ( ! [SY2814: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV198 @ tc_bool ) ) @ SY2814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(2100,plain,
! [SV199: $i] :
( ( ~ ( class_Orderings_Otop @ SV199 )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ SV199 ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(2101,plain,
! [SV200: $i] :
( ( ! [SY2815: $i,SY2816: $i] :
( ( c_lessequals @ SV200 @ SY2815 @ ( tc_fun @ SY2816 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SY2816 ) @ SY2816 @ ( tc_fun @ SY2816 @ tc_bool ) @ tc_bool ) @ SV200 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SY2816 ) @ SY2816 @ ( tc_fun @ SY2816 @ tc_bool ) @ tc_bool ) @ SY2815 ) @ ( tc_fun @ SY2816 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(2102,plain,
! [SV201: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SY2817 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SY2818 ) @ ( tc_fun @ SV201 @ tc_bool ) )
| ~ ( c_lessequals @ SY2817 @ SY2818 @ ( tc_fun @ SV201 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(2103,plain,
! [SV202: $i] :
( ( ! [SY2819: $i,SY2820: $i,SY2821: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SY2819 @ ( c_Set_Oinsert @ SY2820 @ SY2821 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SY2820 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SY2819 @ SY2821 @ SV202 @ SV202 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY2821 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(2104,plain,
! [SV203: $i] :
( ( ! [SY2822: $i,SY2823: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV203 )
| ( c_HOL_Oord__class_Oless @ SY2822 @ SY2823 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SY2823 @ SY2822 @ SV203 )
| ( SY2823 = SY2822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(2105,plain,
! [SV204: $i] :
( ( ! [SY2824: $i,SY2825: $i] :
( ~ ( class_Orderings_Olinorder @ SV204 )
| ( SY2824 = SY2825 )
| ( c_HOL_Oord__class_Oless @ SY2825 @ SY2824 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SY2824 @ SY2825 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(2106,plain,
! [SV205: $i] :
( ( ! [SY2826: $i,SY2827: $i] :
( ( SV205 = SY2826 )
| ~ ( c_lessequals @ SY2826 @ SV205 @ ( tc_fun @ SY2827 @ tc_bool ) )
| ~ ( c_lessequals @ SV205 @ SY2826 @ ( tc_fun @ SY2827 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(2107,plain,
! [SV206: $i] :
( ( ! [SY2828: $i,SY2829: $i] :
( ( SV206 = SY2828 )
| ~ ( c_lessequals @ SY2828 @ SV206 @ ( tc_fun @ SY2829 @ tc_bool ) )
| ~ ( c_lessequals @ SV206 @ SY2828 @ ( tc_fun @ SY2829 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(2108,plain,
! [SV207: $i] :
( ( ! [SY2830: $i,SY2831: $i] :
( ~ ( class_Orderings_Oorder @ SV207 )
| ( SY2830 = SY2831 )
| ~ ( c_lessequals @ SY2831 @ SY2830 @ SV207 )
| ~ ( c_lessequals @ SY2830 @ SY2831 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(2109,plain,
! [SV208: $i] :
( ( ! [SY2832: $i,SY2833: $i] :
( ~ ( class_Orderings_Olinorder @ SV208 )
| ( c_HOL_Oord__class_Oless @ SY2832 @ SY2833 @ SV208 )
| ( c_HOL_Oord__class_Oless @ SY2833 @ SY2832 @ SV208 )
| ( SY2833 = SY2832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(2110,plain,
! [SV209: $i] :
( ( ! [SY2834: $i,SY2835: $i] :
( ~ ( class_Orderings_Oorder @ SV209 )
| ( SY2834 = SY2835 )
| ~ ( c_lessequals @ SY2835 @ SY2834 @ SV209 )
| ~ ( c_lessequals @ SY2834 @ SY2835 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(2111,plain,
! [SV210: $i] :
( ( ! [SY2836: $i,SY2837: $i] :
( ~ ( class_Orderings_Oorder @ SV210 )
| ( SY2836 = SY2837 )
| ~ ( c_lessequals @ SY2836 @ SY2837 @ SV210 )
| ~ ( c_lessequals @ SY2837 @ SY2836 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(2112,plain,
! [SV211: $i] :
( ( ! [SY2838: $i,SY2839: $i] :
( ~ ( class_Orderings_Olinorder @ SV211 )
| ( c_HOL_Oord__class_Oless @ SY2838 @ SY2839 @ SV211 )
| ( SY2839 = SY2838 )
| ( c_HOL_Oord__class_Oless @ SY2839 @ SY2838 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(2113,plain,
! [SV212: $i] :
( ( ! [SY2840: $i,SY2841: $i] :
( ~ ( class_Orderings_Olinorder @ SV212 )
| ( SY2840 = SY2841 )
| ( c_HOL_Oord__class_Oless @ SY2840 @ SY2841 @ SV212 )
| ( c_HOL_Oord__class_Oless @ SY2841 @ SY2840 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(2114,plain,
! [SV213: $i] :
( ( ! [SY2842: $i,SY2843: $i] :
( ~ ( class_Lattices_Olattice @ SV213 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 ) @ SY2842 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 ) @ SY2842 ) @ SY2843 ) )
= SY2842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(2115,plain,
! [SV214: $i] :
( ( ! [SY2844: $i,SY2845: $i,SY2846: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV214 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SY2844 ) @ SY2845 ) @ SY2846 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SY2845 @ SY2846 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(2116,plain,
! [SV215: $i] :
( ( ! [SY2847: $i,SY2848: $i,SY2849: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV215 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SY2847 ) @ SY2848 ) @ SY2849 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ SY2847 @ SY2849 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(2117,plain,
! [SV216: $i] :
( ( ! [SY2850: $i,SY2851: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV216 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2850 @ SY2851 @ ( tc_fun @ SV216 @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV216 @ tc_bool ) ) @ SY2850 ) @ SY2851 ) )
= SY2850 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(2118,plain,
! [SV217: $i] :
( ( ! [SY2852: $i,SY2853: $i] :
( ( c_lessequals @ SV217 @ SY2852 @ ( tc_fun @ SY2853 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV217 @ SY2852 @ ( tc_fun @ SY2853 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(2119,plain,
! [SV218: $i] :
( ( ! [SY2854: $i,SY2855: $i,SY2856: $i] :
( ~ ( class_HOL_Oord @ SV218 )
| ( c_lessequals @ SY2854 @ SY2855 @ ( tc_fun @ SY2856 @ SV218 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2854 @ SY2855 @ ( tc_fun @ SY2856 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(2120,plain,
! [SV219: $i] :
( ( ! [SY2857: $i,SY2858: $i] :
( ~ ( class_Orderings_Oorder @ SV219 )
| ( c_lessequals @ SY2857 @ SY2858 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SY2857 @ SY2858 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(2121,plain,
! [SV220: $i] :
( ( ! [SY2859: $i,SY2860: $i] :
( ~ ( class_Orderings_Opreorder @ SV220 )
| ( c_lessequals @ SY2859 @ SY2860 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SY2859 @ SY2860 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(2122,plain,
! [SV221: $i] :
( ( ! [SY2861: $i,SY2862: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV221 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SY2861 ) @ SY2862 )
= SY2861 )
| ~ ( c_lessequals @ SY2862 @ SY2861 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(2123,plain,
! [SV222: $i] :
( ( ! [SY2863: $i,SY2864: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV222 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SY2863 ) @ SY2864 )
= SY2864 )
| ~ ( c_lessequals @ SY2863 @ SY2864 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(2124,plain,
! [SV223: $i] :
( ( ! [SY2865: $i,SY2866: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV223 @ tc_bool ) ) @ SY2865 ) @ SY2866 )
= SY2866 )
| ~ ( c_lessequals @ SY2865 @ SY2866 @ ( tc_fun @ SV223 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(2125,plain,
! [SV224: $i] :
( ( ! [SY2867: $i,SY2868: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV224 @ tc_bool ) ) @ SY2867 ) @ SY2868 )
= SY2867 )
| ~ ( c_lessequals @ SY2868 @ SY2867 @ ( tc_fun @ SV224 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(2126,plain,
! [SV225: $i] :
( ( ! [SY2869: $i,SY2870: $i,SY2871: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV225 @ SY2869 @ SY2870 @ SY2871 ) @ SY2871 )
| ~ ( c_Finite__Set_Ofinite @ SY2869 @ SY2870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(2127,plain,
! [SV226: $i] :
( ( ! [SY2872: $i,SY2873: $i,SY2874: $i] :
( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SY2872 @ SY2873 @ SY2874 ) @ ( tc_fun @ SY2874 @ tc_bool ) )
| ~ ( c_lessequals @ SV226 @ SY2873 @ ( tc_fun @ SY2874 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY2874 ) @ SY2872 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SY2873 @ ( tc_fun @ SY2874 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(2128,plain,
! [SV227: $i] :
( ( ! [SY2875: $i,SY2876: $i] :
( ~ ( class_Orderings_Olinorder @ SV227 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SY2875 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY2876 @ SV227 ) @ SV227 )
| ~ ( c_Finite__Set_Ofinite @ SY2875 @ SV227 )
| ( SY2876
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2876 @ SY2875 @ ( tc_fun @ SV227 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(2129,plain,
! [SV228: $i] :
( ( ! [SY2877: $i,SY2878: $i,SY2879: $i,SY2880: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV228 @ SY2877 @ SY2878 ) @ SY2879 @ SY2878 @ ( tc_fun @ SY2880 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY2880 @ tc_bool ) ) @ ( hAPP @ SY2879 @ SV228 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2877 @ SY2879 @ SY2878 @ ( tc_fun @ SY2880 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(2130,plain,
! [SV229: $i] :
( ( ! [SY2881: $i,SY2882: $i,SY2883: $i,SY2884: $i,SY2885: $i,SY2886: $i,SY2887: $i,SY2888: $i,SY2889: $i,SY2890: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SY2881 @ SY2882 @ SY2883 ) )
= ( hAPP @ ( hAPP @ SY2884 @ SY2881 ) @ ( hAPP @ SV229 @ SY2882 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2885 @ SV229 @ SY2886 @ SY2887 @ SY2888 @ SY2884 @ SY2889 @ SY2890 @ SY2883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(2131,plain,
! [SV230: $i] :
( ( ! [SY2891: $i,SY2892: $i,SY2893: $i,SY2894: $i,SY2895: $i,SY2896: $i,SY2897: $i,SY2898: $i,SY2899: $i,SY2900: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SY2891 @ SY2892 @ SY2893 ) )
= ( hAPP @ ( hAPP @ SY2894 @ SY2891 ) @ ( hAPP @ SV230 @ SY2892 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SY2895 @ SY2896 @ SY2897 @ SY2894 @ SY2898 @ SY2899 @ SY2900 @ SY2893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(2132,plain,
! [SV231: $i] :
( ( ! [SY2901: $i,SY2902: $i] : ( c_Finite__Set_Ofold1Set @ SV231 @ ( c_Set_Oinsert @ SY2901 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2902 @ tc_bool ) ) @ SY2902 ) @ SY2901 @ SY2902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(2133,plain,
! [SV232: $i] :
( ( ! [SY2903: $i,SY2904: $i,SY2905: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SY2903 @ SY2904 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SY2905 @ SY2904 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2905 @ SY2903 @ SY2904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(2134,plain,
! [SV233: $i] :
( ( ! [SY2906: $i,SY2907: $i,SY2908: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2906 @ SY2907 @ SV233 ) ) @ SY2908 )
= ( c_Set_Oinsert @ SY2906 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ SY2907 ) @ SY2908 ) @ SV233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV233 ) @ SY2906 ) @ SY2908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(2135,plain,
! [SV234: $i] :
( ( ! [SY2909: $i,SY2910: $i,SY2911: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SY2909 ) @ ( c_Set_Oinsert @ SY2910 @ SY2911 @ SV234 ) )
= ( c_Set_Oinsert @ SY2910 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SY2909 ) @ SY2911 ) @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV234 ) @ SY2910 ) @ SY2909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(2136,plain,
! [SV235: $i] :
( ( ! [SY2912: $i,SY2913: $i,SY2914: $i,SY2915: $i] :
( ( c_Set_Oimage @ SV235 @ ( c_Set_Oinsert @ SY2912 @ SY2913 @ SY2914 ) @ SY2914 @ SY2915 )
= ( c_Set_Oinsert @ ( hAPP @ SV235 @ SY2912 ) @ ( c_Set_Oimage @ SV235 @ SY2913 @ SY2914 @ SY2915 ) @ SY2915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(2137,plain,
! [SV236: $i] :
( ( ! [SY2916: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV236 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2916 @ tc_bool ) ) @ ( tc_fun @ SY2916 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2916 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(2138,plain,
! [SV237: $i] :
( ( ! [SY2917: $i,SY2918: $i,SY2919: $i,SY2920: $i,SY2921: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV237 @ SY2917 @ SY2918 @ SY2919 @ SY2920 ) @ SY2921 )
= ( hAPP @ SY2917 @ ( hAPP @ SV237 @ SY2921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(2139,plain,
! [SV238: $i] :
( ( ! [SY2922: $i,SY2923: $i,SY2924: $i,SY2925: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SY2922 ) @ SY2923 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SY2924 ) @ SY2925 ) @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SY2923 @ SY2925 @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SY2922 @ SY2924 @ ( tc_fun @ SV238 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(2140,plain,
! [SV239: $i] :
( ( ! [SY2926: $i,SY2927: $i] :
( ~ ( class_Lattices_Olattice @ SV239 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 ) @ SY2926 ) @ SY2927 ) @ SY2926 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(2141,plain,
! [SV240: $i] :
( ( ! [SY2928: $i,SY2929: $i] :
( ~ ( class_Lattices_Olattice @ SV240 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV240 ) @ SY2928 ) @ SY2929 ) @ SY2929 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(2142,plain,
! [SV241: $i] :
( ( ! [SY2930: $i,SY2931: $i,SY2932: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV241 )
| ( c_lessequals @ SY2930 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SY2931 ) @ SY2932 ) @ SV241 )
| ~ ( c_lessequals @ SY2930 @ SY2932 @ SV241 )
| ~ ( c_lessequals @ SY2930 @ SY2931 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(2143,plain,
! [SV242: $i] :
( ( ! [SY2933: $i,SY2934: $i,SY2935: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV242 )
| ( c_lessequals @ SY2933 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SY2934 ) @ SY2935 ) @ SV242 )
| ~ ( c_lessequals @ SY2933 @ SY2935 @ SV242 )
| ~ ( c_lessequals @ SY2933 @ SY2934 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(2144,plain,
! [SV243: $i] :
( ( ! [SY2936: $i,SY2937: $i,SY2938: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV243 )
| ( c_lessequals @ SY2936 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SY2937 ) @ SY2938 ) @ SV243 )
| ~ ( c_lessequals @ SY2936 @ SY2938 @ SV243 )
| ~ ( c_lessequals @ SY2936 @ SY2937 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(2145,plain,
! [SV244: $i] :
( ( ! [SY2939: $i,SY2940: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV244 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV244 ) @ SY2939 ) @ SY2940 ) @ SY2940 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(2146,plain,
! [SV245: $i] :
( ( ! [SY2941: $i,SY2942: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV245 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 ) @ SY2941 ) @ SY2942 ) @ SY2941 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(2147,plain,
! [SV246: $i] :
( ( ! [SY2943: $i,SY2944: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV246 @ tc_bool ) ) @ SY2943 ) @ SY2944 ) @ SY2943 @ ( tc_fun @ SV246 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(2148,plain,
! [SV247: $i] :
( ( ! [SY2945: $i,SY2946: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV247 @ tc_bool ) ) @ SY2945 ) @ SY2946 ) @ SY2946 @ ( tc_fun @ SV247 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(2149,plain,
! [SV248: $i] :
( ( ! [SY2947: $i,SY2948: $i,SY2949: $i] :
( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2947 @ tc_bool ) ) @ SY2948 ) @ SY2949 ) @ ( tc_fun @ SY2947 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY2949 @ ( tc_fun @ SY2947 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY2948 @ ( tc_fun @ SY2947 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(2150,plain,
! [SV249: $i] :
( ( ! [SY2950: $i,SY2951: $i,SY2952: $i] :
( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2950 @ tc_bool ) ) @ SY2951 ) @ SY2952 ) @ ( tc_fun @ SY2950 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SY2952 @ ( tc_fun @ SY2950 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SY2951 @ ( tc_fun @ SY2950 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(2151,plain,
! [SV250: $i] :
( ( ! [SY2953: $i] : ( c_lessequals @ SV250 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY2953 @ tc_bool ) ) @ ( tc_fun @ SY2953 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(2152,plain,
! [SV251: $i] :
( ( ! [SY2954: $i] :
( ~ ( class_Orderings_Otop @ SV251 )
| ( c_lessequals @ SY2954 @ ( c_Orderings_Otop__class_Otop @ SV251 ) @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(2153,plain,
! [SV252: $i] :
( ( ! [SY2955: $i,SY2956: $i,SY2957: $i,SY2958: $i,SY2959: $i,SY2960: $i] :
( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SY2955 @ SY2956 @ SY2957 @ SY2958 @ SY2959 ) @ SY2958 @ SY2960 @ SY2959 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SY2955 @ SY2958 @ SY2960 @ SY2957 ) @ SY2956 @ SY2957 @ SY2960 @ SY2959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(2154,plain,
! [SV253: $i] :
( ( ! [SY2961: $i,SY2962: $i,SY2963: $i] :
( ( c_Set_Oinsert @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2961 @ tc_bool ) ) @ SY2962 @ SY2961 @ ( tc_fun @ SY2963 @ tc_bool ) ) @ SY2963 )
= ( c_Set_Oinsert @ SV253 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2963 @ tc_bool ) ) @ SY2963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(2155,plain,
! [SV254: $i] :
( ( ! [SY2964: $i,SY2965: $i,SY2966: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ SY2964 ) @ SY2965 ) ) @ SY2966 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SY2964 ) @ SY2966 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SY2965 ) @ SY2966 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(2156,plain,
! [SV255: $i] :
( ( ! [SY2967: $i,SY2968: $i,SY2969: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV255 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SY2967 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ SY2968 ) @ SY2969 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SY2967 ) @ SY2968 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SY2967 ) @ SY2969 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(2157,plain,
! [SV256: $i] :
( ( ! [SY2970: $i,SY2971: $i] :
( ~ ( class_HOL_Ominus @ SV256 )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SY2970 @ SY2971 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SY2970 @ v_x ) @ ( hAPP @ SY2971 @ v_x ) @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(2158,plain,
! [SV257: $i] :
( ( ! [SY2972: $i,SY2973: $i,SY2974: $i] :
( ( c_lessequals @ SV257 @ SY2972 @ ( tc_fun @ SY2973 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2973 @ tc_bool ) ) @ SY2974 ) @ SY2972 ) @ ( tc_fun @ SY2973 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(2159,plain,
! [SV258: $i] :
( ( ! [SY2975: $i,SY2976: $i,SY2977: $i] :
( ( c_lessequals @ SV258 @ SY2975 @ ( tc_fun @ SY2976 @ tc_bool ) )
| ~ ( c_lessequals @ SV258 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY2976 @ tc_bool ) ) @ SY2975 ) @ SY2977 ) @ ( tc_fun @ SY2976 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(2160,plain,
! [SV259: $i] :
( ( ! [SY2978: $i,SY2979: $i,SY2980: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV259 )
| ( c_lessequals @ SY2978 @ SY2979 @ SV259 )
| ~ ( c_lessequals @ SY2978 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SY2979 ) @ SY2980 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(2161,plain,
! [SV260: $i] :
( ( ! [SY2981: $i,SY2982: $i,SY2983: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV260 )
| ( c_lessequals @ SY2981 @ SY2982 @ SV260 )
| ~ ( c_lessequals @ SY2981 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SY2983 ) @ SY2982 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(2162,plain,
! [SV261: $i] :
( ( ! [SY2984: $i,SY2985: $i,SY2986: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV261 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SY2984 ) @ SY2985 ) @ SY2986 @ SV261 )
| ~ ( c_lessequals @ SY2984 @ SY2986 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(2163,plain,
! [SV262: $i] :
( ( ! [SY2987: $i,SY2988: $i,SY2989: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV262 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SY2987 ) @ SY2988 ) @ SY2989 @ SV262 )
| ~ ( c_lessequals @ SY2988 @ SY2989 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(2164,plain,
! [SV263: $i] :
( ( ! [SY2990: $i,SY2991: $i,SY2992: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV263 )
| ( c_lessequals @ SY2990 @ SY2991 @ SV263 )
| ~ ( c_lessequals @ SY2990 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SY2991 ) @ SY2992 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(2165,plain,
! [SV264: $i] :
( ( ! [SY2993: $i,SY2994: $i,SY2995: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV264 )
| ( c_lessequals @ SY2993 @ SY2994 @ SV264 )
| ~ ( c_lessequals @ SY2993 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SY2995 ) @ SY2994 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(2166,plain,
! [SV265: $i] :
( ( ! [SY2996: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ SV265 ) @ SY2996 @ SV265 @ SV265 )
= SY2996 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(2167,plain,
! [SV266: $i] :
( ( ! [SY2997: $i,SY2998: $i,SY2999: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ SY2997 ) @ SY2998 ) @ SY2999 @ ( tc_fun @ SV266 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2997 @ SY2999 @ ( tc_fun @ SV266 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2998 @ SY2999 @ ( tc_fun @ SV266 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(2168,plain,
! [SV267: $i] :
( ( ! [SY3000: $i,SY3001: $i,SY3002: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV267 )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SY3000 @ SY3001 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SY3002 ) @ SY3000 ) @ SV267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SY3002 ) @ SY3001 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3001 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(2169,plain,
! [SV268: $i] :
( ( ! [SY3003: $i,SY3004: $i,SY3005: $i,SY3006: $i,SY3007: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ SV268 @ SY3003 @ SY3004 @ SY3005 @ SY3006 ) @ SY3007 @ SY3006 @ SY3005 )
= ( c_Set_Ovimage @ SY3003 @ ( c_Set_Ovimage @ SV268 @ SY3007 @ SY3004 @ SY3005 ) @ SY3006 @ SY3004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(2170,plain,
! [SV269: $i] :
( ( ! [SY3008: $i,SY3009: $i] :
( ( c_Set_Oinsert @ SV269 @ SY3008 @ SY3009 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3009 @ tc_bool ) ) @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY3009 ) @ SY3009 @ SY3009 @ tc_bool ) @ SV269 ) @ SY3009 ) ) @ SY3008 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(2171,plain,
! [SV270: $i] :
( ( ! [SY3010: $i,SY3011: $i,SY3012: $i] :
( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SY3010 @ SY3011 @ SY3012 ) @ ( tc_fun @ SY3012 @ tc_bool ) )
| ~ ( c_lessequals @ SV270 @ SY3011 @ ( tc_fun @ SY3012 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SY3010 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3012 @ tc_bool ) ) @ SY3012 ) @ ( tc_fun @ SY3012 @ tc_bool ) ) @ SY3011 @ ( tc_fun @ SY3012 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SY3011 @ ( tc_fun @ SY3012 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(2172,plain,
! [SV271: $i] :
( ( ! [SY3013: $i,SY3014: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV271 @ tc_bool ) ) @ SY3013 ) @ SY3014 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV271 @ tc_bool ) ) @ SY3014 ) @ SY3013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(2173,plain,
! [SV272: $i] :
( ( ! [SY3015: $i,SY3016: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SY3015 ) @ SY3016 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SY3016 ) @ SY3015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(2174,plain,
! [SV273: $i] :
( ( ! [SY3017: $i,SY3018: $i] :
( ~ ( class_Lattices_Olattice @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SY3017 ) @ SY3018 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SY3018 ) @ SY3017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(2175,plain,
! [SV274: $i] :
( ( ! [SY3019: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ SV274 ) @ SY3019 @ SV274 @ SV274 )
= SY3019 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(2176,plain,
! [SV275: $i] :
( ( ! [SY3020: $i,SY3021: $i] :
( ( c_Set_Oinsert @ SV275 @ SY3020 @ SY3021 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3021 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV275 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3021 @ tc_bool ) ) @ SY3021 ) ) @ SY3020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(2177,plain,
! [SV276: $i] :
( ( ! [SY3022: $i,SY3023: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SY3022 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SY3022 ) @ SY3023 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SY3022 ) @ SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(2178,plain,
! [SV277: $i] :
( ( ! [SY3024: $i,SY3025: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SY3024 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SY3024 ) @ SY3025 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SY3024 ) @ SY3025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(2179,plain,
! [SV278: $i] :
( ( ! [SY3026: $i,SY3027: $i] :
( ~ ( class_Lattices_Olattice @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SY3026 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SY3026 ) @ SY3027 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SY3026 ) @ SY3027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(2180,plain,
! [SV279: $i] :
( ( ! [SY3028: $i,SY3029: $i,SY3030: $i,SY3031: $i,SY3032: $i] :
( ( c_Finite__Set_Ofold__graph @ SV279 @ SY3028 @ ( c_Set_Oinsert @ SY3029 @ ( c_HOL_Ominus__class_Ominus @ SY3030 @ ( c_Set_Oinsert @ SY3028 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3031 @ tc_bool ) ) @ SY3031 ) @ ( tc_fun @ SY3031 @ tc_bool ) ) @ SY3031 ) @ SY3032 @ SY3031 @ SY3031 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3031 ) @ SY3029 ) @ SY3030 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3031 ) @ SY3028 ) @ SY3030 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SY3029 @ SY3030 @ SY3032 @ SY3031 @ SY3031 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SY3031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(2181,plain,
! [SV280: $i] :
( ( ! [SY3033: $i,SY3034: $i,SY3035: $i,SY3036: $i,SY3037: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SY3033 @ SY3034 @ SY3035 @ SY3036 ) @ SY3037 @ SY3036 @ SY3035 )
| ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SY3033 @ SY3037 @ SY3036 @ SY3034 ) @ SY3034 @ SY3035 )
| ~ ( c_Fun_Oinj__on @ SY3033 @ SY3037 @ SY3036 @ SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2182,plain,
! [SV281: $i] :
( ( ! [SY3038: $i,SY3039: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV281 @ tc_bool ) ) @ SY3038 ) @ ( c_HOL_Ominus__class_Ominus @ SY3039 @ SY3038 @ ( tc_fun @ SV281 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV281 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2183,plain,
! [SV282: $i] :
( ( ! [SY3040: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV282 )
| ( c_Finite__Set_Ofinite @ SY3040 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2184,plain,
! [SV283: $i] :
( ( ! [SY3041: $i,SY3042: $i,SY3043: $i,SY3044: $i,SY3045: $i,SY3046: $i] :
( ( c_Finite__Set_Ofold__graph @ SV283 @ SY3041 @ ( c_Set_Oinsert @ SY3042 @ SY3043 @ SY3044 ) @ ( hAPP @ ( hAPP @ SV283 @ SY3042 ) @ SY3045 ) @ SY3044 @ SY3046 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SY3041 @ SY3043 @ SY3045 @ SY3044 @ SY3046 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3044 ) @ SY3042 ) @ SY3043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(2185,plain,
! [SV284: $i] :
( ( ! [SY3047: $i,SY3048: $i,SY3049: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SY3047 ) @ SY3048 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SY3047 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV284 @ tc_bool ) ) @ SY3048 ) @ ( c_Collect @ SY3049 @ SV284 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(2186,plain,
! [SV285: $i] :
( ( ! [SY3050: $i,SY3051: $i,SY3052: $i,SY3053: $i] :
( ( c_Set_Ovimage @ SV285 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3050 @ tc_bool ) ) @ SY3051 ) @ SY3052 ) @ SY3053 @ SY3050 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3053 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV285 @ SY3051 @ SY3053 @ SY3050 ) ) @ ( c_Set_Ovimage @ SV285 @ SY3052 @ SY3053 @ SY3050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2187,plain,
! [SV286: $i] :
( ( ! [SY3054: $i,SY3055: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY3054 @ ( c_Set_Oinsert @ SY3055 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV286 @ tc_bool ) ) @ SV286 ) @ SV286 ) @ SV286 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 ) @ SY3054 ) @ SY3055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2188,plain,
! [SV287: $i] :
( ( ! [SY3056: $i,SY3057: $i,SY3058: $i,SY3059: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SY3056 @ SY3057 ) ) @ ( c_Set_Oimage @ SY3056 @ ( c_HOL_Ominus__class_Ominus @ SY3058 @ ( c_Set_Oinsert @ SY3057 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3059 @ tc_bool ) ) @ SY3059 ) @ ( tc_fun @ SY3059 @ tc_bool ) ) @ SY3059 @ SV287 ) ) )
| ~ ( c_Fun_Oinj__on @ SY3056 @ ( c_Set_Oinsert @ SY3057 @ SY3058 @ SY3059 ) @ SY3059 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2189,plain,
! [SV288: $i] :
( ( ! [SY3060: $i,SY3061: $i,SY3062: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV288 @ SY3060 @ SY3061 ) @ SY3062 @ ( tc_fun @ SY3061 @ tc_bool ) )
= ( c_Set_Oinsert @ SV288 @ ( c_HOL_Ominus__class_Ominus @ SY3060 @ SY3062 @ ( tc_fun @ SY3061 @ tc_bool ) ) @ SY3061 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3061 ) @ SV288 ) @ SY3062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2190,plain,
! [SV289: $i] :
( ( ! [SY3063: $i,SY3064: $i,SY3065: $i,SY3066: $i,SY3067: $i,SY3068: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV289 @ SY3063 @ SY3064 @ ( hAPP @ ( hAPP @ SV289 @ SY3065 ) @ SY3066 ) @ SY3067 @ SY3068 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SY3063 @ ( c_HOL_Ominus__class_Ominus @ SY3064 @ ( c_Set_Oinsert @ SY3065 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3067 @ tc_bool ) ) @ SY3067 ) @ ( tc_fun @ SY3067 @ tc_bool ) ) @ SY3066 @ SY3067 @ SY3068 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3067 ) @ SY3065 ) @ SY3064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(2191,plain,
! [SV290: $i] :
( ( ! [SY3069: $i,SY3070: $i,SY3071: $i] :
( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SY3069 @ SY3070 @ SY3071 ) @ ( tc_fun @ SY3071 @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ SY3070 @ ( tc_fun @ SY3071 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SY3069 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3071 @ tc_bool ) ) @ SY3071 ) @ ( tc_fun @ SY3071 @ tc_bool ) ) @ SY3070 @ ( tc_fun @ SY3071 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(2192,plain,
! [SV291: $i] :
( ( ! [SY3072: $i,SY3073: $i,SY3074: $i] :
( ( hBOOL @ ( hAPP @ SV291 @ SY3072 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3073 @ tc_bool ) ) @ SY3074 ) @ SV291 ) @ SY3072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(2193,plain,
! [SV292: $i] :
( ( ! [SY3075: $i,SY3076: $i,SY3077: $i] :
( ( hBOOL @ ( hAPP @ SV292 @ SY3075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3076 @ tc_bool ) ) @ SV292 ) @ SY3077 ) @ SY3075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(2194,plain,
! [SV293: $i] :
( ( ! [SY3078: $i,SY3079: $i] :
( ( c_Fun_Oinj__on @ SV293 @ SY3078 @ SY3079 @ SY3079 )
| ~ ( c_lessequals @ SY3078 @ ( c_Set_Oimage @ SV293 @ SY3078 @ SY3079 @ SY3079 ) @ ( tc_fun @ SY3079 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3078 @ SY3079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2195,plain,
! [SV294: $i] :
( ( ! [SY3080: $i,SY3081: $i,SY3082: $i,SY3083: $i] :
( ( c_Fun_Oinj__on @ SV294 @ SY3080 @ SY3081 @ SY3082 )
| ~ ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3081 @ tc_bool ) ) @ SY3083 ) @ SY3080 ) @ SY3081 @ SY3082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2196,plain,
! [SV295: $i] :
( ( ! [SY3084: $i,SY3085: $i,SY3086: $i,SY3087: $i] :
( ( c_Fun_Oinj__on @ SV295 @ SY3084 @ SY3085 @ SY3086 )
| ~ ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3085 @ tc_bool ) ) @ SY3084 ) @ SY3087 ) @ SY3085 @ SY3086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2197,plain,
! [SV296: $i] :
( ( ! [SY3088: $i,SY3089: $i,SY3090: $i,SY3091: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SY3088 @ SY3089 @ SY3090 ) @ SY3091 @ ( tc_fun @ SY3089 @ tc_bool ) )
| ~ ( c_lessequals @ SY3088 @ ( c_Set_Oimage @ SV296 @ SY3091 @ SY3089 @ SY3090 ) @ ( tc_fun @ SY3090 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3089 @ tc_bool ) ) @ SY3089 @ SY3090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2198,plain,
! [SV297: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV297 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV297 @ tc_bool ) ) @ SV297 )
= ( c_Orderings_Otop__class_Otop @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2199,plain,
! [SV298: $i] :
( ( ! [SY3092: $i] :
( ( hAPP @ ( c_Fun_Oid @ SV298 ) @ SY3092 )
= SY3092 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(2200,plain,
! [SV299: $i] :
( ( ! [SY3093: $i,SY3094: $i,SY3095: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV299 @ SY3093 @ ( tc_fun @ SY3094 @ tc_bool ) ) @ SY3095 @ ( tc_fun @ SY3094 @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3094 @ tc_bool ) ) @ SY3093 ) @ SY3095 ) @ ( tc_fun @ SY3094 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2201,plain,
! [SV300: $i] :
( ( ! [SY3096: $i,SY3097: $i,SY3098: $i] :
( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3096 @ tc_bool ) ) @ SY3097 ) @ SY3098 ) @ ( tc_fun @ SY3096 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV300 @ SY3097 @ ( tc_fun @ SY3096 @ tc_bool ) ) @ SY3098 @ ( tc_fun @ SY3096 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(2202,plain,
! [SV301: $i] :
( ( ! [SY3099: $i,SY3100: $i] :
( ( c_Finite__Set_Ofinite @ SV301 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ SY3099 @ SY3100 @ SV301 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2203,plain,
! [SV302: $i] :
( ( ! [SY3101: $i,SY3102: $i] :
( ( c_Finite__Set_Ofinite @ SV302 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ SY3101 @ SV302 @ SY3102 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2204,plain,
! [SV303: $i] :
( ( ! [SY3103: $i,SY3104: $i,SY3105: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV303 )
| ( c_HOL_Oord__class_Oless @ SY3103 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SY3104 ) @ SY3105 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SY3103 @ SY3104 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2205,plain,
! [SV304: $i] :
( ( ! [SY3106: $i,SY3107: $i,SY3108: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV304 )
| ( c_HOL_Oord__class_Oless @ SY3106 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SY3107 ) @ SY3108 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SY3106 @ SY3108 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2206,plain,
! [SV305: $i] :
( ( ! [SY3109: $i,SY3110: $i,SY3111: $i,SY3112: $i] :
( ( c_Set_Ovimage @ SV305 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3109 @ tc_bool ) ) @ SY3110 ) @ SY3111 ) @ SY3112 @ SY3109 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3112 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV305 @ SY3110 @ SY3112 @ SY3109 ) ) @ ( c_Set_Ovimage @ SV305 @ SY3111 @ SY3112 @ SY3109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2207,plain,
! [SV306: $i] :
( ( ! [SY3113: $i,SY3114: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV306 @ tc_bool ) ) @ SY3113 ) @ SY3114 ) @ SV306 )
| ~ ( c_Finite__Set_Ofinite @ SY3114 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2208,plain,
! [SV307: $i] :
( ( ! [SY3115: $i,SY3116: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV307 @ tc_bool ) ) @ SY3115 ) @ SY3116 ) @ SV307 )
| ~ ( c_Finite__Set_Ofinite @ SY3115 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2209,plain,
! [SV308: $i] :
( ( ! [SY3117: $i,SY3118: $i,SY3119: $i,SY3120: $i] :
( ~ ( class_HOL_Oord @ SV308 )
| ( c_lessequals @ ( hAPP @ SY3117 @ SY3118 ) @ ( hAPP @ SY3119 @ SY3118 ) @ SV308 )
| ~ ( c_lessequals @ SY3117 @ SY3119 @ ( tc_fun @ SY3120 @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2210,plain,
! [SV309: $i] :
( ( ! [SY3121: $i,SY3122: $i,SY3123: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SY3121 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SY3122 ) @ SY3123 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SY3121 ) @ SY3123 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SY3121 ) @ SY3122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2211,plain,
! [SV310: $i] :
( ( ! [SY3124: $i,SY3125: $i,SY3126: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SY3124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SY3125 ) @ SY3126 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SY3124 ) @ SY3126 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SY3124 ) @ SY3125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2212,plain,
! [SV311: $i] :
( ( ! [SY3127: $i,SY3128: $i,SY3129: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SY3127 ) @ ( c_Set_Oinsert @ SY3128 @ SY3129 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SY3127 ) @ SY3129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2213,plain,
! [SV312: $i] :
( ( ! [SY3130: $i,SY3131: $i,SY3132: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SY3130 ) @ ( c_Set_Oinsert @ SY3131 @ SY3132 @ SV312 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SY3130 ) @ SY3132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2214,plain,
! [SV313: $i] :
( ( ! [SY3133: $i,SY3134: $i,SY3135: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SY3133 ) @ SY3134 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SY3133 ) @ SY3135 ) )
| ~ ( c_lessequals @ SY3135 @ SY3134 @ ( tc_fun @ SV313 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(2215,plain,
! [SV314: $i] :
( ( ! [SY3136: $i,SY3137: $i,SY3138: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SY3136 ) @ SY3137 ) )
| ~ ( c_lessequals @ SY3138 @ SY3137 @ ( tc_fun @ SV314 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SY3136 ) @ SY3138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(2216,plain,
! [SV315: $i] :
( ( ! [SY3139: $i,SY3140: $i,SY3141: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SY3139 ) @ SY3140 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SY3139 ) @ SY3141 ) )
| ~ ( c_lessequals @ SY3141 @ SY3140 @ ( tc_fun @ SV315 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(2217,plain,
! [SV316: $i] :
( ( ! [SY3142: $i,SY3143: $i,SY3144: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SY3142 ) @ SY3143 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SY3142 ) @ SY3144 ) )
| ~ ( c_lessequals @ SY3144 @ SY3143 @ ( tc_fun @ SV316 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2218,plain,
! [SV317: $i] :
( ( ! [SY3145: $i,SY3146: $i,SY3147: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SY3145 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV317 @ tc_bool ) ) @ SY3146 ) @ SY3147 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SY3145 ) @ SY3146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2219,plain,
! [SV318: $i] :
( ( ! [SY3148: $i,SY3149: $i,SY3150: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SY3148 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV318 @ tc_bool ) ) @ SY3149 ) @ SY3150 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SY3148 ) @ SY3150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2220,plain,
! [SV319: $i] :
( ( ! [SY3151: $i,SY3152: $i,SY3153: $i,SY3154: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SY3151 @ SY3152 @ SY3153 ) @ SY3154 )
= ( hAPP @ SV319 @ SY3154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3152 ) @ SY3154 ) @ SY3151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2221,plain,
! [SV320: $i] :
( ( ! [SY3155: $i,SY3156: $i,SY3157: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SY3155 ) @ SY3156 ) )
| ( SY3155 = SY3157 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SY3155 ) @ ( c_Set_Oinsert @ SY3157 @ SY3156 @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2222,plain,
! [SV321: $i] :
( ( ! [SY3158: $i,SY3159: $i,SY3160: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SY3158 ) @ SY3159 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SY3158 ) @ SY3160 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SY3158 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SY3160 ) @ SY3159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2223,plain,
! [SV322: $i] :
( ( ! [SY3161: $i,SY3162: $i,SY3163: $i,SY3164: $i,SY3165: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SY3161 @ SY3162 @ SY3163 @ SY3164 ) @ SY3165 )
= ( hAPP @ SY3161 @ SY3165 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3163 ) @ SY3165 ) @ SY3162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2224,plain,
! [SV323: $i] :
( ( ! [SY3166: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV323 ) @ SY3166 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV323 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2225,plain,
! [SV324: $i] :
( ( ! [SY3167: $i,SY3168: $i,SY3169: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SY3167 ) @ SY3168 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SY3167 ) @ ( c_HOL_Ominus__class_Ominus @ SY3169 @ SY3168 @ ( tc_fun @ SV324 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2226,plain,
! [SV325: $i] :
( ( ! [SY3170: $i,SY3171: $i,SY3172: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SY3170 ) @ SY3171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SY3170 ) @ ( c_HOL_Ominus__class_Ominus @ SY3171 @ SY3172 @ ( tc_fun @ SV325 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2227,plain,
! [SV326: $i] :
( ( ! [SY3173: $i,SY3174: $i,SY3175: $i,SY3176: $i,SY3177: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SY3173 @ SY3174 @ SY3175 @ SY3176 ) @ SY3177 )
= ( hAPP @ SV326 @ SY3177 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3175 ) @ SY3177 ) @ SY3174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2228,plain,
! [SV327: $i] :
( ( ! [SY3178: $i,SY3179: $i,SY3180: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SY3178 ) @ SY3179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SY3178 ) @ SY3180 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3180 @ SY3179 @ ( tc_fun @ SV327 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2229,plain,
! [SV328: $i] :
( ( ! [SY3181: $i,SY3182: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV328 ) @ SY3181 ) @ ( c_Set_Oinsert @ SY3181 @ SY3182 @ SV328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2230,plain,
! [SV329: $i] :
( ( ! [SY3183: $i,SY3184: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV329 ) @ SY3183 ) @ ( c_Set_Oinsert @ SY3183 @ SY3184 @ SV329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2231,plain,
! [SV330: $i] :
( ( ! [SY3185: $i,SY3186: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV330 ) @ SY3185 ) @ ( c_Set_Oinsert @ SY3185 @ SY3186 @ SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2232,plain,
! [SV331: $i] :
( ( ! [SY3187: $i,SY3188: $i,SY3189: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SY3187 ) @ SY3188 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SY3187 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV331 @ tc_bool ) ) @ SY3189 ) @ SY3188 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2233,plain,
! [SV332: $i] :
( ( ! [SY3190: $i,SY3191: $i,SY3192: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SY3190 ) @ SY3191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SY3190 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV332 @ tc_bool ) ) @ SY3191 ) @ SY3192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2234,plain,
! [SV333: $i] :
( ( ! [SY3193: $i,SY3194: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV333 ) @ SY3193 ) @ ( c_Collect @ SY3194 @ SV333 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY3194 @ SY3193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2235,plain,
! [SV334: $i] :
( ( ! [SY3195: $i,SY3196: $i] :
( ( hBOOL @ ( hAPP @ SV334 @ SY3195 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3196 ) @ SY3195 ) @ ( c_Collect @ SV334 @ SY3196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2236,plain,
! [SV335: $i] :
( ( ! [SY3197: $i,SY3198: $i,SY3199: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SY3197 ) @ ( c_HOL_Ominus__class_Ominus @ SY3198 @ SY3199 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SY3197 ) @ SY3199 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SY3197 ) @ SY3198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2237,plain,
! [SV336: $i] :
( ( ! [SY3200: $i,SY3201: $i,SY3202: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SY3200 ) @ ( c_HOL_Ominus__class_Ominus @ SY3201 @ SY3202 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SY3200 ) @ SY3202 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SY3200 ) @ SY3201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2238,plain,
! [SV337: $i] :
( ( ! [SY3203: $i,SY3204: $i,SY3205: $i,SY3206: $i,SY3207: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SY3203 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3204 @ SY3205 @ SY3206 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SY3203 ) @ ( hAPP @ SY3205 @ SY3207 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3206 ) @ SY3207 ) @ SY3204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2239,plain,
! [SV338: $i] :
( ( ! [SY3208: $i,SY3209: $i,SY3210: $i,SY3211: $i,SY3212: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SY3208 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3209 @ SY3210 @ SY3211 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SY3208 ) @ ( hAPP @ SY3210 @ SY3212 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3211 ) @ SY3212 ) @ SY3209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2240,plain,
! [SV339: $i] :
( ( ! [SY3213: $i,SY3214: $i,SY3215: $i,SY3216: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SY3213 ) @ ( c_Set_Ovimage @ SY3214 @ SY3215 @ SV339 @ SY3216 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3216 ) @ ( hAPP @ SY3214 @ SY3213 ) ) @ SY3215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2241,plain,
! [SV340: $i] :
( ( ! [SY3217: $i,SY3218: $i,SY3219: $i,SY3220: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SY3217 ) @ ( c_Set_Ovimage @ SY3218 @ SY3219 @ SV340 @ SY3220 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3220 ) @ ( hAPP @ SY3218 @ SY3217 ) ) @ SY3219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2242,plain,
! [SV341: $i] :
( ( ! [SY3221: $i,SY3222: $i,SY3223: $i,SY3224: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SY3221 ) @ ( c_Set_Ovimage @ SY3222 @ SY3223 @ SV341 @ SY3224 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3224 ) @ ( hAPP @ SY3222 @ SY3221 ) ) @ SY3223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2243,plain,
! [SV342: $i] :
( ( ! [SY3225: $i,SY3226: $i,SY3227: $i,SY3228: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SY3225 @ SY3226 ) ) @ SY3227 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3228 ) @ SY3226 ) @ ( c_Set_Ovimage @ SY3225 @ SY3227 @ SY3228 @ SV342 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2244,plain,
! [SV343: $i] :
( ( ! [SY3229: $i,SY3230: $i,SY3231: $i,SY3232: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SY3229 @ SY3230 ) ) @ SY3231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3232 ) @ SY3230 ) @ ( c_Set_Ovimage @ SY3229 @ SY3231 @ SY3232 @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2245,plain,
! [SV344: $i] :
( ( ! [SY3233: $i,SY3234: $i,SY3235: $i,SY3236: $i,SY3237: $i,SY3238: $i,SY3239: $i,SY3240: $i,SY3241: $i,SY3242: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SY3233 @ SY3234 ) ) @ SY3235 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3236 ) @ SY3235 ) @ SY3234 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3233 @ SY3237 @ SV344 @ SY3238 @ SY3239 @ SY3240 @ SY3241 @ SY3242 @ SY3236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2246,plain,
! [SV345: $i] :
( ( ! [SY3243: $i,SY3244: $i,SY3245: $i,SY3246: $i,SY3247: $i,SY3248: $i,SY3249: $i,SY3250: $i,SY3251: $i,SY3252: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SY3243 ) @ ( hAPP @ SY3244 @ SY3245 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3246 ) @ SY3243 ) @ SY3245 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3247 @ SY3244 @ SV345 @ SY3248 @ SY3249 @ SY3250 @ SY3251 @ SY3252 @ SY3246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2247,plain,
! [SV346: $i] :
( ( ! [SY3253: $i,SY3254: $i] :
( ( ( c_Set_Oinsert @ SV346 @ SY3253 @ SY3254 )
= SY3253 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3254 ) @ SV346 ) @ SY3253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2248,plain,
! [SV347: $i] :
( ( ! [SY3255: $i,SY3256: $i,SY3257: $i,SY3258: $i,SY3259: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SY3255 @ SY3256 @ ( tc_fun @ SY3257 @ tc_bool ) ) @ SY3258 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3255 @ SY3259 ) @ SY3258 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3256 ) @ SY3259 ) @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2249,plain,
! [SV348: $i] :
( ( ! [SY3260: $i,SY3261: $i,SY3262: $i,SY3263: $i,SY3264: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SY3260 @ SY3261 @ ( tc_fun @ SY3262 @ tc_bool ) ) @ SY3263 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3260 @ SY3264 ) @ SY3263 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3261 ) @ SY3264 ) @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2250,plain,
! [SV349: $i] :
( ( ! [SY3265: $i,SY3266: $i,SY3267: $i,SY3268: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SY3265 ) @ SY3266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3267 ) @ ( hAPP @ SY3268 @ SY3265 ) ) @ ( c_Set_Oimage @ SY3268 @ SY3266 @ SV349 @ SY3267 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2251,plain,
! [SV350: $i] :
( ( ! [SY3269: $i,SY3270: $i,SY3271: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SY3269 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ SY3270 ) @ SY3271 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SY3269 ) @ SY3270 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SY3269 ) @ SY3271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2252,plain,
! [SV351: $i] :
( ( ! [SY3272: $i,SY3273: $i,SY3274: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ SY3272 ) @ SY3273 ) ) @ SY3274 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SY3272 ) @ SY3274 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SY3273 ) @ SY3274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2253,plain,
! [SV352: $i] :
( ( ! [SY3275: $i,SY3276: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV352 @ SY3275 @ SY3276 ) @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2254,plain,
! [SV353: $i] :
( ( ! [SY3277: $i,SY3278: $i,SY3279: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SY3277 @ SY3278 ) @ SY3279 @ ( tc_fun @ SY3278 @ tc_bool ) )
| ~ ( c_lessequals @ SY3277 @ SY3279 @ ( tc_fun @ SY3278 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3278 ) @ SV353 ) @ SY3279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2255,plain,
! [SV354: $i] :
( ( ! [SY3280: $i,SY3281: $i] :
( ~ ( class_Lattices_Olattice @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SY3280 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SY3280 ) @ SY3281 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SY3280 ) @ SY3281 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2256,plain,
! [SV355: $i] :
( ( ! [SY3282: $i,SY3283: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV355 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SY3282 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SY3282 ) @ SY3283 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SY3282 ) @ SY3283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2257,plain,
! [SV356: $i] :
( ( ! [SY3284: $i,SY3285: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SY3284 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SY3284 ) @ SY3285 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SY3284 ) @ SY3285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2258,plain,
! [SV357: $i] :
( ( ! [SY3286: $i,SY3287: $i,SY3288: $i,SY3289: $i,SY3290: $i,SY3291: $i,SY3292: $i,SY3293: $i,SY3294: $i,SY3295: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SY3286 ) @ ( hAPP @ SY3287 @ SY3288 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SY3286 @ SY3288 @ SY3289 @ SY3289 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3288 @ SY3289 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3290 @ SY3287 @ SY3291 @ SY3292 @ SY3293 @ SV357 @ SY3294 @ SY3295 @ SY3289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2259,plain,
! [SV358: $i] :
( ( ! [SY3296: $i,SY3297: $i,SY3298: $i,SY3299: $i,SY3300: $i,SY3301: $i,SY3302: $i,SY3303: $i,SY3304: $i,SY3305: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SY3296 ) @ ( hAPP @ SY3297 @ SY3298 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SY3296 @ SY3298 @ SY3299 @ SY3299 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3298 @ SY3299 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3297 @ SY3300 @ SY3301 @ SY3302 @ SV358 @ SY3303 @ SY3304 @ SY3305 @ SY3299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2260,plain,
! [SV359: $i] :
( ( ! [SY3306: $i,SY3307: $i,SY3308: $i,SY3309: $i,SY3310: $i,SY3311: $i,SY3312: $i,SY3313: $i,SY3314: $i] :
( ( ( hAPP @ SV359 @ SY3306 )
= ( c_Finite__Set_Ofold @ SY3307 @ SY3308 @ SY3306 @ SY3309 @ SY3309 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3306 @ SY3309 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3310 @ SV359 @ SY3311 @ SY3312 @ SY3313 @ SY3307 @ SY3308 @ SY3314 @ SY3309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2261,plain,
! [SV360: $i] :
( ( ! [SY3315: $i,SY3316: $i,SY3317: $i,SY3318: $i,SY3319: $i,SY3320: $i,SY3321: $i,SY3322: $i,SY3323: $i] :
( ( ( hAPP @ SV360 @ SY3315 )
= ( c_Finite__Set_Ofold @ SY3316 @ SY3317 @ SY3315 @ SY3318 @ SY3318 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3315 @ SY3318 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SY3319 @ SY3320 @ SY3321 @ SY3316 @ SY3322 @ SY3323 @ SY3317 @ SY3318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2262,plain,
! [SV361: $i] :
( ( ! [SY3324: $i,SY3325: $i,SY3326: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SY3324 @ ( tc_fun @ SY3325 @ tc_bool ) ) @ SY3325 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SY3326 @ SY3324 @ SY3325 ) @ ( tc_fun @ SY3325 @ tc_bool ) ) @ SY3325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2263,plain,
! [SV362: $i] :
( ( ! [SY3327: $i,SY3328: $i,SY3329: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ ( c_Set_Oinsert @ SY3327 @ SY3328 @ SY3329 ) @ ( tc_fun @ SY3329 @ tc_bool ) ) @ SY3329 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ SY3328 @ ( tc_fun @ SY3329 @ tc_bool ) ) @ SY3329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2264,plain,
! [SV363: $i] :
( ( ! [SY3330: $i,SY3331: $i] :
( ( c_Fun_Ofcomp @ SV363 @ ( c_Fun_Oid @ SY3330 ) @ SY3331 @ SY3330 @ SY3330 )
= SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2265,plain,
! [SV364: $i] :
( ( ! [SY3332: $i,SY3333: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ SV364 ) @ SY3332 @ SV364 @ SV364 @ SY3333 )
= SY3332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2266,plain,
! [SV365: $i] :
( ( ! [SY3334: $i,SY3335: $i,SY3336: $i,SY3337: $i,SY3338: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV365 @ SY3334 @ SY3335 @ SY3336 @ SY3337 ) @ SY3338 @ SY3337 @ SY3336 )
= ( c_Set_Oimage @ SV365 @ ( c_Set_Oimage @ SY3334 @ SY3338 @ SY3337 @ SY3335 ) @ SY3335 @ SY3336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2267,plain,
! [SV366: $i] :
( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV366 )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV366 @ tc_bool ) ) @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2268,plain,
! [SV367: $i] :
( ( ! [SY3339: $i,SY3340: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV367 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SY3339 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SY3340 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SY3339 @ SY3340 @ SV367 @ SV367 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3340 @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2269,plain,
! [SV368: $i] :
( ( ! [SY3341: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV368 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV368 ) @ SY3341 ) @ SY3341 )
= SY3341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2270,plain,
! [SV369: $i] :
( ( ! [SY3342: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV369 @ tc_bool ) ) @ SY3342 ) @ SY3342 )
= SY3342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2271,plain,
! [SV370: $i] :
( ( ! [SY3343: $i,SY3344: $i,SY3345: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV370 )
| ( c_lessequals @ SY3343 @ SY3344 @ SV370 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SY3345 ) @ SY3343 ) @ SY3344 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2272,plain,
! [SV371: $i] :
( ( ! [SY3346: $i,SY3347: $i,SY3348: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV371 )
| ( c_lessequals @ SY3346 @ SY3347 @ SV371 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SY3346 ) @ SY3348 ) @ SY3347 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2273,plain,
! [SV372: $i] :
( ( ! [SY3349: $i,SY3350: $i,SY3351: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV372 )
| ( c_lessequals @ SY3349 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SY3350 ) @ SY3351 ) @ SV372 )
| ~ ( c_lessequals @ SY3349 @ SY3351 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2274,plain,
! [SV373: $i] :
( ( ! [SY3352: $i,SY3353: $i,SY3354: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV373 )
| ( c_lessequals @ SY3352 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SY3353 ) @ SY3354 ) @ SV373 )
| ~ ( c_lessequals @ SY3352 @ SY3353 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2275,plain,
! [SV374: $i] :
( ( ! [SY3355: $i,SY3356: $i,SY3357: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV374 )
| ( c_lessequals @ SY3355 @ SY3356 @ SV374 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SY3357 ) @ SY3355 ) @ SY3356 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2276,plain,
! [SV375: $i] :
( ( ! [SY3358: $i,SY3359: $i,SY3360: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV375 )
| ( c_lessequals @ SY3358 @ SY3359 @ SV375 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SY3358 ) @ SY3360 ) @ SY3359 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2277,plain,
! [SV376: $i] :
( ( ! [SY3361: $i,SY3362: $i,SY3363: $i] :
( ( c_lessequals @ SV376 @ SY3361 @ ( tc_fun @ SY3362 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3362 @ tc_bool ) ) @ SV376 ) @ SY3363 ) @ SY3361 @ ( tc_fun @ SY3362 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2278,plain,
! [SV377: $i] :
( ( ! [SY3364: $i,SY3365: $i,SY3366: $i] :
( ( c_lessequals @ SV377 @ SY3364 @ ( tc_fun @ SY3365 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3365 @ tc_bool ) ) @ SY3366 ) @ SV377 ) @ SY3364 @ ( tc_fun @ SY3365 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2279,plain,
! [SV378: $i] :
( ( ! [SY3367: $i,SY3368: $i] :
( ~ ( class_Lattices_Olattice @ SV378 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ SV378 ) ) @ SY3367 ) @ SY3368 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 ) @ ( hAPP @ SY3367 @ v_x ) ) @ ( hAPP @ SY3368 @ v_x ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2280,plain,
! [SV379: $i] :
( ( ! [SY3369: $i,SY3370: $i,SY3371: $i] :
( ~ ( class_Orderings_Oorder @ SV379 )
| ( c_lessequals @ SY3369 @ SY3370 @ SV379 )
| ~ ( c_lessequals @ SY3369 @ SY3371 @ SV379 )
| ~ ( c_lessequals @ SY3371 @ SY3370 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2281,plain,
! [SV380: $i] :
( ( ! [SY3372: $i,SY3373: $i,SY3374: $i] :
( ~ ( class_Orderings_Oorder @ SV380 )
| ( c_HOL_Oord__class_Oless @ SY3372 @ SY3373 @ SV380 )
| ~ ( c_lessequals @ SY3372 @ SY3374 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SY3374 @ SY3373 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2282,plain,
! [SV381: $i] :
( ( ! [SY3375: $i,SY3376: $i,SY3377: $i] :
( ~ ( class_Orderings_Oorder @ SV381 )
| ( c_HOL_Oord__class_Oless @ SY3375 @ SY3376 @ SV381 )
| ~ ( c_HOL_Oord__class_Oless @ SY3375 @ SY3377 @ SV381 )
| ~ ( c_lessequals @ SY3377 @ SY3376 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2283,plain,
! [SV382: $i] :
( ( ! [SY3378: $i,SY3379: $i,SY3380: $i] :
( ~ ( class_Orderings_Opreorder @ SV382 )
| ( c_lessequals @ SY3378 @ SY3379 @ SV382 )
| ~ ( c_lessequals @ SY3380 @ SY3379 @ SV382 )
| ~ ( c_lessequals @ SY3378 @ SY3380 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2284,plain,
! [SV383: $i] :
( ( ! [SY3381: $i] : ( c_lessequals @ SV383 @ SV383 @ ( tc_fun @ SY3381 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2285,plain,
! [SV384: $i] :
( ( ! [SY3382: $i] : ( c_lessequals @ SV384 @ SV384 @ ( tc_fun @ SY3382 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2286,plain,
! [SV385: $i] :
( ( ! [SY3383: $i,SY3384: $i,SY3385: $i] :
( ( c_lessequals @ SV385 @ SY3383 @ ( tc_fun @ SY3384 @ tc_bool ) )
| ~ ( c_lessequals @ SY3385 @ SY3383 @ ( tc_fun @ SY3384 @ tc_bool ) )
| ~ ( c_lessequals @ SV385 @ SY3385 @ ( tc_fun @ SY3384 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2287,plain,
! [SV386: $i] :
( ( ! [SY3386: $i,SY3387: $i,SY3388: $i,SY3389: $i] :
( ( c_Fun_Oinj__on @ SV386 @ SY3386 @ SY3387 @ SY3388 )
| ~ ( c_lessequals @ SY3386 @ SY3389 @ ( tc_fun @ SY3387 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV386 @ SY3389 @ SY3387 @ SY3388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2288,plain,
! [SV387: $i] :
( ( ! [SY3390: $i,SY3391: $i,SY3392: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ SY3390 ) )
| ~ ( hBOOL @ ( hAPP @ SY3391 @ SY3390 ) )
| ~ ( c_lessequals @ SY3391 @ SV387 @ ( tc_fun @ SY3392 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2289,plain,
! [SV388: $i] :
( ( ! [SY3393: $i] :
( ~ ( class_Orderings_Oorder @ SV388 )
| ( c_lessequals @ SY3393 @ SY3393 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2290,plain,
! [SV389: $i] :
( ( ! [SY3394: $i] :
( ~ ( class_Orderings_Opreorder @ SV389 )
| ( c_lessequals @ SY3394 @ SY3394 @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2291,plain,
! [SV390: $i] :
( ( ! [SY3395: $i,SY3396: $i] :
( ( c_Finite__Set_Ofinite @ SV390 @ SY3395 )
| ~ ( c_Finite__Set_Ofinite @ SY3396 @ SY3395 )
| ~ ( c_lessequals @ SV390 @ SY3396 @ ( tc_fun @ SY3395 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2292,plain,
! [SV391: $i] :
( ( ! [SY3397: $i,SY3398: $i,SY3399: $i] :
( ( c_HOL_Oord__class_Oless @ SV391 @ SY3397 @ ( tc_fun @ SY3398 @ tc_bool ) )
| ~ ( c_lessequals @ SY3399 @ SY3397 @ ( tc_fun @ SY3398 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV391 @ SY3399 @ ( tc_fun @ SY3398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2293,plain,
! [SV392: $i] :
( ( ! [SY3400: $i,SY3401: $i,SY3402: $i] :
( ( c_HOL_Oord__class_Oless @ SV392 @ SY3400 @ ( tc_fun @ SY3401 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3402 @ SY3400 @ ( tc_fun @ SY3401 @ tc_bool ) )
| ~ ( c_lessequals @ SV392 @ SY3402 @ ( tc_fun @ SY3401 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2294,plain,
! [SV393: $i] :
( ( ! [SY3403: $i,SY3404: $i,SY3405: $i] :
( ( hBOOL @ ( hAPP @ SV393 @ SY3403 ) )
| ~ ( c_lessequals @ SY3404 @ SV393 @ ( tc_fun @ SY3405 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY3404 @ SY3403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2295,plain,
! [SV394: $i] :
( ( ! [SY3406: $i,SY3407: $i] :
( ( c_Finite__Set_Ofinite @ SV394 @ SY3406 )
| ~ ( c_lessequals @ SV394 @ SY3407 @ ( tc_fun @ SY3406 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3407 @ SY3406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2296,plain,
! [SV395: $i] :
( ( ! [SY3408: $i,SY3409: $i,SY3410: $i] :
( ~ ( class_Orderings_Opreorder @ SV395 )
| ( c_HOL_Oord__class_Oless @ SY3408 @ SY3409 @ SV395 )
| ~ ( c_HOL_Oord__class_Oless @ SY3410 @ SY3409 @ SV395 )
| ~ ( c_lessequals @ SY3408 @ SY3410 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2297,plain,
! [SV396: $i] :
( ( ! [SY3411: $i,SY3412: $i,SY3413: $i] :
( ~ ( class_Orderings_Opreorder @ SV396 )
| ( c_HOL_Oord__class_Oless @ SY3411 @ SY3412 @ SV396 )
| ~ ( c_lessequals @ SY3413 @ SY3412 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SY3411 @ SY3413 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2298,plain,
! [SV397: $i] :
( ( ! [SY3414: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV397 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY3414 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV397 @ tc_bool ) ) @ SV397 ) @ SV397 )
= SY3414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2299,plain,
! [SV398: $i] :
( ( ! [SY3415: $i,SY3416: $i,SY3417: $i,SY3418: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SY3415 ) @ SY3416 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SY3417 ) @ SY3418 ) @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SY3416 @ SY3418 @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SY3415 @ SY3417 @ ( tc_fun @ SV398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2300,plain,
! [SV399: $i] :
( ( ! [SY3419: $i,SY3420: $i,SY3421: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV399 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3419 @ tc_bool ) ) @ SY3420 ) @ SY3421 ) @ ( tc_fun @ SY3419 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3419 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SY3420 @ ( tc_fun @ SY3419 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SY3421 @ ( tc_fun @ SY3419 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2301,plain,
! [SV400: $i] :
( ( ! [SY3422: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV400 ) @ SV400 @ SV400 @ tc_bool ) @ SY3422 ) @ SV400 )
= ( c_Set_Oinsert @ SY3422 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV400 @ tc_bool ) ) @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2302,plain,
! [SV401: $i] :
( ( ! [SY3423: $i,SY3424: $i,SY3425: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SY3423 ) @ SY3424 ) @ SY3425 @ ( tc_fun @ SV401 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SY3423 ) @ ( c_HOL_Ominus__class_Ominus @ SY3424 @ SY3425 @ ( tc_fun @ SV401 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2303,plain,
! [SV402: $i] :
( ( ! [SY3426: $i,SY3427: $i,SY3428: $i,SY3429: $i,SY3430: $i] :
( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SY3426 @ SY3427 @ ( tc_fun @ SY3428 @ tc_bool ) ) @ SY3428 @ SY3429 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SY3426 @ SY3428 @ SY3429 ) @ ( c_Set_Oimage @ SV402 @ SY3427 @ SY3428 @ SY3429 ) @ ( tc_fun @ SY3429 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY3427 @ SY3430 @ ( tc_fun @ SY3428 @ tc_bool ) )
| ~ ( c_lessequals @ SY3426 @ SY3430 @ ( tc_fun @ SY3428 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SY3430 @ SY3428 @ SY3429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2304,plain,
! [SV403: $i] :
( ( ! [SY3431: $i,SY3432: $i,SY3433: $i,SY3434: $i,SY3435: $i,SY3436: $i,SY3437: $i,SY3438: $i,SY3439: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SY3431 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3432 @ tc_bool ) ) @ SY3432 ) )
= SY3431 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3433 @ SV403 @ SY3434 @ SY3435 @ SY3436 @ SY3437 @ SY3438 @ SY3439 @ SY3432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2305,plain,
! [SV404: $i] :
( ( ! [SY3440: $i,SY3441: $i,SY3442: $i,SY3443: $i,SY3444: $i,SY3445: $i,SY3446: $i,SY3447: $i,SY3448: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SY3440 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3441 @ tc_bool ) ) @ SY3441 ) )
= SY3440 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SY3442 @ SY3443 @ SY3444 @ SY3445 @ SY3446 @ SY3447 @ SY3448 @ SY3441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2306,plain,
! [SV405: $i] :
( ( ! [SY3449: $i,SY3450: $i,SY3451: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SY3449 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SY3450 ) @ ( c_Collect @ SY3451 @ SV405 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SY3451 @ SY3449 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SY3449 ) @ SY3450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2307,plain,
! [SV406: $i] :
( ( ! [SY3452: $i,SY3453: $i] :
( ( SV406
= ( c_Set_Oinsert @ SY3452 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3453 @ tc_bool ) ) @ SY3453 ) )
| ( SV406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3453 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV406 @ ( c_Set_Oinsert @ SY3452 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3453 @ tc_bool ) ) @ SY3453 ) @ ( tc_fun @ SY3453 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2308,plain,
! [SV407: $i] :
( ( ! [SY3454: $i,SY3455: $i,SY3456: $i,SY3457: $i] :
( ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SY3454 @ SY3455 @ SY3456 ) @ SY3457 @ SY3456 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3457 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SY3454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3456 @ tc_bool ) ) @ SY3456 ) @ SY3457 @ SY3456 ) ) @ ( c_Set_Ovimage @ SV407 @ SY3455 @ SY3457 @ SY3456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2309,plain,
! [SV408: $i] :
( ( ! [SY3458: $i,SY3459: $i,SY3460: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV408 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3458 @ tc_bool ) ) @ SY3459 ) @ SY3460 ) @ ( tc_fun @ SY3458 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3458 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SY3459 @ ( tc_fun @ SY3458 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SY3460 @ ( tc_fun @ SY3458 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2310,plain,
! [SV409: $i] :
( ( ! [SY3461: $i,SY3462: $i,SY3463: $i,SY3464: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV409 @ tc_bool ) ) @ SY3461 ) @ SY3462 ) @ SY3463 @ SV409 @ ( tc_fun @ SY3464 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3464 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3461 @ SY3463 @ SV409 @ ( tc_fun @ SY3464 @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3462 @ SY3463 @ SV409 @ ( tc_fun @ SY3464 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2311,plain,
! [SV410: $i] :
( ( ! [SY3465: $i,SY3466: $i,SY3467: $i,SY3468: $i] :
( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SY3465 @ SY3466 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SY3465 @ SV410 @ SY3467 @ SY3468 ) @ SY3466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2312,plain,
! [SV411: $i] :
( ( ! [SY3469: $i,SY3470: $i,SY3471: $i,SY3472: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SY3469 @ SY3470 @ SY3471 ) @ SY3472 ) )
| ~ ( hBOOL @ ( hAPP @ SY3469 @ ( hAPP @ SV411 @ SY3472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2313,plain,
! [SV412: $i] :
( ( ! [SY3473: $i,SY3474: $i] :
( ~ ( class_Orderings_Olinorder @ SV412 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SY3473 @ SV412 ) @ SY3474 @ SV412 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SY3474 ) @ SY3473 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3473 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2314,plain,
! [SV413: $i] :
( ( ! [SY3475: $i,SY3476: $i,SY3477: $i,SY3478: $i,SY3479: $i,SY3480: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV413 @ SY3475 @ SY3476 @ ( c_Set_Oinsert @ SY3477 @ SY3478 @ SY3479 ) @ SY3480 @ SY3479 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SY3475 @ SY3477 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SY3475 @ SY3476 @ SY3478 @ SY3480 @ SY3479 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3479 ) @ SY3477 ) @ SY3478 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3478 @ SY3479 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SY3480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2315,plain,
! [SV414: $i] :
( ( ! [SY3481: $i,SY3482: $i,SY3483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SY3481 ) @ SY3482 ) @ SY3483 ) )
| ~ ( hBOOL @ ( hAPP @ SY3482 @ SY3483 ) )
| ~ ( hBOOL @ ( hAPP @ SY3481 @ SY3483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2316,plain,
! [SV415: $i] :
( ( ! [SY3484: $i,SY3485: $i,SY3486: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV415 @ SY3484 @ SY3485 ) @ SY3486 @ SY3485 @ SY3484 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3485 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3484 ) @ SV415 ) @ SY3486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2317,plain,
! [SV416: $i] :
( ( ! [SY3487: $i,SY3488: $i,SY3489: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SY3487 @ SY3488 @ ( tc_fun @ SY3489 @ tc_bool ) ) @ ( tc_fun @ SY3489 @ tc_bool ) )
= SY3488 )
| ~ ( c_lessequals @ SV416 @ SY3487 @ ( tc_fun @ SY3489 @ tc_bool ) )
| ~ ( c_lessequals @ SY3488 @ SV416 @ ( tc_fun @ SY3489 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2318,plain,
! [SV417: $i] :
( ( ! [SY3490: $i,SY3491: $i,SY3492: $i,SY3493: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SY3490 @ SY3491 @ SY3492 ) @ ( c_Set_Oimage @ SV417 @ SY3493 @ SY3491 @ SY3492 ) @ ( tc_fun @ SY3492 @ tc_bool ) )
| ~ ( c_lessequals @ SY3490 @ SY3493 @ ( tc_fun @ SY3491 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2319,plain,
! [SV418: $i] :
( ( ! [SY3494: $i,SY3495: $i,SY3496: $i,SY3497: $i] :
( ~ ( c_lessequals @ SV418 @ SY3494 @ ( tc_fun @ SY3495 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SY3496 @ SV418 @ SY3495 @ SY3497 ) @ ( c_Set_Oimage @ SY3496 @ SY3494 @ SY3495 @ SY3497 ) @ ( tc_fun @ SY3497 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2320,plain,
! [SV419: $i] :
( ( ! [SY3498: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ SV419 ) @ SY3498 ) @ SV419 )
= ( c_Set_Oinsert @ SY3498 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV419 @ tc_bool ) ) @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2321,plain,
! [SV420: $i] :
( ( ! [SY3499: $i,SY3500: $i,SY3501: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV420 @ SY3499 @ SY3500 ) @ ( c_Set_Oinsert @ SV420 @ SY3501 @ SY3500 ) @ ( tc_fun @ SY3500 @ tc_bool ) )
| ~ ( c_lessequals @ SY3499 @ SY3501 @ ( tc_fun @ SY3500 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2322,plain,
! [SV421: $i] :
( ( ! [SY3502: $i,SY3503: $i,SY3504: $i] :
( ( c_Finite__Set_Ofinite @ SV421 @ SY3502 )
| ~ ( c_Fun_Oinj__on @ SY3503 @ SV421 @ SY3502 @ SY3504 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SY3503 @ SV421 @ SY3502 @ SY3504 ) @ SY3504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2323,plain,
! [SV422: $i] :
( ( ! [SY3505: $i,SY3506: $i] :
( ~ ( class_Orderings_Oorder @ SV422 )
| ( c_HOL_Oord__class_Oless @ SY3505 @ SY3506 @ SV422 )
| ( SY3506 = SY3505 )
| ~ ( c_lessequals @ SY3505 @ SY3506 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2324,plain,
! [SV423: $i] :
( ( ! [SY3507: $i,SY3508: $i] :
( ~ ( class_Orderings_Oorder @ SV423 )
| ( c_HOL_Oord__class_Oless @ SY3507 @ SY3508 @ SV423 )
| ~ ( c_lessequals @ SY3507 @ SY3508 @ SV423 )
| ( SY3508 = SY3507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2325,plain,
! [SV424: $i] :
( ( ! [SY3509: $i,SY3510: $i] :
( ( c_HOL_Oord__class_Oless @ SV424 @ SY3509 @ ( tc_fun @ SY3510 @ tc_bool ) )
| ( SV424 = SY3509 )
| ~ ( c_lessequals @ SV424 @ SY3509 @ ( tc_fun @ SY3510 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2326,plain,
! [SV425: $i] :
( ( ! [SY3511: $i,SY3512: $i] :
( ~ ( class_Orderings_Oorder @ SV425 )
| ( SY3511 = SY3512 )
| ( c_HOL_Oord__class_Oless @ SY3511 @ SY3512 @ SV425 )
| ~ ( c_lessequals @ SY3511 @ SY3512 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2327,plain,
! [SV426: $i] :
( ( ! [SY3513: $i,SY3514: $i] :
( ~ ( class_Orderings_Oorder @ SV426 )
| ( c_HOL_Oord__class_Oless @ SY3513 @ SY3514 @ SV426 )
| ( SY3513 = SY3514 )
| ~ ( c_lessequals @ SY3513 @ SY3514 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2328,plain,
! [SV427: $i] :
( ( ! [SY3515: $i,SY3516: $i] :
( ( SV427 = SY3515 )
| ( c_HOL_Oord__class_Oless @ SV427 @ SY3515 @ ( tc_fun @ SY3516 @ tc_bool ) )
| ~ ( c_lessequals @ SV427 @ SY3515 @ ( tc_fun @ SY3516 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2329,plain,
! [SV428: $i] :
( ( ! [SY3517: $i,SY3518: $i] :
( ~ ( class_Orderings_Oorder @ SV428 )
| ( c_HOL_Oord__class_Oless @ SY3517 @ SY3518 @ SV428 )
| ( SY3517 = SY3518 )
| ~ ( c_lessequals @ SY3517 @ SY3518 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2330,plain,
! [SV429: $i] :
( ( ! [SY3519: $i,SY3520: $i] :
( ~ ( class_Orderings_Oorder @ SV429 )
| ( c_HOL_Oord__class_Oless @ SY3519 @ SY3520 @ SV429 )
| ~ ( c_lessequals @ SY3519 @ SY3520 @ SV429 )
| ( SY3519 = SY3520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2331,plain,
! [SV430: $i] :
( ( ! [SY3521: $i,SY3522: $i] :
( ~ ( class_Orderings_Olinorder @ SV430 )
| ( SY3521 = SY3522 )
| ~ ( c_lessequals @ SY3521 @ SY3522 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SY3521 @ SY3522 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2332,plain,
! [SV431: $i] :
( ( ! [SY3523: $i,SY3524: $i] :
( ~ ( class_Orderings_Olinorder @ SV431 )
| ( SY3523 = SY3524 )
| ( c_HOL_Oord__class_Oless @ SY3523 @ SY3524 @ SV431 )
| ~ ( c_lessequals @ SY3523 @ SY3524 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2333,plain,
! [SV432: $i] :
( ( ! [SY3525: $i,SY3526: $i] :
( ~ ( class_Orderings_Olinorder @ SV432 )
| ( c_lessequals @ SY3525 @ ( c_Finite__Set_Olinorder__class_OMax @ SY3526 @ SV432 ) @ SV432 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SY3525 ) @ SY3526 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3526 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2334,plain,
! [SV433: $i] :
( ( ! [SY3527: $i,SY3528: $i,SY3529: $i,SY3530: $i] :
( ( c_Set_Oimage @ SV433 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3527 @ tc_bool ) ) @ SY3528 ) @ SY3529 ) @ SY3527 @ SY3530 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3530 @ tc_bool ) ) @ ( c_Set_Oimage @ SV433 @ SY3528 @ SY3527 @ SY3530 ) ) @ ( c_Set_Oimage @ SV433 @ SY3529 @ SY3527 @ SY3530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2335,plain,
! [SV434: $i] :
( ( ! [SY3531: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ SV434 ) @ SV434 @ ( tc_fun @ SV434 @ tc_bool ) @ tc_bool ) @ SY3531 ) @ SV434 )
= SY3531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2336,plain,
! [SV435: $i] :
( ( ! [SY3532: $i,SY3533: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV435 )
| ( c_lessequals @ SY3532 @ ( c_Complete__Lattice_OSup__class_OSup @ SY3533 @ SV435 ) @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SY3532 ) @ SY3533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2337,plain,
! [SV436: $i] :
( ( ! [SY3534: $i,SY3535: $i,SY3536: $i,SY3537: $i,SY3538: $i,SY3539: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SY3534 @ SY3535 @ SY3536 @ SY3537 ) @ SY3538 @ SY3535 @ SY3537 @ SY3539 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SY3534 @ SY3538 @ SY3536 @ SY3537 @ SY3539 ) @ SY3535 @ SY3536 @ SY3539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2338,plain,
! [SV437: $i] :
( ( ! [SY3540: $i,SY3541: $i] :
( ~ ( class_Orderings_Oorder @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SY3540 @ SY3541 @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SY3541 @ SY3540 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2339,plain,
! [SV438: $i] :
( ( ! [SY3542: $i,SY3543: $i] :
( ~ ( class_Orderings_Olinorder @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SY3542 @ SY3543 @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SY3543 @ SY3542 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2340,plain,
! [SV439: $i] :
( ( ! [SY3544: $i,SY3545: $i] :
( ~ ( class_Orderings_Olinorder @ SV439 )
| ( c_lessequals @ SY3544 @ SY3545 @ SV439 )
| ( c_lessequals @ SY3545 @ SY3544 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2341,plain,
! [SV440: $i] :
( ( ! [SY3546: $i,SY3547: $i] :
( ~ ( class_Orderings_Opreorder @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SY3546 @ SY3547 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SY3547 @ SY3546 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2342,plain,
! [SV441: $i] :
( ( ! [SY3548: $i,SY3549: $i] :
( ~ ( class_Orderings_Opreorder @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SY3548 @ SY3549 @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SY3549 @ SY3548 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2343,plain,
! [SV442: $i] :
( ( ! [SY3550: $i,SY3551: $i,SY3552: $i,SY3553: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SY3550 ) @ SY3551 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3552 ) @ ( hAPP @ SY3553 @ SY3550 ) ) @ ( c_Set_Oimage @ SY3553 @ SY3551 @ SV442 @ SY3552 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2344,plain,
! [SV443: $i] :
( ( ! [SY3554: $i,SY3555: $i,SY3556: $i,SY3557: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SY3554 @ SY3555 ) ) @ ( c_Set_Oimage @ SY3554 @ SY3556 @ SY3557 @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3557 ) @ SY3555 ) @ SY3556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2345,plain,
! [SV444: $i] :
( ( ! [SY3558: $i,SY3559: $i,SY3560: $i,SY3561: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SY3558 @ SY3559 ) ) @ ( c_Set_Oimage @ SY3558 @ SY3560 @ SY3561 @ SV444 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3561 ) @ SY3559 ) @ SY3560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2346,plain,
! [SV445: $i] :
( ( ! [SY3562: $i] :
( ~ ( class_Orderings_Olinorder @ SV445 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY3562 @ SV445 ) ) @ SY3562 ) )
| ( SY3562
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY3562 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2347,plain,
! [SV446: $i] :
( ( ! [SY3563: $i] :
( ~ ( class_Orderings_Olinorder @ SV446 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY3563 @ SV446 ) ) @ SY3563 ) )
| ( SY3563
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY3563 @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2348,plain,
! [SV447: $i] :
( ( ! [SY3564: $i,SY3565: $i] :
( ( ( c_Set_Oinsert @ SV447 @ ( c_HOL_Ominus__class_Ominus @ SY3564 @ ( c_Set_Oinsert @ SV447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3565 @ tc_bool ) ) @ SY3565 ) @ ( tc_fun @ SY3565 @ tc_bool ) ) @ SY3565 )
= SY3564 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3565 ) @ SV447 ) @ SY3564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2349,plain,
! [SV448: $i] :
( ( ! [SY3566: $i,SY3567: $i,SY3568: $i,SY3569: $i] :
( ( ( hAPP @ SV448 @ SY3566 )
= SY3567 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3568 ) @ SY3566 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SY3567 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3569 @ tc_bool ) ) @ SY3569 ) @ SY3568 @ SY3569 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2350,plain,
! [SV449: $i] :
( ( ! [SY3570: $i,SY3571: $i,SY3572: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV449 @ SY3570 @ SY3571 ) @ SY3572 @ SY3571 @ SY3570 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3571 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3570 ) @ SV449 ) @ SY3572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2351,plain,
! [SV450: $i] :
( ( ! [SY3573: $i,SY3574: $i,SY3575: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV450 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3573 @ SY3574 @ SY3575 @ ( tc_fun @ SV450 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3575 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SY3573 @ SY3574 @ SY3575 @ SV450 ) ) @ SY3573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2352,plain,
! [SV451: $i] :
( ( ! [SY3576: $i,SY3577: $i,SY3578: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SY3576 ) @ ( c_Set_Ovimage @ SY3577 @ ( c_Set_Oinsert @ ( hAPP @ SY3577 @ SY3576 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3578 @ tc_bool ) ) @ SY3578 ) @ SV451 @ SY3578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2353,plain,
! [SV452: $i] :
( ( ! [SY3579: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SY3579 @ SV452 ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SY3579 @ SV452 ) ) )
| ( SY3579
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV452 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2354,plain,
! [SV453: $i] :
( ( ! [SY3580: $i,SY3581: $i,SY3582: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV453 @ SY3580 @ SY3581 @ ( tc_fun @ SY3582 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3582 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3581 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV453 @ SY3580 @ SY3581 @ SY3582 ) ) @ SV453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2355,plain,
! [SV454: $i] :
( ( ! [SY3583: $i,SY3584: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV454 @ SY3583 @ SY3584 ) @ ( c_Set_Oinsert @ SV454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3584 @ tc_bool ) ) @ SY3584 ) @ ( tc_fun @ SY3584 @ tc_bool ) )
= SY3583 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3584 ) @ SV454 ) @ SY3583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2356,plain,
! [SV455: $i] :
( ( ! [SY3585: $i,SY3586: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV455 @ tc_bool ) ) @ SY3585 ) @ SY3586 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV455 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV455 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SY3585 @ SY3586 @ SV455 ) ) @ SY3586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2357,plain,
! [SV456: $i] :
( ( ! [SY3587: $i,SY3588: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV456 @ tc_bool ) ) @ SY3587 ) @ SY3588 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SY3587 @ SY3588 @ SV456 ) ) @ SY3587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2358,plain,
! [SV457: $i] :
( ( ! [SY3589: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV457 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV457 ) @ ( c_Orderings_Obot__class_Obot @ SV457 ) ) @ SY3589 )
= SY3589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2359,plain,
! [SV458: $i] :
( ( ! [SY3590: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV458 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV458 ) @ SY3590 ) @ ( c_Orderings_Obot__class_Obot @ SV458 ) )
= SY3590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2360,plain,
! [SV459: $i] :
( ( ! [SY3591: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV459 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV459 ) @ ( c_Orderings_Obot__class_Obot @ SV459 ) ) @ SY3591 )
= ( c_Orderings_Obot__class_Obot @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2361,plain,
! [SV460: $i] :
( ( ! [SY3592: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV460 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV460 ) @ SY3592 ) @ ( c_Orderings_Obot__class_Obot @ SV460 ) )
= ( c_Orderings_Obot__class_Obot @ SV460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2362,plain,
! [SV461: $i] :
( ( ! [SY3593: $i] :
( ~ ( class_Orderings_Obot @ SV461 )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV461 ) @ SY3593 @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2363,plain,
! [SV462: $i] :
( ( ! [SY3594: $i,SY3595: $i] :
( ( c_Set_Ovimage @ SV462 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3594 @ tc_bool ) ) @ SY3595 @ SY3594 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3595 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2364,plain,
! [SV463: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV463 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV463 @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV463 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV463 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2365,plain,
! [SV464: $i] :
( ( ! [SY3596: $i,SY3597: $i,SY3598: $i,SY3599: $i,SY3600: $i,SY3601: $i,SY3602: $i,SY3603: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3596 @ tc_bool ) ) )
= SY3597 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SY3598 @ SY3599 @ SY3600 @ SY3601 @ SY3602 @ SY3603 @ SY3597 @ SY3596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2366,plain,
! [SV465: $i] :
( ( ! [SY3604: $i,SY3605: $i,SY3606: $i,SY3607: $i,SY3608: $i,SY3609: $i,SY3610: $i,SY3611: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3604 @ tc_bool ) ) )
= SY3605 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3606 @ SV465 @ SY3607 @ SY3608 @ SY3609 @ SY3610 @ SY3605 @ SY3611 @ SY3604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2367,plain,
! [SV466: $i] :
( ( ! [SY3612: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV466 @ tc_bool ) ) @ SY3612 @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2368,plain,
! [SV467: $i] :
( ( ! [SY3613: $i,SY3614: $i,SY3615: $i,SY3616: $i] :
( ( c_Finite__Set_Ofold__image @ SV467 @ SY3613 @ SY3614 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3615 @ tc_bool ) ) @ SY3616 @ SY3615 )
= SY3614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2369,plain,
! [SV468: $i] :
( ( ! [SY3617: $i,SY3618: $i,SY3619: $i] :
( ( c_Finite__Set_Ofold @ SV468 @ SY3617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3618 @ tc_bool ) ) @ SY3618 @ SY3619 )
= SY3617 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2370,plain,
! [SV469: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV469 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV469 @ tc_bool ) ) @ ( tc_fun @ SV469 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2371,plain,
! [SV470: $i] :
( ( ! [SY3620: $i] :
( ( SV470
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3620 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV470 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3620 @ tc_bool ) ) @ ( tc_fun @ SY3620 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2372,plain,
! [SV471: $i] :
( ( ! [SY3621: $i] :
~ ( c_Wellfounded_Omax__extp @ SV471 @ SY3621 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2373,plain,
! [SV472: $i] :
( ( ! [SY3622: $i,SY3623: $i] :
~ ( c_Finite__Set_Ofold1Set @ SV472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3622 @ tc_bool ) ) @ SY3623 @ SY3622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2374,plain,
! [SV473: $i] :
( ( ! [SY3624: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_bool ) ) @ SY3624 @ ( tc_fun @ SV473 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2375,plain,
! [SV474: $i] :
( ( ! [SY3625: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV474 @ tc_bool ) ) @ SY3625 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV474 @ tc_bool ) ) )
= SY3625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2376,plain,
! [SV475: $i] :
( ( ! [SY3626: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV475 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV475 @ tc_bool ) ) ) @ SY3626 )
= SY3626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2377,plain,
! [SV476: $i] :
( ( ! [SY3627: $i] :
~ ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3627 @ tc_bool ) ) @ ( tc_fun @ SY3627 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2378,plain,
! [SV477: $i] :
( ( ! [SY3628: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV477 @ SV477 @ ( tc_fun @ SY3628 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3628 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2379,plain,
! [SV478: $i] :
( ( ! [SY3629: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3629 @ tc_bool ) ) @ ( tc_fun @ SY3629 @ tc_bool ) )
= SV478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2380,plain,
! [SV479: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV479 @ tc_bool ) ) @ SV479 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2381,plain,
! [SV480: $i] :
( ( ! [SY3630: $i,SY3631: $i,SY3632: $i,SY3633: $i] :
( ( SV480 = SY3630 )
| ~ ( c_Finite__Set_Ofold__graph @ SY3631 @ SY3630 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3632 @ tc_bool ) ) @ SV480 @ SY3632 @ SY3633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2382,plain,
! [SV481: $i] :
( ( ! [SY3634: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV481 @ tc_bool ) ) @ SY3634 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV481 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV481 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2383,plain,
! [SV482: $i] :
( ( ! [SY3635: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV482 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_bool ) ) ) @ SY3635 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2384,plain,
! [SV483: $i] :
( ( ! [SY3636: $i,SY3637: $i] :
( ( c_Relation_OImage @ SV483 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3636 @ tc_bool ) ) @ SY3636 @ SY3637 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3637 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2385,plain,
! [SV484: $i] :
( ( ! [SY3638: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV484 @ tc_bool ) ) @ SY3638 @ ( tc_fun @ SV484 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2386,plain,
! [SV485: $i] :
( ( ! [SY3639: $i,SY3640: $i] :
( ( c_Set_Oinsert @ SV485 @ ( c_Set_Oinsert @ SY3639 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3640 @ tc_bool ) ) @ SY3640 ) @ SY3640 )
= ( c_Set_Oinsert @ SY3639 @ ( c_Set_Oinsert @ SV485 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3640 @ tc_bool ) ) @ SY3640 ) @ SY3640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2387,plain,
! [SV486: $i] :
( ( ! [SY3641: $i,SY3642: $i] :
( ( c_Set_Oimage @ SV486 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3641 @ tc_bool ) ) @ SY3641 @ SY3642 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3642 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2388,plain,
! [SV487: $i] :
( ( ! [SY3643: $i,SY3644: $i] : ( c_Fun_Oinj__on @ SV487 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3643 @ tc_bool ) ) @ SY3643 @ SY3644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2389,plain,
! [SV488: $i] :
( ( ! [SY3645: $i,SY3646: $i,SY3647: $i] : ( c_Finite__Set_Ofold__graph @ SV488 @ SY3645 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3646 @ tc_bool ) ) @ SY3645 @ SY3646 @ SY3647 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2390,plain,
! [SV489: $i] :
( ( ! [SY3648: $i,SY3649: $i,SY3650: $i] : ( c_Nitpick_Ofold__graph_H @ SV489 @ SY3648 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3649 @ tc_bool ) ) @ SY3648 @ SY3649 @ SY3650 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2391,plain,
! [SV490: $i] :
( ( ! [SY3651: $i,SY3652: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV490 @ tc_bool ) )
= ( c_Set_Oimage @ SY3651 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3652 @ tc_bool ) ) @ SY3652 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2392,plain,
! [SV491: $i] :
( ( ! [SY3653: $i,SY3654: $i,SY3655: $i] :
( ( c_Fun_Ooverride__on @ SV491 @ SY3653 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3654 @ tc_bool ) ) @ SY3654 @ SY3655 )
= SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2393,plain,
! [SV492: $i] :
( ( ! [SY3656: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SV492 ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SY3656 ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ SV492 ) @ SY3656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2394,plain,
! [SV493: $i] :
( ( ! [SY3657: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SV493 ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SY3657 ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ SV493 ) @ SY3657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2395,plain,
! [SV494: $i] :
( ( ! [SY3658: $i] :
( ( hAPP @ ( c_Map_Orestrict__map @ SV494 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ SY3658 ) @ v_x )
= ( c_Option_Ooption_ONone @ SY3658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2396,plain,
! [SV495: $i] :
( ( ! [SY3659: $i,SY3660: $i,SY3661: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV495 @ SY3659 @ SY3660 @ SY3661 @ t_a ) @ v_x )
= ( hAPP @ SV495 @ ( hAPP @ SY3659 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2397,plain,
! [SV496: $i] :
( ( ! [SY3662: $i,SY3663: $i,SY3664: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV496 @ SY3662 @ t_a @ SY3663 @ SY3664 ) @ v_x )
= ( hAPP @ SY3662 @ ( hAPP @ SV496 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2398,plain,
! [SV497: $i] :
( ( ! [SY3665: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV497 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3665 ) @ tc_bool ) ) @ SY3665 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2399,plain,
! [SV498: $i] :
( ( ! [SY3666: $i,SY3667: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV498 @ SY3666 @ SY3667 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV498 ) @ SY3666 @ SY3667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2400,plain,
! [SV499: $i] :
( ( ! [SY3668: $i,SY3669: $i,SY3670: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SY3668 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SY3668 ) @ SY3669 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SY3670 @ SV499 ) ) @ SY3670 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY3670 @ SY3669 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2401,plain,
! [SV500: $i] :
( ( ! [SY3671: $i,SY3672: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SY3671 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SY3671 ) @ SY3672 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SY3672 ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2402,plain,
! [SV501: $i] :
( ( ! [SY3673: $i,SY3674: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ SV501 @ SY3673 @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ SV501 @ SY3673 ) @ SY3674 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SY3674 ) @ SV501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2403,plain,
! [SV502: $i] :
( ( ! [SY3675: $i,SY3676: $i,SY3677: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SY3675 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SY3675 ) @ SY3676 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SY3677 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY3677 @ SY3676 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2404,plain,
! [SV503: $i] :
( ( ! [SY3678: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV503 ) @ SY3678 ) @ ( c_Set_Oinsert @ SY3678 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV503 @ tc_bool ) ) @ SV503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2405,plain,
! [SV504: $i] :
( ( ! [SY3679: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV504 ) @ ( c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1 @ SY3679 @ SV504 ) ) @ SY3679 ) )
| ( SY3679
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV504 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2406,plain,
! [SV505: $i] :
( ( ! [SY3680: $i] :
( ( SV505
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3680 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3680 ) @ ( c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1 @ SV505 @ SY3680 ) ) @ SV505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2407,plain,
! [SV506: $i] :
( ( ! [SY3681: $i] :
( ( SV506
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3681 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3681 ) @ ( c_ATP__Linkup_Osko__Set__Xequals0I__1__1 @ SV506 @ SY3681 ) ) @ SV506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2408,plain,
! [SV507: $i] :
( ( ! [SY3682: $i,SY3683: $i] :
( ( SV507 = SY3682 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3683 ) @ SV507 ) @ ( c_Set_Oinsert @ SY3682 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3683 @ tc_bool ) ) @ SY3683 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2409,plain,
! [SV508: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV508 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV508 @ tc_bool ) ) @ SV508 )
= ( c_Orderings_Obot__class_Obot @ SV508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2410,plain,
! [SV509: $i] :
( ( ! [SY3684: $i,SY3685: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV509 @ SY3684 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SY3684 ) @ SY3685 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV509 @ SY3685 ) ) @ SY3685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2411,plain,
! [SV510: $i] :
( ( ! [SY3686: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV510 ) @ SY3686 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2412,plain,
! [SV511: $i] :
( ( ! [SY3687: $i,SY3688: $i] :
( ( hBOOL @ ( hAPP @ SV511 @ SY3687 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3688 ) @ SY3687 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3688 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2413,plain,
! [SV512: $i] :
( ( ! [SY3689: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV512 ) @ SY3689 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV512 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2414,plain,
! [SV513: $i] :
( ( ! [SY3690: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV513 ) @ SY3690 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV513 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2415,plain,
! [SV514: $i] :
( ( ! [SY3691: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV514 @ tc_bool ) ) @ SY3691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2416,plain,
! [SV515: $i] :
( ( ~ ( class_Orderings_Obot @ SV515 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV515 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2417,plain,
! [SV516: $i] :
( ( ! [SY3692: $i,SY3693: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV516 ) @ SY3692 ) @ SY3693 ) )
| ~ ( hBOOL @ ( hAPP @ SY3693 @ SY3692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2418,plain,
! [SV517: $i] :
( ( ! [SY3694: $i,SY3695: $i] :
( ( hBOOL @ ( hAPP @ SV517 @ SY3694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3695 ) @ SY3694 ) @ SV517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2419,plain,
! [SV518: $i] :
( ( ! [SY3696: $i,SY3697: $i] :
( ~ ( hBOOL @ ( hAPP @ SV518 @ SY3696 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3697 ) @ SY3696 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3697 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2420,plain,
! [SV519: $i] :
( ( ! [SY3698: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV519 @ SY3698 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY3698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2421,plain,
! [SV520: $i] :
( ( ! [SY3699: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV520 @ SY3699 ) )
| ~ ( class_Lattices_Olattice @ SY3699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2422,plain,
! [SV521: $i] :
( ( ! [SY3700: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV521 @ SY3700 ) )
| ~ ( class_Lattices_Olattice @ SY3700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2423,plain,
! [SV522: $i] :
( ( ! [SY3701: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV522 @ SY3701 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY3701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2424,plain,
! [SV523: $i] :
( ( ! [SY3702: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV523 @ SY3702 ) )
| ~ ( class_Lattices_Obounded__lattice @ SY3702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2425,plain,
! [SV524: $i] :
( ( ! [SY3703: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV524 @ SY3703 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SY3703 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2426,plain,
! [SV525: $i] :
( ( ! [SY3704: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV525 @ SY3704 ) )
| ~ ( class_Orderings_Opreorder @ SY3704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2427,plain,
! [SV526: $i] :
( ( ! [SY3705: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV526 @ SY3705 ) )
| ~ ( class_Lattices_Olattice @ SY3705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2428,plain,
! [SV527: $i] :
( ( ! [SY3706: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV527 @ SY3706 ) )
| ~ ( class_Orderings_Oorder @ SY3706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2429,plain,
! [SV528: $i] :
( ( ! [SY3707: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ SV528 @ SY3707 ) )
| ~ ( class_Orderings_Otop @ SY3707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2430,plain,
! [SV529: $i] :
( ( ! [SY3708: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV529 @ SY3708 ) )
| ~ ( class_Orderings_Obot @ SY3708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2431,plain,
! [SV530: $i] :
( ( ! [SY3709: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ SV530 @ SY3709 ) )
| ~ ( class_HOL_Ominus @ SY3709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2432,plain,
! [SV531: $i] :
( ( ! [SY3710: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV531 @ SY3710 ) )
| ~ ( class_HOL_Oord @ SY3710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2433,plain,
! [SV532: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ SV532 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2434,plain,
! [SV533: $i] :
( ( ! [SY3711: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV533 ) @ SY3711 ) @ SY3711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2435,plain,
! [SV534: $i] :
( ( ! [SY3712: $i,SY3713: $i] :
( ( SV534 = SY3712 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY3713 ) @ SV534 ) @ SY3712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2436,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2437,plain,
! [SV535: $i] :
( ( ! [SY3714: $i,SY3715: $i,SY3716: $i,SY3717: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3714 @ SY3715 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SY3716 @ SY3717 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SY3716 @ SY3717 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SY3714 @ SY3715 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2438,plain,
! [SV536: $i] :
( ( ! [SY3718: $i,SY3719: $i,SY3720: $i,SY3721: $i] :
( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SY3718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3719 @ tc_bool ) ) @ SY3719 ) @ SY3719 )
!= ( c_Set_Oinsert @ SY3720 @ ( c_Set_Oinsert @ SY3721 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3719 @ tc_bool ) ) @ SY3719 ) @ SY3719 ) )
| ( SV536 = SY3721 )
| ( SV536 = SY3720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2439,plain,
! [SV537: $i] :
( ( ! [SY3722: $i,SY3723: $i,SY3724: $i,SY3725: $i] :
( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SY3722 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3723 @ tc_bool ) ) @ SY3723 ) @ SY3723 )
!= ( c_Set_Oinsert @ SY3724 @ ( c_Set_Oinsert @ SY3725 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3723 @ tc_bool ) ) @ SY3723 ) @ SY3723 ) )
| ( SY3722 = SY3724 )
| ( SY3722 = SY3725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2440,plain,
! [SV538: $i] :
( ( ! [SY3726: $i,SY3727: $i,SY3728: $i,SY3729: $i] :
( ( ( hAPP @ SV538 @ SY3726 )
!= ( hAPP @ SV538 @ SY3727 ) )
| ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3728 @ tc_bool ) ) @ SY3728 @ SY3729 )
| ( SY3726 = SY3727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2441,plain,
! [SV539: $i] :
( ( ! [SY3730: $i,SY3731: $i,SY3732: $i,SY3733: $i] :
( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SY3730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3731 @ tc_bool ) ) @ SY3731 ) @ SY3731 )
!= ( c_Set_Oinsert @ SY3732 @ ( c_Set_Oinsert @ SY3733 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3731 @ tc_bool ) ) @ SY3731 ) @ SY3731 ) )
| ( SV539 = SY3733 )
| ( SY3730 = SY3733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2442,plain,
! [SV540: $i] :
( ( ! [SY3734: $i,SY3735: $i,SY3736: $i,SY3737: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SY3734 @ SY3735 @ ( tc_fun @ SY3736 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3736 @ tc_bool ) ) )
| ( ( hAPP @ SY3734 @ SY3737 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3736 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3735 ) @ SY3737 ) @ SV540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2443,plain,
! [SV541: $i] :
( ( ! [SY3738: $i,SY3739: $i,SY3740: $i,SY3741: $i] :
( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SY3738 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3739 @ tc_bool ) ) @ SY3739 ) @ SY3739 )
!= ( c_Set_Oinsert @ SY3740 @ ( c_Set_Oinsert @ SY3741 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3739 @ tc_bool ) ) @ SY3739 ) @ SY3739 ) )
| ( SY3738 = SY3740 )
| ( SV541 = SY3740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2444,plain,
! [SV542: $i] :
( ( ! [SY3742: $i,SY3743: $i,SY3744: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV542 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3742 @ SY3742 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SY3743 @ SY3744 @ SV542 ) )
| ( SY3743 = SY3744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2445,plain,
! [SV543: $i] :
( ( ! [SY3745: $i,SY3746: $i,SY3747: $i] :
( ( ( c_Set_Oinsert @ SV543 @ SY3745 @ SY3746 )
!= ( c_Set_Oinsert @ SV543 @ SY3747 @ SY3746 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3746 ) @ SV543 ) @ SY3747 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3746 ) @ SV543 ) @ SY3745 ) )
| ( SY3745 = SY3747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2446,plain,
! [SV544: $i] :
( ( ! [SY3748: $i,SY3749: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV544 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SY3748 ) @ SY3749 )
!= ( c_Orderings_Obot__class_Obot @ SV544 ) )
| ( SY3749
= ( c_Orderings_Obot__class_Obot @ SV544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2447,plain,
! [SV545: $i] :
( ( ! [SY3750: $i,SY3751: $i,SY3752: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SY3750 ) @ SY3751 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SY3750 ) @ SY3752 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SY3752 ) @ SY3751 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2448,plain,
! [SV546: $i] :
( ( ! [SY3753: $i,SY3754: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV546 @ tc_bool ) ) @ SY3753 ) @ SY3754 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
| ( SY3753
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2449,plain,
! [SV547: $i] :
( ( ! [SY3755: $i,SY3756: $i,SY3757: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SY3755 ) @ SY3756 ) ) @ SY3757 )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SY3755 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ SY3756 ) @ SY3757 ) ) )
| ( c_lessequals @ SY3757 @ SY3755 @ ( tc_fun @ SV547 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2450,plain,
! [SV548: $i] :
( ( ! [SY3758: $i,SY3759: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SY3758 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SY3759 ) )
| ( SY3758 = SY3759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2451,plain,
! [SV549: $i] :
( ( ! [SY3760: $i,SY3761: $i,SY3762: $i,SY3763: $i] :
( ( ( c_Set_Oimage @ SV549 @ SY3760 @ SY3761 @ SY3762 )
!= ( c_Set_Oimage @ SV549 @ SY3763 @ SY3761 @ SY3762 ) )
| ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3761 @ tc_bool ) ) @ SY3761 @ SY3762 )
| ( SY3760 = SY3763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2452,plain,
! [SV550: $i] :
( ( ! [SY3764: $i,SY3765: $i,SY3766: $i,SY3767: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3764 @ SY3765 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SY3766 @ SY3767 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SY3764 @ SY3765 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SY3766 @ SY3767 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2453,plain,
! [SV551: $i] :
( ( ! [SY3768: $i,SY3769: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV551 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SY3768 ) @ SY3769 )
!= ( c_Orderings_Otop__class_Otop @ SV551 ) )
| ( SY3768
= ( c_Orderings_Otop__class_Otop @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2454,plain,
! [SV552: $i] :
( ( ! [SY3770: $i,SY3771: $i] :
( ( ( c_Set_Oinsert @ SV552 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3770 @ tc_bool ) ) @ SY3770 )
!= ( c_Set_Oinsert @ SY3771 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3770 @ tc_bool ) ) @ SY3770 ) )
| ( SV552 = SY3771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2455,plain,
! [SV553: $i] :
( ( ! [SY3772: $i,SY3773: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV553 @ tc_bool ) ) @ SY3772 ) @ SY3773 )
!= SY3773 )
| ( c_lessequals @ SY3772 @ SY3773 @ ( tc_fun @ SV553 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2456,plain,
! [SV554: $i] :
( ( ! [SY3774: $i,SY3775: $i,SY3776: $i,SY3777: $i,SY3778: $i,SY3779: $i,SY3780: $i,SY3781: $i,SY3782: $i,SY3783: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SY3774 @ SY3775 ) )
!= ( hAPP @ SY3776 @ ( hAPP @ SY3777 @ SY3778 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SY3774 @ SY3779 @ SY3780 @ SY3781 ) @ SY3775 )
= ( hAPP @ ( c_Fun_Ocomp @ SY3776 @ SY3777 @ SY3782 @ SY3780 @ SY3783 ) @ SY3778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2457,plain,
! [SV555: $i] :
( ( ! [SY3784: $i,SY3785: $i,SY3786: $i,SY3787: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SY3784 @ ( c_HOL_Ominus__class_Ominus @ SY3785 @ SY3786 @ ( tc_fun @ SY3787 @ tc_bool ) ) @ SY3787 @ SV555 ) ) @ ( c_Set_Oimage @ SY3784 @ ( c_HOL_Ominus__class_Ominus @ SY3786 @ SY3785 @ ( tc_fun @ SY3787 @ tc_bool ) ) @ SY3787 @ SV555 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SY3784 @ SY3786 @ SY3787 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SY3784 @ SY3785 @ SY3787 @ SV555 )
| ( c_Fun_Oinj__on @ SY3784 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3787 @ tc_bool ) ) @ SY3785 ) @ SY3786 ) @ SY3787 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2458,plain,
! [SV556: $i] :
( ( ! [SY3788: $i,SY3789: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV556 @ tc_bool ) ) @ SY3788 ) @ SY3789 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV556 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY3788 @ SY3789 @ ( tc_fun @ SV556 @ tc_bool ) )
= SY3788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2459,plain,
! [SV557: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV557 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV557 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2460,plain,
! [SV558: $i] :
( ( ! [SY3790: $i,SY3791: $i,SY3792: $i] :
( ( ( hAPP @ SV558 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SY3790 @ SV558 @ SY3791 @ SY3792 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3792 @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3792 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3790 @ SV558 @ SY3791 @ ( tc_fun @ SY3792 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2461,plain,
! [SV559: $i] :
( ( ! [SY3793: $i,SY3794: $i,SY3795: $i,SY3796: $i] :
( ( ( c_Set_Oinsert @ SV559 @ SY3793 @ SY3794 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3794 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3794 ) @ SV559 ) @ SY3793 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SY3795 @ SY3796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2462,plain,
! [SV560: $i] :
( ( ! [SY3797: $i,SY3798: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV560 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SY3797 ) @ SY3798 )
!= SY3797 )
| ( c_lessequals @ SY3797 @ SY3798 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2463,plain,
! [SV561: $i] :
( ( ! [SY3799: $i,SY3800: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV561 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SY3799 ) @ SY3800 )
!= ( c_Orderings_Obot__class_Obot @ SV561 ) )
| ( SY3799
= ( c_Orderings_Obot__class_Obot @ SV561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2464,plain,
! [SV562: $i] :
( ( ! [SY3801: $i,SY3802: $i,SY3803: $i,SY3804: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3801 @ SY3802 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SY3803 @ SY3804 @ SV562 ) )
| ( c_lessequals @ SY3804 @ SY3803 @ SV562 )
| ~ ( c_lessequals @ SY3802 @ SY3801 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2465,plain,
! [SV563: $i] :
( ( ! [SY3805: $i,SY3806: $i,SY3807: $i,SY3808: $i,SY3809: $i] :
( ( ( hAPP @ SV563 @ SY3805 )
!= ( hAPP @ SV563 @ SY3806 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3807 ) @ SY3806 ) @ SY3808 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3807 ) @ SY3805 ) @ SY3808 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SY3808 @ SY3807 @ SY3809 )
| ( SY3805 = SY3806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2466,plain,
! [SV564: $i] :
( ( ! [SY3810: $i,SY3811: $i,SY3812: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV564 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3810 @ SY3811 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SY3812 @ SY3812 @ SV564 ) )
| ( SY3810 = SY3811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2467,plain,
! [SV565: $i] :
( ( ! [SY3813: $i,SY3814: $i,SY3815: $i,SY3816: $i,SY3817: $i] :
( ( ( hAPP @ SV565 @ SY3813 )
!= ( hAPP @ SV565 @ SY3814 ) )
| ~ ( c_Fun_Oinj__on @ SV565 @ SY3815 @ SY3816 @ SY3817 )
| ( SY3813 = SY3814 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3816 ) @ SY3814 ) @ SY3815 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3816 ) @ SY3813 ) @ SY3815 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2468,plain,
! [SV566: $i] :
( ( ! [SY3818: $i,SY3819: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV566 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SY3818 ) @ SY3819 )
!= SY3819 )
| ( c_lessequals @ SY3818 @ SY3819 @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2469,plain,
! [SV567: $i] :
( ( ! [SY3820: $i,SY3821: $i,SY3822: $i,SY3823: $i] :
( ( ( c_Set_Oimage @ SV567 @ SY3820 @ SY3821 @ SY3822 )
!= ( c_Set_Oimage @ SV567 @ SY3823 @ SY3821 @ SY3822 ) )
| ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY3821 @ tc_bool ) ) @ SY3820 ) @ SY3823 ) @ SY3821 @ SY3822 )
| ( SY3820 = SY3823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2470,plain,
! [SV568: $i] :
( ( ! [SY3824: $i] :
( ( ( c_Suc @ SV568 )
!= ( c_Suc @ SY3824 ) )
| ( SV568 = SY3824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2471,plain,
! [SV569: $i] :
( ( ! [SY3825: $i,SY3826: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV569 @ tc_bool ) )
!= ( c_Set_Oinsert @ SY3825 @ SY3826 @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2472,plain,
! [SV570: $i] :
( ( ! [SY3827: $i,SY3828: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) )
!= ( c_Collect @ SY3827 @ SV570 ) )
| ~ ( hBOOL @ ( hAPP @ SY3827 @ SY3828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2473,plain,
! [SV571: $i] :
( ( ! [SY3829: $i,SY3830: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV571 @ tc_bool ) ) @ SY3829 ) @ SY3830 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
| ( SY3830
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2474,plain,
! [SV572: $i] :
( ( ! [SY3831: $i,SY3832: $i,SY3833: $i,SY3834: $i,SY3835: $i,SY3836: $i,SY3837: $i,SY3838: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SY3831 @ SY3832 @ SY3833 @ SY3834 )
!= ( c_Fun_Ocomp @ SY3835 @ SY3836 @ SY3837 @ SY3833 @ SY3834 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SY3831 @ SY3838 ) )
= ( hAPP @ SY3835 @ ( hAPP @ SY3836 @ SY3838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2475,plain,
! [SV573: $i] :
( ( ! [SY3839: $i,SY3840: $i] :
( ( ( c_Set_Oinsert @ SV573 @ SY3839 @ SY3840 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3840 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3840 ) @ SV573 ) @ SY3839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2476,plain,
! [SV574: $i] :
( ( ! [SY3841: $i] :
( ( ( c_Suc @ SV574 )
!= ( c_Suc @ SY3841 ) )
| ( SV574 = SY3841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2477,plain,
! [SV575: $i] :
( ( ! [SY3842: $i,SY3843: $i,SY3844: $i,SY3845: $i,SY3846: $i,SY3847: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ SY3842 @ SY3843 @ SY3844 @ SY3845 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SY3844 ) @ SY3846 @ SY3844 @ SY3844 @ SY3845 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SY3842 @ SY3847 ) )
= ( hAPP @ SY3846 @ SY3847 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2478,plain,
! [SV576: $i] :
( ( ! [SY3848: $i,SY3849: $i,SY3850: $i,SY3851: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3848 @ SY3849 @ SY3850 @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ( ( hAPP @ SY3849 @ SY3851 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3850 ) @ SY3851 ) @ SY3848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2479,plain,
! [SV577: $i] :
( ( ( c_Suc @ SV577 )
!= SV577 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2480,plain,
! [SV578: $i] :
( ( ! [SY3852: $i,SY3853: $i,SY3854: $i] :
( ( ( c_Set_Oimage @ SV578 @ SY3852 @ SY3853 @ SY3854 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3854 @ tc_bool ) ) )
| ( SY3852
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3853 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2481,plain,
! [SV579: $i] :
( ( SV579
!= ( c_Suc @ SV579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2482,plain,
! [SV580: $i] :
( ( ! [SY3855: $i,SY3856: $i] :
( ( c_Set_Oinsert @ SV580 @ SY3855 @ SY3856 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3856 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2483,plain,
! [SV581: $i] :
( ( ! [SY3857: $i,SY3858: $i,SY3859: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) )
!= ( c_Set_Oimage @ SY3857 @ SY3858 @ SY3859 @ SV581 ) )
| ( SY3858
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3859 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2484,plain,
! [SV582: $i] :
( ( ! [SY3860: $i,SY3861: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV582 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SY3860 ) @ SY3861 )
!= ( c_Orderings_Otop__class_Otop @ SV582 ) )
| ( SY3861
= ( c_Orderings_Otop__class_Otop @ SV582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2485,plain,
! [SV583: $i] :
( ( ! [SY3862: $i,SY3863: $i] :
( ( ( c_Collect @ SV583 @ SY3862 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3862 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SV583 @ SY3863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2486,plain,
! [SV584: $i] :
( ( ! [SY3864: $i,SY3865: $i,SY3866: $i,SY3867: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3864 @ SY3865 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SY3866 @ SY3867 @ SV584 ) )
| ( c_lessequals @ SY3865 @ SY3864 @ SV584 )
| ~ ( c_lessequals @ SY3867 @ SY3866 @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2487,plain,
! [SV585: $i] :
( ( ! [SY3868: $i,SY3869: $i,SY3870: $i] :
( ( ( hAPP @ SV585 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SY3868 @ SV585 @ SY3869 @ SY3870 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3870 @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3868 @ SV585 @ SY3869 @ ( tc_fun @ SY3870 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3870 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2488,plain,
! [SV586: $i] :
( ( ! [SY3871: $i,SY3872: $i,SY3873: $i,SY3874: $i,SY3875: $i] :
( ( ( hAPP @ SV586 @ SY3871 )
!= ( hAPP @ SV586 @ SY3872 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3873 ) @ SY3872 ) @ SY3874 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3873 ) @ SY3871 ) @ SY3874 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SY3874 @ SY3873 @ SY3875 )
| ( SY3871 = SY3872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2489,plain,
! [SV587: $i] :
( ( ! [SY3876: $i,SY3877: $i,SY3878: $i,SY3879: $i,SY3880: $i] :
( ( ( hAPP @ SV587 @ SY3876 )
!= ( hAPP @ SV587 @ SY3877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3878 ) @ SY3877 ) @ SY3879 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3878 ) @ SY3876 ) @ SY3879 ) )
| ( SY3876 = SY3877 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SY3879 @ SY3878 @ SY3880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2490,plain,
! [SV1: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ SV1 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1 ) @ v_Ga ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2491,plain,
! [SV588: $i,SV2: $i] :
( ( ! [SY3881: $i,SY3882: $i,SY3883: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SY3881 @ SY3882 ) @ ( c_Set_Oimage @ SV2 @ SY3883 @ SY3881 @ SY3882 ) @ ( tc_fun @ SY3882 @ tc_bool ) )
| ~ ( c_lessequals @ SV588 @ SY3883 @ ( tc_fun @ SY3881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3881 @ tc_bool ) ) @ SY3881 @ SY3882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2492,plain,
! [SV589: $i,SV3: $i] :
( ( ! [SY3884: $i,SY3885: $i,SY3886: $i] :
( ( c_Fun_Oinj__on @ SV3 @ SV589 @ SY3884 @ SY3885 )
| ~ ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SY3886 @ SV589 @ SY3884 ) @ SY3884 @ SY3885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2493,plain,
! [SV590: $i,SV4: $i] :
( ( ! [SY3887: $i,SY3888: $i,SY3889: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
| ( c_lessequals @ ( hAPP @ SV590 @ SY3887 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3888 @ SV590 @ SY3889 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3889 ) @ SY3887 ) @ SY3888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2494,plain,
! [SV591: $i,SV5: $i] :
( ( ! [SY3890: $i,SY3891: $i,SY3892: $i] :
( ( c_lessequals @ ( hAPP @ SV5 @ SV591 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3890 @ SV5 @ SY3891 @ ( tc_fun @ SY3892 @ tc_bool ) ) @ ( tc_fun @ SY3892 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3891 ) @ SV591 ) @ SY3890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2495,plain,
! [SV592: $i,SV6: $i] :
( ( ! [SY3893: $i,SY3894: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV6 @ SV592 @ SY3893 ) @ SY3894 @ ( tc_fun @ SY3893 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV592 @ SY3894 @ ( tc_fun @ SY3893 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3893 ) @ SV6 ) @ SY3894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2496,plain,
! [SV593: $i,SV7: $i] :
( ( ! [SY3895: $i,SY3896: $i] :
( ( c_lessequals @ SV7 @ SV593 @ ( tc_fun @ SY3895 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY3896 @ SV7 @ SY3895 ) @ SV593 @ ( tc_fun @ SY3895 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2497,plain,
! [SV594: $i,SV8: $i] :
( ( ! [SY3897: $i,SY3898: $i] :
( ( c_lessequals @ SV8 @ ( c_Set_Oinsert @ SV594 @ SY3897 @ SY3898 ) @ ( tc_fun @ SY3898 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SY3897 @ ( tc_fun @ SY3898 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2498,plain,
! [SV595: $i,SV9: $i] :
( ( ! [SY3899: $i,SY3900: $i,SY3901: $i] :
( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SY3899 @ SY3900 ) @ SY3901 @ SY3900 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3900 ) @ SV595 ) @ SY3899 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SY3899 @ SY3901 @ SY3900 @ SY3900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2499,plain,
! [SV596: $i,SV10: $i] :
( ( ! [SY3902: $i,SY3903: $i,SY3904: $i,SY3905: $i,SY3906: $i,SY3907: $i,SY3908: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SY3902 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3903 @ SV10 @ SY3904 @ SY3905 @ SY3906 @ SY3907 @ SY3908 @ SY3902 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2500,plain,
! [SV597: $i,SV11: $i] :
( ( ! [SY3909: $i,SY3910: $i,SY3911: $i,SY3912: $i,SY3913: $i,SY3914: $i,SY3915: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SY3909 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SY3910 @ SY3911 @ SY3912 @ SY3913 @ SY3914 @ SY3909 @ SY3915 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2501,plain,
! [SV598: $i,SV12: $i] :
( ( ! [SY3916: $i,SY3917: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3916 @ tc_bool ) ) @ SY3916 ) @ ( tc_fun @ SY3916 @ tc_bool ) ) @ SY3917 @ ( tc_fun @ SY3916 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3916 ) @ SV598 ) @ SV12 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3916 ) @ SV598 ) @ SY3917 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SY3917 @ SY3916 ) @ ( tc_fun @ SY3916 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2502,plain,
! [SV599: $i,SV13: $i] :
( ( ! [SY3918: $i,SY3919: $i] :
( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SY3918 @ SY3919 ) @ ( tc_fun @ SY3919 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3919 ) @ SV599 ) @ SV13 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3919 @ tc_bool ) ) @ SY3919 ) @ ( tc_fun @ SY3919 @ tc_bool ) ) @ SY3918 @ ( tc_fun @ SY3919 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3919 ) @ SV599 ) @ SY3918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2503,plain,
! [SV600: $i,SV14: $i] :
( ( ! [SY3920: $i,SY3921: $i,SY3922: $i,SY3923: $i,SY3924: $i,SY3925: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SY3920 @ ( c_Set_Oimage @ SY3921 @ SY3922 @ SY3923 @ SY3924 ) @ SY3925 @ SY3924 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SY3921 @ SY3924 @ SY3925 @ SY3923 ) @ SY3920 @ SY3922 @ SY3925 @ SY3923 ) )
| ~ ( c_Fun_Oinj__on @ SY3921 @ SY3922 @ SY3923 @ SY3924 )
| ~ ( c_Finite__Set_Ofinite @ SY3922 @ SY3923 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY3925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2504,plain,
! [SV601: $i,SV15: $i] :
( ( ! [SY3926: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV601 @ ( tc_fun @ SY3926 @ tc_bool ) ) @ SY3926 )
| ~ ( c_Finite__Set_Ofinite @ SV15 @ SY3926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2505,plain,
! [SV602: $i,SV16: $i] :
( ( ! [SY3927: $i,SY3928: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV16 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SY3927 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SY3927 @ SY3928 @ SV16 @ SV16 ) @ SV16 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SY3928 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3928 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2506,plain,
! [SV603: $i,SV17: $i] :
( ( ! [SY3929: $i,SY3930: $i,SY3931: $i] :
( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SV603 @ SY3929 @ ( tc_fun @ SY3930 @ tc_bool ) ) @ SY3930 @ SY3931 )
| ~ ( c_Fun_Oinj__on @ SV17 @ SV603 @ SY3930 @ SY3931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2507,plain,
! [SV604: $i,SV18: $i] :
( ( ! [SY3932: $i,SY3933: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV604 @ SY3932 @ SV18 ) ) @ SY3933 )
= ( c_Set_Oinsert @ SV604 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ SY3932 ) @ SY3933 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2508,plain,
! [SV605: $i,SV19: $i] :
( ( ! [SY3934: $i,SY3935: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SV605 ) @ ( c_Set_Oinsert @ SY3934 @ SY3935 @ SV19 ) )
= ( c_Set_Oinsert @ SY3934 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SV605 ) @ SY3935 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2509,plain,
! [SV606: $i,SV20: $i] :
( ( ! [SY3936: $i,SY3937: $i,SY3938: $i] :
( ( c_Set_Ovimage @ SV20 @ ( c_HOL_Ominus__class_Ominus @ SV606 @ SY3936 @ ( tc_fun @ SY3937 @ tc_bool ) ) @ SY3938 @ SY3937 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV20 @ SV606 @ SY3938 @ SY3937 ) @ ( c_Set_Ovimage @ SV20 @ SY3936 @ SY3938 @ SY3937 ) @ ( tc_fun @ SY3938 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2510,plain,
! [SV607: $i,SV21: $i] :
( ( ! [SY3939: $i,SY3940: $i] :
( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SY3939 @ SY3940 ) @ ( tc_fun @ SY3940 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3940 ) @ SV607 ) @ SV21 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3940 @ tc_bool ) ) @ SY3940 ) @ ( tc_fun @ SY3940 @ tc_bool ) ) @ SY3939 @ ( tc_fun @ SY3940 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SY3939 @ ( tc_fun @ SY3940 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2511,plain,
! [SV608: $i,SV22: $i] :
( ( ! [SY3941: $i,SY3942: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV22 @ ( c_Set_Ovimage @ SV22 @ SV608 @ SY3941 @ SY3942 ) @ SY3941 @ SY3942 ) @ SV608 @ ( tc_fun @ SY3942 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2512,plain,
! [SV609: $i,SV23: $i] :
( ( ! [SY3943: $i,SY3944: $i] :
( ( ( c_Set_Ovimage @ SV23 @ ( c_Set_Oimage @ SV23 @ SV609 @ SY3943 @ SY3944 ) @ SY3943 @ SY3944 )
= SV609 )
| ~ ( c_Fun_Oinj__on @ SV23 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3943 @ tc_bool ) ) @ SY3943 @ SY3944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2513,plain,
! [SV610: $i,SV24: $i] :
( ( ( c_Collect @ SV24 @ SV610 )
= SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2514,plain,
! [SV611: $i,SV25: $i] :
( ( ! [SY3945: $i,SY3946: $i] :
( ( SV25 = SV611 )
| ~ ( c_Finite__Set_Ofold1Set @ SY3945 @ ( c_Set_Oinsert @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3946 @ tc_bool ) ) @ SY3946 ) @ SV611 @ SY3946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2515,plain,
! [SV612: $i,SV26: $i] :
( ( ! [SY3947: $i] :
( ( c_Set_Ovimage @ SV26 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV612 @ tc_bool ) ) @ SY3947 @ SV612 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY3947 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2516,plain,
! [SV613: $i,SV27: $i] :
( ( ! [SY3948: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV27 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV613 @ SY3948 @ SV27 ) @ SV27 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 ) @ SV613 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SY3948 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2517,plain,
! [SV614: $i,SV28: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV28 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV28 ) @ SV614 ) @ ( c_Orderings_Otop__class_Otop @ SV28 ) )
= ( c_Orderings_Otop__class_Otop @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2518,plain,
! [SV615: $i,SV29: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV29 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV29 ) @ ( c_Orderings_Otop__class_Otop @ SV29 ) ) @ SV615 )
= ( c_Orderings_Otop__class_Otop @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2519,plain,
! [SV616: $i,SV30: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV30 @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV30 @ tc_bool ) ) ) @ SV616 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV30 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2520,plain,
! [SV617: $i,SV31: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV31 @ tc_bool ) ) @ SV617 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV31 @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV31 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2521,plain,
! [SV618: $i,SV32: $i] :
( ( ! [SY3949: $i,SY3950: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV32 @ ( c_Set_Oinsert @ SV618 @ SY3949 @ SY3950 ) @ ( tc_fun @ SY3950 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SY3949 @ ( tc_fun @ SY3950 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3950 @ tc_bool ) ) @ SY3950 ) @ ( tc_fun @ SY3950 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2522,plain,
! [SV619: $i,SV33: $i] :
( ( ! [SY3951: $i,SY3952: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SV619 @ SY3951 @ SY3952 ) @ ( tc_fun @ SY3952 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SV619 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3952 @ tc_bool ) ) @ SY3952 ) @ ( tc_fun @ SY3952 @ tc_bool ) ) @ SY3951 @ ( tc_fun @ SY3952 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2523,plain,
! [SV620: $i,SV34: $i] :
( ( ! [SY3953: $i] :
( ( c_Finite__Set_Ofinite @ SV34 @ SV620 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SY3953 @ ( tc_fun @ SV620 @ tc_bool ) ) @ SV620 )
| ~ ( c_Finite__Set_Ofinite @ SY3953 @ SV620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2524,plain,
! [SV621: $i,SV35: $i] :
( ( ! [SY3954: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SV621 @ ( tc_fun @ SY3954 @ tc_bool ) ) @ SY3954 )
| ~ ( c_Finite__Set_Ofinite @ SV35 @ SY3954 )
| ~ ( c_Finite__Set_Ofinite @ SV621 @ SY3954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2525,plain,
! [SV622: $i,SV36: $i] :
( ( ! [SY3955: $i,SY3956: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV622 @ SY3955 @ SV36 ) ) @ ( c_Set_Oinsert @ SV622 @ SY3956 @ SV36 ) )
= ( c_Set_Oinsert @ SV622 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ SY3955 ) @ SY3956 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2526,plain,
! [SV623: $i,SV37: $i] :
( ( ! [SY3957: $i] :
( ( c_Set_Oinsert @ SV37 @ ( c_Set_Oinsert @ SV37 @ SV623 @ SY3957 ) @ SY3957 )
= ( c_Set_Oinsert @ SV37 @ SV623 @ SY3957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2527,plain,
! [SV624: $i,SV38: $i] :
( ( ! [SY3958: $i,SY3959: $i,SY3960: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SY3958 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3959 ) @ SV624 ) @ SY3960 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3960 @ SV38 @ SY3959 @ ( tc_fun @ SY3958 @ tc_bool ) ) @ SY3958 )
| ~ ( c_Finite__Set_Ofinite @ SY3960 @ SY3959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2528,plain,
! [SV625: $i,SV39: $i] :
( ( ! [SY3961: $i,SY3962: $i] :
( ( hBOOL @ ( hAPP @ SV39 @ SV625 ) )
| ( SY3961 = SV625 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3961 @ SV39 @ SY3962 ) @ SV625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2529,plain,
! [SV626: $i,SV40: $i] :
( ( ( SV40
= ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SV40 @ SV626 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SV40 @ SV626 ) @ SV626 ) )
| ( SV40
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV626 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2530,plain,
! [SV627: $i,SV41: $i] :
( ( ! [SY3963: $i,SY3964: $i,SY3965: $i,SY3966: $i] :
( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SY3963 @ ( tc_fun @ SY3964 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3965 ) @ SV627 ) @ SY3966 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3966 @ SV41 @ SY3965 @ ( tc_fun @ SY3964 @ tc_bool ) ) @ SY3963 @ ( tc_fun @ SY3964 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2531,plain,
! [SV628: $i,SV42: $i] :
( ( ! [SY3967: $i] : ( c_lessequals @ SV42 @ ( c_Set_Oinsert @ SV628 @ SV42 @ SY3967 ) @ ( tc_fun @ SY3967 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2532,plain,
! [SV629: $i,SV43: $i] :
( ( ! [SY3968: $i,SY3969: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV43 @ SV629 @ SY3968 ) @ SY3969 @ SY3968 @ SV629 @ t_a ) @ v_x )
= SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2533,plain,
! [SV630: $i,SV44: $i] :
( ( ! [SY3970: $i] :
( ( c_Finite__Set_Ofinite @ SV44 @ SV630 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY3970 @ SV44 @ SV630 ) @ SV630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2534,plain,
! [SV631: $i,SV45: $i] :
( ( ! [SY3971: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV45 @ SV631 @ SY3971 ) @ SY3971 )
| ~ ( c_Finite__Set_Ofinite @ SV631 @ SY3971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2535,plain,
! [SV632: $i,SV46: $i] :
( ( ! [SY3972: $i,SY3973: $i,SY3974: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SV632 @ SY3972 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3973 @ SV632 @ SY3974 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3973 @ SV632 @ SY3974 @ ( tc_fun @ SV46 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3974 ) @ SY3972 ) @ SY3973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2536,plain,
! [SV633: $i,SV47: $i] :
( ( ! [SY3975: $i,SY3976: $i,SY3977: $i,SY3978: $i,SY3979: $i] :
( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SY3975 @ ( hAPP @ ( hAPP @ SV47 @ SY3976 ) @ SY3977 ) @ SY3978 @ SY3979 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3978 ) @ SY3976 ) @ SY3975 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SY3975 @ ( c_Set_Oinsert @ SY3976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3978 @ tc_bool ) ) @ SY3978 ) @ ( tc_fun @ SY3978 @ tc_bool ) ) @ SY3977 @ SY3978 @ SY3979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2537,plain,
! [SV634: $i,SV48: $i] :
( ( ! [SY3980: $i,SY3981: $i,SY3982: $i] :
( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV634 @ tc_bool ) ) @ SY3980 ) @ SY3981 ) @ SV634 @ SY3982 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY3982 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SY3980 @ SV634 @ SY3982 ) ) @ ( c_Set_Oimage @ SV48 @ SY3981 @ SV634 @ SY3982 ) ) )
| ~ ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV634 @ SY3982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2538,plain,
! [SV635: $i,SV49: $i] :
( ( ! [SY3983: $i,SY3984: $i,SY3985: $i,SY3986: $i,SY3987: $i,SY3988: $i,SY3989: $i,SY3990: $i,SY3991: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SY3983 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3984 @ tc_bool ) ) @ SY3984 ) @ SY3984 ) )
= ( hAPP @ ( hAPP @ SY3985 @ SV635 ) @ SY3983 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3986 @ SV49 @ SY3987 @ SY3988 @ SY3989 @ SY3985 @ SY3990 @ SY3991 @ SY3984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2539,plain,
! [SV636: $i,SV50: $i] :
( ( ! [SY3992: $i,SY3993: $i,SY3994: $i,SY3995: $i,SY3996: $i,SY3997: $i,SY3998: $i,SY3999: $i,SY4000: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SY3992 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3993 @ tc_bool ) ) @ SY3993 ) @ SY3993 ) )
= ( hAPP @ ( hAPP @ SY3994 @ SV636 ) @ SY3992 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SY3995 @ SY3996 @ SY3997 @ SY3994 @ SY3998 @ SY3999 @ SY4000 @ SY3993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2540,plain,
! [SV637: $i,SV51: $i] :
( ( ! [SY4001: $i,SY4002: $i,SY4003: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV51 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV637 @ tc_bool ) ) @ SY4001 ) @ SY4002 ) @ SV637 @ SY4003 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4003 @ tc_bool ) ) @ ( c_Set_Oimage @ SV51 @ SY4001 @ SV637 @ SY4003 ) ) @ ( c_Set_Oimage @ SV51 @ SY4002 @ SV637 @ SY4003 ) ) @ ( tc_fun @ SY4003 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2541,plain,
! [SV638: $i,SV52: $i] :
( ( ! [SY4004: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SV638 ) @ SY4004 ) @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SY4004 @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SV638 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2542,plain,
! [SV639: $i,SV53: $i] :
( ( ! [SY4005: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SV639 ) @ SY4005 ) @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SY4005 @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SV639 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2543,plain,
! [SV640: $i,SV54: $i] :
( ( ! [SY4006: $i,SY4007: $i,SY4008: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV54 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV640 @ tc_bool ) ) @ SY4006 ) @ SY4007 ) @ SV640 @ SY4008 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4008 @ tc_bool ) ) @ ( c_Relation_OImage @ SV54 @ SY4006 @ SV640 @ SY4008 ) ) @ ( c_Relation_OImage @ SV54 @ SY4007 @ SV640 @ SY4008 ) ) @ ( tc_fun @ SY4008 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2544,plain,
! [SV641: $i,SV55: $i] :
( ( ! [SY4009: $i,SY4010: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ SY4009 ) ) @ SY4010 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ SY4009 ) @ SY4010 ) ) )
| ~ ( c_lessequals @ SY4010 @ SV641 @ ( tc_fun @ SV55 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2545,plain,
! [SV642: $i,SV56: $i] :
( ( ! [SY4011: $i,SY4012: $i,SY4013: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV56 @ SV642 @ SY4011 @ SY4012 ) @ SY4013 )
= ( c_Option_Ooption_ONone @ SY4012 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4011 ) @ SY4013 ) @ SV642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2546,plain,
! [SV643: $i,SV57: $i] :
( ( ! [SY4014: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV57 @ tc_bool ) ) @ SV643 ) @ SY4014 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV57 @ tc_bool ) ) )
| ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SV643 @ SY4014 @ SV57 )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SV643 @ SY4014 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2547,plain,
! [SV644: $i,SV58: $i] :
( ( ! [SY4015: $i,SY4016: $i,SY4017: $i,SY4018: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV58 @ SV644 @ SY4015 @ SY4016 @ SY4017 ) @ SY4018 )
= ( hAPP @ SV58 @ ( hAPP @ SV644 @ SY4018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2548,plain,
! [SV645: $i,SV59: $i] :
( ( ! [SY4019: $i,SY4020: $i,SY4021: $i,SY4022: $i] :
( ( hAPP @ SV59 @ ( hAPP @ SV645 @ SY4019 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV59 @ SV645 @ SY4020 @ SY4021 @ SY4022 ) @ SY4019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2549,plain,
! [SV646: $i,SV60: $i] :
( ( ! [SY4023: $i,SY4024: $i,SY4025: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SY4023 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4024 ) @ ( hAPP @ SY4025 @ SV646 ) ) @ ( c_Set_Oimage @ SY4025 @ SY4023 @ SV60 @ SY4024 ) ) )
| ~ ( c_Fun_Oinj__on @ SY4025 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SY4024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2550,plain,
! [SV647: $i,SV61: $i] :
( ( ! [SY4026: $i,SY4027: $i,SY4028: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SY4026 ) ) @ ( c_Set_Oimage @ SV647 @ SY4027 @ SY4028 @ SV61 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4028 ) @ SY4026 ) @ SY4027 ) )
| ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4028 @ tc_bool ) ) @ SY4028 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2551,plain,
! [SV648: $i,SV62: $i] :
( ( ! [SY4029: $i,SY4030: $i,SY4031: $i] :
( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ SY4029 ) ) @ SY4030 )
= ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ ( hAPP @ ( hAPP @ SV62 @ SY4029 ) @ SY4030 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SY4031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2552,plain,
! [SV649: $i,SV63: $i] :
( ( ! [SY4032: $i,SY4033: $i,SY4034: $i] :
( ( ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ ( hAPP @ ( hAPP @ SV63 @ SY4032 ) @ SY4033 ) )
= ( hAPP @ ( hAPP @ SV63 @ SY4032 ) @ ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ SY4033 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SY4034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2553,plain,
! [SV650: $i,SV64: $i] :
( ( ! [SY4035: $i,SY4036: $i] :
( ( ( hAPP @ ( hAPP @ SV64 @ SV650 ) @ SY4035 )
= ( hAPP @ ( hAPP @ SV64 @ SY4035 ) @ SV650 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV64 @ SY4036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2554,plain,
! [SV651: $i,SV65: $i] :
( ( ! [SY4037: $i,SY4038: $i] :
( ( hBOOL @ ( hAPP @ SV65 @ SV651 ) )
| ( hBOOL @ ( hAPP @ SY4037 @ SV651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4038 @ tc_bool ) ) @ SY4037 ) @ SV65 ) @ SV651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2555,plain,
! [SV652: $i,SV66: $i] :
( ( ! [SY4039: $i,SY4040: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV66 @ tc_bool ) ) @ SV652 ) @ SY4039 ) @ SY4040 ) )
| ~ ( hBOOL @ ( hAPP @ SY4039 @ SY4040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2556,plain,
! [SV653: $i,SV67: $i] :
( ( ! [SY4041: $i,SY4042: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV67 @ tc_bool ) ) @ SV653 ) @ SY4041 ) @ SY4042 ) )
| ~ ( hBOOL @ ( hAPP @ SV653 @ SY4042 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2557,plain,
! [SV654: $i,SV68: $i] :
( ( ! [SY4043: $i,SY4044: $i,SY4045: $i] :
( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SY4043 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SY4044 @ SV68 @ SY4043 @ SY4045 ) @ ( c_Set_Oimage @ SY4044 @ SV654 @ SY4043 @ SY4045 ) @ ( tc_fun @ SY4045 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY4044 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4043 @ tc_bool ) ) @ SY4043 @ SY4045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2558,plain,
! [SV655: $i,SV69: $i] :
( ( ! [SY4046: $i,SY4047: $i] :
( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SY4046 @ SY4047 ) @ ( tc_fun @ SY4047 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4047 ) @ SV655 ) @ SV69 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4047 @ tc_bool ) ) @ SY4047 ) @ ( tc_fun @ SY4047 @ tc_bool ) ) @ SY4046 @ ( tc_fun @ SY4047 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2559,plain,
! [SV656: $i,SV70: $i] :
( ( ! [SY4048: $i,SY4049: $i] :
( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SY4048 @ SY4049 ) @ ( tc_fun @ SY4049 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4049 ) @ SV656 ) @ SV70 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4049 @ tc_bool ) ) @ SY4049 ) @ ( tc_fun @ SY4049 @ tc_bool ) ) @ SY4048 @ ( tc_fun @ SY4049 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2560,plain,
! [SV657: $i,SV71: $i] :
( ( ! [SY4050: $i,SY4051: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4050 @ tc_bool ) ) @ SY4050 ) @ ( tc_fun @ SY4050 @ tc_bool ) ) @ SY4051 @ ( tc_fun @ SY4050 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4050 ) @ SV657 ) @ SV71 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SY4051 @ SY4050 ) @ ( tc_fun @ SY4050 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2561,plain,
! [SV658: $i,SV72: $i] :
( ( ! [SY4052: $i,SY4053: $i,SY4054: $i,SY4055: $i] :
( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SY4052 ) @ SY4053 ) @ SV658 @ SY4054 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4054 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SY4052 @ SV658 @ SY4054 ) ) @ ( c_Set_Oimage @ SV72 @ SY4053 @ SV658 @ SY4054 ) ) )
| ~ ( c_lessequals @ SY4053 @ SY4055 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_lessequals @ SY4052 @ SY4055 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SY4055 @ SV658 @ SY4054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2562,plain,
! [SV659: $i,SV73: $i] :
( ( ! [SY4056: $i,SY4057: $i,SY4058: $i] :
( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
| ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SY4056 @ SY4057 @ SY4058 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY4057 @ SY4058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2563,plain,
! [SV660: $i,SV74: $i] :
( ( ! [SY4059: $i,SY4060: $i,SY4061: $i,SY4062: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SY4059 ) ) @ SY4060 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4061 ) @ SY4059 ) @ SY4062 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SY4062 @ SY4061 @ SV74 ) @ SY4060 @ ( tc_fun @ SV74 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2564,plain,
! [SV661: $i,SV75: $i] :
( ( ! [SY4063: $i,SY4064: $i,SY4065: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SV661 @ SY4063 ) @ SY4064 @ SY4063 @ SV661 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV661 @ tc_bool ) ) @ SV661 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4063 ) @ SY4065 ) @ SY4064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2565,plain,
! [SV662: $i,SV76: $i] :
( ( ! [SY4066: $i,SY4067: $i,SY4068: $i,SY4069: $i] :
( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
| ~ ( c_Finite__Set_Ofold__graph @ SY4066 @ SY4067 @ SV76 @ SY4068 @ SV662 @ SY4069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2566,plain,
! [SV663: $i,SV77: $i] :
( ( ! [SY4070: $i] :
( ~ ( class_Lattices_Olattice @ SV77 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ SV77 ) ) @ SV663 ) @ SY4070 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV77 ) @ ( hAPP @ SV663 @ v_x ) ) @ ( hAPP @ SY4070 @ v_x ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2567,plain,
! [SV664: $i,SV78: $i] :
( ( ! [SY4071: $i,SY4072: $i,SY4073: $i,SY4074: $i] :
( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SY4071 @ SY4072 @ SY4073 ) @ SY4073 @ SY4074 )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SY4073 @ SY4074 @ SY4072 ) @ SY4071 @ SY4072 @ SY4074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2568,plain,
! [SV665: $i,SV79: $i] :
( ( ! [SY4075: $i,SY4076: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV665 ) @ SY4075 ) ) @ SY4076 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV665 ) @ SY4076 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SY4075 ) @ SY4076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2569,plain,
! [SV666: $i,SV80: $i] :
( ( ! [SY4077: $i,SY4078: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ SY4077 ) @ SY4078 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ SY4077 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ SY4078 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2570,plain,
! [SV667: $i,SV81: $i] :
( ( ! [SY4079: $i,SY4080: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ SY4079 ) @ SY4080 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SY4079 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SY4080 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2571,plain,
! [SV668: $i,SV82: $i] :
( ( ! [SY4081: $i,SY4082: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ SV668 ) @ SY4081 ) ) @ SY4082 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV668 ) @ SY4082 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SY4081 ) @ SY4082 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2572,plain,
! [SV669: $i,SV83: $i] :
( ( ! [SY4083: $i,SY4084: $i] :
( ( hBOOL @ ( hAPP @ SV83 @ SV669 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4083 ) @ SV669 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4083 @ tc_bool ) ) @ SY4084 ) @ ( c_Collect @ SV83 @ SY4083 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2573,plain,
! [SV670: $i,SV84: $i] :
( ( ! [SY4085: $i] :
( ( c_Fun_Ocomp @ SV84 @ ( c_Fun_Oid @ SV670 ) @ SV670 @ SY4085 @ SV670 )
= SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2574,plain,
! [SV671: $i,SV85: $i] :
( ( ! [SY4086: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV85 ) @ SV671 @ SV85 @ SV85 @ SY4086 )
= SV671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2575,plain,
! [SV672: $i,SV86: $i] :
( ( ! [SY4087: $i,SY4088: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SY4087 @ SY4088 ) @ SY4087 )
| ~ ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4087 @ tc_bool ) ) @ SY4087 @ SY4088 )
| ~ ( c_Finite__Set_Ofinite @ SV672 @ SY4088 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2576,plain,
! [SV673: $i,SV87: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV87 @ tc_bool ) ) @ SV673 ) @ SV673 )
= SV673 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2577,plain,
! [SV674: $i,SV88: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV88 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 ) @ SV674 ) @ SV674 )
= SV674 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2578,plain,
! [SV675: $i,SV89: $i] :
( ( ! [SY4089: $i,SY4090: $i] :
( ~ ( class_Orderings_Opreorder @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV675 @ SY4089 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY4090 @ SY4089 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV675 @ SY4090 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2579,plain,
! [SV676: $i,SV90: $i] :
( ( ! [SY4091: $i,SY4092: $i] :
( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SY4091 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4092 @ SV676 @ ( tc_fun @ SY4091 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ SY4092 @ ( tc_fun @ SY4091 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2580,plain,
! [SV677: $i,SV91: $i] :
( ( ! [SY4093: $i,SY4094: $i] :
( ~ ( class_Orderings_Oorder @ SV91 )
| ( c_HOL_Oord__class_Oless @ SV677 @ SY4093 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY4094 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY4094 @ SY4093 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2581,plain,
! [SV678: $i,SV92: $i] :
( ( ! [SY4095: $i,SY4096: $i,SY4097: $i] :
( ( c_Relation_OImage @ SV92 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV678 @ tc_bool ) ) @ SY4095 ) @ SY4096 ) @ SV678 @ SY4097 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4097 @ tc_bool ) ) @ ( c_Relation_OImage @ SV92 @ SY4095 @ SV678 @ SY4097 ) ) @ ( c_Relation_OImage @ SV92 @ SY4096 @ SV678 @ SY4097 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2582,plain,
! [SV679: $i,SV93: $i] :
( ( ! [SY4098: $i,SY4099: $i,SY4100: $i] :
( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SY4098 @ SY4099 ) @ SY4099 @ SY4100 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4100 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SY4098 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4099 @ tc_bool ) ) @ SY4099 ) @ ( tc_fun @ SY4099 @ tc_bool ) ) @ SY4099 @ SY4100 ) ) )
| ~ ( c_Fun_Oinj__on @ SV93 @ SY4098 @ SY4099 @ SY4100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2583,plain,
! [SV680: $i,SV94: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Oid @ SV94 ) @ SV680 @ SV94 @ SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2584,plain,
! [SV681: $i,SV95: $i] :
( ( ! [SY4101: $i,SY4102: $i] :
( ( c_Set_Oinsert @ SV95 @ ( c_Set_Oinsert @ SV681 @ SY4101 @ SY4102 ) @ SY4102 )
= ( c_Set_Oinsert @ SV681 @ ( c_Set_Oinsert @ SV95 @ SY4101 @ SY4102 ) @ SY4102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2585,plain,
! [SV682: $i,SV96: $i] :
( ( ! [SY4103: $i,SY4104: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV96 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) @ SY4103 @ SV682 @ ( tc_fun @ SY4104 @ tc_bool ) ) @ ( tc_fun @ SY4104 @ tc_bool ) )
= SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2586,plain,
! [SV683: $i,SV97: $i] :
( ( ! [SY4105: $i,SY4106: $i,SY4107: $i,SY4108: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV97 @ SV683 @ SY4105 @ SY4106 ) @ SY4107 ) @ SY4108 )
= ( hAPP @ ( hAPP @ SV97 @ SY4108 ) @ SY4107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2587,plain,
! [SV684: $i,SV98: $i] :
( ( ! [SY4109: $i,SY4110: $i] :
( ( hAPP @ ( c_COMBK @ SV98 @ SV684 @ SY4109 ) @ SY4110 )
= SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2588,plain,
! [SV685: $i,SV99: $i] :
( ( ! [SY4111: $i,SY4112: $i,SY4113: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SY4111 @ SY4112 @ ( tc_fun @ SY4113 @ tc_bool ) ) @ SY4113 @ SV99 ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SY4112 @ SY4111 @ ( tc_fun @ SY4113 @ tc_bool ) ) @ SY4113 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV685 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4113 @ tc_bool ) ) @ SY4111 ) @ SY4112 ) @ SY4113 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2589,plain,
! [SV686: $i,SV100: $i] :
( ( ! [SY4114: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SV686 @ ( tc_fun @ SY4114 @ tc_bool ) ) @ SV686 @ ( tc_fun @ SY4114 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV100 @ SV686 @ ( tc_fun @ SY4114 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2590,plain,
! [SV687: $i,SV101: $i] :
( ( ! [SY4115: $i] :
( ~ ( class_Orderings_Olinorder @ SV101 )
| ( c_HOL_Oord__class_Oless @ SV687 @ SY4115 @ SV101 )
| ( c_lessequals @ SY4115 @ SV687 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2591,plain,
! [SV688: $i,SV102: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV102 )
| ~ ( c_lessequals @ SV688 @ SV688 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV688 @ SV688 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2592,plain,
! [SV689: $i,SV103: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_HOL_Oord__class_Oless @ SV689 @ SV689 @ SV103 )
| ( c_lessequals @ SV689 @ SV689 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2593,plain,
! [SV690: $i,SV104: $i] :
( ( ! [SY4116: $i] :
( ~ ( class_Orderings_Olinorder @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SV690 @ SY4116 @ SV104 )
| ~ ( c_lessequals @ SY4116 @ SV690 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2594,plain,
! [SV691: $i,SV105: $i] :
( ( ! [SY4117: $i] :
( ~ ( class_Orderings_Olinorder @ SV105 )
| ( c_lessequals @ SV691 @ SY4117 @ SV105 )
| ( c_HOL_Oord__class_Oless @ SY4117 @ SV691 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2595,plain,
! [SV692: $i,SV106: $i] :
( ( ! [SY4118: $i] :
( ~ ( class_Orderings_Olinorder @ SV106 )
| ~ ( c_lessequals @ SV692 @ SY4118 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SY4118 @ SV692 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2596,plain,
! [SV693: $i,SV107: $i] :
( ( ! [SY4119: $i] :
( ~ ( class_Orderings_Olinorder @ SV107 )
| ( c_HOL_Oord__class_Oless @ SV693 @ SY4119 @ SV107 )
| ( c_lessequals @ SY4119 @ SV693 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2597,plain,
! [SV694: $i,SV108: $i] :
( ( ! [SY4120: $i,SY4121: $i] :
( ~ ( class_HOL_Oord @ SV108 )
| ~ ( c_lessequals @ SV694 @ SY4120 @ ( tc_fun @ SY4121 @ SV108 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4120 @ SV694 @ ( tc_fun @ SY4121 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2598,plain,
! [SV695: $i,SV109: $i] :
( ( ! [SY4122: $i] :
( ~ ( class_Orderings_Opreorder @ SV109 )
| ~ ( c_lessequals @ SV695 @ SY4122 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY4122 @ SV695 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2599,plain,
! [SV696: $i,SV110: $i] :
( ( ! [SY4123: $i,SY4124: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV110 ) @ ( hAPP @ SV696 @ SY4123 ) ) @ ( c_Set_Oimage @ SV696 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4124 @ tc_bool ) ) @ SY4124 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2600,plain,
! [SV697: $i,SV111: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV111 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ SV697 @ SV111 )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 ) @ ( c_Orderings_Obot__class_Obot @ SV111 ) @ SV697 @ SV111 @ SV111 ) )
| ~ ( c_Finite__Set_Ofinite @ SV697 @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2601,plain,
! [SV698: $i,SV112: $i] :
( ( ! [SY4125: $i] :
( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY4125 @ SV112 ) @ SV112 )
| ~ ( c_Finite__Set_Ofinite @ SY4125 @ SV112 )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SY4125 @ ( tc_fun @ SV112 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2602,plain,
! [SV699: $i,SV113: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV113 )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV699 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV113 @ tc_bool ) ) @ SV113 ) @ SV113 )
= SV699 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2603,plain,
! [SV700: $i,SV114: $i] :
( ( ! [SY4126: $i,SY4127: $i,SY4128: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV114 @ SV700 @ SY4126 @ SY4127 ) @ ( c_Set_Oimage @ SV114 @ SY4128 @ SY4126 @ SY4127 ) @ ( tc_fun @ SY4127 @ tc_bool ) ) @ ( c_Set_Oimage @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV700 @ SY4128 @ ( tc_fun @ SY4126 @ tc_bool ) ) @ SY4126 @ SY4127 ) @ ( tc_fun @ SY4127 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2604,plain,
! [SV701: $i,SV115: $i] :
( ( ! [SY4129: $i,SY4130: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV701 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SY4129 ) @ SY4130 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SY4129 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV701 ) @ SY4130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2605,plain,
! [SV702: $i,SV116: $i] :
( ( ! [SY4131: $i,SY4132: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV702 ) @ SY4131 ) ) @ SY4132 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV702 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SY4131 ) @ SY4132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2606,plain,
! [SV703: $i,SV117: $i] :
( ( ! [SY4133: $i,SY4134: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ SY4133 ) ) @ SY4134 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SY4133 ) @ SY4134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2607,plain,
! [SV704: $i,SV118: $i] :
( ( ! [SY4135: $i,SY4136: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SY4135 ) @ SY4136 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SY4135 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ SY4136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2608,plain,
! [SV705: $i,SV119: $i] :
( ( ! [SY4137: $i,SY4138: $i] :
( ~ ( class_Lattices_Olattice @ SV119 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SY4137 ) @ SY4138 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SY4137 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ SY4138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2609,plain,
! [SV706: $i,SV120: $i] :
( ( ! [SY4139: $i,SY4140: $i] :
( ~ ( class_Lattices_Olattice @ SV120 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ SY4139 ) ) @ SY4140 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SY4139 ) @ SY4140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2610,plain,
! [SV707: $i,SV121: $i] :
( ( ! [SY4141: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV121 @ tc_bool ) ) @ SV707 ) @ SY4141 )
= SV707 )
| ~ ( c_lessequals @ SV707 @ SY4141 @ ( tc_fun @ SV121 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2611,plain,
! [SV708: $i,SV122: $i] :
( ( ! [SY4142: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV122 @ tc_bool ) ) @ SV708 ) @ SY4142 )
= SY4142 )
| ~ ( c_lessequals @ SY4142 @ SV708 @ ( tc_fun @ SV122 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2612,plain,
! [SV709: $i,SV123: $i] :
( ( ! [SY4143: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV123 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SV709 ) @ SY4143 )
= SV709 )
| ~ ( c_lessequals @ SV709 @ SY4143 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2613,plain,
! [SV710: $i,SV124: $i] :
( ( ! [SY4144: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV124 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SV710 ) @ SY4144 )
= SY4144 )
| ~ ( c_lessequals @ SY4144 @ SV710 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2614,plain,
! [SV711: $i,SV125: $i] :
( ( ! [SY4145: $i,SY4146: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SY4145 ) @ SY4146 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SY4145 @ SY4146 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SV711 @ SY4146 @ ( tc_fun @ SV125 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2615,plain,
! [SV712: $i,SV126: $i] :
( ( ! [SY4147: $i] : ( c_lessequals @ SV126 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV712 @ tc_bool ) ) @ SY4147 ) @ SV126 ) @ ( tc_fun @ SV712 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2616,plain,
! [SV713: $i,SV127: $i] :
( ( ! [SY4148: $i] : ( c_lessequals @ SV127 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV713 @ tc_bool ) ) @ SV127 ) @ SY4148 ) @ ( tc_fun @ SV713 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2617,plain,
! [SV714: $i,SV128: $i] :
( ( ! [SY4149: $i,SY4150: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SY4149 ) @ SY4150 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SY4149 @ SY4150 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SY4150 @ ( tc_fun @ SV128 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2618,plain,
! [SV715: $i,SV129: $i] :
( ( ! [SY4151: $i,SY4152: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV129 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SY4151 ) @ SY4152 @ SV129 )
| ~ ( c_lessequals @ SY4151 @ SY4152 @ SV129 )
| ~ ( c_lessequals @ SV715 @ SY4152 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2619,plain,
! [SV716: $i,SV130: $i] :
( ( ! [SY4153: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV130 )
| ( c_lessequals @ SV716 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 ) @ SV716 ) @ SY4153 ) @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2620,plain,
! [SV717: $i,SV131: $i] :
( ( ! [SY4154: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( c_lessequals @ SV717 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 ) @ SY4154 ) @ SV717 ) @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2621,plain,
! [SV718: $i,SV132: $i] :
( ( ! [SY4155: $i,SY4156: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SY4155 ) @ SY4156 @ SV132 )
| ~ ( c_lessequals @ SY4155 @ SY4156 @ SV132 )
| ~ ( c_lessequals @ SV718 @ SY4156 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2622,plain,
! [SV719: $i,SV133: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV133 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SY4157 ) @ SY4158 @ SV133 )
| ~ ( c_lessequals @ SY4157 @ SY4158 @ SV133 )
| ~ ( c_lessequals @ SV719 @ SY4158 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2623,plain,
! [SV720: $i,SV134: $i] :
( ( ! [SY4159: $i] :
( ~ ( class_Lattices_Olattice @ SV134 )
| ( c_lessequals @ SV720 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 ) @ SY4159 ) @ SV720 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2624,plain,
! [SV721: $i,SV135: $i] :
( ( ! [SY4160: $i] :
( ~ ( class_Lattices_Olattice @ SV135 )
| ( c_lessequals @ SV721 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV135 ) @ SV721 ) @ SY4160 ) @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2625,plain,
! [SV722: $i,SV136: $i] :
( ( ! [SY4161: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV136 @ tc_bool ) ) @ SV722 ) @ SY4161 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV136 @ tc_bool ) ) @ SY4161 ) @ SV722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2626,plain,
! [SV723: $i,SV137: $i] :
( ( ! [SY4162: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV137 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV723 ) @ SY4162 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SY4162 ) @ SV723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2627,plain,
! [SV724: $i,SV138: $i] :
( ( ! [SY4163: $i] :
( ~ ( class_Lattices_Olattice @ SV138 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV724 ) @ SY4163 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SY4163 ) @ SV724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2628,plain,
! [SV725: $i,SV139: $i] :
( ( ! [SY4164: $i,SY4165: $i,SY4166: $i,SY4167: $i,SY4168: $i,SY4169: $i,SY4170: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SY4164 @ SY4165 @ SY4165 @ tc_bool ) @ ( c_COMBC @ SY4166 @ SY4165 @ SY4165 @ tc_bool ) @ SY4167 @ SY4168 @ SY4169 @ SY4170 @ SY4165 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SY4164 @ SY4166 @ SY4168 @ SY4167 @ SY4170 @ SY4169 @ SY4165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2629,plain,
! [SV726: $i,SV140: $i] :
( ( ! [SY4171: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV140 @ tc_bool ) ) @ SV726 ) @ ( c_HOL_Ominus__class_Ominus @ SY4171 @ SV726 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= SY4171 )
| ~ ( c_lessequals @ SV726 @ SY4171 @ ( tc_fun @ SV140 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2630,plain,
! [SV727: $i,SV141: $i] :
( ( ! [SY4172: $i,SY4173: $i] :
( ~ ( class_Lattices_Olattice @ SV141 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SY4172 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SY4173 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ SY4172 ) @ SY4173 ) ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2631,plain,
! [SV728: $i,SV142: $i] :
( ( ! [SY4174: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SV728 @ ( tc_fun @ SY4174 @ tc_bool ) ) @ SV142 @ ( tc_fun @ SY4174 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2632,plain,
! [SV729: $i,SV143: $i] :
( ( ! [SY4175: $i] :
( ( c_Set_Oinsert @ SV143 @ ( c_HOL_Ominus__class_Ominus @ SV729 @ ( c_Set_Oinsert @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4175 @ tc_bool ) ) @ SY4175 ) @ ( tc_fun @ SY4175 @ tc_bool ) ) @ SY4175 )
= ( c_Set_Oinsert @ SV143 @ SV729 @ SY4175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2633,plain,
! [SV730: $i,SV144: $i] :
( ( ! [SY4176: $i,SY4177: $i] :
( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SY4176 @ SY4177 ) @ ( tc_fun @ SY4177 @ tc_bool ) )
| ~ ( c_lessequals @ SV144 @ SY4176 @ ( tc_fun @ SY4177 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4177 @ tc_bool ) ) @ SY4177 ) @ ( tc_fun @ SY4177 @ tc_bool ) ) @ SY4176 @ ( tc_fun @ SY4177 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4177 ) @ SV730 ) @ SY4176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2634,plain,
! [SV731: $i,SV145: $i] :
( ( ! [SY4178: $i,SY4179: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV731 ) @ SY4178 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY4178 ) @ SY4179 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY4179 ) @ SV731 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV731 ) @ SY4178 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY4178 ) @ SY4179 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY4179 ) @ SV731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2635,plain,
! [SV732: $i,SV146: $i] :
( ( ! [SY4180: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV146 @ SV732 @ SY4180 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4180 @ tc_bool ) ) @ SY4180 @ SV732 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV732 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2636,plain,
! [SV733: $i,SV147: $i] :
( ( ! [SY4181: $i,SY4182: $i,SY4183: $i,SY4184: $i] :
( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SY4181 @ SY4182 @ SY4183 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SY4184 ) @ SY4183 @ SY4183 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4183 ) @ SY4181 ) @ SY4182 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SY4181 @ SY4182 @ SY4184 @ SY4183 @ SY4183 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SY4183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2637,plain,
! [SV734: $i,SV148: $i] :
( ( ! [SY4185: $i,SY4186: $i,SY4187: $i] :
( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SV734 @ SY4185 @ ( tc_fun @ SY4186 @ tc_bool ) ) @ SY4186 @ SY4187 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SV734 @ SY4186 @ SY4187 ) @ ( c_Set_Oimage @ SV148 @ SY4185 @ SY4186 @ SY4187 ) @ ( tc_fun @ SY4187 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4186 @ tc_bool ) ) @ SY4186 @ SY4187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2638,plain,
! [SV735: $i,SV149: $i] :
( ( ! [SY4188: $i,SY4189: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV149 ) @ SV735 ) @ SY4188 ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV735 @ SY4189 @ SV149 ) @ SY4188 @ ( tc_fun @ SV149 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2639,plain,
! [SV736: $i,SV150: $i] :
( ( ! [SY4190: $i,SY4191: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV150 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV736 @ ( c_COMBK @ SY4190 @ SV150 @ SY4191 ) @ SY4191 @ SV150 )
= SY4190 )
| ( SV736
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4191 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2640,plain,
! [SV737: $i,SV151: $i] :
( ( ! [SY4192: $i,SY4193: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV151 @ SV737 @ SY4192 ) @ SY4193 ) )
| ~ ( hBOOL @ ( hAPP @ SV737 @ SY4193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2641,plain,
! [SV738: $i,SV152: $i] :
( ( ! [SY4194: $i,SY4195: $i,SY4196: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SV738 ) @ ( c_Set_Oimage @ SV152 @ SY4194 @ SY4195 @ SY4196 ) @ SY4196 )
= ( c_Set_Oimage @ SV152 @ SY4194 @ SY4195 @ SY4196 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4195 ) @ SV738 ) @ SY4194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2642,plain,
! [SV739: $i,SV153: $i] :
( ( ! [SY4197: $i,SY4198: $i] :
( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SV739 @ SY4197 @ SY4198 ) @ ( tc_fun @ SY4198 @ tc_bool ) )
| ~ ( c_lessequals @ SV153 @ SY4197 @ ( tc_fun @ SY4198 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4198 ) @ SV739 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2643,plain,
! [SV740: $i,SV154: $i] :
( ( ! [SY4199: $i,SY4200: $i] :
( ( c_lessequals @ SV154 @ SV740 @ ( tc_fun @ SY4199 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4199 ) @ SY4200 ) @ SV154 ) )
| ~ ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SY4200 @ SV740 @ SY4199 ) @ ( tc_fun @ SY4199 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2644,plain,
! [SV741: $i,SV155: $i] :
( ( ! [SY4201: $i,SY4202: $i] :
( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SV741 @ SY4201 @ SY4202 ) @ ( tc_fun @ SY4202 @ tc_bool ) )
| ~ ( c_lessequals @ SV155 @ SY4201 @ ( tc_fun @ SY4202 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4202 ) @ SV741 ) @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2645,plain,
! [SV742: $i,SV156: $i] :
( ( ! [SY4203: $i,SY4204: $i] :
( ( c_lessequals @ SV156 @ SV742 @ ( tc_fun @ SY4203 @ tc_bool ) )
| ~ ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SY4204 @ SV742 @ SY4203 ) @ ( tc_fun @ SY4203 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4203 ) @ SY4204 ) @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2646,plain,
! [SV743: $i,SV157: $i] :
( ( ! [SY4205: $i,SY4206: $i,SY4207: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SV743 @ SY4205 @ SY4206 ) @ ( c_Set_Ovimage @ SV157 @ SY4207 @ SY4205 @ SY4206 ) @ ( tc_fun @ SY4205 @ tc_bool ) )
| ~ ( c_lessequals @ SV743 @ SY4207 @ ( tc_fun @ SY4206 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2647,plain,
! [SV744: $i,SV158: $i] :
( ( ! [SY4208: $i,SY4209: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SY4208 @ SY4209 @ SV158 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ SY4209 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV158 ) @ SY4208 ) @ SV744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2648,plain,
! [SV745: $i,SV159: $i] :
( ( ! [SY4210: $i,SY4211: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV745 @ SY4210 @ SV159 ) ) @ SY4211 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ SY4210 ) @ SY4211 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV159 ) @ SV745 ) @ SY4211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2649,plain,
! [SV746: $i,SV160: $i] :
( ( ! [SY4212: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV160 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV746 @ SY4212 @ ( tc_fun @ SV160 @ tc_bool ) ) ) @ SY4212 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV160 @ tc_bool ) ) @ SV746 ) @ SY4212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2650,plain,
! [SV747: $i,SV161: $i] :
( ( ! [SY4213: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV161 @ tc_bool ) ) @ SV747 ) @ ( c_HOL_Ominus__class_Ominus @ SY4213 @ SV747 @ ( tc_fun @ SV161 @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV161 @ tc_bool ) ) @ SV747 ) @ SY4213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2651,plain,
! [SV748: $i,SV162: $i] :
( ( ! [SY4214: $i] :
( ( ( c_Set_Oimage @ SV162 @ SV748 @ SY4214 @ SY4214 )
= SV748 )
| ~ ( c_Fun_Oinj__on @ SV162 @ SV748 @ SY4214 @ SY4214 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SY4214 @ SY4214 ) @ SV748 @ ( tc_fun @ SY4214 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV748 @ SY4214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2652,plain,
! [SV749: $i,SV163: $i] :
( ( ! [SY4215: $i,SY4216: $i] :
( ~ ( class_Lattices_Olattice @ SV163 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ SY4215 ) ) @ SY4216 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SY4215 ) @ SY4216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2653,plain,
! [SV750: $i,SV164: $i] :
( ( ! [SY4217: $i,SY4218: $i] :
( ~ ( class_Lattices_Olattice @ SV164 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SY4217 ) @ SY4218 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SY4217 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ SY4218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2654,plain,
! [SV751: $i,SV165: $i] :
( ( ! [SY4219: $i,SY4220: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV165 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SY4219 ) @ SY4220 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SY4219 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ SY4220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2655,plain,
! [SV752: $i,SV166: $i] :
( ( ! [SY4221: $i,SY4222: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV166 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ SY4221 ) ) @ SY4222 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SY4221 ) @ SY4222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2656,plain,
! [SV753: $i,SV167: $i] :
( ( ! [SY4223: $i,SY4224: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV753 ) @ SY4223 ) ) @ SY4224 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV753 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SY4223 ) @ SY4224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2657,plain,
! [SV754: $i,SV168: $i] :
( ( ! [SY4225: $i,SY4226: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV754 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SY4225 ) @ SY4226 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SY4225 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV754 ) @ SY4226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2658,plain,
! [SV755: $i,SV169: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV755 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV169 @ tc_bool ) ) @ SV169 ) @ SV169 )
= SV755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2659,plain,
! [SV756: $i,SV170: $i] :
( ( ! [SY4227: $i] :
( ( c_Finite__Set_Ofinite @ SV170 @ SV756 )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV756 @ tc_bool ) ) @ SV170 ) @ SY4227 ) @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2660,plain,
! [SV757: $i,SV171: $i] :
( ( ! [SY4228: $i] :
( ( c_Finite__Set_Ofinite @ SV171 @ SV757 )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV757 @ tc_bool ) ) @ SY4228 ) @ SV171 ) @ SV757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2661,plain,
! [SV758: $i,SV172: $i] :
( ( ! [SY4229: $i,SY4230: $i,SY4231: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ SV172 @ SV758 @ SY4229 @ SY4230 ) @ SY4231 @ SY4229 @ SY4230 )
= ( c_Map_Orestrict__map @ SV172 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4229 @ tc_bool ) ) @ SV758 ) @ SY4231 ) @ SY4229 @ SY4230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2662,plain,
! [SV759: $i,SV173: $i] :
( ( ! [SY4232: $i,SY4233: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV173 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV759 @ tc_bool ) ) @ SY4232 @ SV759 @ ( tc_fun @ SV173 @ tc_bool ) ) ) @ SY4233 )
= SY4233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2663,plain,
! [SV760: $i,SV174: $i] :
( ( ! [SY4234: $i,SY4235: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV174 @ tc_bool ) ) @ SV760 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4234 @ tc_bool ) ) @ SY4235 @ SY4234 @ ( tc_fun @ SV174 @ tc_bool ) ) )
= SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2664,plain,
! [SV761: $i,SV175: $i] :
( ( ! [SY4236: $i,SY4237: $i] :
( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SY4236 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4236 ) @ SY4237 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4236 ) @ SY4237 ) @ SV761 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SY4237 @ SV761 @ SY4236 ) @ ( tc_fun @ SY4236 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2665,plain,
! [SV762: $i,SV176: $i] :
( ( ! [SY4238: $i,SY4239: $i] :
( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SY4238 @ SY4239 ) @ ( tc_fun @ SY4239 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SY4238 @ ( tc_fun @ SY4239 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4239 ) @ SV762 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4239 ) @ SV762 ) @ SY4238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2666,plain,
! [SV763: $i,SV177: $i] :
( ( ! [SY4240: $i,SY4241: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ ( c_HOL_Ominus__class_Ominus @ SY4240 @ SY4241 @ ( tc_fun @ SV177 @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ SY4240 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ SY4241 ) @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2667,plain,
! [SV764: $i,SV178: $i] :
( ( ! [SY4242: $i,SY4243: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV764 @ SY4242 @ ( tc_fun @ SV178 @ tc_bool ) ) ) @ SY4243 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SV764 ) @ SY4243 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SY4242 ) @ SY4243 ) @ ( tc_fun @ SV178 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2668,plain,
! [SV765: $i,SV179: $i] :
( ( ! [SY4244: $i,SY4245: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV179 @ SV765 @ SY4244 ) @ SY4245 @ SY4244 @ SV765 )
= ( c_Set_Oinsert @ SV179 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV765 ) )
| ( SY4245
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4244 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2669,plain,
! [SV766: $i,SV180: $i] :
( ( ! [SY4246: $i,SY4247: $i] :
( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SY4246 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4246 ) @ SY4247 ) @ SV766 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SY4247 @ SV766 @ SY4246 ) @ ( tc_fun @ SY4246 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2670,plain,
! [SV767: $i,SV181: $i] :
( ( ! [SY4248: $i,SY4249: $i] :
( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SY4248 @ SY4249 ) @ ( tc_fun @ SY4249 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4249 ) @ SV767 ) @ SY4248 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SY4248 @ ( tc_fun @ SY4249 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2671,plain,
! [SV768: $i,SV182: $i] :
( ( ! [SY4250: $i,SY4251: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV182 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SY4250 @ SY4251 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SY4250 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SY4251 @ SV182 @ SV182 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY4251 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2672,plain,
! [SV769: $i,SV183: $i] :
( ( ! [SY4252: $i,SY4253: $i,SY4254: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SY4252 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY4253 @ SY4254 @ ( tc_fun @ SY4252 @ tc_bool ) ) @ ( tc_fun @ SY4252 @ tc_bool ) )
| ~ ( c_lessequals @ SY4254 @ SV769 @ ( tc_fun @ SY4252 @ tc_bool ) )
| ~ ( c_lessequals @ SV183 @ SY4253 @ ( tc_fun @ SY4252 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2673,plain,
! [SV770: $i,SV184: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV184 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV184 ) @ SV770 ) @ ( c_Orderings_Otop__class_Otop @ SV184 ) )
= SV770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2674,plain,
! [SV771: $i,SV185: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV185 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV185 ) @ ( c_Orderings_Otop__class_Otop @ SV185 ) ) @ SV771 )
= SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2675,plain,
! [SV772: $i,SV186: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV186 @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV186 @ tc_bool ) ) ) @ SV772 )
= SV772 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2676,plain,
! [SV773: $i,SV187: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV773 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV187 @ tc_bool ) ) )
= SV773 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2677,plain,
! [SV774: $i,SV188: $i] :
( ( ! [SY4255: $i,SY4256: $i] :
( ( c_Set_Oimage @ SV188 @ ( c_Set_Ovimage @ SV188 @ SV774 @ SY4255 @ SY4256 ) @ SY4255 @ SY4256 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4256 @ tc_bool ) ) @ SV774 ) @ ( c_Set_Oimage @ SV188 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4255 @ tc_bool ) ) @ SY4255 @ SY4256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2678,plain,
! [SV775: $i,SV189: $i] :
( ( ! [SY4257: $i,SY4258: $i] :
( ~ ( class_Lattices_Olattice @ SV189 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ SY4257 ) @ SY4258 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SY4257 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SY4258 ) ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2679,plain,
! [SV776: $i,SV190: $i] :
( ( ! [SY4259: $i,SY4260: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV776 ) @ SY4259 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SY4260 ) @ SY4259 ) @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV776 ) @ SY4259 ) @ SY4260 @ ( tc_fun @ SV190 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2680,plain,
! [SV777: $i,SV191: $i] :
( ( ! [SY4261: $i] :
( ~ ( class_Orderings_Opreorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SY4261 @ SV191 )
| ( c_lessequals @ SY4261 @ SV777 @ SV191 )
| ~ ( c_lessequals @ SV777 @ SY4261 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2681,plain,
! [SV778: $i,SV192: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV192 @ SV192 @ ( tc_fun @ SV778 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2682,plain,
! [SV779: $i,SV193: $i] :
( ( ! [SY4262: $i,SY4263: $i] :
( ~ ( class_HOL_Oord @ SV193 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SY4262 @ ( tc_fun @ SY4263 @ SV193 ) )
| ( c_lessequals @ SY4262 @ SV779 @ ( tc_fun @ SY4263 @ SV193 ) )
| ~ ( c_lessequals @ SV779 @ SY4262 @ ( tc_fun @ SY4263 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2683,plain,
! [SV780: $i,SV194: $i] :
( ( ~ ( class_Orderings_Oorder @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ SV780 @ SV780 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2684,plain,
! [SV781: $i,SV195: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV781 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2685,plain,
! [SV782: $i,SV196: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2686,plain,
! [SV783: $i,SV197: $i] :
( ( ! [SY4264: $i] :
( ~ ( class_Lattices_Olattice @ SV197 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 ) @ SV783 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV197 ) @ SV783 ) @ SY4264 ) )
= SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2687,plain,
! [SV784: $i,SV198: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV198 @ tc_bool ) ) @ SV784 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2688,plain,
! [SV199: $i] :
( ( ( ~ ( class_Orderings_Otop @ SV199 ) )
= $true )
| ( ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ SV199 ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2689,plain,
! [SV785: $i,SV200: $i] :
( ( ! [SY4265: $i] :
( ( c_lessequals @ SV200 @ SV785 @ ( tc_fun @ SY4265 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SY4265 ) @ SY4265 @ ( tc_fun @ SY4265 @ tc_bool ) @ tc_bool ) @ SV200 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SY4265 ) @ SY4265 @ ( tc_fun @ SY4265 @ tc_bool ) @ tc_bool ) @ SV785 ) @ ( tc_fun @ SY4265 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2690,plain,
! [SV786: $i,SV201: $i] :
( ( ! [SY4266: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV786 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SY4266 ) @ ( tc_fun @ SV201 @ tc_bool ) )
| ~ ( c_lessequals @ SV786 @ SY4266 @ ( tc_fun @ SV201 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2691,plain,
! [SV787: $i,SV202: $i] :
( ( ! [SY4267: $i,SY4268: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SY4267 @ SY4268 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SY4267 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SY4268 @ SV202 @ SV202 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY4268 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2692,plain,
! [SV788: $i,SV203: $i] :
( ( ! [SY4269: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SY4269 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SY4269 @ SV788 @ SV203 )
| ( SY4269 = SV788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2693,plain,
! [SV789: $i,SV204: $i] :
( ( ! [SY4270: $i] :
( ~ ( class_Orderings_Olinorder @ SV204 )
| ( SV789 = SY4270 )
| ( c_HOL_Oord__class_Oless @ SY4270 @ SV789 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SY4270 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2694,plain,
! [SV790: $i,SV205: $i] :
( ( ! [SY4271: $i] :
( ( SV205 = SV790 )
| ~ ( c_lessequals @ SV790 @ SV205 @ ( tc_fun @ SY4271 @ tc_bool ) )
| ~ ( c_lessequals @ SV205 @ SV790 @ ( tc_fun @ SY4271 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2695,plain,
! [SV791: $i,SV206: $i] :
( ( ! [SY4272: $i] :
( ( SV206 = SV791 )
| ~ ( c_lessequals @ SV791 @ SV206 @ ( tc_fun @ SY4272 @ tc_bool ) )
| ~ ( c_lessequals @ SV206 @ SV791 @ ( tc_fun @ SY4272 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2696,plain,
! [SV792: $i,SV207: $i] :
( ( ! [SY4273: $i] :
( ~ ( class_Orderings_Oorder @ SV207 )
| ( SV792 = SY4273 )
| ~ ( c_lessequals @ SY4273 @ SV792 @ SV207 )
| ~ ( c_lessequals @ SV792 @ SY4273 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2697,plain,
! [SV793: $i,SV208: $i] :
( ( ! [SY4274: $i] :
( ~ ( class_Orderings_Olinorder @ SV208 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SY4274 @ SV208 )
| ( c_HOL_Oord__class_Oless @ SY4274 @ SV793 @ SV208 )
| ( SY4274 = SV793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2698,plain,
! [SV794: $i,SV209: $i] :
( ( ! [SY4275: $i] :
( ~ ( class_Orderings_Oorder @ SV209 )
| ( SV794 = SY4275 )
| ~ ( c_lessequals @ SY4275 @ SV794 @ SV209 )
| ~ ( c_lessequals @ SV794 @ SY4275 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2699,plain,
! [SV795: $i,SV210: $i] :
( ( ! [SY4276: $i] :
( ~ ( class_Orderings_Oorder @ SV210 )
| ( SV795 = SY4276 )
| ~ ( c_lessequals @ SV795 @ SY4276 @ SV210 )
| ~ ( c_lessequals @ SY4276 @ SV795 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2700,plain,
! [SV796: $i,SV211: $i] :
( ( ! [SY4277: $i] :
( ~ ( class_Orderings_Olinorder @ SV211 )
| ( c_HOL_Oord__class_Oless @ SV796 @ SY4277 @ SV211 )
| ( SY4277 = SV796 )
| ( c_HOL_Oord__class_Oless @ SY4277 @ SV796 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2701,plain,
! [SV797: $i,SV212: $i] :
( ( ! [SY4278: $i] :
( ~ ( class_Orderings_Olinorder @ SV212 )
| ( SV797 = SY4278 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SY4278 @ SV212 )
| ( c_HOL_Oord__class_Oless @ SY4278 @ SV797 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2702,plain,
! [SV798: $i,SV213: $i] :
( ( ! [SY4279: $i] :
( ~ ( class_Lattices_Olattice @ SV213 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 ) @ SV798 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 ) @ SV798 ) @ SY4279 ) )
= SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2703,plain,
! [SV799: $i,SV214: $i] :
( ( ! [SY4280: $i,SY4281: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV214 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SY4280 ) @ SY4281 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SY4280 @ SY4281 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2704,plain,
! [SV800: $i,SV215: $i] :
( ( ! [SY4282: $i,SY4283: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV215 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SY4282 ) @ SY4283 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ SV800 @ SY4283 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2705,plain,
! [SV801: $i,SV216: $i] :
( ( ! [SY4284: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV216 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV801 @ SY4284 @ ( tc_fun @ SV216 @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV216 @ tc_bool ) ) @ SV801 ) @ SY4284 ) )
= SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2706,plain,
! [SV802: $i,SV217: $i] :
( ( ! [SY4285: $i] :
( ( c_lessequals @ SV217 @ SV802 @ ( tc_fun @ SY4285 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV217 @ SV802 @ ( tc_fun @ SY4285 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2707,plain,
! [SV803: $i,SV218: $i] :
( ( ! [SY4286: $i,SY4287: $i] :
( ~ ( class_HOL_Oord @ SV218 )
| ( c_lessequals @ SV803 @ SY4286 @ ( tc_fun @ SY4287 @ SV218 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SY4286 @ ( tc_fun @ SY4287 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2708,plain,
! [SV804: $i,SV219: $i] :
( ( ! [SY4288: $i] :
( ~ ( class_Orderings_Oorder @ SV219 )
| ( c_lessequals @ SV804 @ SY4288 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SY4288 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2709,plain,
! [SV805: $i,SV220: $i] :
( ( ! [SY4289: $i] :
( ~ ( class_Orderings_Opreorder @ SV220 )
| ( c_lessequals @ SV805 @ SY4289 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV805 @ SY4289 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2710,plain,
! [SV806: $i,SV221: $i] :
( ( ! [SY4290: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV221 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SV806 ) @ SY4290 )
= SV806 )
| ~ ( c_lessequals @ SY4290 @ SV806 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2711,plain,
! [SV807: $i,SV222: $i] :
( ( ! [SY4291: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV222 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SV807 ) @ SY4291 )
= SY4291 )
| ~ ( c_lessequals @ SV807 @ SY4291 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2712,plain,
! [SV808: $i,SV223: $i] :
( ( ! [SY4292: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV223 @ tc_bool ) ) @ SV808 ) @ SY4292 )
= SY4292 )
| ~ ( c_lessequals @ SV808 @ SY4292 @ ( tc_fun @ SV223 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2713,plain,
! [SV809: $i,SV224: $i] :
( ( ! [SY4293: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV224 @ tc_bool ) ) @ SV809 ) @ SY4293 )
= SV809 )
| ~ ( c_lessequals @ SY4293 @ SV809 @ ( tc_fun @ SV224 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2714,plain,
! [SV810: $i,SV225: $i] :
( ( ! [SY4294: $i,SY4295: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV225 @ SV810 @ SY4294 @ SY4295 ) @ SY4295 )
| ~ ( c_Finite__Set_Ofinite @ SV810 @ SY4294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2715,plain,
! [SV811: $i,SV226: $i] :
( ( ! [SY4296: $i,SY4297: $i] :
( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SY4296 @ SY4297 ) @ ( tc_fun @ SY4297 @ tc_bool ) )
| ~ ( c_lessequals @ SV226 @ SY4296 @ ( tc_fun @ SY4297 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4297 ) @ SV811 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SY4296 @ ( tc_fun @ SY4297 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2716,plain,
! [SV812: $i,SV227: $i] :
( ( ! [SY4298: $i] :
( ~ ( class_Orderings_Olinorder @ SV227 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY4298 @ SV227 ) @ SV227 )
| ~ ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
| ( SY4298
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY4298 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2717,plain,
! [SV813: $i,SV228: $i] :
( ( ! [SY4299: $i,SY4300: $i,SY4301: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV228 @ SV813 @ SY4299 ) @ SY4300 @ SY4299 @ ( tc_fun @ SY4301 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4301 @ tc_bool ) ) @ ( hAPP @ SY4300 @ SV228 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV813 @ SY4300 @ SY4299 @ ( tc_fun @ SY4301 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2718,plain,
! [SV814: $i,SV229: $i] :
( ( ! [SY4302: $i,SY4303: $i,SY4304: $i,SY4305: $i,SY4306: $i,SY4307: $i,SY4308: $i,SY4309: $i,SY4310: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SY4302 @ SY4303 ) )
= ( hAPP @ ( hAPP @ SY4304 @ SV814 ) @ ( hAPP @ SV229 @ SY4302 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4305 @ SV229 @ SY4306 @ SY4307 @ SY4308 @ SY4304 @ SY4309 @ SY4310 @ SY4303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2719,plain,
! [SV815: $i,SV230: $i] :
( ( ! [SY4311: $i,SY4312: $i,SY4313: $i,SY4314: $i,SY4315: $i,SY4316: $i,SY4317: $i,SY4318: $i,SY4319: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SY4311 @ SY4312 ) )
= ( hAPP @ ( hAPP @ SY4313 @ SV815 ) @ ( hAPP @ SV230 @ SY4311 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SY4314 @ SY4315 @ SY4316 @ SY4313 @ SY4317 @ SY4318 @ SY4319 @ SY4312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2720,plain,
! [SV816: $i,SV231: $i] :
( ( ! [SY4320: $i] : ( c_Finite__Set_Ofold1Set @ SV231 @ ( c_Set_Oinsert @ SV816 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4320 @ tc_bool ) ) @ SY4320 ) @ SV816 @ SY4320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2721,plain,
! [SV817: $i,SV232: $i] :
( ( ! [SY4321: $i,SY4322: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SY4321 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SY4322 @ SY4321 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY4322 @ SV817 @ SY4321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2722,plain,
! [SV818: $i,SV233: $i] :
( ( ! [SY4323: $i,SY4324: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV818 @ SY4323 @ SV233 ) ) @ SY4324 )
= ( c_Set_Oinsert @ SV818 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ SY4323 ) @ SY4324 ) @ SV233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV233 ) @ SV818 ) @ SY4324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2723,plain,
! [SV819: $i,SV234: $i] :
( ( ! [SY4325: $i,SY4326: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ ( c_Set_Oinsert @ SY4325 @ SY4326 @ SV234 ) )
= ( c_Set_Oinsert @ SY4325 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ SY4326 ) @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV234 ) @ SY4325 ) @ SV819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2724,plain,
! [SV820: $i,SV235: $i] :
( ( ! [SY4327: $i,SY4328: $i,SY4329: $i] :
( ( c_Set_Oimage @ SV235 @ ( c_Set_Oinsert @ SV820 @ SY4327 @ SY4328 ) @ SY4328 @ SY4329 )
= ( c_Set_Oinsert @ ( hAPP @ SV235 @ SV820 ) @ ( c_Set_Oimage @ SV235 @ SY4327 @ SY4328 @ SY4329 ) @ SY4329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2725,plain,
! [SV821: $i,SV236: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV236 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV821 @ tc_bool ) ) @ ( tc_fun @ SV821 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV821 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2726,plain,
! [SV822: $i,SV237: $i] :
( ( ! [SY4330: $i,SY4331: $i,SY4332: $i,SY4333: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV237 @ SV822 @ SY4330 @ SY4331 @ SY4332 ) @ SY4333 )
= ( hAPP @ SV822 @ ( hAPP @ SV237 @ SY4333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2727,plain,
! [SV823: $i,SV238: $i] :
( ( ! [SY4334: $i,SY4335: $i,SY4336: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SY4334 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SY4335 ) @ SY4336 ) @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SY4334 @ SY4336 @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV823 @ SY4335 @ ( tc_fun @ SV238 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2728,plain,
! [SV824: $i,SV239: $i] :
( ( ! [SY4337: $i] :
( ~ ( class_Lattices_Olattice @ SV239 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 ) @ SV824 ) @ SY4337 ) @ SV824 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2729,plain,
! [SV825: $i,SV240: $i] :
( ( ! [SY4338: $i] :
( ~ ( class_Lattices_Olattice @ SV240 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV240 ) @ SV825 ) @ SY4338 ) @ SY4338 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2730,plain,
! [SV826: $i,SV241: $i] :
( ( ! [SY4339: $i,SY4340: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV241 )
| ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SY4339 ) @ SY4340 ) @ SV241 )
| ~ ( c_lessequals @ SV826 @ SY4340 @ SV241 )
| ~ ( c_lessequals @ SV826 @ SY4339 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2731,plain,
! [SV827: $i,SV242: $i] :
( ( ! [SY4341: $i,SY4342: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV242 )
| ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SY4341 ) @ SY4342 ) @ SV242 )
| ~ ( c_lessequals @ SV827 @ SY4342 @ SV242 )
| ~ ( c_lessequals @ SV827 @ SY4341 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2732,plain,
! [SV828: $i,SV243: $i] :
( ( ! [SY4343: $i,SY4344: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV243 )
| ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SY4343 ) @ SY4344 ) @ SV243 )
| ~ ( c_lessequals @ SV828 @ SY4344 @ SV243 )
| ~ ( c_lessequals @ SV828 @ SY4343 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2733,plain,
! [SV829: $i,SV244: $i] :
( ( ! [SY4345: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV244 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV244 ) @ SV829 ) @ SY4345 ) @ SY4345 @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2734,plain,
! [SV830: $i,SV245: $i] :
( ( ! [SY4346: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV245 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 ) @ SV830 ) @ SY4346 ) @ SV830 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2735,plain,
! [SV831: $i,SV246: $i] :
( ( ! [SY4347: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV246 @ tc_bool ) ) @ SV831 ) @ SY4347 ) @ SV831 @ ( tc_fun @ SV246 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2736,plain,
! [SV832: $i,SV247: $i] :
( ( ! [SY4348: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV247 @ tc_bool ) ) @ SV832 ) @ SY4348 ) @ SY4348 @ ( tc_fun @ SV247 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2737,plain,
! [SV833: $i,SV248: $i] :
( ( ! [SY4349: $i,SY4350: $i] :
( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SY4349 ) @ SY4350 ) @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY4350 @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY4349 @ ( tc_fun @ SV833 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2738,plain,
! [SV834: $i,SV249: $i] :
( ( ! [SY4351: $i,SY4352: $i] :
( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SY4351 ) @ SY4352 ) @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SY4352 @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SY4351 @ ( tc_fun @ SV834 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2739,plain,
! [SV835: $i,SV250: $i] :
( ( c_lessequals @ SV250 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV835 @ tc_bool ) ) @ ( tc_fun @ SV835 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2740,plain,
! [SV836: $i,SV251: $i] :
( ( ~ ( class_Orderings_Otop @ SV251 )
| ( c_lessequals @ SV836 @ ( c_Orderings_Otop__class_Otop @ SV251 ) @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2741,plain,
! [SV837: $i,SV252: $i] :
( ( ! [SY4353: $i,SY4354: $i,SY4355: $i,SY4356: $i,SY4357: $i] :
( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SV837 @ SY4353 @ SY4354 @ SY4355 @ SY4356 ) @ SY4355 @ SY4357 @ SY4356 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SV837 @ SY4355 @ SY4357 @ SY4354 ) @ SY4353 @ SY4354 @ SY4357 @ SY4356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2742,plain,
! [SV838: $i,SV253: $i] :
( ( ! [SY4358: $i,SY4359: $i] :
( ( c_Set_Oinsert @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV838 @ tc_bool ) ) @ SY4358 @ SV838 @ ( tc_fun @ SY4359 @ tc_bool ) ) @ SY4359 )
= ( c_Set_Oinsert @ SV253 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4359 @ tc_bool ) ) @ SY4359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2743,plain,
! [SV839: $i,SV254: $i] :
( ( ! [SY4360: $i,SY4361: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ SV839 ) @ SY4360 ) ) @ SY4361 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV839 ) @ SY4361 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SY4360 ) @ SY4361 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2744,plain,
! [SV840: $i,SV255: $i] :
( ( ! [SY4362: $i,SY4363: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV255 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ SY4362 ) @ SY4363 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SY4362 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SY4363 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2745,plain,
! [SV841: $i,SV256: $i] :
( ( ! [SY4364: $i] :
( ~ ( class_HOL_Ominus @ SV256 )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV841 @ SY4364 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV841 @ v_x ) @ ( hAPP @ SY4364 @ v_x ) @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2746,plain,
! [SV842: $i,SV257: $i] :
( ( ! [SY4365: $i,SY4366: $i] :
( ( c_lessequals @ SV257 @ SV842 @ ( tc_fun @ SY4365 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4365 @ tc_bool ) ) @ SY4366 ) @ SV842 ) @ ( tc_fun @ SY4365 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2747,plain,
! [SV843: $i,SV258: $i] :
( ( ! [SY4367: $i,SY4368: $i] :
( ( c_lessequals @ SV258 @ SV843 @ ( tc_fun @ SY4367 @ tc_bool ) )
| ~ ( c_lessequals @ SV258 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4367 @ tc_bool ) ) @ SV843 ) @ SY4368 ) @ ( tc_fun @ SY4367 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2748,plain,
! [SV844: $i,SV259: $i] :
( ( ! [SY4369: $i,SY4370: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV259 )
| ( c_lessequals @ SV844 @ SY4369 @ SV259 )
| ~ ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SY4369 ) @ SY4370 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2749,plain,
! [SV845: $i,SV260: $i] :
( ( ! [SY4371: $i,SY4372: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV260 )
| ( c_lessequals @ SV845 @ SY4371 @ SV260 )
| ~ ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SY4372 ) @ SY4371 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2750,plain,
! [SV846: $i,SV261: $i] :
( ( ! [SY4373: $i,SY4374: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV261 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SY4373 ) @ SY4374 @ SV261 )
| ~ ( c_lessequals @ SV846 @ SY4374 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2751,plain,
! [SV847: $i,SV262: $i] :
( ( ! [SY4375: $i,SY4376: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV262 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SY4375 ) @ SY4376 @ SV262 )
| ~ ( c_lessequals @ SY4375 @ SY4376 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2752,plain,
! [SV848: $i,SV263: $i] :
( ( ! [SY4377: $i,SY4378: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV263 )
| ( c_lessequals @ SV848 @ SY4377 @ SV263 )
| ~ ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SY4377 ) @ SY4378 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2753,plain,
! [SV849: $i,SV264: $i] :
( ( ! [SY4379: $i,SY4380: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV264 )
| ( c_lessequals @ SV849 @ SY4379 @ SV264 )
| ~ ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SY4380 ) @ SY4379 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2754,plain,
! [SV850: $i,SV265: $i] :
( ( ( c_Set_Ovimage @ ( c_Fun_Oid @ SV265 ) @ SV850 @ SV265 @ SV265 )
= SV850 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2755,plain,
! [SV851: $i,SV266: $i] :
( ( ! [SY4381: $i,SY4382: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ SV851 ) @ SY4381 ) @ SY4382 @ ( tc_fun @ SV266 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SY4382 @ ( tc_fun @ SV266 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SY4381 @ SY4382 @ ( tc_fun @ SV266 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2756,plain,
! [SV852: $i,SV267: $i] :
( ( ! [SY4383: $i,SY4384: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV267 )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SY4383 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SY4384 ) @ SV852 ) @ SV267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SY4384 ) @ SY4383 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4383 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2757,plain,
! [SV853: $i,SV268: $i] :
( ( ! [SY4385: $i,SY4386: $i,SY4387: $i,SY4388: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ SV268 @ SV853 @ SY4385 @ SY4386 @ SY4387 ) @ SY4388 @ SY4387 @ SY4386 )
= ( c_Set_Ovimage @ SV853 @ ( c_Set_Ovimage @ SV268 @ SY4388 @ SY4385 @ SY4386 ) @ SY4387 @ SY4385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2758,plain,
! [SV854: $i,SV269: $i] :
( ( ! [SY4389: $i] :
( ( c_Set_Oinsert @ SV269 @ SV854 @ SY4389 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4389 @ tc_bool ) ) @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY4389 ) @ SY4389 @ SY4389 @ tc_bool ) @ SV269 ) @ SY4389 ) ) @ SV854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2759,plain,
! [SV855: $i,SV270: $i] :
( ( ! [SY4390: $i,SY4391: $i] :
( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SY4390 @ SY4391 ) @ ( tc_fun @ SY4391 @ tc_bool ) )
| ~ ( c_lessequals @ SV270 @ SY4390 @ ( tc_fun @ SY4391 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4391 @ tc_bool ) ) @ SY4391 ) @ ( tc_fun @ SY4391 @ tc_bool ) ) @ SY4390 @ ( tc_fun @ SY4391 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SY4390 @ ( tc_fun @ SY4391 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2760,plain,
! [SV856: $i,SV271: $i] :
( ( ! [SY4392: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV271 @ tc_bool ) ) @ SV856 ) @ SY4392 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV271 @ tc_bool ) ) @ SY4392 ) @ SV856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2761,plain,
! [SV857: $i,SV272: $i] :
( ( ! [SY4393: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV857 ) @ SY4393 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SY4393 ) @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2762,plain,
! [SV858: $i,SV273: $i] :
( ( ! [SY4394: $i] :
( ~ ( class_Lattices_Olattice @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV858 ) @ SY4394 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SY4394 ) @ SV858 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2763,plain,
! [SV859: $i,SV274: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Oid @ SV274 ) @ SV859 @ SV274 @ SV274 )
= SV859 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2764,plain,
! [SV860: $i,SV275: $i] :
( ( ! [SY4395: $i] :
( ( c_Set_Oinsert @ SV275 @ SV860 @ SY4395 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4395 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV275 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4395 @ tc_bool ) ) @ SY4395 ) ) @ SV860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2765,plain,
! [SV861: $i,SV276: $i] :
( ( ! [SY4396: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SV861 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SV861 ) @ SY4396 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SV861 ) @ SY4396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2766,plain,
! [SV862: $i,SV277: $i] :
( ( ! [SY4397: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SY4397 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SY4397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2767,plain,
! [SV863: $i,SV278: $i] :
( ( ! [SY4398: $i] :
( ~ ( class_Lattices_Olattice @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SY4398 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SY4398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2768,plain,
! [SV864: $i,SV279: $i] :
( ( ! [SY4399: $i,SY4400: $i,SY4401: $i,SY4402: $i] :
( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SY4399 @ ( c_HOL_Ominus__class_Ominus @ SY4400 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4401 @ tc_bool ) ) @ SY4401 ) @ ( tc_fun @ SY4401 @ tc_bool ) ) @ SY4401 ) @ SY4402 @ SY4401 @ SY4401 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4401 ) @ SY4399 ) @ SY4400 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4401 ) @ SV864 ) @ SY4400 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SY4399 @ SY4400 @ SY4402 @ SY4401 @ SY4401 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SY4401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2769,plain,
! [SV865: $i,SV280: $i] :
( ( ! [SY4403: $i,SY4404: $i,SY4405: $i,SY4406: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SY4403 @ SY4404 @ SY4405 ) @ SY4406 @ SY4405 @ SY4404 )
| ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SY4406 @ SY4405 @ SY4403 ) @ SY4403 @ SY4404 )
| ~ ( c_Fun_Oinj__on @ SV865 @ SY4406 @ SY4405 @ SY4403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2770,plain,
! [SV866: $i,SV281: $i] :
( ( ! [SY4407: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV281 @ tc_bool ) ) @ SV866 ) @ ( c_HOL_Ominus__class_Ominus @ SY4407 @ SV866 @ ( tc_fun @ SV281 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV281 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2771,plain,
! [SV867: $i,SV282: $i] :
( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV282 )
| ( c_Finite__Set_Ofinite @ SV867 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2772,plain,
! [SV868: $i,SV283: $i] :
( ( ! [SY4408: $i,SY4409: $i,SY4410: $i,SY4411: $i,SY4412: $i] :
( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SY4408 @ SY4409 @ SY4410 ) @ ( hAPP @ ( hAPP @ SV283 @ SY4408 ) @ SY4411 ) @ SY4410 @ SY4412 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SY4409 @ SY4411 @ SY4410 @ SY4412 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4410 ) @ SY4408 ) @ SY4409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2773,plain,
! [SV869: $i,SV284: $i] :
( ( ! [SY4413: $i,SY4414: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ SY4413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV284 @ tc_bool ) ) @ SY4413 ) @ ( c_Collect @ SY4414 @ SV284 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2774,plain,
! [SV870: $i,SV285: $i] :
( ( ! [SY4415: $i,SY4416: $i,SY4417: $i] :
( ( c_Set_Ovimage @ SV285 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV870 @ tc_bool ) ) @ SY4415 ) @ SY4416 ) @ SY4417 @ SV870 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4417 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV285 @ SY4415 @ SY4417 @ SV870 ) ) @ ( c_Set_Ovimage @ SV285 @ SY4416 @ SY4417 @ SV870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2775,plain,
! [SV871: $i,SV286: $i] :
( ( ! [SY4418: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV871 @ ( c_Set_Oinsert @ SY4418 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV286 @ tc_bool ) ) @ SV286 ) @ SV286 ) @ SV286 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 ) @ SV871 ) @ SY4418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2776,plain,
! [SV872: $i,SV287: $i] :
( ( ! [SY4419: $i,SY4420: $i,SY4421: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SY4419 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SY4420 @ ( c_Set_Oinsert @ SY4419 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4421 @ tc_bool ) ) @ SY4421 ) @ ( tc_fun @ SY4421 @ tc_bool ) ) @ SY4421 @ SV287 ) ) )
| ~ ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SY4419 @ SY4420 @ SY4421 ) @ SY4421 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2777,plain,
! [SV873: $i,SV288: $i] :
( ( ! [SY4422: $i,SY4423: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV288 @ SV873 @ SY4422 ) @ SY4423 @ ( tc_fun @ SY4422 @ tc_bool ) )
= ( c_Set_Oinsert @ SV288 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SY4423 @ ( tc_fun @ SY4422 @ tc_bool ) ) @ SY4422 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4422 ) @ SV288 ) @ SY4423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2778,plain,
! [SV874: $i,SV289: $i] :
( ( ! [SY4424: $i,SY4425: $i,SY4426: $i,SY4427: $i,SY4428: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SY4424 @ ( hAPP @ ( hAPP @ SV289 @ SY4425 ) @ SY4426 ) @ SY4427 @ SY4428 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SY4424 @ ( c_Set_Oinsert @ SY4425 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4427 @ tc_bool ) ) @ SY4427 ) @ ( tc_fun @ SY4427 @ tc_bool ) ) @ SY4426 @ SY4427 @ SY4428 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4427 ) @ SY4425 ) @ SY4424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2779,plain,
! [SV875: $i,SV290: $i] :
( ( ! [SY4429: $i,SY4430: $i] :
( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SY4429 @ SY4430 ) @ ( tc_fun @ SY4430 @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ SY4429 @ ( tc_fun @ SY4430 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4430 @ tc_bool ) ) @ SY4430 ) @ ( tc_fun @ SY4430 @ tc_bool ) ) @ SY4429 @ ( tc_fun @ SY4430 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2780,plain,
! [SV876: $i,SV291: $i] :
( ( ! [SY4431: $i,SY4432: $i] :
( ( hBOOL @ ( hAPP @ SV291 @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4431 @ tc_bool ) ) @ SY4432 ) @ SV291 ) @ SV876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2781,plain,
! [SV877: $i,SV292: $i] :
( ( ! [SY4433: $i,SY4434: $i] :
( ( hBOOL @ ( hAPP @ SV292 @ SV877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4433 @ tc_bool ) ) @ SV292 ) @ SY4434 ) @ SV877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2782,plain,
! [SV878: $i,SV293: $i] :
( ( ! [SY4435: $i] :
( ( c_Fun_Oinj__on @ SV293 @ SV878 @ SY4435 @ SY4435 )
| ~ ( c_lessequals @ SV878 @ ( c_Set_Oimage @ SV293 @ SV878 @ SY4435 @ SY4435 ) @ ( tc_fun @ SY4435 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV878 @ SY4435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2783,plain,
! [SV879: $i,SV294: $i] :
( ( ! [SY4436: $i,SY4437: $i,SY4438: $i] :
( ( c_Fun_Oinj__on @ SV294 @ SV879 @ SY4436 @ SY4437 )
| ~ ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4436 @ tc_bool ) ) @ SY4438 ) @ SV879 ) @ SY4436 @ SY4437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2784,plain,
! [SV880: $i,SV295: $i] :
( ( ! [SY4439: $i,SY4440: $i,SY4441: $i] :
( ( c_Fun_Oinj__on @ SV295 @ SV880 @ SY4439 @ SY4440 )
| ~ ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4439 @ tc_bool ) ) @ SV880 ) @ SY4441 ) @ SY4439 @ SY4440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2785,plain,
! [SV881: $i,SV296: $i] :
( ( ! [SY4442: $i,SY4443: $i,SY4444: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SY4442 @ SY4443 ) @ SY4444 @ ( tc_fun @ SY4442 @ tc_bool ) )
| ~ ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SY4444 @ SY4442 @ SY4443 ) @ ( tc_fun @ SY4443 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4442 @ tc_bool ) ) @ SY4442 @ SY4443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2786,plain,
! [SV297: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV297 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV297 @ tc_bool ) ) @ SV297 )
= ( c_Orderings_Otop__class_Otop @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2787,plain,
! [SV882: $i,SV298: $i] :
( ( ( hAPP @ ( c_Fun_Oid @ SV298 ) @ SV882 )
= SV882 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2788,plain,
! [SV883: $i,SV299: $i] :
( ( ! [SY4445: $i,SY4446: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV299 @ SV883 @ ( tc_fun @ SY4445 @ tc_bool ) ) @ SY4446 @ ( tc_fun @ SY4445 @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4445 @ tc_bool ) ) @ SV883 ) @ SY4446 ) @ ( tc_fun @ SY4445 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2789,plain,
! [SV884: $i,SV300: $i] :
( ( ! [SY4447: $i,SY4448: $i] :
( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV884 @ tc_bool ) ) @ SY4447 ) @ SY4448 ) @ ( tc_fun @ SV884 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV300 @ SY4447 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SY4448 @ ( tc_fun @ SV884 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2790,plain,
! [SV885: $i,SV301: $i] :
( ( ! [SY4449: $i] :
( ( c_Finite__Set_Ofinite @ SV301 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ SV885 @ SY4449 @ SV301 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2791,plain,
! [SV886: $i,SV302: $i] :
( ( ! [SY4450: $i] :
( ( c_Finite__Set_Ofinite @ SV302 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ SV886 @ SV302 @ SY4450 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2792,plain,
! [SV887: $i,SV303: $i] :
( ( ! [SY4451: $i,SY4452: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SY4451 ) @ SY4452 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV887 @ SY4451 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2793,plain,
! [SV888: $i,SV304: $i] :
( ( ! [SY4453: $i,SY4454: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SY4453 ) @ SY4454 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV888 @ SY4454 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2794,plain,
! [SV889: $i,SV305: $i] :
( ( ! [SY4455: $i,SY4456: $i,SY4457: $i] :
( ( c_Set_Ovimage @ SV305 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV889 @ tc_bool ) ) @ SY4455 ) @ SY4456 ) @ SY4457 @ SV889 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY4457 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV305 @ SY4455 @ SY4457 @ SV889 ) ) @ ( c_Set_Ovimage @ SV305 @ SY4456 @ SY4457 @ SV889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2795,plain,
! [SV890: $i,SV306: $i] :
( ( ! [SY4458: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV306 @ tc_bool ) ) @ SV890 ) @ SY4458 ) @ SV306 )
| ~ ( c_Finite__Set_Ofinite @ SY4458 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2796,plain,
! [SV891: $i,SV307: $i] :
( ( ! [SY4459: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV307 @ tc_bool ) ) @ SV891 ) @ SY4459 ) @ SV307 )
| ~ ( c_Finite__Set_Ofinite @ SV891 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2797,plain,
! [SV892: $i,SV308: $i] :
( ( ! [SY4460: $i,SY4461: $i,SY4462: $i] :
( ~ ( class_HOL_Oord @ SV308 )
| ( c_lessequals @ ( hAPP @ SV892 @ SY4460 ) @ ( hAPP @ SY4461 @ SY4460 ) @ SV308 )
| ~ ( c_lessequals @ SV892 @ SY4461 @ ( tc_fun @ SY4462 @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2798,plain,
! [SV893: $i,SV309: $i] :
( ( ! [SY4463: $i,SY4464: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SY4463 ) @ SY4464 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SY4464 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SY4463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2799,plain,
! [SV894: $i,SV310: $i] :
( ( ! [SY4465: $i,SY4466: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SY4465 ) @ SY4466 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SY4466 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SY4465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2800,plain,
! [SV895: $i,SV311: $i] :
( ( ! [SY4467: $i,SY4468: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ ( c_Set_Oinsert @ SY4467 @ SY4468 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ SY4468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2801,plain,
! [SV896: $i,SV312: $i] :
( ( ! [SY4469: $i,SY4470: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ ( c_Set_Oinsert @ SY4469 @ SY4470 @ SV312 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ SY4470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2802,plain,
! [SV897: $i,SV313: $i] :
( ( ! [SY4471: $i,SY4472: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SY4471 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SY4472 ) )
| ~ ( c_lessequals @ SY4472 @ SY4471 @ ( tc_fun @ SV313 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2803,plain,
! [SV898: $i,SV314: $i] :
( ( ! [SY4473: $i,SY4474: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SY4473 ) )
| ~ ( c_lessequals @ SY4474 @ SY4473 @ ( tc_fun @ SV314 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SY4474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2804,plain,
! [SV899: $i,SV315: $i] :
( ( ! [SY4475: $i,SY4476: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SY4475 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SY4476 ) )
| ~ ( c_lessequals @ SY4476 @ SY4475 @ ( tc_fun @ SV315 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2805,plain,
! [SV900: $i,SV316: $i] :
( ( ! [SY4477: $i,SY4478: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SY4477 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SY4478 ) )
| ~ ( c_lessequals @ SY4478 @ SY4477 @ ( tc_fun @ SV316 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2806,plain,
! [SV901: $i,SV317: $i] :
( ( ! [SY4479: $i,SY4480: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV317 @ tc_bool ) ) @ SY4479 ) @ SY4480 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ SY4479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2807,plain,
! [SV902: $i,SV318: $i] :
( ( ! [SY4481: $i,SY4482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV318 @ tc_bool ) ) @ SY4481 ) @ SY4482 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ SY4482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2808,plain,
! [SV903: $i,SV319: $i] :
( ( ! [SY4483: $i,SY4484: $i,SY4485: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SV903 @ SY4483 @ SY4484 ) @ SY4485 )
= ( hAPP @ SV319 @ SY4485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4483 ) @ SY4485 ) @ SV903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2809,plain,
! [SV904: $i,SV320: $i] :
( ( ! [SY4486: $i,SY4487: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ SY4486 ) )
| ( SV904 = SY4487 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ ( c_Set_Oinsert @ SY4487 @ SY4486 @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2810,plain,
! [SV905: $i,SV321: $i] :
( ( ! [SY4488: $i,SY4489: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SY4488 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SY4489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SY4489 ) @ SY4488 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2811,plain,
! [SV906: $i,SV322: $i] :
( ( ! [SY4490: $i,SY4491: $i,SY4492: $i,SY4493: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SY4490 @ SY4491 @ SY4492 ) @ SY4493 )
= ( hAPP @ SV906 @ SY4493 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4491 ) @ SY4493 ) @ SY4490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2812,plain,
! [SV907: $i,SV323: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV323 ) @ SV907 ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV323 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2813,plain,
! [SV908: $i,SV324: $i] :
( ( ! [SY4494: $i,SY4495: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ SY4494 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ ( c_HOL_Ominus__class_Ominus @ SY4495 @ SY4494 @ ( tc_fun @ SV324 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2814,plain,
! [SV909: $i,SV325: $i] :
( ( ! [SY4496: $i,SY4497: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ SY4496 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ ( c_HOL_Ominus__class_Ominus @ SY4496 @ SY4497 @ ( tc_fun @ SV325 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2815,plain,
! [SV910: $i,SV326: $i] :
( ( ! [SY4498: $i,SY4499: $i,SY4500: $i,SY4501: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SV910 @ SY4498 @ SY4499 @ SY4500 ) @ SY4501 )
= ( hAPP @ SV326 @ SY4501 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4499 ) @ SY4501 ) @ SY4498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2816,plain,
! [SV911: $i,SV327: $i] :
( ( ! [SY4502: $i,SY4503: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SY4502 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SY4503 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4503 @ SY4502 @ ( tc_fun @ SV327 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2817,plain,
! [SV912: $i,SV328: $i] :
( ( ! [SY4504: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV328 ) @ SV912 ) @ ( c_Set_Oinsert @ SV912 @ SY4504 @ SV328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2818,plain,
! [SV913: $i,SV329: $i] :
( ( ! [SY4505: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV329 ) @ SV913 ) @ ( c_Set_Oinsert @ SV913 @ SY4505 @ SV329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2819,plain,
! [SV914: $i,SV330: $i] :
( ( ! [SY4506: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV330 ) @ SV914 ) @ ( c_Set_Oinsert @ SV914 @ SY4506 @ SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2820,plain,
! [SV915: $i,SV331: $i] :
( ( ! [SY4507: $i,SY4508: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ SY4507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV331 @ tc_bool ) ) @ SY4508 ) @ SY4507 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2821,plain,
! [SV916: $i,SV332: $i] :
( ( ! [SY4509: $i,SY4510: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ SY4509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV332 @ tc_bool ) ) @ SY4509 ) @ SY4510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2822,plain,
! [SV917: $i,SV333: $i] :
( ( ! [SY4511: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV333 ) @ SV917 ) @ ( c_Collect @ SY4511 @ SV333 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY4511 @ SV917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2823,plain,
! [SV918: $i,SV334: $i] :
( ( ! [SY4512: $i] :
( ( hBOOL @ ( hAPP @ SV334 @ SV918 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4512 ) @ SV918 ) @ ( c_Collect @ SV334 @ SY4512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2824,plain,
! [SV919: $i,SV335: $i] :
( ( ! [SY4513: $i,SY4514: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ ( c_HOL_Ominus__class_Ominus @ SY4513 @ SY4514 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SY4514 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SY4513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2825,plain,
! [SV920: $i,SV336: $i] :
( ( ! [SY4515: $i,SY4516: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ ( c_HOL_Ominus__class_Ominus @ SY4515 @ SY4516 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SY4516 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SY4515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2826,plain,
! [SV921: $i,SV337: $i] :
( ( ! [SY4517: $i,SY4518: $i,SY4519: $i,SY4520: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4517 @ SY4518 @ SY4519 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SY4518 @ SY4520 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4519 ) @ SY4520 ) @ SY4517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2827,plain,
! [SV922: $i,SV338: $i] :
( ( ! [SY4521: $i,SY4522: $i,SY4523: $i,SY4524: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4521 @ SY4522 @ SY4523 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SY4522 @ SY4524 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4523 ) @ SY4524 ) @ SY4521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2828,plain,
! [SV923: $i,SV339: $i] :
( ( ! [SY4525: $i,SY4526: $i,SY4527: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SV923 ) @ ( c_Set_Ovimage @ SY4525 @ SY4526 @ SV339 @ SY4527 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4527 ) @ ( hAPP @ SY4525 @ SV923 ) ) @ SY4526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2829,plain,
! [SV924: $i,SV340: $i] :
( ( ! [SY4528: $i,SY4529: $i,SY4530: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SV924 ) @ ( c_Set_Ovimage @ SY4528 @ SY4529 @ SV340 @ SY4530 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4530 ) @ ( hAPP @ SY4528 @ SV924 ) ) @ SY4529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2830,plain,
! [SV925: $i,SV341: $i] :
( ( ! [SY4531: $i,SY4532: $i,SY4533: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SV925 ) @ ( c_Set_Ovimage @ SY4531 @ SY4532 @ SV341 @ SY4533 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4533 ) @ ( hAPP @ SY4531 @ SV925 ) ) @ SY4532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2831,plain,
! [SV926: $i,SV342: $i] :
( ( ! [SY4534: $i,SY4535: $i,SY4536: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SV926 @ SY4534 ) ) @ SY4535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4536 ) @ SY4534 ) @ ( c_Set_Ovimage @ SV926 @ SY4535 @ SY4536 @ SV342 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2832,plain,
! [SV927: $i,SV343: $i] :
( ( ! [SY4537: $i,SY4538: $i,SY4539: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SV927 @ SY4537 ) ) @ SY4538 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4539 ) @ SY4537 ) @ ( c_Set_Ovimage @ SV927 @ SY4538 @ SY4539 @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2833,plain,
! [SV928: $i,SV344: $i] :
( ( ! [SY4540: $i,SY4541: $i,SY4542: $i,SY4543: $i,SY4544: $i,SY4545: $i,SY4546: $i,SY4547: $i,SY4548: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SY4540 ) ) @ SY4541 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4542 ) @ SY4541 ) @ SY4540 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SY4543 @ SV344 @ SY4544 @ SY4545 @ SY4546 @ SY4547 @ SY4548 @ SY4542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2834,plain,
! [SV929: $i,SV345: $i] :
( ( ! [SY4549: $i,SY4550: $i,SY4551: $i,SY4552: $i,SY4553: $i,SY4554: $i,SY4555: $i,SY4556: $i,SY4557: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SY4549 @ SY4550 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4551 ) @ SV929 ) @ SY4550 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4552 @ SY4549 @ SV345 @ SY4553 @ SY4554 @ SY4555 @ SY4556 @ SY4557 @ SY4551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2835,plain,
! [SV930: $i,SV346: $i] :
( ( ! [SY4558: $i] :
( ( ( c_Set_Oinsert @ SV346 @ SV930 @ SY4558 )
= SV930 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4558 ) @ SV346 ) @ SV930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2836,plain,
! [SV931: $i,SV347: $i] :
( ( ! [SY4559: $i,SY4560: $i,SY4561: $i,SY4562: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SY4559 @ ( tc_fun @ SY4560 @ tc_bool ) ) @ SY4561 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SY4562 ) @ SY4561 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4559 ) @ SY4562 ) @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2837,plain,
! [SV932: $i,SV348: $i] :
( ( ! [SY4563: $i,SY4564: $i,SY4565: $i,SY4566: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SY4563 @ ( tc_fun @ SY4564 @ tc_bool ) ) @ SY4565 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SY4566 ) @ SY4565 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4563 ) @ SY4566 ) @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2838,plain,
! [SV933: $i,SV349: $i] :
( ( ! [SY4567: $i,SY4568: $i,SY4569: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SV933 ) @ SY4567 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4568 ) @ ( hAPP @ SY4569 @ SV933 ) ) @ ( c_Set_Oimage @ SY4569 @ SY4567 @ SV349 @ SY4568 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2839,plain,
! [SV934: $i,SV350: $i] :
( ( ! [SY4570: $i,SY4571: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ SY4570 ) @ SY4571 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ SY4570 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ SY4571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2840,plain,
! [SV935: $i,SV351: $i] :
( ( ! [SY4572: $i,SY4573: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV935 ) @ SY4572 ) ) @ SY4573 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV935 ) @ SY4573 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SY4572 ) @ SY4573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2841,plain,
! [SV936: $i,SV352: $i] :
( ( ! [SY4574: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV352 @ SV936 @ SY4574 ) @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2842,plain,
! [SV937: $i,SV353: $i] :
( ( ! [SY4575: $i,SY4576: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SY4575 ) @ SY4576 @ ( tc_fun @ SY4575 @ tc_bool ) )
| ~ ( c_lessequals @ SV937 @ SY4576 @ ( tc_fun @ SY4575 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4575 ) @ SV353 ) @ SY4576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2843,plain,
! [SV938: $i,SV354: $i] :
( ( ! [SY4577: $i] :
( ~ ( class_Lattices_Olattice @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SY4577 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SY4577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2844,plain,
! [SV939: $i,SV355: $i] :
( ( ! [SY4578: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV355 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SY4578 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SY4578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2845,plain,
! [SV940: $i,SV356: $i] :
( ( ! [SY4579: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SV940 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SV940 ) @ SY4579 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SV940 ) @ SY4579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2846,plain,
! [SV941: $i,SV357: $i] :
( ( ! [SY4580: $i,SY4581: $i,SY4582: $i,SY4583: $i,SY4584: $i,SY4585: $i,SY4586: $i,SY4587: $i,SY4588: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SY4580 @ SY4581 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SY4581 @ SY4582 @ SY4582 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4581 @ SY4582 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4583 @ SY4580 @ SY4584 @ SY4585 @ SY4586 @ SV357 @ SY4587 @ SY4588 @ SY4582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2847,plain,
! [SV942: $i,SV358: $i] :
( ( ! [SY4589: $i,SY4590: $i,SY4591: $i,SY4592: $i,SY4593: $i,SY4594: $i,SY4595: $i,SY4596: $i,SY4597: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SY4589 @ SY4590 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SY4590 @ SY4591 @ SY4591 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4590 @ SY4591 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4589 @ SY4592 @ SY4593 @ SY4594 @ SV358 @ SY4595 @ SY4596 @ SY4597 @ SY4591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2848,plain,
! [SV943: $i,SV359: $i] :
( ( ! [SY4598: $i,SY4599: $i,SY4600: $i,SY4601: $i,SY4602: $i,SY4603: $i,SY4604: $i,SY4605: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SY4598 @ SY4599 @ SV943 @ SY4600 @ SY4600 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SY4600 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4601 @ SV359 @ SY4602 @ SY4603 @ SY4604 @ SY4598 @ SY4599 @ SY4605 @ SY4600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2849,plain,
! [SV944: $i,SV360: $i] :
( ( ! [SY4606: $i,SY4607: $i,SY4608: $i,SY4609: $i,SY4610: $i,SY4611: $i,SY4612: $i,SY4613: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SY4606 @ SY4607 @ SV944 @ SY4608 @ SY4608 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SY4608 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SY4609 @ SY4610 @ SY4611 @ SY4606 @ SY4612 @ SY4613 @ SY4607 @ SY4608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2850,plain,
! [SV945: $i,SV361: $i] :
( ( ! [SY4614: $i,SY4615: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV945 @ ( tc_fun @ SY4614 @ tc_bool ) ) @ SY4614 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SY4615 @ SV945 @ SY4614 ) @ ( tc_fun @ SY4614 @ tc_bool ) ) @ SY4614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2851,plain,
! [SV946: $i,SV362: $i] :
( ( ! [SY4616: $i,SY4617: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ ( c_Set_Oinsert @ SV946 @ SY4616 @ SY4617 ) @ ( tc_fun @ SY4617 @ tc_bool ) ) @ SY4617 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ SY4616 @ ( tc_fun @ SY4617 @ tc_bool ) ) @ SY4617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2852,plain,
! [SV947: $i,SV363: $i] :
( ( ! [SY4618: $i] :
( ( c_Fun_Ofcomp @ SV363 @ ( c_Fun_Oid @ SV947 ) @ SY4618 @ SV947 @ SV947 )
= SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2853,plain,
! [SV948: $i,SV364: $i] :
( ( ! [SY4619: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ SV364 ) @ SV948 @ SV364 @ SV364 @ SY4619 )
= SV948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2854,plain,
! [SV949: $i,SV365: $i] :
( ( ! [SY4620: $i,SY4621: $i,SY4622: $i,SY4623: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV365 @ SV949 @ SY4620 @ SY4621 @ SY4622 ) @ SY4623 @ SY4622 @ SY4621 )
= ( c_Set_Oimage @ SV365 @ ( c_Set_Oimage @ SV949 @ SY4623 @ SY4622 @ SY4620 ) @ SY4620 @ SY4621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2855,plain,
! [SV366: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV366 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV366 @ tc_bool ) ) @ SV366 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2856,plain,
! [SV950: $i,SV367: $i] :
( ( ! [SY4624: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV367 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SY4624 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 @ SY4624 @ SV367 @ SV367 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4624 @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2857,plain,
! [SV951: $i,SV368: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV368 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV368 ) @ SV951 ) @ SV951 )
= SV951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2858,plain,
! [SV952: $i,SV369: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV952 ) @ SV952 )
= SV952 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2859,plain,
! [SV953: $i,SV370: $i] :
( ( ! [SY4625: $i,SY4626: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV370 )
| ( c_lessequals @ SV953 @ SY4625 @ SV370 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SY4626 ) @ SV953 ) @ SY4625 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2860,plain,
! [SV954: $i,SV371: $i] :
( ( ! [SY4627: $i,SY4628: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV371 )
| ( c_lessequals @ SV954 @ SY4627 @ SV371 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SY4628 ) @ SY4627 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2861,plain,
! [SV955: $i,SV372: $i] :
( ( ! [SY4629: $i,SY4630: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV372 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SY4629 ) @ SY4630 ) @ SV372 )
| ~ ( c_lessequals @ SV955 @ SY4630 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2862,plain,
! [SV956: $i,SV373: $i] :
( ( ! [SY4631: $i,SY4632: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV373 )
| ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SY4631 ) @ SY4632 ) @ SV373 )
| ~ ( c_lessequals @ SV956 @ SY4631 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2863,plain,
! [SV957: $i,SV374: $i] :
( ( ! [SY4633: $i,SY4634: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV374 )
| ( c_lessequals @ SV957 @ SY4633 @ SV374 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SY4634 ) @ SV957 ) @ SY4633 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2864,plain,
! [SV958: $i,SV375: $i] :
( ( ! [SY4635: $i,SY4636: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV375 )
| ( c_lessequals @ SV958 @ SY4635 @ SV375 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SY4636 ) @ SY4635 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2865,plain,
! [SV959: $i,SV376: $i] :
( ( ! [SY4637: $i,SY4638: $i] :
( ( c_lessequals @ SV376 @ SV959 @ ( tc_fun @ SY4637 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4637 @ tc_bool ) ) @ SV376 ) @ SY4638 ) @ SV959 @ ( tc_fun @ SY4637 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2866,plain,
! [SV960: $i,SV377: $i] :
( ( ! [SY4639: $i,SY4640: $i] :
( ( c_lessequals @ SV377 @ SV960 @ ( tc_fun @ SY4639 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4639 @ tc_bool ) ) @ SY4640 ) @ SV377 ) @ SV960 @ ( tc_fun @ SY4639 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2867,plain,
! [SV961: $i,SV378: $i] :
( ( ! [SY4641: $i] :
( ~ ( class_Lattices_Olattice @ SV378 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ SV378 ) ) @ SV961 ) @ SY4641 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 ) @ ( hAPP @ SV961 @ v_x ) ) @ ( hAPP @ SY4641 @ v_x ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2868,plain,
! [SV962: $i,SV379: $i] :
( ( ! [SY4642: $i,SY4643: $i] :
( ~ ( class_Orderings_Oorder @ SV379 )
| ( c_lessequals @ SV962 @ SY4642 @ SV379 )
| ~ ( c_lessequals @ SV962 @ SY4643 @ SV379 )
| ~ ( c_lessequals @ SY4643 @ SY4642 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2869,plain,
! [SV963: $i,SV380: $i] :
( ( ! [SY4644: $i,SY4645: $i] :
( ~ ( class_Orderings_Oorder @ SV380 )
| ( c_HOL_Oord__class_Oless @ SV963 @ SY4644 @ SV380 )
| ~ ( c_lessequals @ SV963 @ SY4645 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SY4645 @ SY4644 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2870,plain,
! [SV964: $i,SV381: $i] :
( ( ! [SY4646: $i,SY4647: $i] :
( ~ ( class_Orderings_Oorder @ SV381 )
| ( c_HOL_Oord__class_Oless @ SV964 @ SY4646 @ SV381 )
| ~ ( c_HOL_Oord__class_Oless @ SV964 @ SY4647 @ SV381 )
| ~ ( c_lessequals @ SY4647 @ SY4646 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2871,plain,
! [SV965: $i,SV382: $i] :
( ( ! [SY4648: $i,SY4649: $i] :
( ~ ( class_Orderings_Opreorder @ SV382 )
| ( c_lessequals @ SV965 @ SY4648 @ SV382 )
| ~ ( c_lessequals @ SY4649 @ SY4648 @ SV382 )
| ~ ( c_lessequals @ SV965 @ SY4649 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2872,plain,
! [SV966: $i,SV383: $i] :
( ( c_lessequals @ SV383 @ SV383 @ ( tc_fun @ SV966 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2873,plain,
! [SV967: $i,SV384: $i] :
( ( c_lessequals @ SV384 @ SV384 @ ( tc_fun @ SV967 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2874,plain,
! [SV968: $i,SV385: $i] :
( ( ! [SY4650: $i,SY4651: $i] :
( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SY4650 @ tc_bool ) )
| ~ ( c_lessequals @ SY4651 @ SV968 @ ( tc_fun @ SY4650 @ tc_bool ) )
| ~ ( c_lessequals @ SV385 @ SY4651 @ ( tc_fun @ SY4650 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2875,plain,
! [SV969: $i,SV386: $i] :
( ( ! [SY4652: $i,SY4653: $i,SY4654: $i] :
( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SY4652 @ SY4653 )
| ~ ( c_lessequals @ SV969 @ SY4654 @ ( tc_fun @ SY4652 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV386 @ SY4654 @ SY4652 @ SY4653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2876,plain,
! [SV970: $i,SV387: $i] :
( ( ! [SY4655: $i,SY4656: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
| ~ ( hBOOL @ ( hAPP @ SY4655 @ SV970 ) )
| ~ ( c_lessequals @ SY4655 @ SV387 @ ( tc_fun @ SY4656 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2877,plain,
! [SV971: $i,SV388: $i] :
( ( ~ ( class_Orderings_Oorder @ SV388 )
| ( c_lessequals @ SV971 @ SV971 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2878,plain,
! [SV972: $i,SV389: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV389 )
| ( c_lessequals @ SV972 @ SV972 @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2879,plain,
! [SV973: $i,SV390: $i] :
( ( ! [SY4657: $i] :
( ( c_Finite__Set_Ofinite @ SV390 @ SV973 )
| ~ ( c_Finite__Set_Ofinite @ SY4657 @ SV973 )
| ~ ( c_lessequals @ SV390 @ SY4657 @ ( tc_fun @ SV973 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2880,plain,
! [SV974: $i,SV391: $i] :
( ( ! [SY4658: $i,SY4659: $i] :
( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SY4658 @ tc_bool ) )
| ~ ( c_lessequals @ SY4659 @ SV974 @ ( tc_fun @ SY4658 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV391 @ SY4659 @ ( tc_fun @ SY4658 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2881,plain,
! [SV975: $i,SV392: $i] :
( ( ! [SY4660: $i,SY4661: $i] :
( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SY4660 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4661 @ SV975 @ ( tc_fun @ SY4660 @ tc_bool ) )
| ~ ( c_lessequals @ SV392 @ SY4661 @ ( tc_fun @ SY4660 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2882,plain,
! [SV976: $i,SV393: $i] :
( ( ! [SY4662: $i,SY4663: $i] :
( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
| ~ ( c_lessequals @ SY4662 @ SV393 @ ( tc_fun @ SY4663 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4662 @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2883,plain,
! [SV977: $i,SV394: $i] :
( ( ! [SY4664: $i] :
( ( c_Finite__Set_Ofinite @ SV394 @ SV977 )
| ~ ( c_lessequals @ SV394 @ SY4664 @ ( tc_fun @ SV977 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY4664 @ SV977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2884,plain,
! [SV978: $i,SV395: $i] :
( ( ! [SY4665: $i,SY4666: $i] :
( ~ ( class_Orderings_Opreorder @ SV395 )
| ( c_HOL_Oord__class_Oless @ SV978 @ SY4665 @ SV395 )
| ~ ( c_HOL_Oord__class_Oless @ SY4666 @ SY4665 @ SV395 )
| ~ ( c_lessequals @ SV978 @ SY4666 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2885,plain,
! [SV979: $i,SV396: $i] :
( ( ! [SY4667: $i,SY4668: $i] :
( ~ ( class_Orderings_Opreorder @ SV396 )
| ( c_HOL_Oord__class_Oless @ SV979 @ SY4667 @ SV396 )
| ~ ( c_lessequals @ SY4668 @ SY4667 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SV979 @ SY4668 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2886,plain,
! [SV980: $i,SV397: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV397 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV980 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV397 @ tc_bool ) ) @ SV397 ) @ SV397 )
= SV980 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2887,plain,
! [SV981: $i,SV398: $i] :
( ( ! [SY4669: $i,SY4670: $i,SY4671: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SY4669 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SY4670 ) @ SY4671 ) @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SY4669 @ SY4671 @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV981 @ SY4670 @ ( tc_fun @ SV398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2888,plain,
! [SV982: $i,SV399: $i] :
( ( ! [SY4672: $i,SY4673: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV399 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV982 @ tc_bool ) ) @ SY4672 ) @ SY4673 ) @ ( tc_fun @ SV982 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV982 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SY4672 @ ( tc_fun @ SV982 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SY4673 @ ( tc_fun @ SV982 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2889,plain,
! [SV983: $i,SV400: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV400 ) @ SV400 @ SV400 @ tc_bool ) @ SV983 ) @ SV400 )
= ( c_Set_Oinsert @ SV983 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV400 @ tc_bool ) ) @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2890,plain,
! [SV984: $i,SV401: $i] :
( ( ! [SY4674: $i,SY4675: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SV984 ) @ SY4674 ) @ SY4675 @ ( tc_fun @ SV401 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SV984 ) @ ( c_HOL_Ominus__class_Ominus @ SY4674 @ SY4675 @ ( tc_fun @ SV401 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2891,plain,
! [SV985: $i,SV402: $i] :
( ( ! [SY4676: $i,SY4677: $i,SY4678: $i,SY4679: $i] :
( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SY4676 @ ( tc_fun @ SY4677 @ tc_bool ) ) @ SY4677 @ SY4678 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SY4677 @ SY4678 ) @ ( c_Set_Oimage @ SV402 @ SY4676 @ SY4677 @ SY4678 ) @ ( tc_fun @ SY4678 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY4676 @ SY4679 @ ( tc_fun @ SY4677 @ tc_bool ) )
| ~ ( c_lessequals @ SV985 @ SY4679 @ ( tc_fun @ SY4677 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SY4679 @ SY4677 @ SY4678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2892,plain,
! [SV986: $i,SV403: $i] :
( ( ! [SY4680: $i,SY4681: $i,SY4682: $i,SY4683: $i,SY4684: $i,SY4685: $i,SY4686: $i,SY4687: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4680 @ tc_bool ) ) @ SY4680 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4681 @ SV403 @ SY4682 @ SY4683 @ SY4684 @ SY4685 @ SY4686 @ SY4687 @ SY4680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2893,plain,
! [SV987: $i,SV404: $i] :
( ( ! [SY4688: $i,SY4689: $i,SY4690: $i,SY4691: $i,SY4692: $i,SY4693: $i,SY4694: $i,SY4695: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4688 @ tc_bool ) ) @ SY4688 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SY4689 @ SY4690 @ SY4691 @ SY4692 @ SY4693 @ SY4694 @ SY4695 @ SY4688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2894,plain,
! [SV988: $i,SV405: $i] :
( ( ! [SY4696: $i,SY4697: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SY4696 ) @ ( c_Collect @ SY4697 @ SV405 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SY4697 @ SV988 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SY4696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2895,plain,
! [SV989: $i,SV406: $i] :
( ( ! [SY4698: $i] :
( ( SV406
= ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4698 @ tc_bool ) ) @ SY4698 ) )
| ( SV406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4698 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV406 @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4698 @ tc_bool ) ) @ SY4698 ) @ ( tc_fun @ SY4698 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2896,plain,
! [SV990: $i,SV407: $i] :
( ( ! [SY4699: $i,SY4700: $i,SY4701: $i] :
( ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ SY4699 @ SY4700 ) @ SY4701 @ SY4700 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4701 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4700 @ tc_bool ) ) @ SY4700 ) @ SY4701 @ SY4700 ) ) @ ( c_Set_Ovimage @ SV407 @ SY4699 @ SY4701 @ SY4700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2897,plain,
! [SV991: $i,SV408: $i] :
( ( ! [SY4702: $i,SY4703: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV408 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV991 @ tc_bool ) ) @ SY4702 ) @ SY4703 ) @ ( tc_fun @ SV991 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV991 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SY4702 @ ( tc_fun @ SV991 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SY4703 @ ( tc_fun @ SV991 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2898,plain,
! [SV992: $i,SV409: $i] :
( ( ! [SY4704: $i,SY4705: $i,SY4706: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV409 @ tc_bool ) ) @ SV992 ) @ SY4704 ) @ SY4705 @ SV409 @ ( tc_fun @ SY4706 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4706 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV992 @ SY4705 @ SV409 @ ( tc_fun @ SY4706 @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4704 @ SY4705 @ SV409 @ ( tc_fun @ SY4706 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2899,plain,
! [SV993: $i,SV410: $i] :
( ( ! [SY4707: $i,SY4708: $i,SY4709: $i] :
( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SV993 @ SY4707 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV993 @ SV410 @ SY4708 @ SY4709 ) @ SY4707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2900,plain,
! [SV994: $i,SV411: $i] :
( ( ! [SY4710: $i,SY4711: $i,SY4712: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SV994 @ SY4710 @ SY4711 ) @ SY4712 ) )
| ~ ( hBOOL @ ( hAPP @ SV994 @ ( hAPP @ SV411 @ SY4712 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2901,plain,
! [SV995: $i,SV412: $i] :
( ( ! [SY4713: $i] :
( ~ ( class_Orderings_Olinorder @ SV412 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SY4713 @ SV412 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SY4713 ) @ SV995 ) )
| ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2902,plain,
! [SV996: $i,SV413: $i] :
( ( ! [SY4714: $i,SY4715: $i,SY4716: $i,SY4717: $i,SY4718: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SY4714 @ ( c_Set_Oinsert @ SY4715 @ SY4716 @ SY4717 ) @ SY4718 @ SY4717 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SY4715 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SY4714 @ SY4716 @ SY4718 @ SY4717 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4717 ) @ SY4715 ) @ SY4716 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4716 @ SY4717 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SY4718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2903,plain,
! [SV997: $i,SV414: $i] :
( ( ! [SY4719: $i,SY4720: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SY4719 ) @ SY4720 ) )
| ~ ( hBOOL @ ( hAPP @ SY4719 @ SY4720 ) )
| ~ ( hBOOL @ ( hAPP @ SV997 @ SY4720 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2904,plain,
! [SV998: $i,SV415: $i] :
( ( ! [SY4721: $i,SY4722: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV415 @ SV998 @ SY4721 ) @ SY4722 @ SY4721 @ SV998 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4721 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV998 ) @ SV415 ) @ SY4722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2905,plain,
! [SV999: $i,SV416: $i] :
( ( ! [SY4723: $i,SY4724: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SY4723 @ ( tc_fun @ SY4724 @ tc_bool ) ) @ ( tc_fun @ SY4724 @ tc_bool ) )
= SY4723 )
| ~ ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SY4724 @ tc_bool ) )
| ~ ( c_lessequals @ SY4723 @ SV416 @ ( tc_fun @ SY4724 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2906,plain,
! [SV1000: $i,SV417: $i] :
( ( ! [SY4725: $i,SY4726: $i,SY4727: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SV1000 @ SY4725 @ SY4726 ) @ ( c_Set_Oimage @ SV417 @ SY4727 @ SY4725 @ SY4726 ) @ ( tc_fun @ SY4726 @ tc_bool ) )
| ~ ( c_lessequals @ SV1000 @ SY4727 @ ( tc_fun @ SY4725 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2907,plain,
! [SV1001: $i,SV418: $i] :
( ( ! [SY4728: $i,SY4729: $i,SY4730: $i] :
( ~ ( c_lessequals @ SV418 @ SV1001 @ ( tc_fun @ SY4728 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SY4729 @ SV418 @ SY4728 @ SY4730 ) @ ( c_Set_Oimage @ SY4729 @ SV1001 @ SY4728 @ SY4730 ) @ ( tc_fun @ SY4730 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2908,plain,
! [SV1002: $i,SV419: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_fequal @ SV419 ) @ SV1002 ) @ SV419 )
= ( c_Set_Oinsert @ SV1002 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV419 @ tc_bool ) ) @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2909,plain,
! [SV1003: $i,SV420: $i] :
( ( ! [SY4731: $i,SY4732: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV420 @ SV1003 @ SY4731 ) @ ( c_Set_Oinsert @ SV420 @ SY4732 @ SY4731 ) @ ( tc_fun @ SY4731 @ tc_bool ) )
| ~ ( c_lessequals @ SV1003 @ SY4732 @ ( tc_fun @ SY4731 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2910,plain,
! [SV1004: $i,SV421: $i] :
( ( ! [SY4733: $i,SY4734: $i] :
( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
| ~ ( c_Fun_Oinj__on @ SY4733 @ SV421 @ SV1004 @ SY4734 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SY4733 @ SV421 @ SV1004 @ SY4734 ) @ SY4734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2911,plain,
! [SV1005: $i,SV422: $i] :
( ( ! [SY4735: $i] :
( ~ ( class_Orderings_Oorder @ SV422 )
| ( c_HOL_Oord__class_Oless @ SV1005 @ SY4735 @ SV422 )
| ( SY4735 = SV1005 )
| ~ ( c_lessequals @ SV1005 @ SY4735 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2912,plain,
! [SV1006: $i,SV423: $i] :
( ( ! [SY4736: $i] :
( ~ ( class_Orderings_Oorder @ SV423 )
| ( c_HOL_Oord__class_Oless @ SV1006 @ SY4736 @ SV423 )
| ~ ( c_lessequals @ SV1006 @ SY4736 @ SV423 )
| ( SY4736 = SV1006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2913,plain,
! [SV1007: $i,SV424: $i] :
( ( ! [SY4737: $i] :
( ( c_HOL_Oord__class_Oless @ SV424 @ SV1007 @ ( tc_fun @ SY4737 @ tc_bool ) )
| ( SV424 = SV1007 )
| ~ ( c_lessequals @ SV424 @ SV1007 @ ( tc_fun @ SY4737 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2914,plain,
! [SV1008: $i,SV425: $i] :
( ( ! [SY4738: $i] :
( ~ ( class_Orderings_Oorder @ SV425 )
| ( SV1008 = SY4738 )
| ( c_HOL_Oord__class_Oless @ SV1008 @ SY4738 @ SV425 )
| ~ ( c_lessequals @ SV1008 @ SY4738 @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2915,plain,
! [SV1009: $i,SV426: $i] :
( ( ! [SY4739: $i] :
( ~ ( class_Orderings_Oorder @ SV426 )
| ( c_HOL_Oord__class_Oless @ SV1009 @ SY4739 @ SV426 )
| ( SV1009 = SY4739 )
| ~ ( c_lessequals @ SV1009 @ SY4739 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2916,plain,
! [SV1010: $i,SV427: $i] :
( ( ! [SY4740: $i] :
( ( SV427 = SV1010 )
| ( c_HOL_Oord__class_Oless @ SV427 @ SV1010 @ ( tc_fun @ SY4740 @ tc_bool ) )
| ~ ( c_lessequals @ SV427 @ SV1010 @ ( tc_fun @ SY4740 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2917,plain,
! [SV1011: $i,SV428: $i] :
( ( ! [SY4741: $i] :
( ~ ( class_Orderings_Oorder @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1011 @ SY4741 @ SV428 )
| ( SV1011 = SY4741 )
| ~ ( c_lessequals @ SV1011 @ SY4741 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2918,plain,
! [SV1012: $i,SV429: $i] :
( ( ! [SY4742: $i] :
( ~ ( class_Orderings_Oorder @ SV429 )
| ( c_HOL_Oord__class_Oless @ SV1012 @ SY4742 @ SV429 )
| ~ ( c_lessequals @ SV1012 @ SY4742 @ SV429 )
| ( SV1012 = SY4742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2919,plain,
! [SV1013: $i,SV430: $i] :
( ( ! [SY4743: $i] :
( ~ ( class_Orderings_Olinorder @ SV430 )
| ( SV1013 = SY4743 )
| ~ ( c_lessequals @ SV1013 @ SY4743 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1013 @ SY4743 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2920,plain,
! [SV1014: $i,SV431: $i] :
( ( ! [SY4744: $i] :
( ~ ( class_Orderings_Olinorder @ SV431 )
| ( SV1014 = SY4744 )
| ( c_HOL_Oord__class_Oless @ SV1014 @ SY4744 @ SV431 )
| ~ ( c_lessequals @ SV1014 @ SY4744 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2921,plain,
! [SV1015: $i,SV432: $i] :
( ( ! [SY4745: $i] :
( ~ ( class_Orderings_Olinorder @ SV432 )
| ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SY4745 @ SV432 ) @ SV432 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SY4745 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4745 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2922,plain,
! [SV1016: $i,SV433: $i] :
( ( ! [SY4746: $i,SY4747: $i,SY4748: $i] :
( ( c_Set_Oimage @ SV433 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1016 @ tc_bool ) ) @ SY4746 ) @ SY4747 ) @ SV1016 @ SY4748 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4748 @ tc_bool ) ) @ ( c_Set_Oimage @ SV433 @ SY4746 @ SV1016 @ SY4748 ) ) @ ( c_Set_Oimage @ SV433 @ SY4747 @ SV1016 @ SY4748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2923,plain,
! [SV1017: $i,SV434: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ SV434 ) @ SV434 @ ( tc_fun @ SV434 @ tc_bool ) @ tc_bool ) @ SV1017 ) @ SV434 )
= SV1017 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2924,plain,
! [SV1018: $i,SV435: $i] :
( ( ! [SY4749: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV435 )
| ( c_lessequals @ SV1018 @ ( c_Complete__Lattice_OSup__class_OSup @ SY4749 @ SV435 ) @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SV1018 ) @ SY4749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2925,plain,
! [SV1019: $i,SV436: $i] :
( ( ! [SY4750: $i,SY4751: $i,SY4752: $i,SY4753: $i,SY4754: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SV1019 @ SY4750 @ SY4751 @ SY4752 ) @ SY4753 @ SY4750 @ SY4752 @ SY4754 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SV1019 @ SY4753 @ SY4751 @ SY4752 @ SY4754 ) @ SY4750 @ SY4751 @ SY4754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2926,plain,
! [SV1020: $i,SV437: $i] :
( ( ! [SY4755: $i] :
( ~ ( class_Orderings_Oorder @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SV1020 @ SY4755 @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SY4755 @ SV1020 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2927,plain,
! [SV1021: $i,SV438: $i] :
( ( ! [SY4756: $i] :
( ~ ( class_Orderings_Olinorder @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SY4756 @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SY4756 @ SV1021 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2928,plain,
! [SV1022: $i,SV439: $i] :
( ( ! [SY4757: $i] :
( ~ ( class_Orderings_Olinorder @ SV439 )
| ( c_lessequals @ SV1022 @ SY4757 @ SV439 )
| ( c_lessequals @ SY4757 @ SV1022 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2929,plain,
! [SV1023: $i,SV440: $i] :
( ( ! [SY4758: $i] :
( ~ ( class_Orderings_Opreorder @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SV1023 @ SY4758 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SY4758 @ SV1023 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2930,plain,
! [SV1024: $i,SV441: $i] :
( ( ! [SY4759: $i] :
( ~ ( class_Orderings_Opreorder @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1024 @ SY4759 @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SY4759 @ SV1024 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2931,plain,
! [SV1025: $i,SV442: $i] :
( ( ! [SY4760: $i,SY4761: $i,SY4762: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SV1025 ) @ SY4760 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4761 ) @ ( hAPP @ SY4762 @ SV1025 ) ) @ ( c_Set_Oimage @ SY4762 @ SY4760 @ SV442 @ SY4761 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2932,plain,
! [SV1026: $i,SV443: $i] :
( ( ! [SY4763: $i,SY4764: $i,SY4765: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SV1026 @ SY4763 ) ) @ ( c_Set_Oimage @ SV1026 @ SY4764 @ SY4765 @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4765 ) @ SY4763 ) @ SY4764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2933,plain,
! [SV1027: $i,SV444: $i] :
( ( ! [SY4766: $i,SY4767: $i,SY4768: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SV1027 @ SY4766 ) ) @ ( c_Set_Oimage @ SV1027 @ SY4767 @ SY4768 @ SV444 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4768 ) @ SY4766 ) @ SY4767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2934,plain,
! [SV1028: $i,SV445: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV445 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1028 @ SV445 ) ) @ SV1028 ) )
| ( SV1028
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1028 @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2935,plain,
! [SV1029: $i,SV446: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV446 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1029 @ SV446 ) ) @ SV1029 ) )
| ( SV1029
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1029 @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2936,plain,
! [SV1030: $i,SV447: $i] :
( ( ! [SY4769: $i] :
( ( ( c_Set_Oinsert @ SV447 @ ( c_HOL_Ominus__class_Ominus @ SV1030 @ ( c_Set_Oinsert @ SV447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4769 @ tc_bool ) ) @ SY4769 ) @ ( tc_fun @ SY4769 @ tc_bool ) ) @ SY4769 )
= SV1030 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4769 ) @ SV447 ) @ SV1030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2937,plain,
! [SV1031: $i,SV448: $i] :
( ( ! [SY4770: $i,SY4771: $i,SY4772: $i] :
( ( ( hAPP @ SV448 @ SV1031 )
= SY4770 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4771 ) @ SV1031 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SY4770 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4772 @ tc_bool ) ) @ SY4772 ) @ SY4771 @ SY4772 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2938,plain,
! [SV1032: $i,SV449: $i] :
( ( ! [SY4773: $i,SY4774: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV449 @ SV1032 @ SY4773 ) @ SY4774 @ SY4773 @ SV1032 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4773 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1032 ) @ SV449 ) @ SY4774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2939,plain,
! [SV1033: $i,SV450: $i] :
( ( ! [SY4775: $i,SY4776: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV450 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1033 @ SY4775 @ SY4776 @ ( tc_fun @ SV450 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4776 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1033 @ SY4775 @ SY4776 @ SV450 ) ) @ SV1033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2940,plain,
! [SV1034: $i,SV451: $i] :
( ( ! [SY4777: $i,SY4778: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1034 ) @ ( c_Set_Ovimage @ SY4777 @ ( c_Set_Oinsert @ ( hAPP @ SY4777 @ SV1034 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4778 @ tc_bool ) ) @ SY4778 ) @ SV451 @ SY4778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2941,plain,
! [SV1035: $i,SV452: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SV1035 @ SV452 ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SV1035 @ SV452 ) ) )
| ( SV1035
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV452 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2942,plain,
! [SV1036: $i,SV453: $i] :
( ( ! [SY4779: $i,SY4780: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV453 @ SV1036 @ SY4779 @ ( tc_fun @ SY4780 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4780 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4779 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV453 @ SV1036 @ SY4779 @ SY4780 ) ) @ SV453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2943,plain,
! [SV1037: $i,SV454: $i] :
( ( ! [SY4781: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV454 @ SV1037 @ SY4781 ) @ ( c_Set_Oinsert @ SV454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4781 @ tc_bool ) ) @ SY4781 ) @ ( tc_fun @ SY4781 @ tc_bool ) )
= SV1037 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4781 ) @ SV454 ) @ SV1037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2944,plain,
! [SV1038: $i,SV455: $i] :
( ( ! [SY4782: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV455 @ tc_bool ) ) @ SV1038 ) @ SY4782 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV455 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV455 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SV1038 @ SY4782 @ SV455 ) ) @ SY4782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2945,plain,
! [SV1039: $i,SV456: $i] :
( ( ! [SY4783: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV456 @ tc_bool ) ) @ SV1039 ) @ SY4783 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SV1039 @ SY4783 @ SV456 ) ) @ SV1039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2946,plain,
! [SV1040: $i,SV457: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV457 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV457 ) @ ( c_Orderings_Obot__class_Obot @ SV457 ) ) @ SV1040 )
= SV1040 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2947,plain,
! [SV1041: $i,SV458: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV458 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV458 ) @ SV1041 ) @ ( c_Orderings_Obot__class_Obot @ SV458 ) )
= SV1041 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2948,plain,
! [SV1042: $i,SV459: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV459 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV459 ) @ ( c_Orderings_Obot__class_Obot @ SV459 ) ) @ SV1042 )
= ( c_Orderings_Obot__class_Obot @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2949,plain,
! [SV1043: $i,SV460: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV460 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV460 ) @ SV1043 ) @ ( c_Orderings_Obot__class_Obot @ SV460 ) )
= ( c_Orderings_Obot__class_Obot @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2950,plain,
! [SV1044: $i,SV461: $i] :
( ( ~ ( class_Orderings_Obot @ SV461 )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV461 ) @ SV1044 @ SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2951,plain,
! [SV1045: $i,SV462: $i] :
( ( ! [SY4784: $i] :
( ( c_Set_Ovimage @ SV462 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1045 @ tc_bool ) ) @ SY4784 @ SV1045 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4784 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2952,plain,
! [SV1046: $i,SV464: $i] :
( ( ! [SY4785: $i,SY4786: $i,SY4787: $i,SY4788: $i,SY4789: $i,SY4790: $i,SY4791: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SY4785 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SY4786 @ SY4787 @ SY4788 @ SY4789 @ SY4790 @ SY4791 @ SY4785 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2953,plain,
! [SV1047: $i,SV465: $i] :
( ( ! [SY4792: $i,SY4793: $i,SY4794: $i,SY4795: $i,SY4796: $i,SY4797: $i,SY4798: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SY4792 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4793 @ SV465 @ SY4794 @ SY4795 @ SY4796 @ SY4797 @ SY4792 @ SY4798 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2954,plain,
! [SV1048: $i,SV466: $i] :
( ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV466 @ tc_bool ) ) @ SV1048 @ SV466 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2955,plain,
! [SV1049: $i,SV467: $i] :
( ( ! [SY4799: $i,SY4800: $i,SY4801: $i] :
( ( c_Finite__Set_Ofold__image @ SV467 @ SV1049 @ SY4799 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4800 @ tc_bool ) ) @ SY4801 @ SY4800 )
= SY4799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2956,plain,
! [SV1050: $i,SV468: $i] :
( ( ! [SY4802: $i,SY4803: $i] :
( ( c_Finite__Set_Ofold @ SV468 @ SV1050 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4802 @ tc_bool ) ) @ SY4802 @ SY4803 )
= SV1050 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2957,plain,
! [SV1051: $i,SV470: $i] :
( ( ( SV470
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1051 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV470 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1051 @ tc_bool ) ) @ ( tc_fun @ SV1051 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2958,plain,
! [SV1052: $i,SV471: $i] :
( ( ~ ( c_Wellfounded_Omax__extp @ SV471 @ SV1052 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2959,plain,
! [SV1053: $i,SV472: $i] :
( ( ! [SY4804: $i] :
~ ( c_Finite__Set_Ofold1Set @ SV472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1053 @ tc_bool ) ) @ SY4804 @ SV1053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2960,plain,
! [SV1054: $i,SV473: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_bool ) ) @ SV1054 @ ( tc_fun @ SV473 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV473 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2961,plain,
! [SV1055: $i,SV474: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV474 @ tc_bool ) ) @ SV1055 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV474 @ tc_bool ) ) )
= SV1055 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2962,plain,
! [SV1056: $i,SV475: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV475 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV475 @ tc_bool ) ) ) @ SV1056 )
= SV1056 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2963,plain,
! [SV1057: $i,SV476: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ ( tc_fun @ SV1057 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2964,plain,
! [SV1058: $i,SV477: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV477 @ SV477 @ ( tc_fun @ SV1058 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2965,plain,
! [SV1059: $i,SV478: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1059 @ tc_bool ) ) @ ( tc_fun @ SV1059 @ tc_bool ) )
= SV478 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(2966,plain,
! [SV1060: $i,SV480: $i] :
( ( ! [SY4805: $i,SY4806: $i,SY4807: $i] :
( ( SV480 = SV1060 )
| ~ ( c_Finite__Set_Ofold__graph @ SY4805 @ SV1060 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4806 @ tc_bool ) ) @ SV480 @ SY4806 @ SY4807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2967,plain,
! [SV1061: $i,SV481: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV481 @ tc_bool ) ) @ SV1061 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV481 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV481 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2968,plain,
! [SV1062: $i,SV482: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV482 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_bool ) ) ) @ SV1062 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV482 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2969,plain,
! [SV1063: $i,SV483: $i] :
( ( ! [SY4808: $i] :
( ( c_Relation_OImage @ SV483 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1063 @ tc_bool ) ) @ SV1063 @ SY4808 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4808 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2970,plain,
! [SV1064: $i,SV484: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV484 @ tc_bool ) ) @ SV1064 @ ( tc_fun @ SV484 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2971,plain,
! [SV1065: $i,SV485: $i] :
( ( ! [SY4809: $i] :
( ( c_Set_Oinsert @ SV485 @ ( c_Set_Oinsert @ SV1065 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4809 @ tc_bool ) ) @ SY4809 ) @ SY4809 )
= ( c_Set_Oinsert @ SV1065 @ ( c_Set_Oinsert @ SV485 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4809 @ tc_bool ) ) @ SY4809 ) @ SY4809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2972,plain,
! [SV1066: $i,SV486: $i] :
( ( ! [SY4810: $i] :
( ( c_Set_Oimage @ SV486 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1066 @ tc_bool ) ) @ SV1066 @ SY4810 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4810 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2973,plain,
! [SV1067: $i,SV487: $i] :
( ( ! [SY4811: $i] : ( c_Fun_Oinj__on @ SV487 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1067 @ tc_bool ) ) @ SV1067 @ SY4811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2974,plain,
! [SV1068: $i,SV488: $i] :
( ( ! [SY4812: $i,SY4813: $i] : ( c_Finite__Set_Ofold__graph @ SV488 @ SV1068 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4812 @ tc_bool ) ) @ SV1068 @ SY4812 @ SY4813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2975,plain,
! [SV1069: $i,SV489: $i] :
( ( ! [SY4814: $i,SY4815: $i] : ( c_Nitpick_Ofold__graph_H @ SV489 @ SV1069 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4814 @ tc_bool ) ) @ SV1069 @ SY4814 @ SY4815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2976,plain,
! [SV1070: $i,SV490: $i] :
( ( ! [SY4816: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV490 @ tc_bool ) )
= ( c_Set_Oimage @ SV1070 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4816 @ tc_bool ) ) @ SY4816 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2977,plain,
! [SV1071: $i,SV491: $i] :
( ( ! [SY4817: $i,SY4818: $i] :
( ( c_Fun_Ooverride__on @ SV491 @ SV1071 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4817 @ tc_bool ) ) @ SY4817 @ SY4818 )
= SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2978,plain,
! [SV1072: $i,SV492: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SV492 ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SV1072 ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ tc_bool ) ) @ SV492 ) @ SV1072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2979,plain,
! [SV1073: $i,SV493: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SV493 ) ) @ ( hAPP @ ( c_COMBC @ ( c_in @ t_a ) @ t_a @ ( tc_fun @ t_a @ tc_bool ) @ tc_bool ) @ SV1073 ) ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_in @ t_a ) @ v_x ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ tc_bool ) ) @ SV493 ) @ SV1073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2980,plain,
! [SV1074: $i,SV494: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV494 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a @ SV1074 ) @ v_x )
= ( c_Option_Ooption_ONone @ SV1074 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2981,plain,
! [SV1075: $i,SV495: $i] :
( ( ! [SY4819: $i,SY4820: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV495 @ SV1075 @ SY4819 @ SY4820 @ t_a ) @ v_x )
= ( hAPP @ SV495 @ ( hAPP @ SV1075 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2982,plain,
! [SV1076: $i,SV496: $i] :
( ( ! [SY4821: $i,SY4822: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV496 @ SV1076 @ t_a @ SY4821 @ SY4822 ) @ v_x )
= ( hAPP @ SV1076 @ ( hAPP @ SV496 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2983,plain,
! [SV1077: $i,SV497: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV497 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1077 ) @ tc_bool ) ) @ SV1077 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2984,plain,
! [SV1078: $i,SV498: $i] :
( ( ! [SY4823: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV498 @ SV1078 @ SY4823 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV498 ) @ SV1078 @ SY4823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2985,plain,
! [SV1079: $i,SV499: $i] :
( ( ! [SY4824: $i,SY4825: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SY4824 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SY4825 @ SV499 ) ) @ SY4825 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY4825 @ SY4824 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2986,plain,
! [SV1080: $i,SV500: $i] :
( ( ! [SY4826: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SV1080 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1080 ) @ SY4826 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SY4826 ) @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2987,plain,
! [SV1081: $i,SV501: $i] :
( ( ! [SY4827: $i] :
( ( c_Hoare__Mirabelle_Ohoare__valids @ SV501 @ SV1081 @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ SV501 @ SV1081 ) @ SY4827 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SY4827 ) @ SV501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2988,plain,
! [SV1082: $i,SV502: $i] :
( ( ! [SY4828: $i,SY4829: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SY4828 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SY4829 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY4829 @ SY4828 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2989,plain,
! [SV1083: $i,SV503: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV503 ) @ SV1083 ) @ ( c_Set_Oinsert @ SV1083 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV503 @ tc_bool ) ) @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2990,plain,
! [SV1084: $i,SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV504 ) @ ( c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1 @ SV1084 @ SV504 ) ) @ SV1084 ) )
| ( SV1084
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV504 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2991,plain,
! [SV1085: $i,SV505: $i] :
( ( ( SV505
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1085 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1085 ) @ ( c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1 @ SV505 @ SV1085 ) ) @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2992,plain,
! [SV1086: $i,SV506: $i] :
( ( ( SV506
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1086 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1086 ) @ ( c_ATP__Linkup_Osko__Set__Xequals0I__1__1 @ SV506 @ SV1086 ) ) @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2993,plain,
! [SV1087: $i,SV507: $i] :
( ( ! [SY4830: $i] :
( ( SV507 = SV1087 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4830 ) @ SV507 ) @ ( c_Set_Oinsert @ SV1087 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4830 @ tc_bool ) ) @ SY4830 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2994,plain,
! [SV508: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV508 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV508 @ tc_bool ) ) @ SV508 )
= ( c_Orderings_Obot__class_Obot @ SV508 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2995,plain,
! [SV1088: $i,SV509: $i] :
( ( ! [SY4831: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV509 @ SV1088 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1088 ) @ SY4831 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV509 @ SY4831 ) ) @ SY4831 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2996,plain,
! [SV1089: $i,SV510: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV510 ) @ SV1089 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2997,plain,
! [SV1090: $i,SV511: $i] :
( ( ! [SY4832: $i] :
( ( hBOOL @ ( hAPP @ SV511 @ SV1090 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4832 ) @ SV1090 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4832 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2998,plain,
! [SV1091: $i,SV512: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV512 ) @ SV1091 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV512 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2999,plain,
! [SV1092: $i,SV513: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV513 ) @ SV1092 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV513 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3000,plain,
! [SV1093: $i,SV514: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV514 @ tc_bool ) ) @ SV1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3001,plain,
! [SV515: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV515 ) )
= $true )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV515 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(3002,plain,
! [SV1094: $i,SV516: $i] :
( ( ! [SY4833: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV516 ) @ SV1094 ) @ SY4833 ) )
| ~ ( hBOOL @ ( hAPP @ SY4833 @ SV1094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3003,plain,
! [SV1095: $i,SV517: $i] :
( ( ! [SY4834: $i] :
( ( hBOOL @ ( hAPP @ SV517 @ SV1095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4834 ) @ SV1095 ) @ SV517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(3004,plain,
! [SV1096: $i,SV518: $i] :
( ( ! [SY4835: $i] :
( ~ ( hBOOL @ ( hAPP @ SV518 @ SV1096 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4835 ) @ SV1096 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4835 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(3005,plain,
! [SV1097: $i,SV519: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV519 @ SV1097 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV1097 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3006,plain,
! [SV1098: $i,SV520: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV520 @ SV1098 ) )
| ~ ( class_Lattices_Olattice @ SV1098 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3007,plain,
! [SV1099: $i,SV521: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV521 @ SV1099 ) )
| ~ ( class_Lattices_Olattice @ SV1099 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3008,plain,
! [SV1100: $i,SV522: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV522 @ SV1100 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV1100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3009,plain,
! [SV1101: $i,SV523: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV523 @ SV1101 ) )
| ~ ( class_Lattices_Obounded__lattice @ SV1101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3010,plain,
! [SV1102: $i,SV524: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV524 @ SV1102 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1102 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3011,plain,
! [SV1103: $i,SV525: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV525 @ SV1103 ) )
| ~ ( class_Orderings_Opreorder @ SV1103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3012,plain,
! [SV1104: $i,SV526: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV526 @ SV1104 ) )
| ~ ( class_Lattices_Olattice @ SV1104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3013,plain,
! [SV1105: $i,SV527: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV527 @ SV1105 ) )
| ~ ( class_Orderings_Oorder @ SV1105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3014,plain,
! [SV1106: $i,SV528: $i] :
( ( ( class_Orderings_Otop @ ( tc_fun @ SV528 @ SV1106 ) )
| ~ ( class_Orderings_Otop @ SV1106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3015,plain,
! [SV1107: $i,SV529: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV529 @ SV1107 ) )
| ~ ( class_Orderings_Obot @ SV1107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3016,plain,
! [SV1108: $i,SV530: $i] :
( ( ( class_HOL_Ominus @ ( tc_fun @ SV530 @ SV1108 ) )
| ~ ( class_HOL_Ominus @ SV1108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3017,plain,
! [SV1109: $i,SV531: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV531 @ SV1109 ) )
| ~ ( class_HOL_Oord @ SV1109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3018,plain,
! [SV532: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ SV532 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2433]) ).
thf(3019,plain,
! [SV1110: $i,SV533: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV533 ) @ SV1110 ) @ SV1110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3020,plain,
! [SV1111: $i,SV534: $i] :
( ( ! [SY4836: $i] :
( ( SV534 = SV1111 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY4836 ) @ SV534 ) @ SV1111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3021,plain,
! [SV1112: $i,SV535: $i] :
( ( ! [SY4837: $i,SY4838: $i,SY4839: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SY4837 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SY4838 @ SY4839 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SY4838 @ SY4839 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SY4837 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3022,plain,
! [SV1113: $i,SV536: $i] :
( ( ! [SY4840: $i,SY4841: $i,SY4842: $i] :
( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4840 @ tc_bool ) ) @ SY4840 ) @ SY4840 )
!= ( c_Set_Oinsert @ SY4841 @ ( c_Set_Oinsert @ SY4842 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4840 @ tc_bool ) ) @ SY4840 ) @ SY4840 ) )
| ( SV536 = SY4842 )
| ( SV536 = SY4841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3023,plain,
! [SV1114: $i,SV537: $i] :
( ( ! [SY4843: $i,SY4844: $i,SY4845: $i] :
( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4843 @ tc_bool ) ) @ SY4843 ) @ SY4843 )
!= ( c_Set_Oinsert @ SY4844 @ ( c_Set_Oinsert @ SY4845 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4843 @ tc_bool ) ) @ SY4843 ) @ SY4843 ) )
| ( SV1114 = SY4844 )
| ( SV1114 = SY4845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3024,plain,
! [SV1115: $i,SV538: $i] :
( ( ! [SY4846: $i,SY4847: $i,SY4848: $i] :
( ( ( hAPP @ SV538 @ SV1115 )
!= ( hAPP @ SV538 @ SY4846 ) )
| ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4847 @ tc_bool ) ) @ SY4847 @ SY4848 )
| ( SV1115 = SY4846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3025,plain,
! [SV1116: $i,SV539: $i] :
( ( ! [SY4849: $i,SY4850: $i,SY4851: $i] :
( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4849 @ tc_bool ) ) @ SY4849 ) @ SY4849 )
!= ( c_Set_Oinsert @ SY4850 @ ( c_Set_Oinsert @ SY4851 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4849 @ tc_bool ) ) @ SY4849 ) @ SY4849 ) )
| ( SV539 = SY4851 )
| ( SV1116 = SY4851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3026,plain,
! [SV1117: $i,SV540: $i] :
( ( ! [SY4852: $i,SY4853: $i,SY4854: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SY4852 @ ( tc_fun @ SY4853 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4853 @ tc_bool ) ) )
| ( ( hAPP @ SV1117 @ SY4854 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4853 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4852 ) @ SY4854 ) @ SV540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3027,plain,
! [SV1118: $i,SV541: $i] :
( ( ! [SY4855: $i,SY4856: $i,SY4857: $i] :
( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4855 @ tc_bool ) ) @ SY4855 ) @ SY4855 )
!= ( c_Set_Oinsert @ SY4856 @ ( c_Set_Oinsert @ SY4857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4855 @ tc_bool ) ) @ SY4855 ) @ SY4855 ) )
| ( SV1118 = SY4856 )
| ( SV541 = SY4856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3028,plain,
! [SV1119: $i,SV542: $i] :
( ( ! [SY4858: $i,SY4859: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV542 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SY4858 @ SY4859 @ SV542 ) )
| ( SY4858 = SY4859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3029,plain,
! [SV1120: $i,SV543: $i] :
( ( ! [SY4860: $i,SY4861: $i] :
( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SY4860 )
!= ( c_Set_Oinsert @ SV543 @ SY4861 @ SY4860 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4860 ) @ SV543 ) @ SY4861 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4860 ) @ SV543 ) @ SV1120 ) )
| ( SV1120 = SY4861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3030,plain,
! [SV1121: $i,SV544: $i] :
( ( ! [SY4862: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV544 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SV1121 ) @ SY4862 )
!= ( c_Orderings_Obot__class_Obot @ SV544 ) )
| ( SY4862
= ( c_Orderings_Obot__class_Obot @ SV544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3031,plain,
! [SV1122: $i,SV545: $i] :
( ( ! [SY4863: $i,SY4864: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SY4863 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SY4864 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SY4864 ) @ SY4863 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3032,plain,
! [SV1123: $i,SV546: $i] :
( ( ! [SY4865: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV546 @ tc_bool ) ) @ SV1123 ) @ SY4865 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
| ( SV1123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3033,plain,
! [SV1124: $i,SV547: $i] :
( ( ! [SY4866: $i,SY4867: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ SY4866 ) ) @ SY4867 )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ SY4866 ) @ SY4867 ) ) )
| ( c_lessequals @ SY4867 @ SV1124 @ ( tc_fun @ SV547 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3034,plain,
! [SV1125: $i,SV548: $i] :
( ( ! [SY4868: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1125 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SY4868 ) )
| ( SV1125 = SY4868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3035,plain,
! [SV1126: $i,SV549: $i] :
( ( ! [SY4869: $i,SY4870: $i,SY4871: $i] :
( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SY4869 @ SY4870 )
!= ( c_Set_Oimage @ SV549 @ SY4871 @ SY4869 @ SY4870 ) )
| ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY4869 @ tc_bool ) ) @ SY4869 @ SY4870 )
| ( SV1126 = SY4871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3036,plain,
! [SV1127: $i,SV550: $i] :
( ( ! [SY4872: $i,SY4873: $i,SY4874: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SY4872 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SY4873 @ SY4874 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SY4872 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SY4873 @ SY4874 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3037,plain,
! [SV1128: $i,SV551: $i] :
( ( ! [SY4875: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV551 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SV1128 ) @ SY4875 )
!= ( c_Orderings_Otop__class_Otop @ SV551 ) )
| ( SV1128
= ( c_Orderings_Otop__class_Otop @ SV551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3038,plain,
! [SV1129: $i,SV552: $i] :
( ( ! [SY4876: $i] :
( ( ( c_Set_Oinsert @ SV552 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 )
!= ( c_Set_Oinsert @ SY4876 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 ) )
| ( SV552 = SY4876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3039,plain,
! [SV1130: $i,SV553: $i] :
( ( ! [SY4877: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV553 @ tc_bool ) ) @ SV1130 ) @ SY4877 )
!= SY4877 )
| ( c_lessequals @ SV1130 @ SY4877 @ ( tc_fun @ SV553 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3040,plain,
! [SV1131: $i,SV554: $i] :
( ( ! [SY4878: $i,SY4879: $i,SY4880: $i,SY4881: $i,SY4882: $i,SY4883: $i,SY4884: $i,SY4885: $i,SY4886: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SY4878 ) )
!= ( hAPP @ SY4879 @ ( hAPP @ SY4880 @ SY4881 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SY4882 @ SY4883 @ SY4884 ) @ SY4878 )
= ( hAPP @ ( c_Fun_Ocomp @ SY4879 @ SY4880 @ SY4885 @ SY4883 @ SY4886 ) @ SY4881 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3041,plain,
! [SV1132: $i,SV555: $i] :
( ( ! [SY4887: $i,SY4888: $i,SY4889: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SY4887 @ SY4888 @ ( tc_fun @ SY4889 @ tc_bool ) ) @ SY4889 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SY4888 @ SY4887 @ ( tc_fun @ SY4889 @ tc_bool ) ) @ SY4889 @ SV555 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SY4888 @ SY4889 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SY4887 @ SY4889 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4889 @ tc_bool ) ) @ SY4887 ) @ SY4888 ) @ SY4889 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3042,plain,
! [SV1133: $i,SV556: $i] :
( ( ! [SY4890: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV556 @ tc_bool ) ) @ SV1133 ) @ SY4890 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV556 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1133 @ SY4890 @ ( tc_fun @ SV556 @ tc_bool ) )
= SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3043,plain,
! [SV557: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV557 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV557 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(3044,plain,
! [SV1134: $i,SV558: $i] :
( ( ! [SY4891: $i,SY4892: $i] :
( ( ( hAPP @ SV558 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1134 @ SV558 @ SY4891 @ SY4892 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4892 @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4892 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1134 @ SV558 @ SY4891 @ ( tc_fun @ SY4892 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3045,plain,
! [SV1135: $i,SV559: $i] :
( ( ! [SY4893: $i,SY4894: $i,SY4895: $i] :
( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SY4893 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4893 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4893 ) @ SV559 ) @ SV1135 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SY4894 @ SY4895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3046,plain,
! [SV1136: $i,SV560: $i] :
( ( ! [SY4896: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV560 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SV1136 ) @ SY4896 )
!= SV1136 )
| ( c_lessequals @ SV1136 @ SY4896 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3047,plain,
! [SV1137: $i,SV561: $i] :
( ( ! [SY4897: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV561 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SV1137 ) @ SY4897 )
!= ( c_Orderings_Obot__class_Obot @ SV561 ) )
| ( SV1137
= ( c_Orderings_Obot__class_Obot @ SV561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3048,plain,
! [SV1138: $i,SV562: $i] :
( ( ! [SY4898: $i,SY4899: $i,SY4900: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SY4898 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SY4899 @ SY4900 @ SV562 ) )
| ( c_lessequals @ SY4900 @ SY4899 @ SV562 )
| ~ ( c_lessequals @ SY4898 @ SV1138 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3049,plain,
! [SV1139: $i,SV563: $i] :
( ( ! [SY4901: $i,SY4902: $i,SY4903: $i,SY4904: $i] :
( ( ( hAPP @ SV563 @ SV1139 )
!= ( hAPP @ SV563 @ SY4901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4902 ) @ SY4901 ) @ SY4903 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4902 ) @ SV1139 ) @ SY4903 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SY4903 @ SY4902 @ SY4904 )
| ( SV1139 = SY4901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3050,plain,
! [SV1140: $i,SV564: $i] :
( ( ! [SY4905: $i,SY4906: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV564 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SY4905 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SY4906 @ SY4906 @ SV564 ) )
| ( SV1140 = SY4905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3051,plain,
! [SV1141: $i,SV565: $i] :
( ( ! [SY4907: $i,SY4908: $i,SY4909: $i,SY4910: $i] :
( ( ( hAPP @ SV565 @ SV1141 )
!= ( hAPP @ SV565 @ SY4907 ) )
| ~ ( c_Fun_Oinj__on @ SV565 @ SY4908 @ SY4909 @ SY4910 )
| ( SV1141 = SY4907 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4909 ) @ SY4907 ) @ SY4908 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4909 ) @ SV1141 ) @ SY4908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3052,plain,
! [SV1142: $i,SV566: $i] :
( ( ! [SY4911: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV566 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SV1142 ) @ SY4911 )
!= SY4911 )
| ( c_lessequals @ SV1142 @ SY4911 @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3053,plain,
! [SV1143: $i,SV567: $i] :
( ( ! [SY4912: $i,SY4913: $i,SY4914: $i] :
( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SY4912 @ SY4913 )
!= ( c_Set_Oimage @ SV567 @ SY4914 @ SY4912 @ SY4913 ) )
| ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY4912 @ tc_bool ) ) @ SV1143 ) @ SY4914 ) @ SY4912 @ SY4913 )
| ( SV1143 = SY4914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(3054,plain,
! [SV1144: $i,SV568: $i] :
( ( ( ( c_Suc @ SV568 )
!= ( c_Suc @ SV1144 ) )
| ( SV568 = SV1144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3055,plain,
! [SV1145: $i,SV569: $i] :
( ( ! [SY4915: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV569 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV1145 @ SY4915 @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3056,plain,
! [SV1146: $i,SV570: $i] :
( ( ! [SY4916: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) )
!= ( c_Collect @ SV1146 @ SV570 ) )
| ~ ( hBOOL @ ( hAPP @ SV1146 @ SY4916 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3057,plain,
! [SV1147: $i,SV571: $i] :
( ( ! [SY4917: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV571 @ tc_bool ) ) @ SV1147 ) @ SY4917 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
| ( SY4917
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3058,plain,
! [SV1148: $i,SV572: $i] :
( ( ! [SY4918: $i,SY4919: $i,SY4920: $i,SY4921: $i,SY4922: $i,SY4923: $i,SY4924: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SY4918 @ SY4919 @ SY4920 )
!= ( c_Fun_Ocomp @ SY4921 @ SY4922 @ SY4923 @ SY4919 @ SY4920 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY4924 ) )
= ( hAPP @ SY4921 @ ( hAPP @ SY4922 @ SY4924 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3059,plain,
! [SV1149: $i,SV573: $i] :
( ( ! [SY4925: $i] :
( ( ( c_Set_Oinsert @ SV573 @ SV1149 @ SY4925 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4925 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4925 ) @ SV573 ) @ SV1149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3060,plain,
! [SV1150: $i,SV574: $i] :
( ( ( ( c_Suc @ SV574 )
!= ( c_Suc @ SV1150 ) )
| ( SV574 = SV1150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3061,plain,
! [SV1151: $i,SV575: $i] :
( ( ! [SY4926: $i,SY4927: $i,SY4928: $i,SY4929: $i,SY4930: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SY4926 @ SY4927 @ SY4928 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SY4927 ) @ SY4929 @ SY4927 @ SY4927 @ SY4928 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SY4930 ) )
= ( hAPP @ SY4929 @ SY4930 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3062,plain,
! [SV1152: $i,SV576: $i] :
( ( ! [SY4931: $i,SY4932: $i,SY4933: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SY4931 @ SY4932 @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ( ( hAPP @ SY4931 @ SY4933 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4932 ) @ SY4933 ) @ SV1152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3063,plain,
! [SV577: $i] :
( ( ( c_Suc @ SV577 )
= SV577 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(3064,plain,
! [SV1153: $i,SV578: $i] :
( ( ! [SY4934: $i,SY4935: $i] :
( ( ( c_Set_Oimage @ SV578 @ SV1153 @ SY4934 @ SY4935 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4935 @ tc_bool ) ) )
| ( SV1153
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4934 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3065,plain,
! [SV579: $i] :
( ( SV579
= ( c_Suc @ SV579 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(3066,plain,
! [SV1154: $i,SV580: $i] :
( ( ! [SY4936: $i] :
( ( c_Set_Oinsert @ SV580 @ SV1154 @ SY4936 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4936 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3067,plain,
! [SV1155: $i,SV581: $i] :
( ( ! [SY4937: $i,SY4938: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) )
!= ( c_Set_Oimage @ SV1155 @ SY4937 @ SY4938 @ SV581 ) )
| ( SY4937
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4938 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3068,plain,
! [SV1156: $i,SV582: $i] :
( ( ! [SY4939: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV582 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SV1156 ) @ SY4939 )
!= ( c_Orderings_Otop__class_Otop @ SV582 ) )
| ( SY4939
= ( c_Orderings_Otop__class_Otop @ SV582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3069,plain,
! [SV1157: $i,SV583: $i] :
( ( ! [SY4940: $i] :
( ( ( c_Collect @ SV583 @ SV1157 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1157 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SV583 @ SY4940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3070,plain,
! [SV1158: $i,SV584: $i] :
( ( ! [SY4941: $i,SY4942: $i,SY4943: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SY4941 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SY4942 @ SY4943 @ SV584 ) )
| ( c_lessequals @ SY4941 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SY4943 @ SY4942 @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3071,plain,
! [SV1159: $i,SV585: $i] :
( ( ! [SY4944: $i,SY4945: $i] :
( ( ( hAPP @ SV585 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV1159 @ SV585 @ SY4944 @ SY4945 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4945 @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1159 @ SV585 @ SY4944 @ ( tc_fun @ SY4945 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4945 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3072,plain,
! [SV1160: $i,SV586: $i] :
( ( ! [SY4946: $i,SY4947: $i,SY4948: $i,SY4949: $i] :
( ( ( hAPP @ SV586 @ SV1160 )
!= ( hAPP @ SV586 @ SY4946 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4947 ) @ SY4946 ) @ SY4948 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4947 ) @ SV1160 ) @ SY4948 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SY4948 @ SY4947 @ SY4949 )
| ( SV1160 = SY4946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3073,plain,
! [SV1161: $i,SV587: $i] :
( ( ! [SY4950: $i,SY4951: $i,SY4952: $i,SY4953: $i] :
( ( ( hAPP @ SV587 @ SV1161 )
!= ( hAPP @ SV587 @ SY4950 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4951 ) @ SY4950 ) @ SY4952 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4951 ) @ SV1161 ) @ SY4952 ) )
| ( SV1161 = SY4950 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SY4952 @ SY4951 @ SY4953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3074,plain,
! [SV1: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1 ) @ v_Ga ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ v_x @ SV1 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(3075,plain,
! [SV1162: $i,SV588: $i,SV2: $i] :
( ( ! [SY4954: $i,SY4955: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SY4954 ) @ ( c_Set_Oimage @ SV2 @ SY4955 @ SV1162 @ SY4954 ) @ ( tc_fun @ SY4954 @ tc_bool ) )
| ~ ( c_lessequals @ SV588 @ SY4955 @ ( tc_fun @ SV1162 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SY4954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3076,plain,
! [SV1163: $i,SV589: $i,SV3: $i] :
( ( ! [SY4956: $i,SY4957: $i] :
( ( c_Fun_Oinj__on @ SV3 @ SV589 @ SV1163 @ SY4956 )
| ~ ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SY4957 @ SV589 @ SV1163 ) @ SV1163 @ SY4956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3077,plain,
! [SV1164: $i,SV590: $i,SV4: $i] :
( ( ! [SY4958: $i,SY4959: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
| ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4958 @ SV590 @ SY4959 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4959 ) @ SV1164 ) @ SY4958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3078,plain,
! [SV1165: $i,SV591: $i,SV5: $i] :
( ( ! [SY4960: $i,SY4961: $i] :
( ( c_lessequals @ ( hAPP @ SV5 @ SV591 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1165 @ SV5 @ SY4960 @ ( tc_fun @ SY4961 @ tc_bool ) ) @ ( tc_fun @ SY4961 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4960 ) @ SV591 ) @ SV1165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3079,plain,
! [SV1166: $i,SV592: $i,SV6: $i] :
( ( ! [SY4962: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV6 @ SV592 @ SV1166 ) @ SY4962 @ ( tc_fun @ SV1166 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV592 @ SY4962 @ ( tc_fun @ SV1166 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1166 ) @ SV6 ) @ SY4962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3080,plain,
! [SV1167: $i,SV593: $i,SV7: $i] :
( ( ! [SY4963: $i] :
( ( c_lessequals @ SV7 @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SY4963 @ SV7 @ SV1167 ) @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3081,plain,
! [SV1168: $i,SV594: $i,SV8: $i] :
( ( ! [SY4964: $i] :
( ( c_lessequals @ SV8 @ ( c_Set_Oinsert @ SV594 @ SV1168 @ SY4964 ) @ ( tc_fun @ SY4964 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SV1168 @ ( tc_fun @ SY4964 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3082,plain,
! [SV1169: $i,SV595: $i,SV9: $i] :
( ( ! [SY4965: $i,SY4966: $i] :
( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SV1169 @ SY4965 ) @ SY4966 @ SY4965 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4965 ) @ SV595 ) @ SV1169 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SV1169 @ SY4966 @ SY4965 @ SY4965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3083,plain,
! [SV1170: $i,SV596: $i,SV10: $i] :
( ( ! [SY4967: $i,SY4968: $i,SY4969: $i,SY4970: $i,SY4971: $i,SY4972: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4967 @ SV10 @ SY4968 @ SY4969 @ SY4970 @ SY4971 @ SY4972 @ SV1170 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3084,plain,
! [SV1171: $i,SV597: $i,SV11: $i] :
( ( ! [SY4973: $i,SY4974: $i,SY4975: $i,SY4976: $i,SY4977: $i,SY4978: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SY4973 @ SY4974 @ SY4975 @ SY4976 @ SY4977 @ SV1171 @ SY4978 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3085,plain,
! [SV1172: $i,SV598: $i,SV12: $i] :
( ( ! [SY4979: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SY4979 @ ( tc_fun @ SV1172 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SY4979 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SY4979 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3086,plain,
! [SV1173: $i,SV599: $i,SV13: $i] :
( ( ! [SY4980: $i] :
( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SY4980 ) @ ( tc_fun @ SY4980 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4980 ) @ SV599 ) @ SV13 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4980 @ tc_bool ) ) @ SY4980 ) @ ( tc_fun @ SY4980 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SY4980 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4980 ) @ SV599 ) @ SV1173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3087,plain,
! [SV1174: $i,SV600: $i,SV14: $i] :
( ( ! [SY4981: $i,SY4982: $i,SY4983: $i,SY4984: $i,SY4985: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SY4981 @ SY4982 @ SY4983 @ SY4984 ) @ SY4985 @ SY4984 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SY4981 @ SY4984 @ SY4985 @ SY4983 ) @ SV1174 @ SY4982 @ SY4985 @ SY4983 ) )
| ~ ( c_Fun_Oinj__on @ SY4981 @ SY4982 @ SY4983 @ SY4984 )
| ~ ( c_Finite__Set_Ofinite @ SY4982 @ SY4983 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY4985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3088,plain,
! [SV1175: $i,SV601: $i,SV15: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV601 @ ( tc_fun @ SV1175 @ tc_bool ) ) @ SV1175 )
| ~ ( c_Finite__Set_Ofinite @ SV15 @ SV1175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3089,plain,
! [SV1176: $i,SV602: $i,SV16: $i] :
( ( ! [SY4986: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV16 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SY4986 @ SV16 @ SV16 ) @ SV16 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SY4986 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4986 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3090,plain,
! [SV1177: $i,SV603: $i,SV17: $i] :
( ( ! [SY4987: $i,SY4988: $i] :
( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SV603 @ SV1177 @ ( tc_fun @ SY4987 @ tc_bool ) ) @ SY4987 @ SY4988 )
| ~ ( c_Fun_Oinj__on @ SV17 @ SV603 @ SY4987 @ SY4988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3091,plain,
! [SV1178: $i,SV604: $i,SV18: $i] :
( ( ! [SY4989: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV604 @ SV1178 @ SV18 ) ) @ SY4989 )
= ( c_Set_Oinsert @ SV604 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ SV1178 ) @ SY4989 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3092,plain,
! [SV1179: $i,SV605: $i,SV19: $i] :
( ( ! [SY4990: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SV605 ) @ ( c_Set_Oinsert @ SV1179 @ SY4990 @ SV19 ) )
= ( c_Set_Oinsert @ SV1179 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SV605 ) @ SY4990 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3093,plain,
! [SV1180: $i,SV606: $i,SV20: $i] :
( ( ! [SY4991: $i,SY4992: $i] :
( ( c_Set_Ovimage @ SV20 @ ( c_HOL_Ominus__class_Ominus @ SV606 @ SV1180 @ ( tc_fun @ SY4991 @ tc_bool ) ) @ SY4992 @ SY4991 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV20 @ SV606 @ SY4992 @ SY4991 ) @ ( c_Set_Ovimage @ SV20 @ SV1180 @ SY4992 @ SY4991 ) @ ( tc_fun @ SY4992 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3094,plain,
! [SV1181: $i,SV607: $i,SV21: $i] :
( ( ! [SY4993: $i] :
( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SY4993 ) @ ( tc_fun @ SY4993 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4993 ) @ SV607 ) @ SV21 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4993 @ tc_bool ) ) @ SY4993 ) @ ( tc_fun @ SY4993 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SY4993 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SY4993 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3095,plain,
! [SV1182: $i,SV608: $i,SV22: $i] :
( ( ! [SY4994: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV22 @ ( c_Set_Ovimage @ SV22 @ SV608 @ SV1182 @ SY4994 ) @ SV1182 @ SY4994 ) @ SV608 @ ( tc_fun @ SY4994 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(3096,plain,
! [SV1183: $i,SV609: $i,SV23: $i] :
( ( ! [SY4995: $i] :
( ( ( c_Set_Ovimage @ SV23 @ ( c_Set_Oimage @ SV23 @ SV609 @ SV1183 @ SY4995 ) @ SV1183 @ SY4995 )
= SV609 )
| ~ ( c_Fun_Oinj__on @ SV23 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1183 @ SY4995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3097,plain,
! [SV1184: $i,SV611: $i,SV25: $i] :
( ( ! [SY4996: $i] :
( ( SV25 = SV611 )
| ~ ( c_Finite__Set_Ofold1Set @ SV1184 @ ( c_Set_Oinsert @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4996 @ tc_bool ) ) @ SY4996 ) @ SV611 @ SY4996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3098,plain,
! [SV1185: $i,SV612: $i,SV26: $i] :
( ( ( c_Set_Ovimage @ SV26 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV612 @ tc_bool ) ) @ SV1185 @ SV612 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1185 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3099,plain,
! [SV1186: $i,SV613: $i,SV27: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV27 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV613 @ SV1186 @ SV27 ) @ SV27 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 ) @ SV613 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1186 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3100,plain,
! [SV614: $i,SV28: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV28 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV28 ) @ SV614 ) @ ( c_Orderings_Otop__class_Otop @ SV28 ) )
= ( c_Orderings_Otop__class_Otop @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(3101,plain,
! [SV615: $i,SV29: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV29 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV29 ) @ ( c_Orderings_Otop__class_Otop @ SV29 ) ) @ SV615 )
= ( c_Orderings_Otop__class_Otop @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(3102,plain,
! [SV1187: $i,SV618: $i,SV32: $i] :
( ( ! [SY4997: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV32 @ ( c_Set_Oinsert @ SV618 @ SV1187 @ SY4997 ) @ ( tc_fun @ SY4997 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV1187 @ ( tc_fun @ SY4997 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4997 @ tc_bool ) ) @ SY4997 ) @ ( tc_fun @ SY4997 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3103,plain,
! [SV1188: $i,SV619: $i,SV33: $i] :
( ( ! [SY4998: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SV619 @ SV1188 @ SY4998 ) @ ( tc_fun @ SY4998 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SV619 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4998 @ tc_bool ) ) @ SY4998 ) @ ( tc_fun @ SY4998 @ tc_bool ) ) @ SV1188 @ ( tc_fun @ SY4998 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3104,plain,
! [SV1189: $i,SV620: $i,SV34: $i] :
( ( ( c_Finite__Set_Ofinite @ SV34 @ SV620 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV1189 @ ( tc_fun @ SV620 @ tc_bool ) ) @ SV620 )
| ~ ( c_Finite__Set_Ofinite @ SV1189 @ SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3105,plain,
! [SV1190: $i,SV621: $i,SV35: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SV621 @ ( tc_fun @ SV1190 @ tc_bool ) ) @ SV1190 )
| ~ ( c_Finite__Set_Ofinite @ SV35 @ SV1190 )
| ~ ( c_Finite__Set_Ofinite @ SV621 @ SV1190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3106,plain,
! [SV1191: $i,SV622: $i,SV36: $i] :
( ( ! [SY4999: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV622 @ SV1191 @ SV36 ) ) @ ( c_Set_Oinsert @ SV622 @ SY4999 @ SV36 ) )
= ( c_Set_Oinsert @ SV622 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ SV1191 ) @ SY4999 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3107,plain,
! [SV1192: $i,SV623: $i,SV37: $i] :
( ( ( c_Set_Oinsert @ SV37 @ ( c_Set_Oinsert @ SV37 @ SV623 @ SV1192 ) @ SV1192 )
= ( c_Set_Oinsert @ SV37 @ SV623 @ SV1192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3108,plain,
! [SV1193: $i,SV624: $i,SV38: $i] :
( ( ! [SY5000: $i,SY5001: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5000 ) @ SV624 ) @ SY5001 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5001 @ SV38 @ SY5000 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
| ~ ( c_Finite__Set_Ofinite @ SY5001 @ SY5000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3109,plain,
! [SV1194: $i,SV625: $i,SV39: $i] :
( ( ! [SY5002: $i] :
( ( hBOOL @ ( hAPP @ SV39 @ SV625 ) )
| ( SV1194 = SV625 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1194 @ SV39 @ SY5002 ) @ SV625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3110,plain,
! [SV626: $i,SV40: $i] :
( ( ( SV40
= ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SV40 @ SV626 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SV40 @ SV626 ) @ SV626 ) )
= $true )
| ( ( SV40
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV626 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(3111,plain,
! [SV1195: $i,SV627: $i,SV41: $i] :
( ( ! [SY5003: $i,SY5004: $i,SY5005: $i] :
( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SY5003 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5004 ) @ SV627 ) @ SY5005 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5005 @ SV41 @ SY5004 @ ( tc_fun @ SY5003 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SY5003 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3112,plain,
! [SV1196: $i,SV628: $i,SV42: $i] :
( ( c_lessequals @ SV42 @ ( c_Set_Oinsert @ SV628 @ SV42 @ SV1196 ) @ ( tc_fun @ SV1196 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3113,plain,
! [SV1197: $i,SV629: $i,SV43: $i] :
( ( ! [SY5006: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV43 @ SV629 @ SV1197 ) @ SY5006 @ SV1197 @ SV629 @ t_a ) @ v_x )
= SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3114,plain,
! [SV1198: $i,SV630: $i,SV44: $i] :
( ( ( c_Finite__Set_Ofinite @ SV44 @ SV630 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1198 @ SV44 @ SV630 ) @ SV630 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3115,plain,
! [SV1199: $i,SV631: $i,SV45: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV45 @ SV631 @ SV1199 ) @ SV1199 )
| ~ ( c_Finite__Set_Ofinite @ SV631 @ SV1199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3116,plain,
! [SV1200: $i,SV632: $i,SV46: $i] :
( ( ! [SY5007: $i,SY5008: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SV632 @ SV1200 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5007 @ SV632 @ SY5008 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5007 @ SV632 @ SY5008 @ ( tc_fun @ SV46 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5008 ) @ SV1200 ) @ SY5007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3117,plain,
! [SV1201: $i,SV633: $i,SV47: $i] :
( ( ! [SY5009: $i,SY5010: $i,SY5011: $i,SY5012: $i] :
( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SY5009 ) @ SY5010 ) @ SY5011 @ SY5012 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5011 ) @ SY5009 ) @ SV1201 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SY5009 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5011 @ tc_bool ) ) @ SY5011 ) @ ( tc_fun @ SY5011 @ tc_bool ) ) @ SY5010 @ SY5011 @ SY5012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3118,plain,
! [SV1202: $i,SV634: $i,SV48: $i] :
( ( ! [SY5013: $i,SY5014: $i] :
( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV1202 ) @ SY5013 ) @ SV634 @ SY5014 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5014 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SV1202 @ SV634 @ SY5014 ) ) @ ( c_Set_Oimage @ SV48 @ SY5013 @ SV634 @ SY5014 ) ) )
| ~ ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV634 @ SY5014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3119,plain,
! [SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY5015: $i,SY5016: $i,SY5017: $i,SY5018: $i,SY5019: $i,SY5020: $i,SY5021: $i,SY5022: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5015 @ tc_bool ) ) @ SY5015 ) @ SY5015 ) )
= ( hAPP @ ( hAPP @ SY5016 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5017 @ SV49 @ SY5018 @ SY5019 @ SY5020 @ SY5016 @ SY5021 @ SY5022 @ SY5015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3120,plain,
! [SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY5023: $i,SY5024: $i,SY5025: $i,SY5026: $i,SY5027: $i,SY5028: $i,SY5029: $i,SY5030: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5023 @ tc_bool ) ) @ SY5023 ) @ SY5023 ) )
= ( hAPP @ ( hAPP @ SY5024 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SY5025 @ SY5026 @ SY5027 @ SY5024 @ SY5028 @ SY5029 @ SY5030 @ SY5023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3121,plain,
! [SV1205: $i,SV637: $i,SV51: $i] :
( ( ! [SY5031: $i,SY5032: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV51 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV637 @ tc_bool ) ) @ SV1205 ) @ SY5031 ) @ SV637 @ SY5032 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5032 @ tc_bool ) ) @ ( c_Set_Oimage @ SV51 @ SV1205 @ SV637 @ SY5032 ) ) @ ( c_Set_Oimage @ SV51 @ SY5031 @ SV637 @ SY5032 ) ) @ ( tc_fun @ SY5032 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3122,plain,
! [SV1206: $i,SV638: $i,SV52: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SV638 ) @ SV1206 ) @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SV1206 @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SV638 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3123,plain,
! [SV1207: $i,SV639: $i,SV53: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SV639 ) @ SV1207 ) @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SV1207 @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SV639 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3124,plain,
! [SV1208: $i,SV640: $i,SV54: $i] :
( ( ! [SY5033: $i,SY5034: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV54 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV640 @ tc_bool ) ) @ SV1208 ) @ SY5033 ) @ SV640 @ SY5034 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5034 @ tc_bool ) ) @ ( c_Relation_OImage @ SV54 @ SV1208 @ SV640 @ SY5034 ) ) @ ( c_Relation_OImage @ SV54 @ SY5033 @ SV640 @ SY5034 ) ) @ ( tc_fun @ SY5034 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3125,plain,
! [SV1209: $i,SV641: $i,SV55: $i] :
( ( ! [SY5035: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ SV1209 ) ) @ SY5035 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV1209 ) @ SY5035 ) ) )
| ~ ( c_lessequals @ SY5035 @ SV641 @ ( tc_fun @ SV55 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3126,plain,
! [SV1210: $i,SV642: $i,SV56: $i] :
( ( ! [SY5036: $i,SY5037: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV56 @ SV642 @ SV1210 @ SY5036 ) @ SY5037 )
= ( c_Option_Ooption_ONone @ SY5036 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1210 ) @ SY5037 ) @ SV642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3127,plain,
! [SV1211: $i,SV643: $i,SV57: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV57 @ tc_bool ) ) @ SV643 ) @ SV1211 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV57 @ tc_bool ) ) )
| ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SV643 @ SV1211 @ SV57 )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SV643 @ SV1211 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3128,plain,
! [SV1212: $i,SV644: $i,SV58: $i] :
( ( ! [SY5038: $i,SY5039: $i,SY5040: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV58 @ SV644 @ SV1212 @ SY5038 @ SY5039 ) @ SY5040 )
= ( hAPP @ SV58 @ ( hAPP @ SV644 @ SY5040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3129,plain,
! [SV1213: $i,SV645: $i,SV59: $i] :
( ( ! [SY5041: $i,SY5042: $i,SY5043: $i] :
( ( hAPP @ SV59 @ ( hAPP @ SV645 @ SV1213 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV59 @ SV645 @ SY5041 @ SY5042 @ SY5043 ) @ SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3130,plain,
! [SV1214: $i,SV646: $i,SV60: $i] :
( ( ! [SY5044: $i,SY5045: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5044 ) @ ( hAPP @ SY5045 @ SV646 ) ) @ ( c_Set_Oimage @ SY5045 @ SV1214 @ SV60 @ SY5044 ) ) )
| ~ ( c_Fun_Oinj__on @ SY5045 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SY5044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3131,plain,
! [SV1215: $i,SV647: $i,SV61: $i] :
( ( ! [SY5046: $i,SY5047: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SY5046 @ SY5047 @ SV61 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5047 ) @ SV1215 ) @ SY5046 ) )
| ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY5047 @ tc_bool ) ) @ SY5047 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3132,plain,
! [SV1216: $i,SV648: $i,SV62: $i] :
( ( ! [SY5048: $i,SY5049: $i] :
( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ SV1216 ) ) @ SY5048 )
= ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ ( hAPP @ ( hAPP @ SV62 @ SV1216 ) @ SY5048 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SY5049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3133,plain,
! [SV1217: $i,SV649: $i,SV63: $i] :
( ( ! [SY5050: $i,SY5051: $i] :
( ( ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ SY5050 ) )
= ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ SY5050 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SY5051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3134,plain,
! [SV1218: $i,SV650: $i,SV64: $i] :
( ( ! [SY5052: $i] :
( ( ( hAPP @ ( hAPP @ SV64 @ SV650 ) @ SV1218 )
= ( hAPP @ ( hAPP @ SV64 @ SV1218 ) @ SV650 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV64 @ SY5052 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3135,plain,
! [SV1219: $i,SV651: $i,SV65: $i] :
( ( ! [SY5053: $i] :
( ( hBOOL @ ( hAPP @ SV65 @ SV651 ) )
| ( hBOOL @ ( hAPP @ SV1219 @ SV651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5053 @ tc_bool ) ) @ SV1219 ) @ SV65 ) @ SV651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3136,plain,
! [SV1220: $i,SV652: $i,SV66: $i] :
( ( ! [SY5054: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV66 @ tc_bool ) ) @ SV652 ) @ SV1220 ) @ SY5054 ) )
| ~ ( hBOOL @ ( hAPP @ SV1220 @ SY5054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3137,plain,
! [SV1221: $i,SV653: $i,SV67: $i] :
( ( ! [SY5055: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV67 @ tc_bool ) ) @ SV653 ) @ SV1221 ) @ SY5055 ) )
| ~ ( hBOOL @ ( hAPP @ SV653 @ SY5055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3138,plain,
! [SV1222: $i,SV654: $i,SV68: $i] :
( ( ! [SY5056: $i,SY5057: $i] :
( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SY5056 @ SV68 @ SV1222 @ SY5057 ) @ ( c_Set_Oimage @ SY5056 @ SV654 @ SV1222 @ SY5057 ) @ ( tc_fun @ SY5057 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY5056 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SY5057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3139,plain,
! [SV1223: $i,SV655: $i,SV69: $i] :
( ( ! [SY5058: $i] :
( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SV1223 @ SY5058 ) @ ( tc_fun @ SY5058 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5058 ) @ SV655 ) @ SV69 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5058 @ tc_bool ) ) @ SY5058 ) @ ( tc_fun @ SY5058 @ tc_bool ) ) @ SV1223 @ ( tc_fun @ SY5058 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3140,plain,
! [SV1224: $i,SV656: $i,SV70: $i] :
( ( ! [SY5059: $i] :
( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SV1224 @ SY5059 ) @ ( tc_fun @ SY5059 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5059 ) @ SV656 ) @ SV70 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5059 @ tc_bool ) ) @ SY5059 ) @ ( tc_fun @ SY5059 @ tc_bool ) ) @ SV1224 @ ( tc_fun @ SY5059 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3141,plain,
! [SV1225: $i,SV657: $i,SV71: $i] :
( ( ! [SY5060: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SY5060 @ ( tc_fun @ SV1225 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1225 ) @ SV657 ) @ SV71 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SY5060 @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3142,plain,
! [SV1226: $i,SV658: $i,SV72: $i] :
( ( ! [SY5061: $i,SY5062: $i,SY5063: $i] :
( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SY5061 ) @ SV658 @ SY5062 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5062 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SY5062 ) ) @ ( c_Set_Oimage @ SV72 @ SY5061 @ SV658 @ SY5062 ) ) )
| ~ ( c_lessequals @ SY5061 @ SY5063 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_lessequals @ SV1226 @ SY5063 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SY5063 @ SV658 @ SY5062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3143,plain,
! [SV1227: $i,SV659: $i,SV73: $i] :
( ( ! [SY5064: $i,SY5065: $i] :
( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
| ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SY5064 @ SY5065 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY5064 @ SY5065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3144,plain,
! [SV1228: $i,SV660: $i,SV74: $i] :
( ( ! [SY5066: $i,SY5067: $i,SY5068: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SY5066 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5067 ) @ SV1228 ) @ SY5068 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SY5068 @ SY5067 @ SV74 ) @ SY5066 @ ( tc_fun @ SV74 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3145,plain,
! [SV1229: $i,SV661: $i,SV75: $i] :
( ( ! [SY5069: $i,SY5070: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SV661 @ SV1229 ) @ SY5069 @ SV1229 @ SV661 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV661 @ tc_bool ) ) @ SV661 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1229 ) @ SY5070 ) @ SY5069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3146,plain,
! [SV1230: $i,SV662: $i,SV76: $i] :
( ( ! [SY5071: $i,SY5072: $i,SY5073: $i] :
( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1230 @ SY5071 @ SV76 @ SY5072 @ SV662 @ SY5073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3147,plain,
! [SV1231: $i,SV663: $i,SV77: $i] :
( ( ~ ( class_Lattices_Olattice @ SV77 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ SV77 ) ) @ SV663 ) @ SV1231 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV77 ) @ ( hAPP @ SV663 @ v_x ) ) @ ( hAPP @ SV1231 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3148,plain,
! [SV1232: $i,SV664: $i,SV78: $i] :
( ( ! [SY5074: $i,SY5075: $i,SY5076: $i] :
( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SV1232 @ SY5074 @ SY5075 ) @ SY5075 @ SY5076 )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SY5075 @ SY5076 @ SY5074 ) @ SV1232 @ SY5074 @ SY5076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3149,plain,
! [SV1233: $i,SV665: $i,SV79: $i] :
( ( ! [SY5077: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV665 ) @ SV1233 ) ) @ SY5077 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV665 ) @ SY5077 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV1233 ) @ SY5077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3150,plain,
! [SV1234: $i,SV666: $i,SV80: $i] :
( ( ! [SY5078: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV1234 ) @ SY5078 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ SV1234 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ SY5078 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3151,plain,
! [SV1235: $i,SV667: $i,SV81: $i] :
( ( ! [SY5079: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ SV1235 ) @ SY5079 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1235 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SY5079 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3152,plain,
! [SV1236: $i,SV668: $i,SV82: $i] :
( ( ! [SY5080: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ SV668 ) @ SV1236 ) ) @ SY5080 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV668 ) @ SY5080 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV1236 ) @ SY5080 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3153,plain,
! [SV1237: $i,SV669: $i,SV83: $i] :
( ( ! [SY5081: $i] :
( ( hBOOL @ ( hAPP @ SV83 @ SV669 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1237 ) @ SV669 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1237 @ tc_bool ) ) @ SY5081 ) @ ( c_Collect @ SV83 @ SV1237 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3154,plain,
! [SV1238: $i,SV670: $i,SV84: $i] :
( ( ( c_Fun_Ocomp @ SV84 @ ( c_Fun_Oid @ SV670 ) @ SV670 @ SV1238 @ SV670 )
= SV84 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3155,plain,
! [SV1239: $i,SV671: $i,SV85: $i] :
( ( ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV85 ) @ SV671 @ SV85 @ SV85 @ SV1239 )
= SV671 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3156,plain,
! [SV1240: $i,SV672: $i,SV86: $i] :
( ( ! [SY5082: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SV1240 @ SY5082 ) @ SV1240 )
| ~ ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1240 @ tc_bool ) ) @ SV1240 @ SY5082 )
| ~ ( c_Finite__Set_Ofinite @ SV672 @ SY5082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3157,plain,
! [SV674: $i,SV88: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV88 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 ) @ SV674 ) @ SV674 )
= SV674 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(3158,plain,
! [SV1241: $i,SV675: $i,SV89: $i] :
( ( ! [SY5083: $i] :
( ~ ( class_Orderings_Opreorder @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY5083 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV675 @ SY5083 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3159,plain,
! [SV1242: $i,SV676: $i,SV90: $i] :
( ( ! [SY5084: $i] :
( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5084 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ SY5084 @ ( tc_fun @ SV1242 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3160,plain,
! [SV1243: $i,SV677: $i,SV91: $i] :
( ( ! [SY5085: $i] :
( ~ ( class_Orderings_Oorder @ SV91 )
| ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY5085 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY5085 @ SV1243 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3161,plain,
! [SV1244: $i,SV678: $i,SV92: $i] :
( ( ! [SY5086: $i,SY5087: $i] :
( ( c_Relation_OImage @ SV92 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV678 @ tc_bool ) ) @ SV1244 ) @ SY5086 ) @ SV678 @ SY5087 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5087 @ tc_bool ) ) @ ( c_Relation_OImage @ SV92 @ SV1244 @ SV678 @ SY5087 ) ) @ ( c_Relation_OImage @ SV92 @ SY5086 @ SV678 @ SY5087 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3162,plain,
! [SV1245: $i,SV679: $i,SV93: $i] :
( ( ! [SY5088: $i,SY5089: $i] :
( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SV1245 @ SY5088 ) @ SY5088 @ SY5089 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5089 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5088 @ tc_bool ) ) @ SY5088 ) @ ( tc_fun @ SY5088 @ tc_bool ) ) @ SY5088 @ SY5089 ) ) )
| ~ ( c_Fun_Oinj__on @ SV93 @ SV1245 @ SY5088 @ SY5089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3163,plain,
! [SV1246: $i,SV681: $i,SV95: $i] :
( ( ! [SY5090: $i] :
( ( c_Set_Oinsert @ SV95 @ ( c_Set_Oinsert @ SV681 @ SV1246 @ SY5090 ) @ SY5090 )
= ( c_Set_Oinsert @ SV681 @ ( c_Set_Oinsert @ SV95 @ SV1246 @ SY5090 ) @ SY5090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3164,plain,
! [SV1247: $i,SV682: $i,SV96: $i] :
( ( ! [SY5091: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV96 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) @ SV1247 @ SV682 @ ( tc_fun @ SY5091 @ tc_bool ) ) @ ( tc_fun @ SY5091 @ tc_bool ) )
= SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3165,plain,
! [SV1248: $i,SV683: $i,SV97: $i] :
( ( ! [SY5092: $i,SY5093: $i,SY5094: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV97 @ SV683 @ SV1248 @ SY5092 ) @ SY5093 ) @ SY5094 )
= ( hAPP @ ( hAPP @ SV97 @ SY5094 ) @ SY5093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3166,plain,
! [SV1249: $i,SV684: $i,SV98: $i] :
( ( ! [SY5095: $i] :
( ( hAPP @ ( c_COMBK @ SV98 @ SV684 @ SV1249 ) @ SY5095 )
= SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3167,plain,
! [SV1250: $i,SV685: $i,SV99: $i] :
( ( ! [SY5096: $i,SY5097: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SY5096 @ ( tc_fun @ SY5097 @ tc_bool ) ) @ SY5097 @ SV99 ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SY5096 @ SV1250 @ ( tc_fun @ SY5097 @ tc_bool ) ) @ SY5097 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV685 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5097 @ tc_bool ) ) @ SV1250 ) @ SY5096 ) @ SY5097 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3168,plain,
! [SV1251: $i,SV686: $i,SV100: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV100 @ SV686 @ ( tc_fun @ SV1251 @ tc_bool ) ) @ SV686 @ ( tc_fun @ SV1251 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV100 @ SV686 @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3169,plain,
! [SV1252: $i,SV687: $i,SV101: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV101 )
| ( c_HOL_Oord__class_Oless @ SV687 @ SV1252 @ SV101 )
| ( c_lessequals @ SV1252 @ SV687 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3170,plain,
! [SV688: $i,SV102: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV102 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV688 @ SV688 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV688 @ SV688 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2591]) ).
thf(3171,plain,
! [SV689: $i,SV103: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV103 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV689 @ SV689 @ SV103 )
| ( c_lessequals @ SV689 @ SV689 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(3172,plain,
! [SV1253: $i,SV690: $i,SV104: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ SV690 @ SV1253 @ SV104 )
| ~ ( c_lessequals @ SV1253 @ SV690 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3173,plain,
! [SV1254: $i,SV691: $i,SV105: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV105 )
| ( c_lessequals @ SV691 @ SV1254 @ SV105 )
| ( c_HOL_Oord__class_Oless @ SV1254 @ SV691 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3174,plain,
! [SV1255: $i,SV692: $i,SV106: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV106 )
| ~ ( c_lessequals @ SV692 @ SV1255 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV1255 @ SV692 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3175,plain,
! [SV1256: $i,SV693: $i,SV107: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV107 )
| ( c_HOL_Oord__class_Oless @ SV693 @ SV1256 @ SV107 )
| ( c_lessequals @ SV1256 @ SV693 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3176,plain,
! [SV1257: $i,SV694: $i,SV108: $i] :
( ( ! [SY5098: $i] :
( ~ ( class_HOL_Oord @ SV108 )
| ~ ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SY5098 @ SV108 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SY5098 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3177,plain,
! [SV1258: $i,SV695: $i,SV109: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV109 )
| ~ ( c_lessequals @ SV695 @ SV1258 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1258 @ SV695 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3178,plain,
! [SV1259: $i,SV696: $i,SV110: $i] :
( ( ! [SY5099: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV110 ) @ ( hAPP @ SV696 @ SV1259 ) ) @ ( c_Set_Oimage @ SV696 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY5099 @ tc_bool ) ) @ SY5099 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3179,plain,
! [SV697: $i,SV111: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV111 ) )
= $true )
| ( ( ( ( c_Complete__Lattice_OSup__class_OSup @ SV697 @ SV111 )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 ) @ ( c_Orderings_Obot__class_Obot @ SV111 ) @ SV697 @ SV111 @ SV111 ) )
| ~ ( c_Finite__Set_Ofinite @ SV697 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(3180,plain,
! [SV1260: $i,SV698: $i,SV112: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
| ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3181,plain,
! [SV699: $i,SV113: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV113 ) )
= $true )
| ( ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV699 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV113 @ tc_bool ) ) @ SV113 ) @ SV113 )
= SV699 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(3182,plain,
! [SV1261: $i,SV700: $i,SV114: $i] :
( ( ! [SY5100: $i,SY5101: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV114 @ SV700 @ SV1261 @ SY5100 ) @ ( c_Set_Oimage @ SV114 @ SY5101 @ SV1261 @ SY5100 ) @ ( tc_fun @ SY5100 @ tc_bool ) ) @ ( c_Set_Oimage @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV700 @ SY5101 @ ( tc_fun @ SV1261 @ tc_bool ) ) @ SV1261 @ SY5100 ) @ ( tc_fun @ SY5100 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3183,plain,
! [SV1262: $i,SV701: $i,SV115: $i] :
( ( ! [SY5102: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV701 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV1262 ) @ SY5102 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV1262 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV701 ) @ SY5102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3184,plain,
! [SV1263: $i,SV702: $i,SV116: $i] :
( ( ! [SY5103: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV702 ) @ SV1263 ) ) @ SY5103 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV702 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV1263 ) @ SY5103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3185,plain,
! [SV1264: $i,SV703: $i,SV117: $i] :
( ( ! [SY5104: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ SV1264 ) ) @ SY5104 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV1264 ) @ SY5104 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3186,plain,
! [SV1265: $i,SV704: $i,SV118: $i] :
( ( ! [SY5105: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ SY5105 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ SY5105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3187,plain,
! [SV1266: $i,SV705: $i,SV119: $i] :
( ( ! [SY5106: $i] :
( ~ ( class_Lattices_Olattice @ SV119 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ SY5106 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ SY5106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3188,plain,
! [SV1267: $i,SV706: $i,SV120: $i] :
( ( ! [SY5107: $i] :
( ~ ( class_Lattices_Olattice @ SV120 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ SV1267 ) ) @ SY5107 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV1267 ) @ SY5107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3189,plain,
! [SV1268: $i,SV707: $i,SV121: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV121 @ tc_bool ) ) @ SV707 ) @ SV1268 )
= SV707 )
| ~ ( c_lessequals @ SV707 @ SV1268 @ ( tc_fun @ SV121 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3190,plain,
! [SV1269: $i,SV708: $i,SV122: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV122 @ tc_bool ) ) @ SV708 ) @ SV1269 )
= SV1269 )
| ~ ( c_lessequals @ SV1269 @ SV708 @ ( tc_fun @ SV122 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3191,plain,
! [SV1270: $i,SV709: $i,SV123: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV123 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SV709 ) @ SV1270 )
= SV709 )
| ~ ( c_lessequals @ SV709 @ SV1270 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3192,plain,
! [SV1271: $i,SV710: $i,SV124: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV124 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SV710 ) @ SV1271 )
= SV1271 )
| ~ ( c_lessequals @ SV1271 @ SV710 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3193,plain,
! [SV1272: $i,SV711: $i,SV125: $i] :
( ( ! [SY5108: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SV1272 ) @ SY5108 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SV1272 @ SY5108 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SV711 @ SY5108 @ ( tc_fun @ SV125 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3194,plain,
! [SV1273: $i,SV712: $i,SV126: $i] :
( ( c_lessequals @ SV126 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV712 @ tc_bool ) ) @ SV1273 ) @ SV126 ) @ ( tc_fun @ SV712 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3195,plain,
! [SV1274: $i,SV713: $i,SV127: $i] :
( ( c_lessequals @ SV127 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV713 @ tc_bool ) ) @ SV127 ) @ SV1274 ) @ ( tc_fun @ SV713 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3196,plain,
! [SV1275: $i,SV714: $i,SV128: $i] :
( ( ! [SY5109: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SV1275 ) @ SY5109 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SV1275 @ SY5109 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SY5109 @ ( tc_fun @ SV128 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3197,plain,
! [SV1276: $i,SV715: $i,SV129: $i] :
( ( ! [SY5110: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV129 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SY5110 @ SV129 )
| ~ ( c_lessequals @ SV1276 @ SY5110 @ SV129 )
| ~ ( c_lessequals @ SV715 @ SY5110 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3198,plain,
! [SV1277: $i,SV716: $i,SV130: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV130 )
| ( c_lessequals @ SV716 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 ) @ SV716 ) @ SV1277 ) @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3199,plain,
! [SV1278: $i,SV717: $i,SV131: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( c_lessequals @ SV717 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 ) @ SV1278 ) @ SV717 ) @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3200,plain,
! [SV1279: $i,SV718: $i,SV132: $i] :
( ( ! [SY5111: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SY5111 @ SV132 )
| ~ ( c_lessequals @ SV1279 @ SY5111 @ SV132 )
| ~ ( c_lessequals @ SV718 @ SY5111 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3201,plain,
! [SV1280: $i,SV719: $i,SV133: $i] :
( ( ! [SY5112: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV133 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SY5112 @ SV133 )
| ~ ( c_lessequals @ SV1280 @ SY5112 @ SV133 )
| ~ ( c_lessequals @ SV719 @ SY5112 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3202,plain,
! [SV1281: $i,SV720: $i,SV134: $i] :
( ( ~ ( class_Lattices_Olattice @ SV134 )
| ( c_lessequals @ SV720 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 ) @ SV1281 ) @ SV720 ) @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3203,plain,
! [SV1282: $i,SV721: $i,SV135: $i] :
( ( ~ ( class_Lattices_Olattice @ SV135 )
| ( c_lessequals @ SV721 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV135 ) @ SV721 ) @ SV1282 ) @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3204,plain,
! [SV1283: $i,SV722: $i,SV136: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV136 @ tc_bool ) ) @ SV722 ) @ SV1283 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV136 @ tc_bool ) ) @ SV1283 ) @ SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3205,plain,
! [SV1284: $i,SV723: $i,SV137: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV137 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV723 ) @ SV1284 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV1284 ) @ SV723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3206,plain,
! [SV1285: $i,SV724: $i,SV138: $i] :
( ( ~ ( class_Lattices_Olattice @ SV138 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV724 ) @ SV1285 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV1285 ) @ SV724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3207,plain,
! [SV1286: $i,SV725: $i,SV139: $i] :
( ( ! [SY5113: $i,SY5114: $i,SY5115: $i,SY5116: $i,SY5117: $i,SY5118: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SY5113 @ SY5113 @ tc_bool ) @ ( c_COMBC @ SY5114 @ SY5113 @ SY5113 @ tc_bool ) @ SY5115 @ SY5116 @ SY5117 @ SY5118 @ SY5113 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SY5114 @ SY5116 @ SY5115 @ SY5118 @ SY5117 @ SY5113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3208,plain,
! [SV1287: $i,SV726: $i,SV140: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV140 @ tc_bool ) ) @ SV726 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SV726 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= SV1287 )
| ~ ( c_lessequals @ SV726 @ SV1287 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3209,plain,
! [SV1288: $i,SV727: $i,SV141: $i] :
( ( ! [SY5119: $i] :
( ~ ( class_Lattices_Olattice @ SV141 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1288 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SY5119 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ SV1288 ) @ SY5119 ) ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3210,plain,
! [SV1289: $i,SV728: $i,SV142: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV142 @ SV728 @ ( tc_fun @ SV1289 @ tc_bool ) ) @ SV142 @ ( tc_fun @ SV1289 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3211,plain,
! [SV1290: $i,SV729: $i,SV143: $i] :
( ( ( c_Set_Oinsert @ SV143 @ ( c_HOL_Ominus__class_Ominus @ SV729 @ ( c_Set_Oinsert @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1290 @ tc_bool ) ) @ SV1290 ) @ ( tc_fun @ SV1290 @ tc_bool ) ) @ SV1290 )
= ( c_Set_Oinsert @ SV143 @ SV729 @ SV1290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3212,plain,
! [SV1291: $i,SV730: $i,SV144: $i] :
( ( ! [SY5120: $i] :
( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SY5120 ) @ ( tc_fun @ SY5120 @ tc_bool ) )
| ~ ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SY5120 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5120 @ tc_bool ) ) @ SY5120 ) @ ( tc_fun @ SY5120 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SY5120 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5120 ) @ SV730 ) @ SV1291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3213,plain,
! [SV1292: $i,SV731: $i,SV145: $i] :
( ( ! [SY5121: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV731 ) @ SV1292 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV1292 ) @ SY5121 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY5121 ) @ SV731 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV731 ) @ SV1292 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV1292 ) @ SY5121 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SY5121 ) @ SV731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3214,plain,
! [SV1293: $i,SV732: $i,SV146: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV146 @ SV732 @ SV1293 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1293 @ tc_bool ) ) @ SV1293 @ SV732 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV732 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3215,plain,
! [SV1294: $i,SV733: $i,SV147: $i] :
( ( ! [SY5122: $i,SY5123: $i,SY5124: $i] :
( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SY5122 @ SY5123 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SY5124 ) @ SY5123 @ SY5123 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5123 ) @ SV1294 ) @ SY5122 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SY5122 @ SY5124 @ SY5123 @ SY5123 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SY5123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3216,plain,
! [SV1295: $i,SV734: $i,SV148: $i] :
( ( ! [SY5125: $i,SY5126: $i] :
( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SV734 @ SV1295 @ ( tc_fun @ SY5125 @ tc_bool ) ) @ SY5125 @ SY5126 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SV734 @ SY5125 @ SY5126 ) @ ( c_Set_Oimage @ SV148 @ SV1295 @ SY5125 @ SY5126 ) @ ( tc_fun @ SY5126 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY5125 @ tc_bool ) ) @ SY5125 @ SY5126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3217,plain,
! [SV1296: $i,SV735: $i,SV149: $i] :
( ( ! [SY5127: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV149 ) @ SV735 ) @ SV1296 ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV735 @ SY5127 @ SV149 ) @ SV1296 @ ( tc_fun @ SV149 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3218,plain,
! [SV1297: $i,SV736: $i,SV150: $i] :
( ( ! [SY5128: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV150 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV736 @ ( c_COMBK @ SV1297 @ SV150 @ SY5128 ) @ SY5128 @ SV150 )
= SV1297 )
| ( SV736
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5128 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3219,plain,
! [SV1298: $i,SV737: $i,SV151: $i] :
( ( ! [SY5129: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV151 @ SV737 @ SV1298 ) @ SY5129 ) )
| ~ ( hBOOL @ ( hAPP @ SV737 @ SY5129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3220,plain,
! [SV1299: $i,SV738: $i,SV152: $i] :
( ( ! [SY5130: $i,SY5131: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SV738 ) @ ( c_Set_Oimage @ SV152 @ SV1299 @ SY5130 @ SY5131 ) @ SY5131 )
= ( c_Set_Oimage @ SV152 @ SV1299 @ SY5130 @ SY5131 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5130 ) @ SV738 ) @ SV1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3221,plain,
! [SV1300: $i,SV739: $i,SV153: $i] :
( ( ! [SY5132: $i] :
( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SV739 @ SV1300 @ SY5132 ) @ ( tc_fun @ SY5132 @ tc_bool ) )
| ~ ( c_lessequals @ SV153 @ SV1300 @ ( tc_fun @ SY5132 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5132 ) @ SV739 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3222,plain,
! [SV1301: $i,SV740: $i,SV154: $i] :
( ( ! [SY5133: $i] :
( ( c_lessequals @ SV154 @ SV740 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1301 ) @ SY5133 ) @ SV154 ) )
| ~ ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SY5133 @ SV740 @ SV1301 ) @ ( tc_fun @ SV1301 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3223,plain,
! [SV1302: $i,SV741: $i,SV155: $i] :
( ( ! [SY5134: $i] :
( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SV741 @ SV1302 @ SY5134 ) @ ( tc_fun @ SY5134 @ tc_bool ) )
| ~ ( c_lessequals @ SV155 @ SV1302 @ ( tc_fun @ SY5134 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5134 ) @ SV741 ) @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3224,plain,
! [SV1303: $i,SV742: $i,SV156: $i] :
( ( ! [SY5135: $i] :
( ( c_lessequals @ SV156 @ SV742 @ ( tc_fun @ SV1303 @ tc_bool ) )
| ~ ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SY5135 @ SV742 @ SV1303 ) @ ( tc_fun @ SV1303 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1303 ) @ SY5135 ) @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3225,plain,
! [SV1304: $i,SV743: $i,SV157: $i] :
( ( ! [SY5136: $i,SY5137: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SV743 @ SV1304 @ SY5136 ) @ ( c_Set_Ovimage @ SV157 @ SY5137 @ SV1304 @ SY5136 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_lessequals @ SV743 @ SY5137 @ ( tc_fun @ SY5136 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3226,plain,
! [SV1305: $i,SV744: $i,SV158: $i] :
( ( ! [SY5138: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1305 @ SY5138 @ SV158 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ SY5138 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV158 ) @ SV1305 ) @ SV744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3227,plain,
! [SV1306: $i,SV745: $i,SV159: $i] :
( ( ! [SY5139: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV745 @ SV1306 @ SV159 ) ) @ SY5139 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ SV1306 ) @ SY5139 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV159 ) @ SV745 ) @ SY5139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3228,plain,
! [SV1307: $i,SV746: $i,SV160: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV160 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV746 @ SV1307 @ ( tc_fun @ SV160 @ tc_bool ) ) ) @ SV1307 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV160 @ tc_bool ) ) @ SV746 ) @ SV1307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3229,plain,
! [SV1308: $i,SV747: $i,SV161: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV161 @ tc_bool ) ) @ SV747 ) @ ( c_HOL_Ominus__class_Ominus @ SV1308 @ SV747 @ ( tc_fun @ SV161 @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV161 @ tc_bool ) ) @ SV747 ) @ SV1308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3230,plain,
! [SV1309: $i,SV748: $i,SV162: $i] :
( ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
| ~ ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV748 @ SV1309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3231,plain,
! [SV1310: $i,SV749: $i,SV163: $i] :
( ( ! [SY5140: $i] :
( ~ ( class_Lattices_Olattice @ SV163 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ SV1310 ) ) @ SY5140 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV1310 ) @ SY5140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3232,plain,
! [SV1311: $i,SV750: $i,SV164: $i] :
( ( ! [SY5141: $i] :
( ~ ( class_Lattices_Olattice @ SV164 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ SY5141 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ SY5141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3233,plain,
! [SV1312: $i,SV751: $i,SV165: $i] :
( ( ! [SY5142: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV165 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ SY5142 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ SY5142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3234,plain,
! [SV1313: $i,SV752: $i,SV166: $i] :
( ( ! [SY5143: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV166 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ SV1313 ) ) @ SY5143 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV1313 ) @ SY5143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3235,plain,
! [SV1314: $i,SV753: $i,SV167: $i] :
( ( ! [SY5144: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV753 ) @ SV1314 ) ) @ SY5144 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV753 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV1314 ) @ SY5144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3236,plain,
! [SV1315: $i,SV754: $i,SV168: $i] :
( ( ! [SY5145: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV754 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV1315 ) @ SY5145 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV1315 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV754 ) @ SY5145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3237,plain,
! [SV755: $i,SV169: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV169 ) )
= $true )
| ( ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV755 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV169 @ tc_bool ) ) @ SV169 ) @ SV169 )
= SV755 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(3238,plain,
! [SV1316: $i,SV756: $i,SV170: $i] :
( ( ( c_Finite__Set_Ofinite @ SV170 @ SV756 )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV756 @ tc_bool ) ) @ SV170 ) @ SV1316 ) @ SV756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3239,plain,
! [SV1317: $i,SV757: $i,SV171: $i] :
( ( ( c_Finite__Set_Ofinite @ SV171 @ SV757 )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV757 @ tc_bool ) ) @ SV1317 ) @ SV171 ) @ SV757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3240,plain,
! [SV1318: $i,SV758: $i,SV172: $i] :
( ( ! [SY5146: $i,SY5147: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ SV172 @ SV758 @ SV1318 @ SY5146 ) @ SY5147 @ SV1318 @ SY5146 )
= ( c_Map_Orestrict__map @ SV172 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1318 @ tc_bool ) ) @ SV758 ) @ SY5147 ) @ SV1318 @ SY5146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3241,plain,
! [SV1319: $i,SV759: $i,SV173: $i] :
( ( ! [SY5148: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV173 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV759 @ tc_bool ) ) @ SV1319 @ SV759 @ ( tc_fun @ SV173 @ tc_bool ) ) ) @ SY5148 )
= SY5148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3242,plain,
! [SV1320: $i,SV760: $i,SV174: $i] :
( ( ! [SY5149: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV174 @ tc_bool ) ) @ SV760 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SY5149 @ SV1320 @ ( tc_fun @ SV174 @ tc_bool ) ) )
= SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3243,plain,
! [SV1321: $i,SV761: $i,SV175: $i] :
( ( ! [SY5150: $i] :
( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SV1321 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SY5150 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SY5150 ) @ SV761 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SY5150 @ SV761 @ SV1321 ) @ ( tc_fun @ SV1321 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3244,plain,
! [SV1322: $i,SV762: $i,SV176: $i] :
( ( ! [SY5151: $i] :
( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SV1322 @ SY5151 ) @ ( tc_fun @ SY5151 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV1322 @ ( tc_fun @ SY5151 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5151 ) @ SV762 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5151 ) @ SV762 ) @ SV1322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3245,plain,
! [SV1323: $i,SV763: $i,SV177: $i] :
( ( ! [SY5152: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ ( c_HOL_Ominus__class_Ominus @ SV1323 @ SY5152 @ ( tc_fun @ SV177 @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ SY5152 ) @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3246,plain,
! [SV1324: $i,SV764: $i,SV178: $i] :
( ( ! [SY5153: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV764 @ SV1324 @ ( tc_fun @ SV178 @ tc_bool ) ) ) @ SY5153 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SV764 ) @ SY5153 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SV1324 ) @ SY5153 ) @ ( tc_fun @ SV178 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3247,plain,
! [SV1325: $i,SV765: $i,SV179: $i] :
( ( ! [SY5154: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV179 @ SV765 @ SV1325 ) @ SY5154 @ SV1325 @ SV765 )
= ( c_Set_Oinsert @ SV179 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV765 ) )
| ( SY5154
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3248,plain,
! [SV1326: $i,SV766: $i,SV180: $i] :
( ( ! [SY5155: $i] :
( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SV1326 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1326 ) @ SY5155 ) @ SV766 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SY5155 @ SV766 @ SV1326 ) @ ( tc_fun @ SV1326 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3249,plain,
! [SV1327: $i,SV767: $i,SV181: $i] :
( ( ! [SY5156: $i] :
( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SV1327 @ SY5156 ) @ ( tc_fun @ SY5156 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5156 ) @ SV767 ) @ SV1327 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1327 @ ( tc_fun @ SY5156 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3250,plain,
! [SV1328: $i,SV768: $i,SV182: $i] :
( ( ! [SY5157: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV182 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SV1328 @ SY5157 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV1328 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SY5157 @ SV182 @ SV182 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY5157 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3251,plain,
! [SV1329: $i,SV769: $i,SV183: $i] :
( ( ! [SY5158: $i,SY5159: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY5158 @ SY5159 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SY5159 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SV183 @ SY5158 @ ( tc_fun @ SV1329 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3252,plain,
! [SV770: $i,SV184: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV184 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV184 ) @ SV770 ) @ ( c_Orderings_Otop__class_Otop @ SV184 ) )
= SV770 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(3253,plain,
! [SV771: $i,SV185: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV185 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV185 ) @ ( c_Orderings_Otop__class_Otop @ SV185 ) ) @ SV771 )
= SV771 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(3254,plain,
! [SV1330: $i,SV774: $i,SV188: $i] :
( ( ! [SY5160: $i] :
( ( c_Set_Oimage @ SV188 @ ( c_Set_Ovimage @ SV188 @ SV774 @ SV1330 @ SY5160 ) @ SV1330 @ SY5160 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5160 @ tc_bool ) ) @ SV774 ) @ ( c_Set_Oimage @ SV188 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1330 @ tc_bool ) ) @ SV1330 @ SY5160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3255,plain,
! [SV1331: $i,SV775: $i,SV189: $i] :
( ( ! [SY5161: $i] :
( ~ ( class_Lattices_Olattice @ SV189 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ SV1331 ) @ SY5161 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1331 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SY5161 ) ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3256,plain,
! [SV1332: $i,SV776: $i,SV190: $i] :
( ( ! [SY5162: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV776 ) @ SV1332 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SY5162 ) @ SV1332 ) @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV776 ) @ SV1332 ) @ SY5162 @ ( tc_fun @ SV190 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3257,plain,
! [SV1333: $i,SV777: $i,SV191: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV191 )
| ( c_HOL_Oord__class_Oless @ SV777 @ SV1333 @ SV191 )
| ( c_lessequals @ SV1333 @ SV777 @ SV191 )
| ~ ( c_lessequals @ SV777 @ SV1333 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3258,plain,
! [SV778: $i,SV192: $i] :
( ( c_HOL_Oord__class_Oless @ SV192 @ SV192 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(3259,plain,
! [SV1334: $i,SV779: $i,SV193: $i] :
( ( ! [SY5163: $i] :
( ~ ( class_HOL_Oord @ SV193 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SY5163 @ SV193 ) )
| ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SY5163 @ SV193 ) )
| ~ ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SY5163 @ SV193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3260,plain,
! [SV780: $i,SV194: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV194 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV780 @ SV780 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(3261,plain,
! [SV781: $i,SV195: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV195 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV781 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2684]) ).
thf(3262,plain,
! [SV782: $i,SV196: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV196 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(3263,plain,
! [SV1335: $i,SV783: $i,SV197: $i] :
( ( ~ ( class_Lattices_Olattice @ SV197 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 ) @ SV783 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV197 ) @ SV783 ) @ SV1335 ) )
= SV783 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3264,plain,
! [SV199: $i] :
( ( ( class_Orderings_Otop @ SV199 )
= $false )
| ( ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ SV199 ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(3265,plain,
! [SV1336: $i,SV785: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV785 @ ( tc_fun @ SV1336 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1336 ) @ SV1336 @ ( tc_fun @ SV1336 @ tc_bool ) @ tc_bool ) @ SV200 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1336 ) @ SV1336 @ ( tc_fun @ SV1336 @ tc_bool ) @ tc_bool ) @ SV785 ) @ ( tc_fun @ SV1336 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3266,plain,
! [SV1337: $i,SV786: $i,SV201: $i] :
( ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV786 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV1337 ) @ ( tc_fun @ SV201 @ tc_bool ) )
| ~ ( c_lessequals @ SV786 @ SV1337 @ ( tc_fun @ SV201 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3267,plain,
! [SV1338: $i,SV787: $i,SV202: $i] :
( ( ! [SY5164: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SV1338 @ SY5164 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV1338 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SY5164 @ SV202 @ SV202 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY5164 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3268,plain,
! [SV1339: $i,SV788: $i,SV203: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV1339 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ SV788 @ SV203 )
| ( SV1339 = SV788 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3269,plain,
! [SV1340: $i,SV789: $i,SV204: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV204 )
| ( SV789 = SV1340 )
| ( c_HOL_Oord__class_Oless @ SV1340 @ SV789 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SV1340 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3270,plain,
! [SV1341: $i,SV790: $i,SV205: $i] :
( ( ( SV205 = SV790 )
| ~ ( c_lessequals @ SV790 @ SV205 @ ( tc_fun @ SV1341 @ tc_bool ) )
| ~ ( c_lessequals @ SV205 @ SV790 @ ( tc_fun @ SV1341 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3271,plain,
! [SV1342: $i,SV791: $i,SV206: $i] :
( ( ( SV206 = SV791 )
| ~ ( c_lessequals @ SV791 @ SV206 @ ( tc_fun @ SV1342 @ tc_bool ) )
| ~ ( c_lessequals @ SV206 @ SV791 @ ( tc_fun @ SV1342 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3272,plain,
! [SV1343: $i,SV792: $i,SV207: $i] :
( ( ~ ( class_Orderings_Oorder @ SV207 )
| ( SV792 = SV1343 )
| ~ ( c_lessequals @ SV1343 @ SV792 @ SV207 )
| ~ ( c_lessequals @ SV792 @ SV1343 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3273,plain,
! [SV1344: $i,SV793: $i,SV208: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV208 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV1344 @ SV208 )
| ( c_HOL_Oord__class_Oless @ SV1344 @ SV793 @ SV208 )
| ( SV1344 = SV793 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3274,plain,
! [SV1345: $i,SV794: $i,SV209: $i] :
( ( ~ ( class_Orderings_Oorder @ SV209 )
| ( SV794 = SV1345 )
| ~ ( c_lessequals @ SV1345 @ SV794 @ SV209 )
| ~ ( c_lessequals @ SV794 @ SV1345 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3275,plain,
! [SV1346: $i,SV795: $i,SV210: $i] :
( ( ~ ( class_Orderings_Oorder @ SV210 )
| ( SV795 = SV1346 )
| ~ ( c_lessequals @ SV795 @ SV1346 @ SV210 )
| ~ ( c_lessequals @ SV1346 @ SV795 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3276,plain,
! [SV1347: $i,SV796: $i,SV211: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV211 )
| ( c_HOL_Oord__class_Oless @ SV796 @ SV1347 @ SV211 )
| ( SV1347 = SV796 )
| ( c_HOL_Oord__class_Oless @ SV1347 @ SV796 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3277,plain,
! [SV1348: $i,SV797: $i,SV212: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV212 )
| ( SV797 = SV1348 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SV1348 @ SV212 )
| ( c_HOL_Oord__class_Oless @ SV1348 @ SV797 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3278,plain,
! [SV1349: $i,SV798: $i,SV213: $i] :
( ( ~ ( class_Lattices_Olattice @ SV213 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 ) @ SV798 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 ) @ SV798 ) @ SV1349 ) )
= SV798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3279,plain,
! [SV1350: $i,SV799: $i,SV214: $i] :
( ( ! [SY5165: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV214 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SV1350 ) @ SY5165 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SY5165 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3280,plain,
! [SV1351: $i,SV800: $i,SV215: $i] :
( ( ! [SY5166: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV215 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SV1351 ) @ SY5166 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ SV800 @ SY5166 @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3281,plain,
! [SV1352: $i,SV801: $i,SV216: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV216 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV801 @ SV1352 @ ( tc_fun @ SV216 @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV216 @ tc_bool ) ) @ SV801 ) @ SV1352 ) )
= SV801 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3282,plain,
! [SV1353: $i,SV802: $i,SV217: $i] :
( ( ( c_lessequals @ SV217 @ SV802 @ ( tc_fun @ SV1353 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV217 @ SV802 @ ( tc_fun @ SV1353 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3283,plain,
! [SV1354: $i,SV803: $i,SV218: $i] :
( ( ! [SY5167: $i] :
( ~ ( class_HOL_Oord @ SV218 )
| ( c_lessequals @ SV803 @ SV1354 @ ( tc_fun @ SY5167 @ SV218 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1354 @ ( tc_fun @ SY5167 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3284,plain,
! [SV1355: $i,SV804: $i,SV219: $i] :
( ( ~ ( class_Orderings_Oorder @ SV219 )
| ( c_lessequals @ SV804 @ SV1355 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1355 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3285,plain,
! [SV1356: $i,SV805: $i,SV220: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV220 )
| ( c_lessequals @ SV805 @ SV1356 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV805 @ SV1356 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3286,plain,
! [SV1357: $i,SV806: $i,SV221: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV221 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SV806 ) @ SV1357 )
= SV806 )
| ~ ( c_lessequals @ SV1357 @ SV806 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3287,plain,
! [SV1358: $i,SV807: $i,SV222: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV222 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SV807 ) @ SV1358 )
= SV1358 )
| ~ ( c_lessequals @ SV807 @ SV1358 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3288,plain,
! [SV1359: $i,SV808: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV223 @ tc_bool ) ) @ SV808 ) @ SV1359 )
= SV1359 )
| ~ ( c_lessequals @ SV808 @ SV1359 @ ( tc_fun @ SV223 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3289,plain,
! [SV1360: $i,SV809: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV224 @ tc_bool ) ) @ SV809 ) @ SV1360 )
= SV809 )
| ~ ( c_lessequals @ SV1360 @ SV809 @ ( tc_fun @ SV224 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3290,plain,
! [SV1361: $i,SV810: $i,SV225: $i] :
( ( ! [SY5168: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV225 @ SV810 @ SV1361 @ SY5168 ) @ SY5168 )
| ~ ( c_Finite__Set_Ofinite @ SV810 @ SV1361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3291,plain,
! [SV1362: $i,SV811: $i,SV226: $i] :
( ( ! [SY5169: $i] :
( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SY5169 ) @ ( tc_fun @ SY5169 @ tc_bool ) )
| ~ ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SY5169 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5169 ) @ SV811 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SY5169 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3292,plain,
! [SV1363: $i,SV812: $i,SV227: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV227 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
| ~ ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
| ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3293,plain,
! [SV1364: $i,SV813: $i,SV228: $i] :
( ( ! [SY5170: $i,SY5171: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV228 @ SV813 @ SV1364 ) @ SY5170 @ SV1364 @ ( tc_fun @ SY5171 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5171 @ tc_bool ) ) @ ( hAPP @ SY5170 @ SV228 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV813 @ SY5170 @ SV1364 @ ( tc_fun @ SY5171 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3294,plain,
! [SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY5172: $i,SY5173: $i,SY5174: $i,SY5175: $i,SY5176: $i,SY5177: $i,SY5178: $i,SY5179: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SY5172 ) )
= ( hAPP @ ( hAPP @ SY5173 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5174 @ SV229 @ SY5175 @ SY5176 @ SY5177 @ SY5173 @ SY5178 @ SY5179 @ SY5172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3295,plain,
! [SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY5180: $i,SY5181: $i,SY5182: $i,SY5183: $i,SY5184: $i,SY5185: $i,SY5186: $i,SY5187: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SY5180 ) )
= ( hAPP @ ( hAPP @ SY5181 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SY5182 @ SY5183 @ SY5184 @ SY5181 @ SY5185 @ SY5186 @ SY5187 @ SY5180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3296,plain,
! [SV1367: $i,SV816: $i,SV231: $i] :
( ( c_Finite__Set_Ofold1Set @ SV231 @ ( c_Set_Oinsert @ SV816 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1367 @ tc_bool ) ) @ SV1367 ) @ SV816 @ SV1367 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3297,plain,
! [SV1368: $i,SV817: $i,SV232: $i] :
( ( ! [SY5188: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SV1368 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SY5188 @ SV1368 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY5188 @ SV817 @ SV1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3298,plain,
! [SV1369: $i,SV818: $i,SV233: $i] :
( ( ! [SY5189: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV818 @ SV1369 @ SV233 ) ) @ SY5189 )
= ( c_Set_Oinsert @ SV818 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ SV1369 ) @ SY5189 ) @ SV233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV233 ) @ SV818 ) @ SY5189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3299,plain,
! [SV1370: $i,SV819: $i,SV234: $i] :
( ( ! [SY5190: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ ( c_Set_Oinsert @ SV1370 @ SY5190 @ SV234 ) )
= ( c_Set_Oinsert @ SV1370 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ SY5190 ) @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV234 ) @ SV1370 ) @ SV819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3300,plain,
! [SV1371: $i,SV820: $i,SV235: $i] :
( ( ! [SY5191: $i,SY5192: $i] :
( ( c_Set_Oimage @ SV235 @ ( c_Set_Oinsert @ SV820 @ SV1371 @ SY5191 ) @ SY5191 @ SY5192 )
= ( c_Set_Oinsert @ ( hAPP @ SV235 @ SV820 ) @ ( c_Set_Oimage @ SV235 @ SV1371 @ SY5191 @ SY5192 ) @ SY5192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3301,plain,
! [SV1372: $i,SV822: $i,SV237: $i] :
( ( ! [SY5193: $i,SY5194: $i,SY5195: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV237 @ SV822 @ SV1372 @ SY5193 @ SY5194 ) @ SY5195 )
= ( hAPP @ SV822 @ ( hAPP @ SV237 @ SY5195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3302,plain,
! [SV1373: $i,SV823: $i,SV238: $i] :
( ( ! [SY5196: $i,SY5197: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SY5196 ) @ SY5197 ) @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV1373 @ SY5197 @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV823 @ SY5196 @ ( tc_fun @ SV238 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3303,plain,
! [SV1374: $i,SV824: $i,SV239: $i] :
( ( ~ ( class_Lattices_Olattice @ SV239 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 ) @ SV824 ) @ SV1374 ) @ SV824 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3304,plain,
! [SV1375: $i,SV825: $i,SV240: $i] :
( ( ~ ( class_Lattices_Olattice @ SV240 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV240 ) @ SV825 ) @ SV1375 ) @ SV1375 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3305,plain,
! [SV1376: $i,SV826: $i,SV241: $i] :
( ( ! [SY5198: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV241 )
| ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SY5198 ) @ SV241 )
| ~ ( c_lessequals @ SV826 @ SY5198 @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3306,plain,
! [SV1377: $i,SV827: $i,SV242: $i] :
( ( ! [SY5199: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV242 )
| ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SY5199 ) @ SV242 )
| ~ ( c_lessequals @ SV827 @ SY5199 @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3307,plain,
! [SV1378: $i,SV828: $i,SV243: $i] :
( ( ! [SY5200: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV243 )
| ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SY5200 ) @ SV243 )
| ~ ( c_lessequals @ SV828 @ SY5200 @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3308,plain,
! [SV1379: $i,SV829: $i,SV244: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV244 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV244 ) @ SV829 ) @ SV1379 ) @ SV1379 @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3309,plain,
! [SV1380: $i,SV830: $i,SV245: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV245 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 ) @ SV830 ) @ SV1380 ) @ SV830 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3310,plain,
! [SV1381: $i,SV831: $i,SV246: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV246 @ tc_bool ) ) @ SV831 ) @ SV1381 ) @ SV831 @ ( tc_fun @ SV246 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3311,plain,
! [SV1382: $i,SV832: $i,SV247: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV247 @ tc_bool ) ) @ SV832 ) @ SV1382 ) @ SV1382 @ ( tc_fun @ SV247 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3312,plain,
! [SV1383: $i,SV833: $i,SV248: $i] :
( ( ! [SY5201: $i] :
( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SV1383 ) @ SY5201 ) @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY5201 @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV1383 @ ( tc_fun @ SV833 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3313,plain,
! [SV1384: $i,SV834: $i,SV249: $i] :
( ( ! [SY5202: $i] :
( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV1384 ) @ SY5202 ) @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SY5202 @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SV1384 @ ( tc_fun @ SV834 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3314,plain,
! [SV836: $i,SV251: $i] :
( ( ( ~ ( class_Orderings_Otop @ SV251 ) )
= $true )
| ( ( c_lessequals @ SV836 @ ( c_Orderings_Otop__class_Otop @ SV251 ) @ SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(3315,plain,
! [SV1385: $i,SV837: $i,SV252: $i] :
( ( ! [SY5203: $i,SY5204: $i,SY5205: $i,SY5206: $i] :
( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SV837 @ SV1385 @ SY5203 @ SY5204 @ SY5205 ) @ SY5204 @ SY5206 @ SY5205 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SV837 @ SY5204 @ SY5206 @ SY5203 ) @ SV1385 @ SY5203 @ SY5206 @ SY5205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3316,plain,
! [SV1386: $i,SV838: $i,SV253: $i] :
( ( ! [SY5207: $i] :
( ( c_Set_Oinsert @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV838 @ tc_bool ) ) @ SV1386 @ SV838 @ ( tc_fun @ SY5207 @ tc_bool ) ) @ SY5207 )
= ( c_Set_Oinsert @ SV253 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5207 @ tc_bool ) ) @ SY5207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3317,plain,
! [SV1387: $i,SV839: $i,SV254: $i] :
( ( ! [SY5208: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ SV839 ) @ SV1387 ) ) @ SY5208 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV839 ) @ SY5208 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV1387 ) @ SY5208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3318,plain,
! [SV1388: $i,SV840: $i,SV255: $i] :
( ( ! [SY5209: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV255 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ SV1388 ) @ SY5209 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1388 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SY5209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3319,plain,
! [SV1389: $i,SV841: $i,SV256: $i] :
( ( ~ ( class_HOL_Ominus @ SV256 )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV841 @ SV1389 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV841 @ v_x ) @ ( hAPP @ SV1389 @ v_x ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3320,plain,
! [SV1390: $i,SV842: $i,SV257: $i] :
( ( ! [SY5210: $i] :
( ( c_lessequals @ SV257 @ SV842 @ ( tc_fun @ SV1390 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1390 @ tc_bool ) ) @ SY5210 ) @ SV842 ) @ ( tc_fun @ SV1390 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3321,plain,
! [SV1391: $i,SV843: $i,SV258: $i] :
( ( ! [SY5211: $i] :
( ( c_lessequals @ SV258 @ SV843 @ ( tc_fun @ SV1391 @ tc_bool ) )
| ~ ( c_lessequals @ SV258 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1391 @ tc_bool ) ) @ SV843 ) @ SY5211 ) @ ( tc_fun @ SV1391 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3322,plain,
! [SV1392: $i,SV844: $i,SV259: $i] :
( ( ! [SY5212: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV259 )
| ( c_lessequals @ SV844 @ SV1392 @ SV259 )
| ~ ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SV1392 ) @ SY5212 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3323,plain,
! [SV1393: $i,SV845: $i,SV260: $i] :
( ( ! [SY5213: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV260 )
| ( c_lessequals @ SV845 @ SV1393 @ SV260 )
| ~ ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SY5213 ) @ SV1393 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3324,plain,
! [SV1394: $i,SV846: $i,SV261: $i] :
( ( ! [SY5214: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV261 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SV1394 ) @ SY5214 @ SV261 )
| ~ ( c_lessequals @ SV846 @ SY5214 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3325,plain,
! [SV1395: $i,SV847: $i,SV262: $i] :
( ( ! [SY5215: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV262 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SV1395 ) @ SY5215 @ SV262 )
| ~ ( c_lessequals @ SV1395 @ SY5215 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3326,plain,
! [SV1396: $i,SV848: $i,SV263: $i] :
( ( ! [SY5216: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV263 )
| ( c_lessequals @ SV848 @ SV1396 @ SV263 )
| ~ ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SV1396 ) @ SY5216 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3327,plain,
! [SV1397: $i,SV849: $i,SV264: $i] :
( ( ! [SY5217: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV264 )
| ( c_lessequals @ SV849 @ SV1397 @ SV264 )
| ~ ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SY5217 ) @ SV1397 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3328,plain,
! [SV1398: $i,SV851: $i,SV266: $i] :
( ( ! [SY5218: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ SV851 ) @ SV1398 ) @ SY5218 @ ( tc_fun @ SV266 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SY5218 @ ( tc_fun @ SV266 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1398 @ SY5218 @ ( tc_fun @ SV266 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3329,plain,
! [SV1399: $i,SV852: $i,SV267: $i] :
( ( ! [SY5219: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV267 )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SY5219 ) @ SV852 ) @ SV267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SY5219 ) @ SV1399 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3330,plain,
! [SV1400: $i,SV853: $i,SV268: $i] :
( ( ! [SY5220: $i,SY5221: $i,SY5222: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ SV268 @ SV853 @ SV1400 @ SY5220 @ SY5221 ) @ SY5222 @ SY5221 @ SY5220 )
= ( c_Set_Ovimage @ SV853 @ ( c_Set_Ovimage @ SV268 @ SY5222 @ SV1400 @ SY5220 ) @ SY5221 @ SV1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3331,plain,
! [SV1401: $i,SV854: $i,SV269: $i] :
( ( ( c_Set_Oinsert @ SV269 @ SV854 @ SV1401 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1401 @ tc_bool ) ) @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV1401 ) @ SV1401 @ SV1401 @ tc_bool ) @ SV269 ) @ SV1401 ) ) @ SV854 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3332,plain,
! [SV1402: $i,SV855: $i,SV270: $i] :
( ( ! [SY5223: $i] :
( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SY5223 ) @ ( tc_fun @ SY5223 @ tc_bool ) )
| ~ ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SY5223 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5223 @ tc_bool ) ) @ SY5223 ) @ ( tc_fun @ SY5223 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SY5223 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SY5223 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3333,plain,
! [SV1403: $i,SV856: $i,SV271: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV271 @ tc_bool ) ) @ SV856 ) @ SV1403 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV271 @ tc_bool ) ) @ SV1403 ) @ SV856 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3334,plain,
! [SV1404: $i,SV857: $i,SV272: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV857 ) @ SV1404 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV1404 ) @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3335,plain,
! [SV1405: $i,SV858: $i,SV273: $i] :
( ( ~ ( class_Lattices_Olattice @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV858 ) @ SV1405 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV1405 ) @ SV858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3336,plain,
! [SV1406: $i,SV860: $i,SV275: $i] :
( ( ( c_Set_Oinsert @ SV275 @ SV860 @ SV1406 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1406 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV275 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) ) @ SV860 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3337,plain,
! [SV1407: $i,SV861: $i,SV276: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SV861 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SV861 ) @ SV1407 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV276 @ tc_bool ) ) @ SV861 ) @ SV1407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3338,plain,
! [SV1408: $i,SV862: $i,SV277: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SV1408 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SV1408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3339,plain,
! [SV1409: $i,SV863: $i,SV278: $i] :
( ( ~ ( class_Lattices_Olattice @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SV1409 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SV1409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3340,plain,
! [SV1410: $i,SV864: $i,SV279: $i] :
( ( ! [SY5224: $i,SY5225: $i,SY5226: $i] :
( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SY5224 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5225 @ tc_bool ) ) @ SY5225 ) @ ( tc_fun @ SY5225 @ tc_bool ) ) @ SY5225 ) @ SY5226 @ SY5225 @ SY5225 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5225 ) @ SV1410 ) @ SY5224 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5225 ) @ SV864 ) @ SY5224 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SY5224 @ SY5226 @ SY5225 @ SY5225 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SY5225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3341,plain,
! [SV1411: $i,SV865: $i,SV280: $i] :
( ( ! [SY5227: $i,SY5228: $i,SY5229: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SY5227 @ SY5228 ) @ SY5229 @ SY5228 @ SY5227 )
| ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SY5229 @ SY5228 @ SV1411 ) @ SV1411 @ SY5227 )
| ~ ( c_Fun_Oinj__on @ SV865 @ SY5229 @ SY5228 @ SV1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3342,plain,
! [SV1412: $i,SV866: $i,SV281: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV281 @ tc_bool ) ) @ SV866 ) @ ( c_HOL_Ominus__class_Ominus @ SV1412 @ SV866 @ ( tc_fun @ SV281 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV281 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3343,plain,
! [SV867: $i,SV282: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV282 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV867 @ SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(3344,plain,
! [SV1413: $i,SV868: $i,SV283: $i] :
( ( ! [SY5230: $i,SY5231: $i,SY5232: $i,SY5233: $i] :
( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SY5230 @ SY5231 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SY5232 ) @ SY5231 @ SY5233 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SY5230 @ SY5232 @ SY5231 @ SY5233 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5231 ) @ SV1413 ) @ SY5230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3345,plain,
! [SV1414: $i,SV869: $i,SV284: $i] :
( ( ! [SY5234: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ SV1414 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV284 @ tc_bool ) ) @ SV1414 ) @ ( c_Collect @ SY5234 @ SV284 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3346,plain,
! [SV1415: $i,SV870: $i,SV285: $i] :
( ( ! [SY5235: $i,SY5236: $i] :
( ( c_Set_Ovimage @ SV285 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV870 @ tc_bool ) ) @ SV1415 ) @ SY5235 ) @ SY5236 @ SV870 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5236 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV285 @ SV1415 @ SY5236 @ SV870 ) ) @ ( c_Set_Ovimage @ SV285 @ SY5235 @ SY5236 @ SV870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3347,plain,
! [SV1416: $i,SV871: $i,SV286: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV871 @ ( c_Set_Oinsert @ SV1416 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV286 @ tc_bool ) ) @ SV286 ) @ SV286 ) @ SV286 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 ) @ SV871 ) @ SV1416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3348,plain,
! [SV1417: $i,SV872: $i,SV287: $i] :
( ( ! [SY5237: $i,SY5238: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SV1417 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SY5237 @ ( c_Set_Oinsert @ SV1417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5238 @ tc_bool ) ) @ SY5238 ) @ ( tc_fun @ SY5238 @ tc_bool ) ) @ SY5238 @ SV287 ) ) )
| ~ ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SV1417 @ SY5237 @ SY5238 ) @ SY5238 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3349,plain,
! [SV1418: $i,SV873: $i,SV288: $i] :
( ( ! [SY5239: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV288 @ SV873 @ SV1418 ) @ SY5239 @ ( tc_fun @ SV1418 @ tc_bool ) )
= ( c_Set_Oinsert @ SV288 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SY5239 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV288 ) @ SY5239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3350,plain,
! [SV1419: $i,SV874: $i,SV289: $i] :
( ( ! [SY5240: $i,SY5241: $i,SY5242: $i,SY5243: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SY5240 ) @ SY5241 ) @ SY5242 @ SY5243 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SY5240 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5242 @ tc_bool ) ) @ SY5242 ) @ ( tc_fun @ SY5242 @ tc_bool ) ) @ SY5241 @ SY5242 @ SY5243 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5242 ) @ SY5240 ) @ SV1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3351,plain,
! [SV1420: $i,SV875: $i,SV290: $i] :
( ( ! [SY5244: $i] :
( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SV1420 @ SY5244 ) @ ( tc_fun @ SY5244 @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ SV1420 @ ( tc_fun @ SY5244 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5244 @ tc_bool ) ) @ SY5244 ) @ ( tc_fun @ SY5244 @ tc_bool ) ) @ SV1420 @ ( tc_fun @ SY5244 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3352,plain,
! [SV1421: $i,SV876: $i,SV291: $i] :
( ( ! [SY5245: $i] :
( ( hBOOL @ ( hAPP @ SV291 @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SY5245 ) @ SV291 ) @ SV876 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3353,plain,
! [SV1422: $i,SV877: $i,SV292: $i] :
( ( ! [SY5246: $i] :
( ( hBOOL @ ( hAPP @ SV292 @ SV877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1422 @ tc_bool ) ) @ SV292 ) @ SY5246 ) @ SV877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3354,plain,
! [SV1423: $i,SV878: $i,SV293: $i] :
( ( ( c_Fun_Oinj__on @ SV293 @ SV878 @ SV1423 @ SV1423 )
| ~ ( c_lessequals @ SV878 @ ( c_Set_Oimage @ SV293 @ SV878 @ SV1423 @ SV1423 ) @ ( tc_fun @ SV1423 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV878 @ SV1423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3355,plain,
! [SV1424: $i,SV879: $i,SV294: $i] :
( ( ! [SY5247: $i,SY5248: $i] :
( ( c_Fun_Oinj__on @ SV294 @ SV879 @ SV1424 @ SY5247 )
| ~ ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SY5248 ) @ SV879 ) @ SV1424 @ SY5247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3356,plain,
! [SV1425: $i,SV880: $i,SV295: $i] :
( ( ! [SY5249: $i,SY5250: $i] :
( ( c_Fun_Oinj__on @ SV295 @ SV880 @ SV1425 @ SY5249 )
| ~ ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1425 @ tc_bool ) ) @ SV880 ) @ SY5250 ) @ SV1425 @ SY5249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3357,plain,
! [SV1426: $i,SV881: $i,SV296: $i] :
( ( ! [SY5251: $i,SY5252: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SY5251 ) @ SY5252 @ ( tc_fun @ SV1426 @ tc_bool ) )
| ~ ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SY5252 @ SV1426 @ SY5251 ) @ ( tc_fun @ SY5251 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SY5251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3358,plain,
! [SV297: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV297 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV297 @ tc_bool ) ) @ SV297 )
= ( c_Orderings_Otop__class_Otop @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(3359,plain,
! [SV1427: $i,SV883: $i,SV299: $i] :
( ( ! [SY5253: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV299 @ SV883 @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SY5253 @ ( tc_fun @ SV1427 @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV883 ) @ SY5253 ) @ ( tc_fun @ SV1427 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3360,plain,
! [SV1428: $i,SV884: $i,SV300: $i] :
( ( ! [SY5254: $i] :
( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1428 ) @ SY5254 ) @ ( tc_fun @ SV884 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV300 @ SV1428 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SY5254 @ ( tc_fun @ SV884 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3361,plain,
! [SV1429: $i,SV885: $i,SV301: $i] :
( ( ( c_Finite__Set_Ofinite @ SV301 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ SV885 @ SV1429 @ SV301 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3362,plain,
! [SV1430: $i,SV886: $i,SV302: $i] :
( ( ( c_Finite__Set_Ofinite @ SV302 @ t_a )
| ~ ( c_Wellfounded_Omax__extp @ SV886 @ SV302 @ SV1430 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3363,plain,
! [SV1431: $i,SV887: $i,SV303: $i] :
( ( ! [SY5255: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SV1431 ) @ SY5255 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV887 @ SV1431 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3364,plain,
! [SV1432: $i,SV888: $i,SV304: $i] :
( ( ! [SY5256: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SV1432 ) @ SY5256 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV888 @ SY5256 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3365,plain,
! [SV1433: $i,SV889: $i,SV305: $i] :
( ( ! [SY5257: $i,SY5258: $i] :
( ( c_Set_Ovimage @ SV305 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV889 @ tc_bool ) ) @ SV1433 ) @ SY5257 ) @ SY5258 @ SV889 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5258 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV305 @ SV1433 @ SY5258 @ SV889 ) ) @ ( c_Set_Ovimage @ SV305 @ SY5257 @ SY5258 @ SV889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3366,plain,
! [SV1434: $i,SV890: $i,SV306: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV306 @ tc_bool ) ) @ SV890 ) @ SV1434 ) @ SV306 )
| ~ ( c_Finite__Set_Ofinite @ SV1434 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3367,plain,
! [SV1435: $i,SV891: $i,SV307: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV307 @ tc_bool ) ) @ SV891 ) @ SV1435 ) @ SV307 )
| ~ ( c_Finite__Set_Ofinite @ SV891 @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3368,plain,
! [SV1436: $i,SV892: $i,SV308: $i] :
( ( ! [SY5259: $i,SY5260: $i] :
( ~ ( class_HOL_Oord @ SV308 )
| ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SY5259 @ SV1436 ) @ SV308 )
| ~ ( c_lessequals @ SV892 @ SY5259 @ ( tc_fun @ SY5260 @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3369,plain,
! [SV1437: $i,SV893: $i,SV309: $i] :
( ( ! [SY5261: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV1437 ) @ SY5261 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SY5261 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3370,plain,
! [SV1438: $i,SV894: $i,SV310: $i] :
( ( ! [SY5262: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SV1438 ) @ SY5262 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SY5262 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3371,plain,
! [SV1439: $i,SV895: $i,SV311: $i] :
( ( ! [SY5263: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ ( c_Set_Oinsert @ SV1439 @ SY5263 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ SY5263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3372,plain,
! [SV1440: $i,SV896: $i,SV312: $i] :
( ( ! [SY5264: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ ( c_Set_Oinsert @ SV1440 @ SY5264 @ SV312 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ SY5264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3373,plain,
! [SV1441: $i,SV897: $i,SV313: $i] :
( ( ! [SY5265: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SY5265 ) )
| ~ ( c_lessequals @ SY5265 @ SV1441 @ ( tc_fun @ SV313 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3374,plain,
! [SV1442: $i,SV898: $i,SV314: $i] :
( ( ! [SY5266: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1442 ) )
| ~ ( c_lessequals @ SY5266 @ SV1442 @ ( tc_fun @ SV314 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SY5266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3375,plain,
! [SV1443: $i,SV899: $i,SV315: $i] :
( ( ! [SY5267: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1443 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SY5267 ) )
| ~ ( c_lessequals @ SY5267 @ SV1443 @ ( tc_fun @ SV315 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3376,plain,
! [SV1444: $i,SV900: $i,SV316: $i] :
( ( ! [SY5268: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SY5268 ) )
| ~ ( c_lessequals @ SY5268 @ SV1444 @ ( tc_fun @ SV316 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3377,plain,
! [SV1445: $i,SV901: $i,SV317: $i] :
( ( ! [SY5269: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV317 @ tc_bool ) ) @ SV1445 ) @ SY5269 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ SV1445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3378,plain,
! [SV1446: $i,SV902: $i,SV318: $i] :
( ( ! [SY5270: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV1446 ) @ SY5270 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ SY5270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3379,plain,
! [SV1447: $i,SV903: $i,SV319: $i] :
( ( ! [SY5271: $i,SY5272: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SV903 @ SV1447 @ SY5271 ) @ SY5272 )
= ( hAPP @ SV319 @ SY5272 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1447 ) @ SY5272 ) @ SV903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3380,plain,
! [SV1448: $i,SV904: $i,SV320: $i] :
( ( ! [SY5273: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ SV1448 ) )
| ( SV904 = SY5273 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ ( c_Set_Oinsert @ SY5273 @ SV1448 @ SV320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3381,plain,
! [SV1449: $i,SV905: $i,SV321: $i] :
( ( ! [SY5274: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1449 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SY5274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SY5274 ) @ SV1449 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3382,plain,
! [SV1450: $i,SV906: $i,SV322: $i] :
( ( ! [SY5275: $i,SY5276: $i,SY5277: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SV1450 @ SY5275 @ SY5276 ) @ SY5277 )
= ( hAPP @ SV906 @ SY5277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5275 ) @ SY5277 ) @ SV1450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3383,plain,
! [SV1451: $i,SV908: $i,SV324: $i] :
( ( ! [SY5278: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ SV1451 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ ( c_HOL_Ominus__class_Ominus @ SY5278 @ SV1451 @ ( tc_fun @ SV324 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3384,plain,
! [SV1452: $i,SV909: $i,SV325: $i] :
( ( ! [SY5279: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ SV1452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ ( c_HOL_Ominus__class_Ominus @ SV1452 @ SY5279 @ ( tc_fun @ SV325 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3385,plain,
! [SV1453: $i,SV910: $i,SV326: $i] :
( ( ! [SY5280: $i,SY5281: $i,SY5282: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SV910 @ SV1453 @ SY5280 @ SY5281 ) @ SY5282 )
= ( hAPP @ SV326 @ SY5282 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5280 ) @ SY5282 ) @ SV1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3386,plain,
! [SV1454: $i,SV911: $i,SV327: $i] :
( ( ! [SY5283: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1454 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SY5283 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5283 @ SV1454 @ ( tc_fun @ SV327 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3387,plain,
! [SV1455: $i,SV912: $i,SV328: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV328 ) @ SV912 ) @ ( c_Set_Oinsert @ SV912 @ SV1455 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3388,plain,
! [SV1456: $i,SV913: $i,SV329: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV329 ) @ SV913 ) @ ( c_Set_Oinsert @ SV913 @ SV1456 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3389,plain,
! [SV1457: $i,SV914: $i,SV330: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV330 ) @ SV914 ) @ ( c_Set_Oinsert @ SV914 @ SV1457 @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3390,plain,
! [SV1458: $i,SV915: $i,SV331: $i] :
( ( ! [SY5284: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ SV1458 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV331 @ tc_bool ) ) @ SY5284 ) @ SV1458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3391,plain,
! [SV1459: $i,SV916: $i,SV332: $i] :
( ( ! [SY5285: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ SV1459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV332 @ tc_bool ) ) @ SV1459 ) @ SY5285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3392,plain,
! [SV1460: $i,SV917: $i,SV333: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV333 ) @ SV917 ) @ ( c_Collect @ SV1460 @ SV333 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV1460 @ SV917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3393,plain,
! [SV1461: $i,SV918: $i,SV334: $i] :
( ( ( hBOOL @ ( hAPP @ SV334 @ SV918 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1461 ) @ SV918 ) @ ( c_Collect @ SV334 @ SV1461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3394,plain,
! [SV1462: $i,SV919: $i,SV335: $i] :
( ( ! [SY5286: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ ( c_HOL_Ominus__class_Ominus @ SV1462 @ SY5286 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SY5286 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3395,plain,
! [SV1463: $i,SV920: $i,SV336: $i] :
( ( ! [SY5287: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ ( c_HOL_Ominus__class_Ominus @ SV1463 @ SY5287 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SY5287 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3396,plain,
! [SV1464: $i,SV921: $i,SV337: $i] :
( ( ! [SY5288: $i,SY5289: $i,SY5290: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SY5288 @ SY5289 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SY5288 @ SY5290 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5289 ) @ SY5290 ) @ SV1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3397,plain,
! [SV1465: $i,SV922: $i,SV338: $i] :
( ( ! [SY5291: $i,SY5292: $i,SY5293: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SY5291 @ SY5292 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SY5291 @ SY5293 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5292 ) @ SY5293 ) @ SV1465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3398,plain,
! [SV1466: $i,SV923: $i,SV339: $i] :
( ( ! [SY5294: $i,SY5295: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SV923 ) @ ( c_Set_Ovimage @ SV1466 @ SY5294 @ SV339 @ SY5295 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5295 ) @ ( hAPP @ SV1466 @ SV923 ) ) @ SY5294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3399,plain,
! [SV1467: $i,SV924: $i,SV340: $i] :
( ( ! [SY5296: $i,SY5297: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SV924 ) @ ( c_Set_Ovimage @ SV1467 @ SY5296 @ SV340 @ SY5297 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5297 ) @ ( hAPP @ SV1467 @ SV924 ) ) @ SY5296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3400,plain,
! [SV1468: $i,SV925: $i,SV341: $i] :
( ( ! [SY5298: $i,SY5299: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SV925 ) @ ( c_Set_Ovimage @ SV1468 @ SY5298 @ SV341 @ SY5299 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5299 ) @ ( hAPP @ SV1468 @ SV925 ) ) @ SY5298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3401,plain,
! [SV1469: $i,SV926: $i,SV342: $i] :
( ( ! [SY5300: $i,SY5301: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SV926 @ SV1469 ) ) @ SY5300 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5301 ) @ SV1469 ) @ ( c_Set_Ovimage @ SV926 @ SY5300 @ SY5301 @ SV342 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3402,plain,
! [SV1470: $i,SV927: $i,SV343: $i] :
( ( ! [SY5302: $i,SY5303: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SV927 @ SV1470 ) ) @ SY5302 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5303 ) @ SV1470 ) @ ( c_Set_Ovimage @ SV927 @ SY5302 @ SY5303 @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3403,plain,
! [SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY5304: $i,SY5305: $i,SY5306: $i,SY5307: $i,SY5308: $i,SY5309: $i,SY5310: $i,SY5311: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SY5304 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5305 ) @ SY5304 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SY5306 @ SV344 @ SY5307 @ SY5308 @ SY5309 @ SY5310 @ SY5311 @ SY5305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3404,plain,
! [SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY5312: $i,SY5313: $i,SY5314: $i,SY5315: $i,SY5316: $i,SY5317: $i,SY5318: $i,SY5319: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SY5312 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5313 ) @ SV929 ) @ SY5312 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5314 @ SV1472 @ SV345 @ SY5315 @ SY5316 @ SY5317 @ SY5318 @ SY5319 @ SY5313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3405,plain,
! [SV1473: $i,SV930: $i,SV346: $i] :
( ( ( ( c_Set_Oinsert @ SV346 @ SV930 @ SV1473 )
= SV930 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1473 ) @ SV346 ) @ SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3406,plain,
! [SV1474: $i,SV931: $i,SV347: $i] :
( ( ! [SY5320: $i,SY5321: $i,SY5322: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SY5320 @ tc_bool ) ) @ SY5321 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SY5322 ) @ SY5321 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SY5322 ) @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3407,plain,
! [SV1475: $i,SV932: $i,SV348: $i] :
( ( ! [SY5323: $i,SY5324: $i,SY5325: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SY5323 @ tc_bool ) ) @ SY5324 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SY5325 ) @ SY5324 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SY5325 ) @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3408,plain,
! [SV1476: $i,SV933: $i,SV349: $i] :
( ( ! [SY5326: $i,SY5327: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SV933 ) @ SV1476 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5326 ) @ ( hAPP @ SY5327 @ SV933 ) ) @ ( c_Set_Oimage @ SY5327 @ SV1476 @ SV349 @ SY5326 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3409,plain,
! [SV1477: $i,SV934: $i,SV350: $i] :
( ( ! [SY5328: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV1477 ) @ SY5328 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ SV1477 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ SY5328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3410,plain,
! [SV1478: $i,SV935: $i,SV351: $i] :
( ( ! [SY5329: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV935 ) @ SV1478 ) ) @ SY5329 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV935 ) @ SY5329 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV1478 ) @ SY5329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3411,plain,
! [SV1479: $i,SV936: $i,SV352: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV352 @ SV936 @ SV1479 ) @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3412,plain,
! [SV1480: $i,SV937: $i,SV353: $i] :
( ( ! [SY5330: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SV1480 ) @ SY5330 @ ( tc_fun @ SV1480 @ tc_bool ) )
| ~ ( c_lessequals @ SV937 @ SY5330 @ ( tc_fun @ SV1480 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1480 ) @ SV353 ) @ SY5330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3413,plain,
! [SV1481: $i,SV938: $i,SV354: $i] :
( ( ~ ( class_Lattices_Olattice @ SV354 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SV1481 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SV1481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3414,plain,
! [SV1482: $i,SV939: $i,SV355: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV355 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SV1482 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SV1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3415,plain,
! [SV1483: $i,SV940: $i,SV356: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SV940 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SV940 ) @ SV1483 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV356 @ tc_bool ) ) @ SV940 ) @ SV1483 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3416,plain,
! [SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY5331: $i,SY5332: $i,SY5333: $i,SY5334: $i,SY5335: $i,SY5336: $i,SY5337: $i,SY5338: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SY5331 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SY5331 @ SY5332 @ SY5332 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5331 @ SY5332 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5333 @ SV1484 @ SY5334 @ SY5335 @ SY5336 @ SV357 @ SY5337 @ SY5338 @ SY5332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3417,plain,
! [SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY5339: $i,SY5340: $i,SY5341: $i,SY5342: $i,SY5343: $i,SY5344: $i,SY5345: $i,SY5346: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SY5339 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SY5339 @ SY5340 @ SY5340 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5339 @ SY5340 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SY5341 @ SY5342 @ SY5343 @ SV358 @ SY5344 @ SY5345 @ SY5346 @ SY5340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3418,plain,
! [SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY5347: $i,SY5348: $i,SY5349: $i,SY5350: $i,SY5351: $i,SY5352: $i,SY5353: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SY5347 @ SV943 @ SY5348 @ SY5348 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SY5348 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5349 @ SV359 @ SY5350 @ SY5351 @ SY5352 @ SV1486 @ SY5347 @ SY5353 @ SY5348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3419,plain,
! [SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY5354: $i,SY5355: $i,SY5356: $i,SY5357: $i,SY5358: $i,SY5359: $i,SY5360: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SY5354 @ SV944 @ SY5355 @ SY5355 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SY5355 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SY5356 @ SY5357 @ SY5358 @ SV1487 @ SY5359 @ SY5360 @ SY5354 @ SY5355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3420,plain,
! [SV1488: $i,SV945: $i,SV361: $i] :
( ( ! [SY5361: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV945 @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SY5361 @ SV945 @ SV1488 ) @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3421,plain,
! [SV1489: $i,SV946: $i,SV362: $i] :
( ( ! [SY5362: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ ( c_Set_Oinsert @ SV946 @ SV1489 @ SY5362 ) @ ( tc_fun @ SY5362 @ tc_bool ) ) @ SY5362 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ SV1489 @ ( tc_fun @ SY5362 @ tc_bool ) ) @ SY5362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3422,plain,
! [SV1490: $i,SV947: $i,SV363: $i] :
( ( ( c_Fun_Ofcomp @ SV363 @ ( c_Fun_Oid @ SV947 ) @ SV1490 @ SV947 @ SV947 )
= SV363 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3423,plain,
! [SV1491: $i,SV948: $i,SV364: $i] :
( ( ( c_Fun_Ofcomp @ ( c_Fun_Oid @ SV364 ) @ SV948 @ SV364 @ SV364 @ SV1491 )
= SV948 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3424,plain,
! [SV1492: $i,SV949: $i,SV365: $i] :
( ( ! [SY5363: $i,SY5364: $i,SY5365: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV365 @ SV949 @ SV1492 @ SY5363 @ SY5364 ) @ SY5365 @ SY5364 @ SY5363 )
= ( c_Set_Oimage @ SV365 @ ( c_Set_Oimage @ SV949 @ SY5365 @ SY5364 @ SV1492 ) @ SV1492 @ SY5363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3425,plain,
! [SV366: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV366 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV366 @ tc_bool ) ) @ SV366 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(3426,plain,
! [SV1493: $i,SV950: $i,SV367: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV367 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1493 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 @ SV1493 @ SV367 @ SV367 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1493 @ SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3427,plain,
! [SV951: $i,SV368: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV368 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV368 ) @ SV951 ) @ SV951 )
= SV951 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3428,plain,
! [SV1494: $i,SV953: $i,SV370: $i] :
( ( ! [SY5366: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV370 )
| ( c_lessequals @ SV953 @ SV1494 @ SV370 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SY5366 ) @ SV953 ) @ SV1494 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3429,plain,
! [SV1495: $i,SV954: $i,SV371: $i] :
( ( ! [SY5367: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV371 )
| ( c_lessequals @ SV954 @ SV1495 @ SV371 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SY5367 ) @ SV1495 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3430,plain,
! [SV1496: $i,SV955: $i,SV372: $i] :
( ( ! [SY5368: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV372 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SV1496 ) @ SY5368 ) @ SV372 )
| ~ ( c_lessequals @ SV955 @ SY5368 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3431,plain,
! [SV1497: $i,SV956: $i,SV373: $i] :
( ( ! [SY5369: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV373 )
| ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SV1497 ) @ SY5369 ) @ SV373 )
| ~ ( c_lessequals @ SV956 @ SV1497 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3432,plain,
! [SV1498: $i,SV957: $i,SV374: $i] :
( ( ! [SY5370: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV374 )
| ( c_lessequals @ SV957 @ SV1498 @ SV374 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SY5370 ) @ SV957 ) @ SV1498 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3433,plain,
! [SV1499: $i,SV958: $i,SV375: $i] :
( ( ! [SY5371: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV375 )
| ( c_lessequals @ SV958 @ SV1499 @ SV375 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SY5371 ) @ SV1499 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3434,plain,
! [SV1500: $i,SV959: $i,SV376: $i] :
( ( ! [SY5372: $i] :
( ( c_lessequals @ SV376 @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1500 @ tc_bool ) ) @ SV376 ) @ SY5372 ) @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3435,plain,
! [SV1501: $i,SV960: $i,SV377: $i] :
( ( ! [SY5373: $i] :
( ( c_lessequals @ SV377 @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1501 @ tc_bool ) ) @ SY5373 ) @ SV377 ) @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3436,plain,
! [SV1502: $i,SV961: $i,SV378: $i] :
( ( ~ ( class_Lattices_Olattice @ SV378 )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ SV378 ) ) @ SV961 ) @ SV1502 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 ) @ ( hAPP @ SV961 @ v_x ) ) @ ( hAPP @ SV1502 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3437,plain,
! [SV1503: $i,SV962: $i,SV379: $i] :
( ( ! [SY5374: $i] :
( ~ ( class_Orderings_Oorder @ SV379 )
| ( c_lessequals @ SV962 @ SV1503 @ SV379 )
| ~ ( c_lessequals @ SV962 @ SY5374 @ SV379 )
| ~ ( c_lessequals @ SY5374 @ SV1503 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3438,plain,
! [SV1504: $i,SV963: $i,SV380: $i] :
( ( ! [SY5375: $i] :
( ~ ( class_Orderings_Oorder @ SV380 )
| ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
| ~ ( c_lessequals @ SV963 @ SY5375 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SY5375 @ SV1504 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3439,plain,
! [SV1505: $i,SV964: $i,SV381: $i] :
( ( ! [SY5376: $i] :
( ~ ( class_Orderings_Oorder @ SV381 )
| ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
| ~ ( c_HOL_Oord__class_Oless @ SV964 @ SY5376 @ SV381 )
| ~ ( c_lessequals @ SY5376 @ SV1505 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3440,plain,
! [SV1506: $i,SV965: $i,SV382: $i] :
( ( ! [SY5377: $i] :
( ~ ( class_Orderings_Opreorder @ SV382 )
| ( c_lessequals @ SV965 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SY5377 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV965 @ SY5377 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3441,plain,
! [SV1507: $i,SV968: $i,SV385: $i] :
( ( ! [SY5378: $i] :
( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
| ~ ( c_lessequals @ SY5378 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
| ~ ( c_lessequals @ SV385 @ SY5378 @ ( tc_fun @ SV1507 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3442,plain,
! [SV1508: $i,SV969: $i,SV386: $i] :
( ( ! [SY5379: $i,SY5380: $i] :
( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SY5379 )
| ~ ( c_lessequals @ SV969 @ SY5380 @ ( tc_fun @ SV1508 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV386 @ SY5380 @ SV1508 @ SY5379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3443,plain,
! [SV1509: $i,SV970: $i,SV387: $i] :
( ( ! [SY5381: $i] :
( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
| ~ ( hBOOL @ ( hAPP @ SV1509 @ SV970 ) )
| ~ ( c_lessequals @ SV1509 @ SV387 @ ( tc_fun @ SY5381 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3444,plain,
! [SV971: $i,SV388: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV388 ) )
= $true )
| ( ( c_lessequals @ SV971 @ SV971 @ SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(3445,plain,
! [SV972: $i,SV389: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV389 ) )
= $true )
| ( ( c_lessequals @ SV972 @ SV972 @ SV389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3446,plain,
! [SV1510: $i,SV973: $i,SV390: $i] :
( ( ( c_Finite__Set_Ofinite @ SV390 @ SV973 )
| ~ ( c_Finite__Set_Ofinite @ SV1510 @ SV973 )
| ~ ( c_lessequals @ SV390 @ SV1510 @ ( tc_fun @ SV973 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3447,plain,
! [SV1511: $i,SV974: $i,SV391: $i] :
( ( ! [SY5382: $i] :
( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
| ~ ( c_lessequals @ SY5382 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV391 @ SY5382 @ ( tc_fun @ SV1511 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3448,plain,
! [SV1512: $i,SV975: $i,SV392: $i] :
( ( ! [SY5383: $i] :
( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5383 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
| ~ ( c_lessequals @ SV392 @ SY5383 @ ( tc_fun @ SV1512 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3449,plain,
! [SV1513: $i,SV976: $i,SV393: $i] :
( ( ! [SY5384: $i] :
( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
| ~ ( c_lessequals @ SV1513 @ SV393 @ ( tc_fun @ SY5384 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1513 @ SV976 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3450,plain,
! [SV1514: $i,SV977: $i,SV394: $i] :
( ( ( c_Finite__Set_Ofinite @ SV394 @ SV977 )
| ~ ( c_lessequals @ SV394 @ SV1514 @ ( tc_fun @ SV977 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1514 @ SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3451,plain,
! [SV1515: $i,SV978: $i,SV395: $i] :
( ( ! [SY5385: $i] :
( ~ ( class_Orderings_Opreorder @ SV395 )
| ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
| ~ ( c_HOL_Oord__class_Oless @ SY5385 @ SV1515 @ SV395 )
| ~ ( c_lessequals @ SV978 @ SY5385 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3452,plain,
! [SV1516: $i,SV979: $i,SV396: $i] :
( ( ! [SY5386: $i] :
( ~ ( class_Orderings_Opreorder @ SV396 )
| ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
| ~ ( c_lessequals @ SY5386 @ SV1516 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SV979 @ SY5386 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3453,plain,
! [SV980: $i,SV397: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV397 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV980 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV397 @ tc_bool ) ) @ SV397 ) @ SV397 )
= SV980 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3454,plain,
! [SV1517: $i,SV981: $i,SV398: $i] :
( ( ! [SY5387: $i,SY5388: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SY5387 ) @ SY5388 ) @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV1517 @ SY5388 @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV981 @ SY5387 @ ( tc_fun @ SV398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3455,plain,
! [SV1518: $i,SV982: $i,SV399: $i] :
( ( ! [SY5389: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV399 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV982 @ tc_bool ) ) @ SV1518 ) @ SY5389 ) @ ( tc_fun @ SV982 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV982 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SV1518 @ ( tc_fun @ SV982 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SY5389 @ ( tc_fun @ SV982 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3456,plain,
! [SV1519: $i,SV984: $i,SV401: $i] :
( ( ! [SY5390: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SV984 ) @ SV1519 ) @ SY5390 @ ( tc_fun @ SV401 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SV984 ) @ ( c_HOL_Ominus__class_Ominus @ SV1519 @ SY5390 @ ( tc_fun @ SV401 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3457,plain,
! [SV1520: $i,SV985: $i,SV402: $i] :
( ( ! [SY5391: $i,SY5392: $i,SY5393: $i] :
( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SY5391 @ tc_bool ) ) @ SY5391 @ SY5392 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SY5391 @ SY5392 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SY5391 @ SY5392 ) @ ( tc_fun @ SY5392 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1520 @ SY5393 @ ( tc_fun @ SY5391 @ tc_bool ) )
| ~ ( c_lessequals @ SV985 @ SY5393 @ ( tc_fun @ SY5391 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SY5393 @ SY5391 @ SY5392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3458,plain,
! [SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY5394: $i,SY5395: $i,SY5396: $i,SY5397: $i,SY5398: $i,SY5399: $i,SY5400: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5394 @ SV403 @ SY5395 @ SY5396 @ SY5397 @ SY5398 @ SY5399 @ SY5400 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3459,plain,
! [SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY5401: $i,SY5402: $i,SY5403: $i,SY5404: $i,SY5405: $i,SY5406: $i,SY5407: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SY5401 @ SY5402 @ SY5403 @ SY5404 @ SY5405 @ SY5406 @ SY5407 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3460,plain,
! [SV1523: $i,SV988: $i,SV405: $i] :
( ( ! [SY5408: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SV1523 ) @ ( c_Collect @ SY5408 @ SV405 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SY5408 @ SV988 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SV1523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3461,plain,
! [SV1524: $i,SV989: $i,SV406: $i] :
( ( ( SV406
= ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) )
| ( SV406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV406 @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) @ ( tc_fun @ SV1524 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3462,plain,
! [SV1525: $i,SV990: $i,SV407: $i] :
( ( ! [SY5409: $i,SY5410: $i] :
( ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ SV1525 @ SY5409 ) @ SY5410 @ SY5409 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5410 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5409 @ tc_bool ) ) @ SY5409 ) @ SY5410 @ SY5409 ) ) @ ( c_Set_Ovimage @ SV407 @ SV1525 @ SY5410 @ SY5409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3463,plain,
! [SV1526: $i,SV991: $i,SV408: $i] :
( ( ! [SY5411: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV408 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV991 @ tc_bool ) ) @ SV1526 ) @ SY5411 ) @ ( tc_fun @ SV991 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV991 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SV1526 @ ( tc_fun @ SV991 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SY5411 @ ( tc_fun @ SV991 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3464,plain,
! [SV1527: $i,SV992: $i,SV409: $i] :
( ( ! [SY5412: $i,SY5413: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV409 @ tc_bool ) ) @ SV992 ) @ SV1527 ) @ SY5412 @ SV409 @ ( tc_fun @ SY5413 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5413 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV992 @ SY5412 @ SV409 @ ( tc_fun @ SY5413 @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1527 @ SY5412 @ SV409 @ ( tc_fun @ SY5413 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3465,plain,
! [SV1528: $i,SV993: $i,SV410: $i] :
( ( ! [SY5414: $i,SY5415: $i] :
( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SV993 @ SV1528 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV993 @ SV410 @ SY5414 @ SY5415 ) @ SV1528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3466,plain,
! [SV1529: $i,SV994: $i,SV411: $i] :
( ( ! [SY5416: $i,SY5417: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SV994 @ SV1529 @ SY5416 ) @ SY5417 ) )
| ~ ( hBOOL @ ( hAPP @ SV994 @ ( hAPP @ SV411 @ SY5417 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3467,plain,
! [SV1530: $i,SV995: $i,SV412: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV412 )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) )
| ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3468,plain,
! [SV1531: $i,SV996: $i,SV413: $i] :
( ( ! [SY5418: $i,SY5419: $i,SY5420: $i,SY5421: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SY5418 @ SY5419 @ SY5420 ) @ SY5421 @ SY5420 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SY5418 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SY5419 @ SY5421 @ SY5420 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5420 ) @ SY5418 ) @ SY5419 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5419 @ SY5420 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SY5421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3469,plain,
! [SV1532: $i,SV997: $i,SV414: $i] :
( ( ! [SY5422: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SV1532 ) @ SY5422 ) )
| ~ ( hBOOL @ ( hAPP @ SV1532 @ SY5422 ) )
| ~ ( hBOOL @ ( hAPP @ SV997 @ SY5422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3470,plain,
! [SV1533: $i,SV998: $i,SV415: $i] :
( ( ! [SY5423: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV415 @ SV998 @ SV1533 ) @ SY5423 @ SV1533 @ SV998 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1533 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV998 ) @ SV415 ) @ SY5423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3471,plain,
! [SV1534: $i,SV999: $i,SV416: $i] :
( ( ! [SY5424: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SV1534 @ ( tc_fun @ SY5424 @ tc_bool ) ) @ ( tc_fun @ SY5424 @ tc_bool ) )
= SV1534 )
| ~ ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SY5424 @ tc_bool ) )
| ~ ( c_lessequals @ SV1534 @ SV416 @ ( tc_fun @ SY5424 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3472,plain,
! [SV1535: $i,SV1000: $i,SV417: $i] :
( ( ! [SY5425: $i,SY5426: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SV1000 @ SV1535 @ SY5425 ) @ ( c_Set_Oimage @ SV417 @ SY5426 @ SV1535 @ SY5425 ) @ ( tc_fun @ SY5425 @ tc_bool ) )
| ~ ( c_lessequals @ SV1000 @ SY5426 @ ( tc_fun @ SV1535 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3473,plain,
! [SV1536: $i,SV1001: $i,SV418: $i] :
( ( ! [SY5427: $i,SY5428: $i] :
( ~ ( c_lessequals @ SV418 @ SV1001 @ ( tc_fun @ SV1536 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SY5427 @ SV418 @ SV1536 @ SY5428 ) @ ( c_Set_Oimage @ SY5427 @ SV1001 @ SV1536 @ SY5428 ) @ ( tc_fun @ SY5428 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3474,plain,
! [SV1537: $i,SV1003: $i,SV420: $i] :
( ( ! [SY5429: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV420 @ SV1003 @ SV1537 ) @ ( c_Set_Oinsert @ SV420 @ SY5429 @ SV1537 ) @ ( tc_fun @ SV1537 @ tc_bool ) )
| ~ ( c_lessequals @ SV1003 @ SY5429 @ ( tc_fun @ SV1537 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3475,plain,
! [SV1538: $i,SV1004: $i,SV421: $i] :
( ( ! [SY5430: $i] :
( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
| ~ ( c_Fun_Oinj__on @ SV1538 @ SV421 @ SV1004 @ SY5430 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV1538 @ SV421 @ SV1004 @ SY5430 ) @ SY5430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3476,plain,
! [SV1539: $i,SV1005: $i,SV422: $i] :
( ( ~ ( class_Orderings_Oorder @ SV422 )
| ( c_HOL_Oord__class_Oless @ SV1005 @ SV1539 @ SV422 )
| ( SV1539 = SV1005 )
| ~ ( c_lessequals @ SV1005 @ SV1539 @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3477,plain,
! [SV1540: $i,SV1006: $i,SV423: $i] :
( ( ~ ( class_Orderings_Oorder @ SV423 )
| ( c_HOL_Oord__class_Oless @ SV1006 @ SV1540 @ SV423 )
| ~ ( c_lessequals @ SV1006 @ SV1540 @ SV423 )
| ( SV1540 = SV1006 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3478,plain,
! [SV1541: $i,SV1007: $i,SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) )
| ( SV424 = SV1007 )
| ~ ( c_lessequals @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3479,plain,
! [SV1542: $i,SV1008: $i,SV425: $i] :
( ( ~ ( class_Orderings_Oorder @ SV425 )
| ( SV1008 = SV1542 )
| ( c_HOL_Oord__class_Oless @ SV1008 @ SV1542 @ SV425 )
| ~ ( c_lessequals @ SV1008 @ SV1542 @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3480,plain,
! [SV1543: $i,SV1009: $i,SV426: $i] :
( ( ~ ( class_Orderings_Oorder @ SV426 )
| ( c_HOL_Oord__class_Oless @ SV1009 @ SV1543 @ SV426 )
| ( SV1009 = SV1543 )
| ~ ( c_lessequals @ SV1009 @ SV1543 @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3481,plain,
! [SV1544: $i,SV1010: $i,SV427: $i] :
( ( ( SV427 = SV1010 )
| ( c_HOL_Oord__class_Oless @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) )
| ~ ( c_lessequals @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3482,plain,
! [SV1545: $i,SV1011: $i,SV428: $i] :
( ( ~ ( class_Orderings_Oorder @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1011 @ SV1545 @ SV428 )
| ( SV1011 = SV1545 )
| ~ ( c_lessequals @ SV1011 @ SV1545 @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3483,plain,
! [SV1546: $i,SV1012: $i,SV429: $i] :
( ( ~ ( class_Orderings_Oorder @ SV429 )
| ( c_HOL_Oord__class_Oless @ SV1012 @ SV1546 @ SV429 )
| ~ ( c_lessequals @ SV1012 @ SV1546 @ SV429 )
| ( SV1012 = SV1546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3484,plain,
! [SV1547: $i,SV1013: $i,SV430: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV430 )
| ( SV1013 = SV1547 )
| ~ ( c_lessequals @ SV1013 @ SV1547 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1013 @ SV1547 @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3485,plain,
! [SV1548: $i,SV1014: $i,SV431: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV431 )
| ( SV1014 = SV1548 )
| ( c_HOL_Oord__class_Oless @ SV1014 @ SV1548 @ SV431 )
| ~ ( c_lessequals @ SV1014 @ SV1548 @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3486,plain,
! [SV1549: $i,SV1015: $i,SV432: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV432 )
| ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1549 @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3487,plain,
! [SV1550: $i,SV1016: $i,SV433: $i] :
( ( ! [SY5431: $i,SY5432: $i] :
( ( c_Set_Oimage @ SV433 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1016 @ tc_bool ) ) @ SV1550 ) @ SY5431 ) @ SV1016 @ SY5432 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5432 @ tc_bool ) ) @ ( c_Set_Oimage @ SV433 @ SV1550 @ SV1016 @ SY5432 ) ) @ ( c_Set_Oimage @ SV433 @ SY5431 @ SV1016 @ SY5432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3488,plain,
! [SV1551: $i,SV1018: $i,SV435: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV435 )
| ( c_lessequals @ SV1018 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1551 @ SV435 ) @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SV1018 ) @ SV1551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3489,plain,
! [SV1552: $i,SV1019: $i,SV436: $i] :
( ( ! [SY5433: $i,SY5434: $i,SY5435: $i,SY5436: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SV1019 @ SV1552 @ SY5433 @ SY5434 ) @ SY5435 @ SV1552 @ SY5434 @ SY5436 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SV1019 @ SY5435 @ SY5433 @ SY5434 @ SY5436 ) @ SV1552 @ SY5433 @ SY5436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3490,plain,
! [SV1553: $i,SV1020: $i,SV437: $i] :
( ( ~ ( class_Orderings_Oorder @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SV1020 @ SV1553 @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SV1553 @ SV1020 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3491,plain,
! [SV1554: $i,SV1021: $i,SV438: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SV1554 @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1021 @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3492,plain,
! [SV1555: $i,SV1022: $i,SV439: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV439 )
| ( c_lessequals @ SV1022 @ SV1555 @ SV439 )
| ( c_lessequals @ SV1555 @ SV1022 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3493,plain,
! [SV1556: $i,SV1023: $i,SV440: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SV1023 @ SV1556 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1023 @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3494,plain,
! [SV1557: $i,SV1024: $i,SV441: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1024 @ SV1557 @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV1024 @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3495,plain,
! [SV1558: $i,SV1025: $i,SV442: $i] :
( ( ! [SY5437: $i,SY5438: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SV1025 ) @ SV1558 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5437 ) @ ( hAPP @ SY5438 @ SV1025 ) ) @ ( c_Set_Oimage @ SY5438 @ SV1558 @ SV442 @ SY5437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3496,plain,
! [SV1559: $i,SV1026: $i,SV443: $i] :
( ( ! [SY5439: $i,SY5440: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SV1026 @ SV1559 ) ) @ ( c_Set_Oimage @ SV1026 @ SY5439 @ SY5440 @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5440 ) @ SV1559 ) @ SY5439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3497,plain,
! [SV1560: $i,SV1027: $i,SV444: $i] :
( ( ! [SY5441: $i,SY5442: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SV1027 @ SV1560 ) ) @ ( c_Set_Oimage @ SV1027 @ SY5441 @ SY5442 @ SV444 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5442 ) @ SV1560 ) @ SY5441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3498,plain,
! [SV1028: $i,SV445: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV445 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1028 @ SV445 ) ) @ SV1028 ) )
| ( SV1028
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1028 @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3499,plain,
! [SV1029: $i,SV446: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV446 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1029 @ SV446 ) ) @ SV1029 ) )
| ( SV1029
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1029 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3500,plain,
! [SV1561: $i,SV1030: $i,SV447: $i] :
( ( ( ( c_Set_Oinsert @ SV447 @ ( c_HOL_Ominus__class_Ominus @ SV1030 @ ( c_Set_Oinsert @ SV447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1561 @ tc_bool ) ) @ SV1561 ) @ ( tc_fun @ SV1561 @ tc_bool ) ) @ SV1561 )
= SV1030 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV447 ) @ SV1030 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3501,plain,
! [SV1562: $i,SV1031: $i,SV448: $i] :
( ( ! [SY5443: $i,SY5444: $i] :
( ( ( hAPP @ SV448 @ SV1031 )
= SV1562 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5443 ) @ SV1031 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SV1562 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5444 @ tc_bool ) ) @ SY5444 ) @ SY5443 @ SY5444 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3502,plain,
! [SV1563: $i,SV1032: $i,SV449: $i] :
( ( ! [SY5445: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV449 @ SV1032 @ SV1563 ) @ SY5445 @ SV1563 @ SV1032 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1563 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1032 ) @ SV449 ) @ SY5445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3503,plain,
! [SV1564: $i,SV1033: $i,SV450: $i] :
( ( ! [SY5446: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV450 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1033 @ SV1564 @ SY5446 @ ( tc_fun @ SV450 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5446 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1033 @ SV1564 @ SY5446 @ SV450 ) ) @ SV1033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3504,plain,
! [SV1565: $i,SV1034: $i,SV451: $i] :
( ( ! [SY5447: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1034 ) @ ( c_Set_Ovimage @ SV1565 @ ( c_Set_Oinsert @ ( hAPP @ SV1565 @ SV1034 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5447 @ tc_bool ) ) @ SY5447 ) @ SV451 @ SY5447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3505,plain,
! [SV1035: $i,SV452: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SV1035 @ SV452 ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SV1035 @ SV452 ) ) ) )
= $true )
| ( ( SV1035
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV452 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3506,plain,
! [SV1566: $i,SV1036: $i,SV453: $i] :
( ( ! [SY5448: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV453 @ SV1036 @ SV1566 @ ( tc_fun @ SY5448 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5448 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1566 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV453 @ SV1036 @ SV1566 @ SY5448 ) ) @ SV453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3507,plain,
! [SV1567: $i,SV1037: $i,SV454: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV454 @ SV1037 @ SV1567 ) @ ( c_Set_Oinsert @ SV454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1567 @ tc_bool ) ) @ SV1567 ) @ ( tc_fun @ SV1567 @ tc_bool ) )
= SV1037 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1567 ) @ SV454 ) @ SV1037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3508,plain,
! [SV1568: $i,SV1038: $i,SV455: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV455 @ tc_bool ) ) @ SV1038 ) @ SV1568 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV455 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV455 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SV1038 @ SV1568 @ SV455 ) ) @ SV1568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3509,plain,
! [SV1569: $i,SV1039: $i,SV456: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV456 @ tc_bool ) ) @ SV1039 ) @ SV1569 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SV1039 @ SV1569 @ SV456 ) ) @ SV1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3510,plain,
! [SV1040: $i,SV457: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV457 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV457 ) @ ( c_Orderings_Obot__class_Obot @ SV457 ) ) @ SV1040 )
= SV1040 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3511,plain,
! [SV1041: $i,SV458: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV458 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV458 ) @ SV1041 ) @ ( c_Orderings_Obot__class_Obot @ SV458 ) )
= SV1041 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3512,plain,
! [SV1042: $i,SV459: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV459 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV459 ) @ ( c_Orderings_Obot__class_Obot @ SV459 ) ) @ SV1042 )
= ( c_Orderings_Obot__class_Obot @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3513,plain,
! [SV1043: $i,SV460: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV460 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV460 ) @ SV1043 ) @ ( c_Orderings_Obot__class_Obot @ SV460 ) )
= ( c_Orderings_Obot__class_Obot @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3514,plain,
! [SV1044: $i,SV461: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV461 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV461 ) @ SV1044 @ SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3515,plain,
! [SV1570: $i,SV1045: $i,SV462: $i] :
( ( ( c_Set_Ovimage @ SV462 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1045 @ tc_bool ) ) @ SV1570 @ SV1045 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1570 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3516,plain,
! [SV1571: $i,SV1046: $i,SV464: $i] :
( ( ! [SY5449: $i,SY5450: $i,SY5451: $i,SY5452: $i,SY5453: $i,SY5454: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SY5449 @ SY5450 @ SY5451 @ SY5452 @ SY5453 @ SY5454 @ SV1571 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3517,plain,
! [SV1572: $i,SV1047: $i,SV465: $i] :
( ( ! [SY5455: $i,SY5456: $i,SY5457: $i,SY5458: $i,SY5459: $i,SY5460: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5455 @ SV465 @ SY5456 @ SY5457 @ SY5458 @ SY5459 @ SV1572 @ SY5460 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3518,plain,
! [SV1573: $i,SV1049: $i,SV467: $i] :
( ( ! [SY5461: $i,SY5462: $i] :
( ( c_Finite__Set_Ofold__image @ SV467 @ SV1049 @ SV1573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5461 @ tc_bool ) ) @ SY5462 @ SY5461 )
= SV1573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3519,plain,
! [SV1574: $i,SV1050: $i,SV468: $i] :
( ( ! [SY5463: $i] :
( ( c_Finite__Set_Ofold @ SV468 @ SV1050 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1574 @ tc_bool ) ) @ SV1574 @ SY5463 )
= SV1050 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3520,plain,
! [SV1051: $i,SV470: $i] :
( ( ( SV470
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1051 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV470 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1051 @ tc_bool ) ) @ ( tc_fun @ SV1051 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3521,plain,
! [SV1052: $i,SV471: $i] :
( ( c_Wellfounded_Omax__extp @ SV471 @ SV1052 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3522,plain,
! [SV1575: $i,SV1053: $i,SV472: $i] :
( ( ~ ( c_Finite__Set_Ofold1Set @ SV472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1053 @ tc_bool ) ) @ SV1575 @ SV1053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3523,plain,
! [SV1057: $i,SV476: $i] :
( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ ( tc_fun @ SV1057 @ tc_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3524,plain,
! [SV1576: $i,SV1060: $i,SV480: $i] :
( ( ! [SY5464: $i,SY5465: $i] :
( ( SV480 = SV1060 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1576 @ SV1060 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5464 @ tc_bool ) ) @ SV480 @ SY5464 @ SY5465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3525,plain,
! [SV1577: $i,SV1063: $i,SV483: $i] :
( ( ( c_Relation_OImage @ SV483 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1063 @ tc_bool ) ) @ SV1063 @ SV1577 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1577 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3526,plain,
! [SV1578: $i,SV1065: $i,SV485: $i] :
( ( ( c_Set_Oinsert @ SV485 @ ( c_Set_Oinsert @ SV1065 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1578 @ tc_bool ) ) @ SV1578 ) @ SV1578 )
= ( c_Set_Oinsert @ SV1065 @ ( c_Set_Oinsert @ SV485 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1578 @ tc_bool ) ) @ SV1578 ) @ SV1578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3527,plain,
! [SV1579: $i,SV1066: $i,SV486: $i] :
( ( ( c_Set_Oimage @ SV486 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1066 @ tc_bool ) ) @ SV1066 @ SV1579 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1579 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3528,plain,
! [SV1580: $i,SV1067: $i,SV487: $i] :
( ( c_Fun_Oinj__on @ SV487 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1067 @ tc_bool ) ) @ SV1067 @ SV1580 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3529,plain,
! [SV1581: $i,SV1068: $i,SV488: $i] :
( ( ! [SY5466: $i] : ( c_Finite__Set_Ofold__graph @ SV488 @ SV1068 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1581 @ tc_bool ) ) @ SV1068 @ SV1581 @ SY5466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3530,plain,
! [SV1582: $i,SV1069: $i,SV489: $i] :
( ( ! [SY5467: $i] : ( c_Nitpick_Ofold__graph_H @ SV489 @ SV1069 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1582 @ tc_bool ) ) @ SV1069 @ SV1582 @ SY5467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3531,plain,
! [SV1583: $i,SV1070: $i,SV490: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV490 @ tc_bool ) )
= ( c_Set_Oimage @ SV1070 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1583 @ tc_bool ) ) @ SV1583 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3532,plain,
! [SV1584: $i,SV1071: $i,SV491: $i] :
( ( ! [SY5468: $i] :
( ( c_Fun_Ooverride__on @ SV491 @ SV1071 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1584 @ tc_bool ) ) @ SV1584 @ SY5468 )
= SV491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3533,plain,
! [SV1585: $i,SV1075: $i,SV495: $i] :
( ( ! [SY5469: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV495 @ SV1075 @ SV1585 @ SY5469 @ t_a ) @ v_x )
= ( hAPP @ SV495 @ ( hAPP @ SV1075 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3534,plain,
! [SV1586: $i,SV1076: $i,SV496: $i] :
( ( ! [SY5470: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV496 @ SV1076 @ t_a @ SV1586 @ SY5470 ) @ v_x )
= ( hAPP @ SV1076 @ ( hAPP @ SV496 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3535,plain,
! [SV1587: $i,SV1078: $i,SV498: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV498 @ SV1078 @ SV1587 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV498 ) @ SV1078 @ SV1587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3536,plain,
! [SV1588: $i,SV1079: $i,SV499: $i] :
( ( ! [SY5471: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SY5471 @ SV499 ) ) @ SY5471 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY5471 @ SV1588 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3537,plain,
! [SV1589: $i,SV1080: $i,SV500: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SV1080 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1080 ) @ SV1589 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SV1589 ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3538,plain,
! [SV1590: $i,SV1081: $i,SV501: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV501 @ SV1081 @ t_a )
| ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ SV501 @ SV1081 ) @ SV1590 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1590 ) @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3539,plain,
! [SV1591: $i,SV1082: $i,SV502: $i] :
( ( ! [SY5472: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SY5472 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SY5472 @ SV1591 @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3540,plain,
! [SV1084: $i,SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV504 ) @ ( c_ATP__Linkup_Osko__Set__Xex__in__conv__1__1 @ SV1084 @ SV504 ) ) @ SV1084 ) )
= $true )
| ( ( SV1084
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV504 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2990]) ).
thf(3541,plain,
! [SV1085: $i,SV505: $i] :
( ( ( SV505
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1085 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1085 ) @ ( c_ATP__Linkup_Osko__Set__Xall__not__in__conv__1__1 @ SV505 @ SV1085 ) ) @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2991]) ).
thf(3542,plain,
! [SV1086: $i,SV506: $i] :
( ( ( SV506
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1086 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1086 ) @ ( c_ATP__Linkup_Osko__Set__Xequals0I__1__1 @ SV506 @ SV1086 ) ) @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3543,plain,
! [SV1592: $i,SV1087: $i,SV507: $i] :
( ( ( SV507 = SV1087 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1592 ) @ SV507 ) @ ( c_Set_Oinsert @ SV1087 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3544,plain,
! [SV508: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV508 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV508 @ tc_bool ) ) @ SV508 )
= ( c_Orderings_Obot__class_Obot @ SV508 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3545,plain,
! [SV1593: $i,SV1088: $i,SV509: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV509 @ SV1088 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1088 ) @ SV1593 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV509 @ SV1593 ) ) @ SV1593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3546,plain,
! [SV1089: $i,SV510: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV510 ) @ SV1089 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3547,plain,
! [SV1594: $i,SV1090: $i,SV511: $i] :
( ( ( hBOOL @ ( hAPP @ SV511 @ SV1090 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1594 ) @ SV1090 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1594 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3548,plain,
! [SV1091: $i,SV512: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV512 ) @ SV1091 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV512 @ tc_bool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3549,plain,
! [SV1092: $i,SV513: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV513 ) @ SV1092 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV513 @ tc_bool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3550,plain,
! [SV1093: $i,SV514: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV514 @ tc_bool ) ) @ SV1093 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3551,plain,
! [SV515: $i] :
( ( ( class_Orderings_Obot @ SV515 )
= $false )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV515 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3552,plain,
! [SV1595: $i,SV1094: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV516 ) @ SV1094 ) @ SV1595 ) )
| ~ ( hBOOL @ ( hAPP @ SV1595 @ SV1094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3553,plain,
! [SV1596: $i,SV1095: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ SV517 @ SV1095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1596 ) @ SV1095 ) @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3554,plain,
! [SV1597: $i,SV1096: $i,SV518: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV518 @ SV1096 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1597 ) @ SV1096 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1597 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3555,plain,
! [SV1097: $i,SV519: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV519 @ SV1097 ) )
= $true )
| ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV1097 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3556,plain,
! [SV1098: $i,SV520: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV520 @ SV1098 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1098 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3557,plain,
! [SV1099: $i,SV521: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV521 @ SV1099 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1099 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3558,plain,
! [SV1100: $i,SV522: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV522 @ SV1100 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV1100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3559,plain,
! [SV1101: $i,SV523: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV523 @ SV1101 ) )
= $true )
| ( ( ~ ( class_Lattices_Obounded__lattice @ SV1101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3560,plain,
! [SV1102: $i,SV524: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV524 @ SV1102 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1102 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3561,plain,
! [SV1103: $i,SV525: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV525 @ SV1103 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3562,plain,
! [SV1104: $i,SV526: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV526 @ SV1104 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3563,plain,
! [SV1105: $i,SV527: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV527 @ SV1105 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3564,plain,
! [SV1106: $i,SV528: $i] :
( ( ( class_Orderings_Otop @ ( tc_fun @ SV528 @ SV1106 ) )
= $true )
| ( ( ~ ( class_Orderings_Otop @ SV1106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3565,plain,
! [SV1107: $i,SV529: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV529 @ SV1107 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV1107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3015]) ).
thf(3566,plain,
! [SV1108: $i,SV530: $i] :
( ( ( class_HOL_Ominus @ ( tc_fun @ SV530 @ SV1108 ) )
= $true )
| ( ( ~ ( class_HOL_Ominus @ SV1108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3567,plain,
! [SV1109: $i,SV531: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV531 @ SV1109 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV1109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3568,plain,
! [SV532: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV532 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ SV532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3569,plain,
! [SV1598: $i,SV1111: $i,SV534: $i] :
( ( ( SV534 = SV1111 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1598 ) @ SV534 ) @ SV1111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3570,plain,
! [SV1599: $i,SV1112: $i,SV535: $i] :
( ( ! [SY5473: $i,SY5474: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SY5473 @ SY5474 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SY5473 @ SY5474 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3571,plain,
! [SV1600: $i,SV1113: $i,SV536: $i] :
( ( ! [SY5475: $i,SY5476: $i] :
( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 )
!= ( c_Set_Oinsert @ SY5475 @ ( c_Set_Oinsert @ SY5476 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 ) )
| ( SV536 = SY5476 )
| ( SV536 = SY5475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3572,plain,
! [SV1601: $i,SV1114: $i,SV537: $i] :
( ( ! [SY5477: $i,SY5478: $i] :
( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 )
!= ( c_Set_Oinsert @ SY5477 @ ( c_Set_Oinsert @ SY5478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 ) )
| ( SV1114 = SY5477 )
| ( SV1114 = SY5478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3573,plain,
! [SV1602: $i,SV1115: $i,SV538: $i] :
( ( ! [SY5479: $i,SY5480: $i] :
( ( ( hAPP @ SV538 @ SV1115 )
!= ( hAPP @ SV538 @ SV1602 ) )
| ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY5479 @ tc_bool ) ) @ SY5479 @ SY5480 )
| ( SV1115 = SV1602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3574,plain,
! [SV1603: $i,SV1116: $i,SV539: $i] :
( ( ! [SY5481: $i,SY5482: $i] :
( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 )
!= ( c_Set_Oinsert @ SY5481 @ ( c_Set_Oinsert @ SY5482 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 ) )
| ( SV539 = SY5482 )
| ( SV1116 = SY5482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3575,plain,
! [SV1604: $i,SV1117: $i,SV540: $i] :
( ( ! [SY5483: $i,SY5484: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SY5483 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5483 @ tc_bool ) ) )
| ( ( hAPP @ SV1117 @ SY5484 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5483 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SY5484 ) @ SV540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3576,plain,
! [SV1605: $i,SV1118: $i,SV541: $i] :
( ( ! [SY5485: $i,SY5486: $i] :
( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 )
!= ( c_Set_Oinsert @ SY5485 @ ( c_Set_Oinsert @ SY5486 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 ) )
| ( SV1118 = SY5485 )
| ( SV541 = SY5485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3577,plain,
! [SV1606: $i,SV1119: $i,SV542: $i] :
( ( ! [SY5487: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV542 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SV1606 @ SY5487 @ SV542 ) )
| ( SV1606 = SY5487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3578,plain,
! [SV1607: $i,SV1120: $i,SV543: $i] :
( ( ! [SY5488: $i] :
( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SV1607 )
!= ( c_Set_Oinsert @ SV543 @ SY5488 @ SV1607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SY5488 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1120 ) )
| ( SV1120 = SY5488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3579,plain,
! [SV1608: $i,SV1121: $i,SV544: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV544 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SV1121 ) @ SV1608 )
!= ( c_Orderings_Obot__class_Obot @ SV544 ) )
| ( SV1608
= ( c_Orderings_Obot__class_Obot @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3580,plain,
! [SV1609: $i,SV1122: $i,SV545: $i] :
( ( ! [SY5489: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SY5489 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SY5489 ) @ SV1609 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3581,plain,
! [SV1610: $i,SV1123: $i,SV546: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV546 @ tc_bool ) ) @ SV1123 ) @ SV1610 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
| ( SV1123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3582,plain,
! [SV1611: $i,SV1124: $i,SV547: $i] :
( ( ! [SY5490: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ SV1611 ) ) @ SY5490 )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1611 ) @ SY5490 ) ) )
| ( c_lessequals @ SY5490 @ SV1124 @ ( tc_fun @ SV547 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3583,plain,
! [SV1612: $i,SV1125: $i,SV548: $i] :
( ( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1125 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1612 ) )
| ( SV1125 = SV1612 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3584,plain,
! [SV1613: $i,SV1126: $i,SV549: $i] :
( ( ! [SY5491: $i,SY5492: $i] :
( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SY5491 )
!= ( c_Set_Oimage @ SV549 @ SY5492 @ SV1613 @ SY5491 ) )
| ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SY5491 )
| ( SV1126 = SY5492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3585,plain,
! [SV1614: $i,SV1127: $i,SV550: $i] :
( ( ! [SY5493: $i,SY5494: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SY5493 @ SY5494 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SY5493 @ SY5494 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3586,plain,
! [SV1615: $i,SV1128: $i,SV551: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV551 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SV1128 ) @ SV1615 )
!= ( c_Orderings_Otop__class_Otop @ SV551 ) )
| ( SV1128
= ( c_Orderings_Otop__class_Otop @ SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3587,plain,
! [SV1616: $i,SV1129: $i,SV552: $i] :
( ( ( ( c_Set_Oinsert @ SV552 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 )
!= ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 ) )
| ( SV552 = SV1616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3588,plain,
! [SV1617: $i,SV1130: $i,SV553: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV553 @ tc_bool ) ) @ SV1130 ) @ SV1617 )
!= SV1617 )
| ( c_lessequals @ SV1130 @ SV1617 @ ( tc_fun @ SV553 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3589,plain,
! [SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY5495: $i,SY5496: $i,SY5497: $i,SY5498: $i,SY5499: $i,SY5500: $i,SY5501: $i,SY5502: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SY5495 @ ( hAPP @ SY5496 @ SY5497 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SY5498 @ SY5499 @ SY5500 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SY5495 @ SY5496 @ SY5501 @ SY5499 @ SY5502 ) @ SY5497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3590,plain,
! [SV1619: $i,SV1132: $i,SV555: $i] :
( ( ! [SY5503: $i,SY5504: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SY5503 @ ( tc_fun @ SY5504 @ tc_bool ) ) @ SY5504 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SY5503 @ SV1619 @ ( tc_fun @ SY5504 @ tc_bool ) ) @ SY5504 @ SV555 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SY5503 @ SY5504 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SY5504 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5504 @ tc_bool ) ) @ SV1619 ) @ SY5503 ) @ SY5504 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3591,plain,
! [SV1620: $i,SV1133: $i,SV556: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV556 @ tc_bool ) ) @ SV1133 ) @ SV1620 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV556 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1133 @ SV1620 @ ( tc_fun @ SV556 @ tc_bool ) )
= SV1133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3592,plain,
! [SV1621: $i,SV1134: $i,SV558: $i] :
( ( ! [SY5505: $i] :
( ( ( hAPP @ SV558 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1134 @ SV558 @ SV1621 @ SY5505 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5505 @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5505 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1134 @ SV558 @ SV1621 @ ( tc_fun @ SY5505 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3593,plain,
! [SV1622: $i,SV1135: $i,SV559: $i] :
( ( ! [SY5506: $i,SY5507: $i] :
( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SY5506 @ SY5507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3594,plain,
! [SV1623: $i,SV1136: $i,SV560: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV560 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SV1136 ) @ SV1623 )
!= SV1136 )
| ( c_lessequals @ SV1136 @ SV1623 @ SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3595,plain,
! [SV1624: $i,SV1137: $i,SV561: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV561 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SV1137 ) @ SV1624 )
!= ( c_Orderings_Obot__class_Obot @ SV561 ) )
| ( SV1137
= ( c_Orderings_Obot__class_Obot @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3596,plain,
! [SV1625: $i,SV1138: $i,SV562: $i] :
( ( ! [SY5508: $i,SY5509: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SY5508 @ SY5509 @ SV562 ) )
| ( c_lessequals @ SY5509 @ SY5508 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3597,plain,
! [SV1626: $i,SV1139: $i,SV563: $i] :
( ( ! [SY5510: $i,SY5511: $i,SY5512: $i] :
( ( ( hAPP @ SV563 @ SV1139 )
!= ( hAPP @ SV563 @ SV1626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5510 ) @ SV1626 ) @ SY5511 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5510 ) @ SV1139 ) @ SY5511 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SY5511 @ SY5510 @ SY5512 )
| ( SV1139 = SV1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3598,plain,
! [SV1627: $i,SV1140: $i,SV564: $i] :
( ( ! [SY5513: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV564 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SV1627 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SY5513 @ SY5513 @ SV564 ) )
| ( SV1140 = SV1627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3599,plain,
! [SV1628: $i,SV1141: $i,SV565: $i] :
( ( ! [SY5514: $i,SY5515: $i,SY5516: $i] :
( ( ( hAPP @ SV565 @ SV1141 )
!= ( hAPP @ SV565 @ SV1628 ) )
| ~ ( c_Fun_Oinj__on @ SV565 @ SY5514 @ SY5515 @ SY5516 )
| ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5515 ) @ SV1628 ) @ SY5514 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5515 ) @ SV1141 ) @ SY5514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3600,plain,
! [SV1629: $i,SV1142: $i,SV566: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV566 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SV1142 ) @ SV1629 )
!= SV1629 )
| ( c_lessequals @ SV1142 @ SV1629 @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3601,plain,
! [SV1630: $i,SV1143: $i,SV567: $i] :
( ( ! [SY5517: $i,SY5518: $i] :
( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SY5517 )
!= ( c_Set_Oimage @ SV567 @ SY5518 @ SV1630 @ SY5517 ) )
| ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SY5518 ) @ SV1630 @ SY5517 )
| ( SV1143 = SY5518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3602,plain,
! [SV1144: $i,SV568: $i] :
( ( ( ( c_Suc @ SV568 )
!= ( c_Suc @ SV1144 ) )
= $true )
| ( ( SV568 = SV1144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3603,plain,
! [SV1631: $i,SV1145: $i,SV569: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV569 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV1145 @ SV1631 @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3604,plain,
! [SV1632: $i,SV1146: $i,SV570: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) )
!= ( c_Collect @ SV1146 @ SV570 ) )
| ~ ( hBOOL @ ( hAPP @ SV1146 @ SV1632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3605,plain,
! [SV1633: $i,SV1147: $i,SV571: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV571 @ tc_bool ) ) @ SV1147 ) @ SV1633 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
| ( SV1633
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3606,plain,
! [SV1634: $i,SV1148: $i,SV572: $i] :
( ( ! [SY5519: $i,SY5520: $i,SY5521: $i,SY5522: $i,SY5523: $i,SY5524: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SY5519 @ SY5520 )
!= ( c_Fun_Ocomp @ SY5521 @ SY5522 @ SY5523 @ SY5519 @ SY5520 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY5524 ) )
= ( hAPP @ SY5521 @ ( hAPP @ SY5522 @ SY5524 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3607,plain,
! [SV1635: $i,SV1149: $i,SV573: $i] :
( ( ( ( c_Set_Oinsert @ SV573 @ SV1149 @ SV1635 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1635 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1635 ) @ SV573 ) @ SV1149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3608,plain,
! [SV1150: $i,SV574: $i] :
( ( ( ( c_Suc @ SV574 )
!= ( c_Suc @ SV1150 ) )
= $true )
| ( ( SV574 = SV1150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3609,plain,
! [SV1636: $i,SV1151: $i,SV575: $i] :
( ( ! [SY5525: $i,SY5526: $i,SY5527: $i,SY5528: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SY5525 @ SY5526 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SY5525 ) @ SY5527 @ SY5525 @ SY5525 @ SY5526 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SY5528 ) )
= ( hAPP @ SY5527 @ SY5528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3610,plain,
! [SV1637: $i,SV1152: $i,SV576: $i] :
( ( ! [SY5529: $i,SY5530: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SY5529 @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ( ( hAPP @ SV1637 @ SY5530 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5529 ) @ SY5530 ) @ SV1152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3611,plain,
! [SV1638: $i,SV1153: $i,SV578: $i] :
( ( ! [SY5531: $i] :
( ( ( c_Set_Oimage @ SV578 @ SV1153 @ SV1638 @ SY5531 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5531 @ tc_bool ) ) )
| ( SV1153
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1638 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3612,plain,
! [SV1639: $i,SV1154: $i,SV580: $i] :
( ( ( c_Set_Oinsert @ SV580 @ SV1154 @ SV1639 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1639 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3613,plain,
! [SV1640: $i,SV1155: $i,SV581: $i] :
( ( ! [SY5532: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) )
!= ( c_Set_Oimage @ SV1155 @ SV1640 @ SY5532 @ SV581 ) )
| ( SV1640
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5532 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3614,plain,
! [SV1641: $i,SV1156: $i,SV582: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV582 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SV1156 ) @ SV1641 )
!= ( c_Orderings_Otop__class_Otop @ SV582 ) )
| ( SV1641
= ( c_Orderings_Otop__class_Otop @ SV582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3615,plain,
! [SV1642: $i,SV1157: $i,SV583: $i] :
( ( ( ( c_Collect @ SV583 @ SV1157 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1157 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SV583 @ SV1642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3616,plain,
! [SV1643: $i,SV1158: $i,SV584: $i] :
( ( ! [SY5533: $i,SY5534: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SY5533 @ SY5534 @ SV584 ) )
| ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SY5534 @ SY5533 @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3617,plain,
! [SV1644: $i,SV1159: $i,SV585: $i] :
( ( ! [SY5535: $i] :
( ( ( hAPP @ SV585 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV1159 @ SV585 @ SV1644 @ SY5535 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5535 @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1159 @ SV585 @ SV1644 @ ( tc_fun @ SY5535 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5535 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3618,plain,
! [SV1645: $i,SV1160: $i,SV586: $i] :
( ( ! [SY5536: $i,SY5537: $i,SY5538: $i] :
( ( ( hAPP @ SV586 @ SV1160 )
!= ( hAPP @ SV586 @ SV1645 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5536 ) @ SV1645 ) @ SY5537 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5536 ) @ SV1160 ) @ SY5537 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SY5537 @ SY5536 @ SY5538 )
| ( SV1160 = SV1645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3619,plain,
! [SV1646: $i,SV1161: $i,SV587: $i] :
( ( ! [SY5539: $i,SY5540: $i,SY5541: $i] :
( ( ( hAPP @ SV587 @ SV1161 )
!= ( hAPP @ SV587 @ SV1646 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5539 ) @ SV1646 ) @ SY5540 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5539 ) @ SV1161 ) @ SY5540 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SY5540 @ SY5539 @ SY5541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3620,plain,
! [SV1647: $i,SV1162: $i,SV588: $i,SV2: $i] :
( ( ! [SY5542: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SV1647 ) @ ( c_Set_Oimage @ SV2 @ SY5542 @ SV1162 @ SV1647 ) @ ( tc_fun @ SV1647 @ tc_bool ) )
| ~ ( c_lessequals @ SV588 @ SY5542 @ ( tc_fun @ SV1162 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SV1647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3621,plain,
! [SV1648: $i,SV1163: $i,SV589: $i,SV3: $i] :
( ( ! [SY5543: $i] :
( ( c_Fun_Oinj__on @ SV3 @ SV589 @ SV1163 @ SV1648 )
| ~ ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SY5543 @ SV589 @ SV1163 ) @ SV1163 @ SV1648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3622,plain,
! [SV1649: $i,SV1164: $i,SV590: $i,SV4: $i] :
( ( ! [SY5544: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
| ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1649 @ SV590 @ SY5544 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5544 ) @ SV1164 ) @ SV1649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3623,plain,
! [SV1650: $i,SV1165: $i,SV591: $i,SV5: $i] :
( ( ! [SY5545: $i] :
( ( c_lessequals @ ( hAPP @ SV5 @ SV591 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1165 @ SV5 @ SV1650 @ ( tc_fun @ SY5545 @ tc_bool ) ) @ ( tc_fun @ SY5545 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV591 ) @ SV1165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3624,plain,
! [SV1651: $i,SV1166: $i,SV592: $i,SV6: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV6 @ SV592 @ SV1166 ) @ SV1651 @ ( tc_fun @ SV1166 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV592 @ SV1651 @ ( tc_fun @ SV1166 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1166 ) @ SV6 ) @ SV1651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3625,plain,
! [SV1652: $i,SV1167: $i,SV593: $i,SV7: $i] :
( ( ( c_lessequals @ SV7 @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1652 @ SV7 @ SV1167 ) @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3626,plain,
! [SV1653: $i,SV1168: $i,SV594: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ ( c_Set_Oinsert @ SV594 @ SV1168 @ SV1653 ) @ ( tc_fun @ SV1653 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SV1168 @ ( tc_fun @ SV1653 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3627,plain,
! [SV1654: $i,SV1169: $i,SV595: $i,SV9: $i] :
( ( ! [SY5546: $i] :
( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SV1169 @ SV1654 ) @ SY5546 @ SV1654 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1654 ) @ SV595 ) @ SV1169 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SV1169 @ SY5546 @ SV1654 @ SV1654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3628,plain,
! [SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ! [SY5547: $i,SY5548: $i,SY5549: $i,SY5550: $i,SY5551: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SY5547 @ SY5548 @ SY5549 @ SY5550 @ SY5551 @ SV1170 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3629,plain,
! [SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ! [SY5552: $i,SY5553: $i,SY5554: $i,SY5555: $i,SY5556: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SY5552 @ SY5553 @ SY5554 @ SY5555 @ SV1171 @ SY5556 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3630,plain,
! [SV1657: $i,SV1172: $i,SV598: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1657 @ ( tc_fun @ SV1172 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV1657 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SV1657 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3631,plain,
! [SV1658: $i,SV1173: $i,SV599: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV13 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SV1658 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3632,plain,
! [SV1659: $i,SV1174: $i,SV600: $i,SV14: $i] :
( ( ! [SY5557: $i,SY5558: $i,SY5559: $i,SY5560: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SY5557 @ SY5558 @ SY5559 ) @ SY5560 @ SY5559 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SY5559 @ SY5560 @ SY5558 ) @ SV1174 @ SY5557 @ SY5560 @ SY5558 ) )
| ~ ( c_Fun_Oinj__on @ SV1659 @ SY5557 @ SY5558 @ SY5559 )
| ~ ( c_Finite__Set_Ofinite @ SY5557 @ SY5558 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY5560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3633,plain,
! [SV1175: $i,SV601: $i,SV15: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV601 @ ( tc_fun @ SV1175 @ tc_bool ) ) @ SV1175 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV15 @ SV1175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3634,plain,
! [SV1660: $i,SV1176: $i,SV602: $i,SV16: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV16 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1660 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3635,plain,
! [SV1661: $i,SV1177: $i,SV603: $i,SV17: $i] :
( ( ! [SY5561: $i] :
( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SV603 @ SV1177 @ ( tc_fun @ SV1661 @ tc_bool ) ) @ SV1661 @ SY5561 )
| ~ ( c_Fun_Oinj__on @ SV17 @ SV603 @ SV1661 @ SY5561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3636,plain,
! [SV1662: $i,SV1178: $i,SV604: $i,SV18: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV604 @ SV1178 @ SV18 ) ) @ SV1662 )
= ( c_Set_Oinsert @ SV604 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV18 @ tc_bool ) ) @ SV1178 ) @ SV1662 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3637,plain,
! [SV1663: $i,SV1179: $i,SV605: $i,SV19: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SV605 ) @ ( c_Set_Oinsert @ SV1179 @ SV1663 @ SV19 ) )
= ( c_Set_Oinsert @ SV1179 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV19 @ tc_bool ) ) @ SV605 ) @ SV1663 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3638,plain,
! [SV1664: $i,SV1180: $i,SV606: $i,SV20: $i] :
( ( ! [SY5562: $i] :
( ( c_Set_Ovimage @ SV20 @ ( c_HOL_Ominus__class_Ominus @ SV606 @ SV1180 @ ( tc_fun @ SV1664 @ tc_bool ) ) @ SY5562 @ SV1664 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV20 @ SV606 @ SY5562 @ SV1664 ) @ ( c_Set_Ovimage @ SV20 @ SV1180 @ SY5562 @ SV1664 ) @ ( tc_fun @ SY5562 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3639,plain,
! [SV1665: $i,SV1181: $i,SV607: $i,SV21: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3640,plain,
! [SV1666: $i,SV1182: $i,SV608: $i,SV22: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV22 @ ( c_Set_Ovimage @ SV22 @ SV608 @ SV1182 @ SV1666 ) @ SV1182 @ SV1666 ) @ SV608 @ ( tc_fun @ SV1666 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3641,plain,
! [SV1667: $i,SV1183: $i,SV609: $i,SV23: $i] :
( ( ( ( c_Set_Ovimage @ SV23 @ ( c_Set_Oimage @ SV23 @ SV609 @ SV1183 @ SV1667 ) @ SV1183 @ SV1667 )
= SV609 )
| ~ ( c_Fun_Oinj__on @ SV23 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1183 @ SV1667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3642,plain,
! [SV1668: $i,SV1184: $i,SV611: $i,SV25: $i] :
( ( ( SV25 = SV611 )
| ~ ( c_Finite__Set_Ofold1Set @ SV1184 @ ( c_Set_Oinsert @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1668 @ tc_bool ) ) @ SV1668 ) @ SV611 @ SV1668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3643,plain,
! [SV1186: $i,SV613: $i,SV27: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV27 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV613 @ SV1186 @ SV27 ) @ SV27 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 ) @ SV613 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1186 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3644,plain,
! [SV614: $i,SV28: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV28 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV28 ) @ SV614 ) @ ( c_Orderings_Otop__class_Otop @ SV28 ) )
= ( c_Orderings_Otop__class_Otop @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3645,plain,
! [SV615: $i,SV29: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV29 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV29 ) @ ( c_Orderings_Otop__class_Otop @ SV29 ) ) @ SV615 )
= ( c_Orderings_Otop__class_Otop @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3646,plain,
! [SV1669: $i,SV1187: $i,SV618: $i,SV32: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV32 @ ( c_Set_Oinsert @ SV618 @ SV1187 @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV32 @ SV1187 @ ( tc_fun @ SV1669 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV618 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1669 @ tc_bool ) ) @ SV1669 ) @ ( tc_fun @ SV1669 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3647,plain,
! [SV1670: $i,SV1188: $i,SV619: $i,SV33: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SV619 @ SV1188 @ SV1670 ) @ ( tc_fun @ SV1670 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV33 @ ( c_Set_Oinsert @ SV619 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1670 @ tc_bool ) ) @ SV1670 ) @ ( tc_fun @ SV1670 @ tc_bool ) ) @ SV1188 @ ( tc_fun @ SV1670 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3648,plain,
! [SV1189: $i,SV620: $i,SV34: $i] :
( ( ( c_Finite__Set_Ofinite @ SV34 @ SV620 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV1189 @ ( tc_fun @ SV620 @ tc_bool ) ) @ SV620 )
| ~ ( c_Finite__Set_Ofinite @ SV1189 @ SV620 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3649,plain,
! [SV1190: $i,SV621: $i,SV35: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SV621 @ ( tc_fun @ SV1190 @ tc_bool ) ) @ SV1190 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV35 @ SV1190 )
| ~ ( c_Finite__Set_Ofinite @ SV621 @ SV1190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3650,plain,
! [SV1671: $i,SV1191: $i,SV622: $i,SV36: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV622 @ SV1191 @ SV36 ) ) @ ( c_Set_Oinsert @ SV622 @ SV1671 @ SV36 ) )
= ( c_Set_Oinsert @ SV622 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV36 @ tc_bool ) ) @ SV1191 ) @ SV1671 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3651,plain,
! [SV1672: $i,SV1193: $i,SV624: $i,SV38: $i] :
( ( ! [SY5563: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SY5563 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5563 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
| ~ ( c_Finite__Set_Ofinite @ SY5563 @ SV1672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3652,plain,
! [SV1673: $i,SV1194: $i,SV625: $i,SV39: $i] :
( ( ( hBOOL @ ( hAPP @ SV39 @ SV625 ) )
| ( SV1194 = SV625 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1194 @ SV39 @ SV1673 ) @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3653,plain,
! [SV1674: $i,SV1195: $i,SV627: $i,SV41: $i] :
( ( ! [SY5564: $i,SY5565: $i] :
( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5564 ) @ SV627 ) @ SY5565 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5565 @ SV41 @ SY5564 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3654,plain,
! [SV1675: $i,SV1197: $i,SV629: $i,SV43: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV43 @ SV629 @ SV1197 ) @ SV1675 @ SV1197 @ SV629 @ t_a ) @ v_x )
= SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3655,plain,
! [SV1198: $i,SV630: $i,SV44: $i] :
( ( ( c_Finite__Set_Ofinite @ SV44 @ SV630 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1198 @ SV44 @ SV630 ) @ SV630 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3656,plain,
! [SV1199: $i,SV631: $i,SV45: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV45 @ SV631 @ SV1199 ) @ SV1199 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV631 @ SV1199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3657,plain,
! [SV1676: $i,SV1200: $i,SV632: $i,SV46: $i] :
( ( ! [SY5566: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SV632 @ SV1200 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SY5566 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SY5566 @ ( tc_fun @ SV46 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5566 ) @ SV1200 ) @ SV1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3658,plain,
! [SV1677: $i,SV1201: $i,SV633: $i,SV47: $i] :
( ( ! [SY5567: $i,SY5568: $i,SY5569: $i] :
( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SY5567 ) @ SY5568 @ SY5569 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5568 ) @ SV1677 ) @ SV1201 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5568 @ tc_bool ) ) @ SY5568 ) @ ( tc_fun @ SY5568 @ tc_bool ) ) @ SY5567 @ SY5568 @ SY5569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3659,plain,
! [SV1678: $i,SV1202: $i,SV634: $i,SV48: $i] :
( ( ! [SY5570: $i] :
( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV1202 ) @ SV1678 ) @ SV634 @ SY5570 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5570 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SV1202 @ SV634 @ SY5570 ) ) @ ( c_Set_Oimage @ SV48 @ SV1678 @ SV634 @ SY5570 ) ) )
| ~ ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV634 @ SY5570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3660,plain,
! [SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY5571: $i,SY5572: $i,SY5573: $i,SY5574: $i,SY5575: $i,SY5576: $i,SY5577: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SY5571 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5572 @ SV49 @ SY5573 @ SY5574 @ SY5575 @ SY5571 @ SY5576 @ SY5577 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3661,plain,
! [SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY5578: $i,SY5579: $i,SY5580: $i,SY5581: $i,SY5582: $i,SY5583: $i,SY5584: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SY5578 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SY5579 @ SY5580 @ SY5581 @ SY5578 @ SY5582 @ SY5583 @ SY5584 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3662,plain,
! [SV1681: $i,SV1205: $i,SV637: $i,SV51: $i] :
( ( ! [SY5585: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV51 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV637 @ tc_bool ) ) @ SV1205 ) @ SV1681 ) @ SV637 @ SY5585 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5585 @ tc_bool ) ) @ ( c_Set_Oimage @ SV51 @ SV1205 @ SV637 @ SY5585 ) ) @ ( c_Set_Oimage @ SV51 @ SV1681 @ SV637 @ SY5585 ) ) @ ( tc_fun @ SY5585 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3663,plain,
! [SV1206: $i,SV638: $i,SV52: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SV638 ) @ SV1206 ) @ SV52 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1206 @ SV52 )
| ~ ( c_Finite__Set_Ofinite @ SV638 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3122]) ).
thf(3664,plain,
! [SV1207: $i,SV639: $i,SV53: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SV639 ) @ SV1207 ) @ SV53 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1207 @ SV53 )
| ~ ( c_Finite__Set_Ofinite @ SV639 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3665,plain,
! [SV1682: $i,SV1208: $i,SV640: $i,SV54: $i] :
( ( ! [SY5586: $i] : ( c_lessequals @ ( c_Relation_OImage @ SV54 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV640 @ tc_bool ) ) @ SV1208 ) @ SV1682 ) @ SV640 @ SY5586 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5586 @ tc_bool ) ) @ ( c_Relation_OImage @ SV54 @ SV1208 @ SV640 @ SY5586 ) ) @ ( c_Relation_OImage @ SV54 @ SV1682 @ SV640 @ SY5586 ) ) @ ( tc_fun @ SY5586 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3666,plain,
! [SV1683: $i,SV1209: $i,SV641: $i,SV55: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ SV1209 ) ) @ SV1683 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV1209 ) @ SV1683 ) ) )
| ~ ( c_lessequals @ SV1683 @ SV641 @ ( tc_fun @ SV55 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3667,plain,
! [SV1684: $i,SV1210: $i,SV642: $i,SV56: $i] :
( ( ! [SY5587: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV56 @ SV642 @ SV1210 @ SV1684 ) @ SY5587 )
= ( c_Option_Ooption_ONone @ SV1684 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1210 ) @ SY5587 ) @ SV642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3668,plain,
! [SV1211: $i,SV643: $i,SV57: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV57 @ tc_bool ) ) @ SV643 ) @ SV1211 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV57 @ tc_bool ) ) )
= $true )
| ( ( ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SV643 @ SV1211 @ SV57 )
= ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SV643 @ SV1211 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3669,plain,
! [SV1685: $i,SV1212: $i,SV644: $i,SV58: $i] :
( ( ! [SY5588: $i,SY5589: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV58 @ SV644 @ SV1212 @ SV1685 @ SY5588 ) @ SY5589 )
= ( hAPP @ SV58 @ ( hAPP @ SV644 @ SY5589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3670,plain,
! [SV1686: $i,SV1213: $i,SV645: $i,SV59: $i] :
( ( ! [SY5590: $i,SY5591: $i] :
( ( hAPP @ SV59 @ ( hAPP @ SV645 @ SV1213 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV59 @ SV645 @ SV1686 @ SY5590 @ SY5591 ) @ SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3671,plain,
! [SV1687: $i,SV1214: $i,SV646: $i,SV60: $i] :
( ( ! [SY5592: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ ( hAPP @ SY5592 @ SV646 ) ) @ ( c_Set_Oimage @ SY5592 @ SV1214 @ SV60 @ SV1687 ) ) )
| ~ ( c_Fun_Oinj__on @ SY5592 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SV1687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3672,plain,
! [SV1688: $i,SV1215: $i,SV647: $i,SV61: $i] :
( ( ! [SY5593: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SV1688 @ SY5593 @ SV61 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5593 ) @ SV1215 ) @ SV1688 ) )
| ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SY5593 @ tc_bool ) ) @ SY5593 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3673,plain,
! [SV1689: $i,SV1216: $i,SV648: $i,SV62: $i] :
( ( ! [SY5594: $i] :
( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ SV1216 ) ) @ SV1689 )
= ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ ( hAPP @ ( hAPP @ SV62 @ SV1216 ) @ SV1689 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SY5594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3674,plain,
! [SV1690: $i,SV1217: $i,SV649: $i,SV63: $i] :
( ( ! [SY5595: $i] :
( ( ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ SV1690 ) )
= ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ SV1690 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SY5595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3675,plain,
! [SV1691: $i,SV1218: $i,SV650: $i,SV64: $i] :
( ( ( ( hAPP @ ( hAPP @ SV64 @ SV650 ) @ SV1218 )
= ( hAPP @ ( hAPP @ SV64 @ SV1218 ) @ SV650 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV64 @ SV1691 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3676,plain,
! [SV1692: $i,SV1219: $i,SV651: $i,SV65: $i] :
( ( ( hBOOL @ ( hAPP @ SV65 @ SV651 ) )
| ( hBOOL @ ( hAPP @ SV1219 @ SV651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1692 @ tc_bool ) ) @ SV1219 ) @ SV65 ) @ SV651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3677,plain,
! [SV1693: $i,SV1220: $i,SV652: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV66 @ tc_bool ) ) @ SV652 ) @ SV1220 ) @ SV1693 ) )
| ~ ( hBOOL @ ( hAPP @ SV1220 @ SV1693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3678,plain,
! [SV1694: $i,SV1221: $i,SV653: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV67 @ tc_bool ) ) @ SV653 ) @ SV1221 ) @ SV1694 ) )
| ~ ( hBOOL @ ( hAPP @ SV653 @ SV1694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(3679,plain,
! [SV1695: $i,SV1222: $i,SV654: $i,SV68: $i] :
( ( ! [SY5596: $i] :
( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV1695 @ SV68 @ SV1222 @ SY5596 ) @ ( c_Set_Oimage @ SV1695 @ SV654 @ SV1222 @ SY5596 ) @ ( tc_fun @ SY5596 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV1695 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SY5596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3680,plain,
! [SV1696: $i,SV1223: $i,SV655: $i,SV69: $i] :
( ( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SV1223 @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1696 ) @ SV655 ) @ SV69 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1223 @ ( tc_fun @ SV1696 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3681,plain,
! [SV1697: $i,SV1224: $i,SV656: $i,SV70: $i] :
( ( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SV1224 @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV656 ) @ SV70 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1224 @ ( tc_fun @ SV1697 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3682,plain,
! [SV1698: $i,SV1225: $i,SV657: $i,SV71: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1698 @ ( tc_fun @ SV1225 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1225 ) @ SV657 ) @ SV71 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SV1698 @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3683,plain,
! [SV1699: $i,SV1226: $i,SV658: $i,SV72: $i] :
( ( ! [SY5597: $i,SY5598: $i] :
( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SY5597 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5597 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SY5597 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SY5597 ) ) )
| ~ ( c_lessequals @ SV1699 @ SY5598 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_lessequals @ SV1226 @ SY5598 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SY5598 @ SV658 @ SY5597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3684,plain,
! [SV1700: $i,SV1227: $i,SV659: $i,SV73: $i] :
( ( ! [SY5599: $i] :
( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
| ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SV1700 @ SY5599 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1700 @ SY5599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3685,plain,
! [SV1701: $i,SV1228: $i,SV660: $i,SV74: $i] :
( ( ! [SY5600: $i,SY5601: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5600 ) @ SV1228 ) @ SY5601 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SY5601 @ SY5600 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3686,plain,
! [SV1702: $i,SV1229: $i,SV661: $i,SV75: $i] :
( ( ! [SY5602: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SV661 @ SV1229 ) @ SV1702 @ SV1229 @ SV661 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV661 @ tc_bool ) ) @ SV661 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1229 ) @ SY5602 ) @ SV1702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3687,plain,
! [SV1703: $i,SV1230: $i,SV662: $i,SV76: $i] :
( ( ! [SY5603: $i,SY5604: $i] :
( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1230 @ SV1703 @ SV76 @ SY5603 @ SV662 @ SY5604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3688,plain,
! [SV1231: $i,SV663: $i,SV77: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV77 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ SV77 ) ) @ SV663 ) @ SV1231 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV77 ) @ ( hAPP @ SV663 @ v_x ) ) @ ( hAPP @ SV1231 @ v_x ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3689,plain,
! [SV1704: $i,SV1232: $i,SV664: $i,SV78: $i] :
( ( ! [SY5605: $i,SY5606: $i] :
( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SV1232 @ SV1704 @ SY5605 ) @ SY5605 @ SY5606 )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SY5605 @ SY5606 @ SV1704 ) @ SV1232 @ SV1704 @ SY5606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3690,plain,
! [SV1705: $i,SV1233: $i,SV665: $i,SV79: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV665 ) @ SV1233 ) ) @ SV1705 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV79 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV665 ) @ SV1705 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV79 @ tc_bool ) ) @ SV1233 ) @ SV1705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3691,plain,
! [SV1706: $i,SV1234: $i,SV666: $i,SV80: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV1234 ) @ SV1706 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV80 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ SV1234 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV80 @ tc_bool ) ) @ SV666 ) @ SV1706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3692,plain,
! [SV1707: $i,SV1235: $i,SV667: $i,SV81: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV81 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ SV1235 ) @ SV1707 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1235 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3693,plain,
! [SV1708: $i,SV1236: $i,SV668: $i,SV82: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV82 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ SV668 ) @ SV1236 ) ) @ SV1708 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV668 ) @ SV1708 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV1236 ) @ SV1708 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3694,plain,
! [SV1709: $i,SV1237: $i,SV669: $i,SV83: $i] :
( ( ( hBOOL @ ( hAPP @ SV83 @ SV669 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1237 ) @ SV669 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1237 @ tc_bool ) ) @ SV1709 ) @ ( c_Collect @ SV83 @ SV1237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3695,plain,
! [SV1710: $i,SV1240: $i,SV672: $i,SV86: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SV1240 @ SV1710 ) @ SV1240 )
| ~ ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1240 @ tc_bool ) ) @ SV1240 @ SV1710 )
| ~ ( c_Finite__Set_Ofinite @ SV672 @ SV1710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3696,plain,
! [SV674: $i,SV88: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV88 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 ) @ SV674 ) @ SV674 )
= SV674 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3697,plain,
! [SV1711: $i,SV1241: $i,SV675: $i,SV89: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3698,plain,
! [SV1712: $i,SV1242: $i,SV676: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1712 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ SV1712 @ ( tc_fun @ SV1242 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3699,plain,
! [SV1713: $i,SV1243: $i,SV677: $i,SV91: $i] :
( ( ~ ( class_Orderings_Oorder @ SV91 )
| ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3700,plain,
! [SV1714: $i,SV1244: $i,SV678: $i,SV92: $i] :
( ( ! [SY5607: $i] :
( ( c_Relation_OImage @ SV92 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV678 @ tc_bool ) ) @ SV1244 ) @ SV1714 ) @ SV678 @ SY5607 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5607 @ tc_bool ) ) @ ( c_Relation_OImage @ SV92 @ SV1244 @ SV678 @ SY5607 ) ) @ ( c_Relation_OImage @ SV92 @ SV1714 @ SV678 @ SY5607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3701,plain,
! [SV1715: $i,SV1245: $i,SV679: $i,SV93: $i] :
( ( ! [SY5608: $i] :
( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SV1245 @ SV1715 ) @ SV1715 @ SY5608 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5608 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 ) @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 @ SY5608 ) ) )
| ~ ( c_Fun_Oinj__on @ SV93 @ SV1245 @ SV1715 @ SY5608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(3702,plain,
! [SV1716: $i,SV1246: $i,SV681: $i,SV95: $i] :
( ( ( c_Set_Oinsert @ SV95 @ ( c_Set_Oinsert @ SV681 @ SV1246 @ SV1716 ) @ SV1716 )
= ( c_Set_Oinsert @ SV681 @ ( c_Set_Oinsert @ SV95 @ SV1246 @ SV1716 ) @ SV1716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3703,plain,
! [SV1717: $i,SV1247: $i,SV682: $i,SV96: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV96 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) @ SV1247 @ SV682 @ ( tc_fun @ SV1717 @ tc_bool ) ) @ ( tc_fun @ SV1717 @ tc_bool ) )
= SV96 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3704,plain,
! [SV1718: $i,SV1248: $i,SV683: $i,SV97: $i] :
( ( ! [SY5609: $i,SY5610: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV97 @ SV683 @ SV1248 @ SV1718 ) @ SY5609 ) @ SY5610 )
= ( hAPP @ ( hAPP @ SV97 @ SY5610 ) @ SY5609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3705,plain,
! [SV1719: $i,SV1249: $i,SV684: $i,SV98: $i] :
( ( ( hAPP @ ( c_COMBK @ SV98 @ SV684 @ SV1249 ) @ SV1719 )
= SV98 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3706,plain,
! [SV1720: $i,SV1250: $i,SV685: $i,SV99: $i] :
( ( ! [SY5611: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1720 @ ( tc_fun @ SY5611 @ tc_bool ) ) @ SY5611 @ SV99 ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1720 @ SV1250 @ ( tc_fun @ SY5611 @ tc_bool ) ) @ SY5611 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV685 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5611 @ tc_bool ) ) @ SV1250 ) @ SV1720 ) @ SY5611 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3707,plain,
! [SV1252: $i,SV687: $i,SV101: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV101 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV687 @ SV1252 @ SV101 )
| ( c_lessequals @ SV1252 @ SV687 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3708,plain,
! [SV688: $i,SV102: $i] :
( ( ( class_Orderings_Olinorder @ SV102 )
= $false )
| ( ( ~ ( c_lessequals @ SV688 @ SV688 @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ SV688 @ SV688 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3170]) ).
thf(3709,plain,
! [SV689: $i,SV103: $i] :
( ( ( class_Orderings_Olinorder @ SV103 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV689 @ SV689 @ SV103 )
| ( c_lessequals @ SV689 @ SV689 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3710,plain,
! [SV1253: $i,SV690: $i,SV104: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV104 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV690 @ SV1253 @ SV104 )
| ~ ( c_lessequals @ SV1253 @ SV690 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3711,plain,
! [SV1254: $i,SV691: $i,SV105: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV105 ) )
= $true )
| ( ( ( c_lessequals @ SV691 @ SV1254 @ SV105 )
| ( c_HOL_Oord__class_Oless @ SV1254 @ SV691 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3712,plain,
! [SV1255: $i,SV692: $i,SV106: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV106 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV692 @ SV1255 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV1255 @ SV692 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3713,plain,
! [SV1256: $i,SV693: $i,SV107: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV107 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1256 @ SV107 )
| ( c_lessequals @ SV1256 @ SV693 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3714,plain,
! [SV1721: $i,SV1257: $i,SV694: $i,SV108: $i] :
( ( ~ ( class_HOL_Oord @ SV108 )
| ~ ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SV1721 @ SV108 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SV1721 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3715,plain,
! [SV1258: $i,SV695: $i,SV109: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV109 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV695 @ SV1258 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1258 @ SV695 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3716,plain,
! [SV1722: $i,SV1259: $i,SV696: $i,SV110: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV110 ) @ ( hAPP @ SV696 @ SV1259 ) ) @ ( c_Set_Oimage @ SV696 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1722 @ tc_bool ) ) @ SV1722 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3717,plain,
! [SV697: $i,SV111: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV111 )
= $false )
| ( ( ( ( c_Complete__Lattice_OSup__class_OSup @ SV697 @ SV111 )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 ) @ ( c_Orderings_Obot__class_Obot @ SV111 ) @ SV697 @ SV111 @ SV111 ) )
| ~ ( c_Finite__Set_Ofinite @ SV697 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3718,plain,
! [SV1260: $i,SV698: $i,SV112: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV112 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
| ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3180]) ).
thf(3719,plain,
! [SV699: $i,SV113: $i] :
( ( ( class_Orderings_Olinorder @ SV113 )
= $false )
| ( ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV699 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV113 @ tc_bool ) ) @ SV113 ) @ SV113 )
= SV699 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3720,plain,
! [SV1723: $i,SV1261: $i,SV700: $i,SV114: $i] :
( ( ! [SY5612: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV114 @ SV700 @ SV1261 @ SV1723 ) @ ( c_Set_Oimage @ SV114 @ SY5612 @ SV1261 @ SV1723 ) @ ( tc_fun @ SV1723 @ tc_bool ) ) @ ( c_Set_Oimage @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV700 @ SY5612 @ ( tc_fun @ SV1261 @ tc_bool ) ) @ SV1261 @ SV1723 ) @ ( tc_fun @ SV1723 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3721,plain,
! [SV1724: $i,SV1262: $i,SV701: $i,SV115: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV701 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV1262 ) @ SV1724 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV1262 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV115 @ tc_bool ) ) @ SV701 ) @ SV1724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3722,plain,
! [SV1725: $i,SV1263: $i,SV702: $i,SV116: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV702 ) @ SV1263 ) ) @ SV1725 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV702 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV116 @ tc_bool ) ) @ SV1263 ) @ SV1725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3723,plain,
! [SV1726: $i,SV1264: $i,SV703: $i,SV117: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV117 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ SV1264 ) ) @ SV1726 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV1264 ) @ SV1726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3724,plain,
! [SV1727: $i,SV1265: $i,SV704: $i,SV118: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV118 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ SV1727 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ SV1727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3725,plain,
! [SV1728: $i,SV1266: $i,SV705: $i,SV119: $i] :
( ( ~ ( class_Lattices_Olattice @ SV119 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ SV1728 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ SV1728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3726,plain,
! [SV1729: $i,SV1267: $i,SV706: $i,SV120: $i] :
( ( ~ ( class_Lattices_Olattice @ SV120 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ SV1267 ) ) @ SV1729 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV1267 ) @ SV1729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3727,plain,
! [SV1268: $i,SV707: $i,SV121: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV121 @ tc_bool ) ) @ SV707 ) @ SV1268 )
= SV707 )
= $true )
| ( ( ~ ( c_lessequals @ SV707 @ SV1268 @ ( tc_fun @ SV121 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3728,plain,
! [SV1269: $i,SV708: $i,SV122: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV122 @ tc_bool ) ) @ SV708 ) @ SV1269 )
= SV1269 )
= $true )
| ( ( ~ ( c_lessequals @ SV1269 @ SV708 @ ( tc_fun @ SV122 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3729,plain,
! [SV1270: $i,SV709: $i,SV123: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV123 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SV709 ) @ SV1270 )
= SV709 )
| ~ ( c_lessequals @ SV709 @ SV1270 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3191]) ).
thf(3730,plain,
! [SV1271: $i,SV710: $i,SV124: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV124 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SV710 ) @ SV1271 )
= SV1271 )
| ~ ( c_lessequals @ SV1271 @ SV710 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3192]) ).
thf(3731,plain,
! [SV1730: $i,SV1272: $i,SV711: $i,SV125: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SV1272 ) @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SV1272 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SV711 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3732,plain,
! [SV1731: $i,SV1275: $i,SV714: $i,SV128: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SV1275 ) @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SV1275 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3733,plain,
! [SV1732: $i,SV1276: $i,SV715: $i,SV129: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV129 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV1276 @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV715 @ SV1732 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3734,plain,
! [SV1277: $i,SV716: $i,SV130: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV130 ) )
= $true )
| ( ( c_lessequals @ SV716 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 ) @ SV716 ) @ SV1277 ) @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3735,plain,
! [SV1278: $i,SV717: $i,SV131: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV131 ) )
= $true )
| ( ( c_lessequals @ SV717 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 ) @ SV1278 ) @ SV717 ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3199]) ).
thf(3736,plain,
! [SV1733: $i,SV1279: $i,SV718: $i,SV132: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV1279 @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV718 @ SV1733 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3737,plain,
! [SV1734: $i,SV1280: $i,SV719: $i,SV133: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV133 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV1280 @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV719 @ SV1734 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3738,plain,
! [SV1281: $i,SV720: $i,SV134: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV134 ) )
= $true )
| ( ( c_lessequals @ SV720 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 ) @ SV1281 ) @ SV720 ) @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3739,plain,
! [SV1282: $i,SV721: $i,SV135: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV135 ) )
= $true )
| ( ( c_lessequals @ SV721 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV135 ) @ SV721 ) @ SV1282 ) @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3740,plain,
! [SV1284: $i,SV723: $i,SV137: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV137 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV723 ) @ SV1284 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV1284 ) @ SV723 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3741,plain,
! [SV1285: $i,SV724: $i,SV138: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV138 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV724 ) @ SV1285 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV1285 ) @ SV724 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3742,plain,
! [SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ! [SY5613: $i,SY5614: $i,SY5615: $i,SY5616: $i,SY5617: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SY5613 @ SV1735 @ SV1735 @ tc_bool ) @ SY5614 @ SY5615 @ SY5616 @ SY5617 @ SV1735 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SY5613 @ SY5615 @ SY5614 @ SY5617 @ SY5616 @ SV1735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3743,plain,
! [SV1287: $i,SV726: $i,SV140: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV140 @ tc_bool ) ) @ SV726 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SV726 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= SV1287 )
= $true )
| ( ( ~ ( c_lessequals @ SV726 @ SV1287 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3744,plain,
! [SV1736: $i,SV1288: $i,SV727: $i,SV141: $i] :
( ( ~ ( class_Lattices_Olattice @ SV141 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1288 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1736 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ SV1288 ) @ SV1736 ) ) @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3745,plain,
! [SV1737: $i,SV1291: $i,SV730: $i,SV144: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) )
| ~ ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1737 ) @ SV730 ) @ SV1291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3746,plain,
! [SV1738: $i,SV1292: $i,SV731: $i,SV145: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV731 ) @ SV1292 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV1292 ) @ SV1738 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV1738 ) @ SV731 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV145 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV731 ) @ SV1292 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV1292 ) @ SV1738 ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV145 @ tc_bool ) ) @ SV1738 ) @ SV731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3747,plain,
! [SV1739: $i,SV1294: $i,SV733: $i,SV147: $i] :
( ( ! [SY5618: $i,SY5619: $i] :
( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SY5618 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SY5619 ) @ SY5618 @ SY5618 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5618 ) @ SV1294 ) @ SV1739 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SY5619 @ SY5618 @ SY5618 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SY5618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3748,plain,
! [SV1740: $i,SV1295: $i,SV734: $i,SV148: $i] :
( ( ! [SY5620: $i] :
( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SV734 @ SV1295 @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SY5620 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SV734 @ SV1740 @ SY5620 ) @ ( c_Set_Oimage @ SV148 @ SV1295 @ SV1740 @ SY5620 ) @ ( tc_fun @ SY5620 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SY5620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3749,plain,
! [SV1741: $i,SV1296: $i,SV735: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV149 ) @ SV735 ) @ SV1296 ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ SV735 @ SV1741 @ SV149 ) @ SV1296 @ ( tc_fun @ SV149 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3750,plain,
! [SV1742: $i,SV1297: $i,SV736: $i,SV150: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV150 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV736 @ ( c_COMBK @ SV1297 @ SV150 @ SV1742 ) @ SV1742 @ SV150 )
= SV1297 )
| ( SV736
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1742 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3751,plain,
! [SV1743: $i,SV1298: $i,SV737: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV151 @ SV737 @ SV1298 ) @ SV1743 ) )
| ~ ( hBOOL @ ( hAPP @ SV737 @ SV1743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3752,plain,
! [SV1744: $i,SV1299: $i,SV738: $i,SV152: $i] :
( ( ! [SY5621: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SV738 ) @ ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SY5621 ) @ SY5621 )
= ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SY5621 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1744 ) @ SV738 ) @ SV1299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3753,plain,
! [SV1745: $i,SV1300: $i,SV739: $i,SV153: $i] :
( ( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SV739 @ SV1300 @ SV1745 ) @ ( tc_fun @ SV1745 @ tc_bool ) )
| ~ ( c_lessequals @ SV153 @ SV1300 @ ( tc_fun @ SV1745 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1745 ) @ SV739 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3754,plain,
! [SV1746: $i,SV1301: $i,SV740: $i,SV154: $i] :
( ( ( c_lessequals @ SV154 @ SV740 @ ( tc_fun @ SV1301 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1301 ) @ SV1746 ) @ SV154 ) )
| ~ ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SV1746 @ SV740 @ SV1301 ) @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3755,plain,
! [SV1747: $i,SV1302: $i,SV741: $i,SV155: $i] :
( ( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SV741 @ SV1302 @ SV1747 ) @ ( tc_fun @ SV1747 @ tc_bool ) )
| ~ ( c_lessequals @ SV155 @ SV1302 @ ( tc_fun @ SV1747 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1747 ) @ SV741 ) @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3756,plain,
! [SV1748: $i,SV1303: $i,SV742: $i,SV156: $i] :
( ( ( c_lessequals @ SV156 @ SV742 @ ( tc_fun @ SV1303 @ tc_bool ) )
| ~ ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SV1748 @ SV742 @ SV1303 ) @ ( tc_fun @ SV1303 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1303 ) @ SV1748 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3757,plain,
! [SV1749: $i,SV1304: $i,SV743: $i,SV157: $i] :
( ( ! [SY5622: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SV743 @ SV1304 @ SV1749 ) @ ( c_Set_Ovimage @ SV157 @ SY5622 @ SV1304 @ SV1749 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_lessequals @ SV743 @ SY5622 @ ( tc_fun @ SV1749 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3758,plain,
! [SV1750: $i,SV1305: $i,SV744: $i,SV158: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1305 @ SV1750 @ SV158 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ SV1750 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV158 ) @ SV1305 ) @ SV744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3759,plain,
! [SV1751: $i,SV1306: $i,SV745: $i,SV159: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV745 @ SV1306 @ SV159 ) ) @ SV1751 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ SV1306 ) @ SV1751 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV159 ) @ SV745 ) @ SV1751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3760,plain,
! [SV1309: $i,SV748: $i,SV162: $i] :
( ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV748 @ SV1309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3761,plain,
! [SV1752: $i,SV1310: $i,SV749: $i,SV163: $i] :
( ( ~ ( class_Lattices_Olattice @ SV163 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ SV1310 ) ) @ SV1752 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV1310 ) @ SV1752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3762,plain,
! [SV1753: $i,SV1311: $i,SV750: $i,SV164: $i] :
( ( ~ ( class_Lattices_Olattice @ SV164 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ SV1753 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ SV1753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3763,plain,
! [SV1754: $i,SV1312: $i,SV751: $i,SV165: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV165 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ SV1754 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ SV1754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3764,plain,
! [SV1755: $i,SV1313: $i,SV752: $i,SV166: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV166 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ SV1313 ) ) @ SV1755 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV1313 ) @ SV1755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3765,plain,
! [SV1756: $i,SV1314: $i,SV753: $i,SV167: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV753 ) @ SV1314 ) ) @ SV1756 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV753 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV167 @ tc_bool ) ) @ SV1314 ) @ SV1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3766,plain,
! [SV1757: $i,SV1315: $i,SV754: $i,SV168: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV754 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV1315 ) @ SV1757 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV1315 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV168 @ tc_bool ) ) @ SV754 ) @ SV1757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3767,plain,
! [SV755: $i,SV169: $i] :
( ( ( class_Orderings_Olinorder @ SV169 )
= $false )
| ( ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV755 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV169 @ tc_bool ) ) @ SV169 ) @ SV169 )
= SV755 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3768,plain,
! [SV1316: $i,SV756: $i,SV170: $i] :
( ( ( c_Finite__Set_Ofinite @ SV170 @ SV756 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV756 @ tc_bool ) ) @ SV170 ) @ SV1316 ) @ SV756 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3769,plain,
! [SV1317: $i,SV757: $i,SV171: $i] :
( ( ( c_Finite__Set_Ofinite @ SV171 @ SV757 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV757 @ tc_bool ) ) @ SV1317 ) @ SV171 ) @ SV757 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3770,plain,
! [SV1758: $i,SV1318: $i,SV758: $i,SV172: $i] :
( ( ! [SY5623: $i] :
( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ SV172 @ SV758 @ SV1318 @ SV1758 ) @ SY5623 @ SV1318 @ SV1758 )
= ( c_Map_Orestrict__map @ SV172 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1318 @ tc_bool ) ) @ SV758 ) @ SY5623 ) @ SV1318 @ SV1758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3771,plain,
! [SV1759: $i,SV1319: $i,SV759: $i,SV173: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV173 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV759 @ tc_bool ) ) @ SV1319 @ SV759 @ ( tc_fun @ SV173 @ tc_bool ) ) ) @ SV1759 )
= SV1759 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3772,plain,
! [SV1760: $i,SV1320: $i,SV760: $i,SV174: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV174 @ tc_bool ) ) @ SV760 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1760 @ SV1320 @ ( tc_fun @ SV174 @ tc_bool ) ) )
= SV760 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3773,plain,
! [SV1761: $i,SV1321: $i,SV761: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SV1321 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV761 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SV1761 @ SV761 @ SV1321 ) @ ( tc_fun @ SV1321 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3774,plain,
! [SV1762: $i,SV1322: $i,SV762: $i,SV176: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SV1322 @ SV1762 ) @ ( tc_fun @ SV1762 @ tc_bool ) )
| ~ ( c_lessequals @ SV176 @ SV1322 @ ( tc_fun @ SV1762 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV1322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3775,plain,
! [SV1763: $i,SV1323: $i,SV763: $i,SV177: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ ( c_HOL_Ominus__class_Ominus @ SV1323 @ SV1763 @ ( tc_fun @ SV177 @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV763 ) @ SV1763 ) @ ( tc_fun @ SV177 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3776,plain,
! [SV1764: $i,SV1324: $i,SV764: $i,SV178: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV764 @ SV1324 @ ( tc_fun @ SV178 @ tc_bool ) ) ) @ SV1764 )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SV764 ) @ SV1764 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV178 @ tc_bool ) ) @ SV1324 ) @ SV1764 ) @ ( tc_fun @ SV178 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3777,plain,
! [SV1765: $i,SV1325: $i,SV765: $i,SV179: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV179 @ SV765 @ SV1325 ) @ SV1765 @ SV1325 @ SV765 )
= ( c_Set_Oinsert @ SV179 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV765 ) )
| ( SV1765
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3778,plain,
! [SV1766: $i,SV1326: $i,SV766: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SV1326 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1326 ) @ SV1766 ) @ SV766 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SV1766 @ SV766 @ SV1326 ) @ ( tc_fun @ SV1326 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3779,plain,
! [SV1767: $i,SV1327: $i,SV767: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SV1327 @ SV1767 ) @ ( tc_fun @ SV1767 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1767 ) @ SV767 ) @ SV1327 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1327 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3780,plain,
! [SV1768: $i,SV1328: $i,SV768: $i,SV182: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV182 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SV1328 @ SV1768 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV1328 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SV1768 @ SV182 @ SV182 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1768 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3781,plain,
! [SV1769: $i,SV1329: $i,SV769: $i,SV183: $i] :
( ( ! [SY5624: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1769 @ SY5624 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SY5624 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SV183 @ SV1769 @ ( tc_fun @ SV1329 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3782,plain,
! [SV770: $i,SV184: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV184 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV184 ) @ SV770 ) @ ( c_Orderings_Otop__class_Otop @ SV184 ) )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3783,plain,
! [SV771: $i,SV185: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV185 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV185 ) @ ( c_Orderings_Otop__class_Otop @ SV185 ) ) @ SV771 )
= SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3784,plain,
! [SV1770: $i,SV1330: $i,SV774: $i,SV188: $i] :
( ( ( c_Set_Oimage @ SV188 @ ( c_Set_Ovimage @ SV188 @ SV774 @ SV1330 @ SV1770 ) @ SV1330 @ SV1770 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1770 @ tc_bool ) ) @ SV774 ) @ ( c_Set_Oimage @ SV188 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1330 @ tc_bool ) ) @ SV1330 @ SV1770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3785,plain,
! [SV1771: $i,SV1331: $i,SV775: $i,SV189: $i] :
( ( ~ ( class_Lattices_Olattice @ SV189 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ SV1331 ) @ SV1771 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1331 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1771 ) ) @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3786,plain,
! [SV1772: $i,SV1332: $i,SV776: $i,SV190: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV776 ) @ SV1332 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV1772 ) @ SV1332 ) @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV776 ) @ SV1332 ) @ SV1772 @ ( tc_fun @ SV190 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(3787,plain,
! [SV1333: $i,SV777: $i,SV191: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV191 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV777 @ SV1333 @ SV191 )
| ( c_lessequals @ SV1333 @ SV777 @ SV191 )
| ~ ( c_lessequals @ SV777 @ SV1333 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3788,plain,
! [SV1773: $i,SV1334: $i,SV779: $i,SV193: $i] :
( ( ~ ( class_HOL_Oord @ SV193 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
| ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SV1773 @ SV193 ) )
| ~ ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3789,plain,
! [SV780: $i,SV194: $i] :
( ( ( class_Orderings_Oorder @ SV194 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV780 @ SV780 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3790,plain,
! [SV781: $i,SV195: $i] :
( ( ( class_Orderings_Olinorder @ SV195 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV781 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3791,plain,
! [SV782: $i,SV196: $i] :
( ( ( class_Orderings_Opreorder @ SV196 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3792,plain,
! [SV1335: $i,SV783: $i,SV197: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV197 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 ) @ SV783 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV197 ) @ SV783 ) @ SV1335 ) )
= SV783 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3793,plain,
! [SV1336: $i,SV785: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV785 @ ( tc_fun @ SV1336 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1336 ) @ SV1336 @ ( tc_fun @ SV1336 @ tc_bool ) @ tc_bool ) @ SV200 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1336 ) @ SV1336 @ ( tc_fun @ SV1336 @ tc_bool ) @ tc_bool ) @ SV785 ) @ ( tc_fun @ SV1336 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3794,plain,
! [SV1337: $i,SV786: $i,SV201: $i] :
( ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV786 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV1337 ) @ ( tc_fun @ SV201 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV786 @ SV1337 @ ( tc_fun @ SV201 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3795,plain,
! [SV1774: $i,SV1338: $i,SV787: $i,SV202: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SV1338 @ SV1774 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV1338 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SV1774 @ SV202 @ SV202 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1774 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3796,plain,
! [SV1339: $i,SV788: $i,SV203: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV203 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1339 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ SV788 @ SV203 )
| ( SV1339 = SV788 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3797,plain,
! [SV1340: $i,SV789: $i,SV204: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV204 ) )
= $true )
| ( ( ( SV789 = SV1340 )
| ( c_HOL_Oord__class_Oless @ SV1340 @ SV789 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SV1340 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3798,plain,
! [SV1341: $i,SV790: $i,SV205: $i] :
( ( ( SV205 = SV790 )
= $true )
| ( ( ~ ( c_lessequals @ SV790 @ SV205 @ ( tc_fun @ SV1341 @ tc_bool ) )
| ~ ( c_lessequals @ SV205 @ SV790 @ ( tc_fun @ SV1341 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3799,plain,
! [SV1342: $i,SV791: $i,SV206: $i] :
( ( ( SV206 = SV791 )
= $true )
| ( ( ~ ( c_lessequals @ SV791 @ SV206 @ ( tc_fun @ SV1342 @ tc_bool ) )
| ~ ( c_lessequals @ SV206 @ SV791 @ ( tc_fun @ SV1342 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3800,plain,
! [SV1343: $i,SV792: $i,SV207: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV207 ) )
= $true )
| ( ( ( SV792 = SV1343 )
| ~ ( c_lessequals @ SV1343 @ SV792 @ SV207 )
| ~ ( c_lessequals @ SV792 @ SV1343 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3801,plain,
! [SV1344: $i,SV793: $i,SV208: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV208 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV793 @ SV1344 @ SV208 )
| ( c_HOL_Oord__class_Oless @ SV1344 @ SV793 @ SV208 )
| ( SV1344 = SV793 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3273]) ).
thf(3802,plain,
! [SV1345: $i,SV794: $i,SV209: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV209 ) )
= $true )
| ( ( ( SV794 = SV1345 )
| ~ ( c_lessequals @ SV1345 @ SV794 @ SV209 )
| ~ ( c_lessequals @ SV794 @ SV1345 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3803,plain,
! [SV1346: $i,SV795: $i,SV210: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV210 ) )
= $true )
| ( ( ( SV795 = SV1346 )
| ~ ( c_lessequals @ SV795 @ SV1346 @ SV210 )
| ~ ( c_lessequals @ SV1346 @ SV795 @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3804,plain,
! [SV1347: $i,SV796: $i,SV211: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV211 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV796 @ SV1347 @ SV211 )
| ( SV1347 = SV796 )
| ( c_HOL_Oord__class_Oless @ SV1347 @ SV796 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3805,plain,
! [SV1348: $i,SV797: $i,SV212: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV212 ) )
= $true )
| ( ( ( SV797 = SV1348 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SV1348 @ SV212 )
| ( c_HOL_Oord__class_Oless @ SV1348 @ SV797 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3806,plain,
! [SV1349: $i,SV798: $i,SV213: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV213 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 ) @ SV798 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 ) @ SV798 ) @ SV1349 ) )
= SV798 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3807,plain,
! [SV1775: $i,SV1350: $i,SV799: $i,SV214: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV214 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SV1350 ) @ SV1775 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV1775 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3808,plain,
! [SV1776: $i,SV1351: $i,SV800: $i,SV215: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV215 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SV1351 ) @ SV1776 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ SV800 @ SV1776 @ SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3809,plain,
! [SV1353: $i,SV802: $i,SV217: $i] :
( ( ( c_lessequals @ SV217 @ SV802 @ ( tc_fun @ SV1353 @ tc_bool ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV217 @ SV802 @ ( tc_fun @ SV1353 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3810,plain,
! [SV1777: $i,SV1354: $i,SV803: $i,SV218: $i] :
( ( ~ ( class_HOL_Oord @ SV218 )
| ( c_lessequals @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(3811,plain,
! [SV1355: $i,SV804: $i,SV219: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV219 ) )
= $true )
| ( ( ( c_lessequals @ SV804 @ SV1355 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1355 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3284]) ).
thf(3812,plain,
! [SV1356: $i,SV805: $i,SV220: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV220 ) )
= $true )
| ( ( ( c_lessequals @ SV805 @ SV1356 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV805 @ SV1356 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3813,plain,
! [SV1357: $i,SV806: $i,SV221: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV221 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SV806 ) @ SV1357 )
= SV806 )
| ~ ( c_lessequals @ SV1357 @ SV806 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3814,plain,
! [SV1358: $i,SV807: $i,SV222: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV222 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SV807 ) @ SV1358 )
= SV1358 )
| ~ ( c_lessequals @ SV807 @ SV1358 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3815,plain,
! [SV1359: $i,SV808: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV223 @ tc_bool ) ) @ SV808 ) @ SV1359 )
= SV1359 )
= $true )
| ( ( ~ ( c_lessequals @ SV808 @ SV1359 @ ( tc_fun @ SV223 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3816,plain,
! [SV1360: $i,SV809: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV224 @ tc_bool ) ) @ SV809 ) @ SV1360 )
= SV809 )
= $true )
| ( ( ~ ( c_lessequals @ SV1360 @ SV809 @ ( tc_fun @ SV224 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3817,plain,
! [SV1778: $i,SV1361: $i,SV810: $i,SV225: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV225 @ SV810 @ SV1361 @ SV1778 ) @ SV1778 )
| ~ ( c_Finite__Set_Ofinite @ SV810 @ SV1361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3818,plain,
! [SV1779: $i,SV1362: $i,SV811: $i,SV226: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SV1779 ) @ ( tc_fun @ SV1779 @ tc_bool ) )
| ~ ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1779 ) @ SV811 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3291]) ).
thf(3819,plain,
! [SV1363: $i,SV812: $i,SV227: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV227 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
| ~ ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
| ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3820,plain,
! [SV1780: $i,SV1364: $i,SV813: $i,SV228: $i] :
( ( ! [SY5625: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV228 @ SV813 @ SV1364 ) @ SV1780 @ SV1364 @ ( tc_fun @ SY5625 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5625 @ tc_bool ) ) @ ( hAPP @ SV1780 @ SV228 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV813 @ SV1780 @ SV1364 @ ( tc_fun @ SY5625 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3293]) ).
thf(3821,plain,
! [SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY5626: $i,SY5627: $i,SY5628: $i,SY5629: $i,SY5630: $i,SY5631: $i,SY5632: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SY5626 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5627 @ SV229 @ SY5628 @ SY5629 @ SY5630 @ SY5626 @ SY5631 @ SY5632 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(3822,plain,
! [SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY5633: $i,SY5634: $i,SY5635: $i,SY5636: $i,SY5637: $i,SY5638: $i,SY5639: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SY5633 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SY5634 @ SY5635 @ SY5636 @ SY5633 @ SY5637 @ SY5638 @ SY5639 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(3823,plain,
! [SV1783: $i,SV1368: $i,SV817: $i,SV232: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SV1368 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV1783 @ SV1368 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1783 @ SV817 @ SV1368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(3824,plain,
! [SV1784: $i,SV1369: $i,SV818: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV818 @ SV1369 @ SV233 ) ) @ SV1784 )
= ( c_Set_Oinsert @ SV818 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ SV1369 ) @ SV1784 ) @ SV233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV233 ) @ SV818 ) @ SV1784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(3825,plain,
! [SV1785: $i,SV1370: $i,SV819: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ ( c_Set_Oinsert @ SV1370 @ SV1785 @ SV234 ) )
= ( c_Set_Oinsert @ SV1370 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ SV1785 ) @ SV234 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV234 ) @ SV1370 ) @ SV819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3826,plain,
! [SV1786: $i,SV1371: $i,SV820: $i,SV235: $i] :
( ( ! [SY5640: $i] :
( ( c_Set_Oimage @ SV235 @ ( c_Set_Oinsert @ SV820 @ SV1371 @ SV1786 ) @ SV1786 @ SY5640 )
= ( c_Set_Oinsert @ ( hAPP @ SV235 @ SV820 ) @ ( c_Set_Oimage @ SV235 @ SV1371 @ SV1786 @ SY5640 ) @ SY5640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3827,plain,
! [SV1787: $i,SV1372: $i,SV822: $i,SV237: $i] :
( ( ! [SY5641: $i,SY5642: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV237 @ SV822 @ SV1372 @ SV1787 @ SY5641 ) @ SY5642 )
= ( hAPP @ SV822 @ ( hAPP @ SV237 @ SY5642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3828,plain,
! [SV1788: $i,SV1373: $i,SV823: $i,SV238: $i] :
( ( ! [SY5643: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV1788 ) @ SY5643 ) @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV1373 @ SY5643 @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV823 @ SV1788 @ ( tc_fun @ SV238 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3829,plain,
! [SV1374: $i,SV824: $i,SV239: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV239 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 ) @ SV824 ) @ SV1374 ) @ SV824 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(3830,plain,
! [SV1375: $i,SV825: $i,SV240: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV240 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV240 ) @ SV825 ) @ SV1375 ) @ SV1375 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3831,plain,
! [SV1789: $i,SV1376: $i,SV826: $i,SV241: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV241 )
| ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1789 @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3832,plain,
! [SV1790: $i,SV1377: $i,SV827: $i,SV242: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV242 )
| ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1790 @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3833,plain,
! [SV1791: $i,SV1378: $i,SV828: $i,SV243: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV243 )
| ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1791 @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3834,plain,
! [SV1379: $i,SV829: $i,SV244: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV244 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV244 ) @ SV829 ) @ SV1379 ) @ SV1379 @ SV244 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3835,plain,
! [SV1380: $i,SV830: $i,SV245: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV245 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 ) @ SV830 ) @ SV1380 ) @ SV830 @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3836,plain,
! [SV1792: $i,SV1383: $i,SV833: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SV1383 ) @ SV1792 ) @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV1792 @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV1383 @ ( tc_fun @ SV833 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3837,plain,
! [SV1793: $i,SV1384: $i,SV834: $i,SV249: $i] :
( ( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV1384 ) @ SV1793 ) @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SV1793 @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SV1384 @ ( tc_fun @ SV834 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3838,plain,
! [SV836: $i,SV251: $i] :
( ( ( class_Orderings_Otop @ SV251 )
= $false )
| ( ( c_lessequals @ SV836 @ ( c_Orderings_Otop__class_Otop @ SV251 ) @ SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3839,plain,
! [SV1794: $i,SV1385: $i,SV837: $i,SV252: $i] :
( ( ! [SY5644: $i,SY5645: $i,SY5646: $i] :
( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SV837 @ SV1385 @ SV1794 @ SY5644 @ SY5645 ) @ SY5644 @ SY5646 @ SY5645 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SV837 @ SY5644 @ SY5646 @ SV1794 ) @ SV1385 @ SV1794 @ SY5646 @ SY5645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3840,plain,
! [SV1795: $i,SV1386: $i,SV838: $i,SV253: $i] :
( ( ( c_Set_Oinsert @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV838 @ tc_bool ) ) @ SV1386 @ SV838 @ ( tc_fun @ SV1795 @ tc_bool ) ) @ SV1795 )
= ( c_Set_Oinsert @ SV253 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1795 @ tc_bool ) ) @ SV1795 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3841,plain,
! [SV1796: $i,SV1387: $i,SV839: $i,SV254: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV254 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ SV839 ) @ SV1387 ) ) @ SV1796 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV839 ) @ SV1796 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV1387 ) @ SV1796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3842,plain,
! [SV1797: $i,SV1388: $i,SV840: $i,SV255: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV255 )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ SV1388 ) @ SV1797 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1388 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1797 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3843,plain,
! [SV1389: $i,SV841: $i,SV256: $i] :
( ( ( ~ ( class_HOL_Ominus @ SV256 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV841 @ SV1389 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV841 @ v_x ) @ ( hAPP @ SV1389 @ v_x ) @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3844,plain,
! [SV1798: $i,SV1390: $i,SV842: $i,SV257: $i] :
( ( ( c_lessequals @ SV257 @ SV842 @ ( tc_fun @ SV1390 @ tc_bool ) )
| ~ ( c_lessequals @ SV257 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1390 @ tc_bool ) ) @ SV1798 ) @ SV842 ) @ ( tc_fun @ SV1390 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3845,plain,
! [SV1799: $i,SV1391: $i,SV843: $i,SV258: $i] :
( ( ( c_lessequals @ SV258 @ SV843 @ ( tc_fun @ SV1391 @ tc_bool ) )
| ~ ( c_lessequals @ SV258 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1391 @ tc_bool ) ) @ SV843 ) @ SV1799 ) @ ( tc_fun @ SV1391 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3846,plain,
! [SV1800: $i,SV1392: $i,SV844: $i,SV259: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV259 )
| ( c_lessequals @ SV844 @ SV1392 @ SV259 )
| ~ ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SV1392 ) @ SV1800 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3847,plain,
! [SV1801: $i,SV1393: $i,SV845: $i,SV260: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV260 )
| ( c_lessequals @ SV845 @ SV1393 @ SV260 )
| ~ ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SV1801 ) @ SV1393 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3848,plain,
! [SV1802: $i,SV1394: $i,SV846: $i,SV261: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV261 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SV1394 ) @ SV1802 @ SV261 )
| ~ ( c_lessequals @ SV846 @ SV1802 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3849,plain,
! [SV1803: $i,SV1395: $i,SV847: $i,SV262: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV262 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SV1395 ) @ SV1803 @ SV262 )
| ~ ( c_lessequals @ SV1395 @ SV1803 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3850,plain,
! [SV1804: $i,SV1396: $i,SV848: $i,SV263: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV263 )
| ( c_lessequals @ SV848 @ SV1396 @ SV263 )
| ~ ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SV1396 ) @ SV1804 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(3851,plain,
! [SV1805: $i,SV1397: $i,SV849: $i,SV264: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV264 )
| ( c_lessequals @ SV849 @ SV1397 @ SV264 )
| ~ ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SV1805 ) @ SV1397 ) @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(3852,plain,
! [SV1806: $i,SV1398: $i,SV851: $i,SV266: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ SV851 ) @ SV1398 ) @ SV1806 @ ( tc_fun @ SV266 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV266 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1806 @ ( tc_fun @ SV266 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1806 @ ( tc_fun @ SV266 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(3853,plain,
! [SV1807: $i,SV1399: $i,SV852: $i,SV267: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV267 )
| ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(3854,plain,
! [SV1808: $i,SV1400: $i,SV853: $i,SV268: $i] :
( ( ! [SY5647: $i,SY5648: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ SV268 @ SV853 @ SV1400 @ SV1808 @ SY5647 ) @ SY5648 @ SY5647 @ SV1808 )
= ( c_Set_Ovimage @ SV853 @ ( c_Set_Ovimage @ SV268 @ SY5648 @ SV1400 @ SV1808 ) @ SY5647 @ SV1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(3855,plain,
! [SV1809: $i,SV1402: $i,SV855: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3856,plain,
! [SV1404: $i,SV857: $i,SV272: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV272 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV857 ) @ SV1404 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV1404 ) @ SV857 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3334]) ).
thf(3857,plain,
! [SV1405: $i,SV858: $i,SV273: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV273 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV858 ) @ SV1405 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV1405 ) @ SV858 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3858,plain,
! [SV1408: $i,SV862: $i,SV277: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV277 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SV1408 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SV1408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3859,plain,
! [SV1409: $i,SV863: $i,SV278: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV278 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SV1409 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SV1409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3860,plain,
! [SV1810: $i,SV1410: $i,SV864: $i,SV279: $i] :
( ( ! [SY5649: $i,SY5650: $i] :
( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5649 @ tc_bool ) ) @ SY5649 ) @ ( tc_fun @ SY5649 @ tc_bool ) ) @ SY5649 ) @ SY5650 @ SY5649 @ SY5649 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5649 ) @ SV1410 ) @ SV1810 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5649 ) @ SV864 ) @ SV1810 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SY5650 @ SY5649 @ SY5649 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SY5649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(3861,plain,
! [SV1811: $i,SV1411: $i,SV865: $i,SV280: $i] :
( ( ! [SY5651: $i,SY5652: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SY5651 ) @ SY5652 @ SY5651 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SY5652 @ SY5651 @ SV1411 ) @ SV1411 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV865 @ SY5652 @ SY5651 @ SV1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(3862,plain,
! [SV867: $i,SV282: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV282 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV867 @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3863,plain,
! [SV1812: $i,SV1413: $i,SV868: $i,SV283: $i] :
( ( ! [SY5653: $i,SY5654: $i,SY5655: $i] :
( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SY5653 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SY5654 ) @ SY5653 @ SY5655 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SY5654 @ SY5653 @ SY5655 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5653 ) @ SV1413 ) @ SV1812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3864,plain,
! [SV1813: $i,SV1414: $i,SV869: $i,SV284: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ SV1414 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV284 @ tc_bool ) ) @ SV1414 ) @ ( c_Collect @ SV1813 @ SV284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3865,plain,
! [SV1814: $i,SV1415: $i,SV870: $i,SV285: $i] :
( ( ! [SY5656: $i] :
( ( c_Set_Ovimage @ SV285 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV870 @ tc_bool ) ) @ SV1415 ) @ SV1814 ) @ SY5656 @ SV870 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5656 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV285 @ SV1415 @ SY5656 @ SV870 ) ) @ ( c_Set_Ovimage @ SV285 @ SV1814 @ SY5656 @ SV870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3866,plain,
! [SV1416: $i,SV871: $i,SV286: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV871 @ ( c_Set_Oinsert @ SV1416 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV286 @ tc_bool ) ) @ SV286 ) @ SV286 ) @ SV286 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 ) @ SV871 ) @ SV1416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3867,plain,
! [SV1815: $i,SV1417: $i,SV872: $i,SV287: $i] :
( ( ! [SY5657: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SV1417 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Set_Oinsert @ SV1417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5657 @ tc_bool ) ) @ SY5657 ) @ ( tc_fun @ SY5657 @ tc_bool ) ) @ SY5657 @ SV287 ) ) )
| ~ ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SV1417 @ SV1815 @ SY5657 ) @ SY5657 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3868,plain,
! [SV1816: $i,SV1418: $i,SV873: $i,SV288: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV288 @ SV873 @ SV1418 ) @ SV1816 @ ( tc_fun @ SV1418 @ tc_bool ) )
= ( c_Set_Oinsert @ SV288 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SV1816 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV288 ) @ SV1816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3869,plain,
! [SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ! [SY5658: $i,SY5659: $i,SY5660: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SY5658 ) @ SY5659 @ SY5660 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5659 @ tc_bool ) ) @ SY5659 ) @ ( tc_fun @ SY5659 @ tc_bool ) ) @ SY5658 @ SY5659 @ SY5660 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5659 ) @ SV1817 ) @ SV1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3870,plain,
! [SV1818: $i,SV1420: $i,SV875: $i,SV290: $i] :
( ( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SV1420 @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) )
| ~ ( c_lessequals @ SV290 @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3871,plain,
! [SV1819: $i,SV1421: $i,SV876: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ SV876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1819 ) @ SV291 ) @ SV876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3872,plain,
! [SV1820: $i,SV1422: $i,SV877: $i,SV292: $i] :
( ( ( hBOOL @ ( hAPP @ SV292 @ SV877 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1422 @ tc_bool ) ) @ SV292 ) @ SV1820 ) @ SV877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3873,plain,
! [SV1423: $i,SV878: $i,SV293: $i] :
( ( ( c_Fun_Oinj__on @ SV293 @ SV878 @ SV1423 @ SV1423 )
= $true )
| ( ( ~ ( c_lessequals @ SV878 @ ( c_Set_Oimage @ SV293 @ SV878 @ SV1423 @ SV1423 ) @ ( tc_fun @ SV1423 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV878 @ SV1423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3874,plain,
! [SV1821: $i,SV1424: $i,SV879: $i,SV294: $i] :
( ( ! [SY5661: $i] :
( ( c_Fun_Oinj__on @ SV294 @ SV879 @ SV1424 @ SV1821 )
| ~ ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SY5661 ) @ SV879 ) @ SV1424 @ SV1821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3875,plain,
! [SV1822: $i,SV1425: $i,SV880: $i,SV295: $i] :
( ( ! [SY5662: $i] :
( ( c_Fun_Oinj__on @ SV295 @ SV880 @ SV1425 @ SV1822 )
| ~ ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1425 @ tc_bool ) ) @ SV880 ) @ SY5662 ) @ SV1425 @ SV1822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3876,plain,
! [SV1823: $i,SV1426: $i,SV881: $i,SV296: $i] :
( ( ! [SY5663: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SV1823 ) @ SY5663 @ ( tc_fun @ SV1426 @ tc_bool ) )
| ~ ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SY5663 @ SV1426 @ SV1823 ) @ ( tc_fun @ SV1823 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SV1823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(3877,plain,
! [SV1824: $i,SV1427: $i,SV883: $i,SV299: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV299 @ SV883 @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV1824 @ ( tc_fun @ SV1427 @ tc_bool ) )
| ~ ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV883 ) @ SV1824 ) @ ( tc_fun @ SV1427 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3878,plain,
! [SV1825: $i,SV1428: $i,SV884: $i,SV300: $i] :
( ( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1428 ) @ SV1825 ) @ ( tc_fun @ SV884 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV300 @ SV1428 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1825 @ ( tc_fun @ SV884 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3879,plain,
! [SV1429: $i,SV885: $i,SV301: $i] :
( ( ( c_Finite__Set_Ofinite @ SV301 @ t_a )
= $true )
| ( ( ~ ( c_Wellfounded_Omax__extp @ SV885 @ SV1429 @ SV301 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3880,plain,
! [SV1430: $i,SV886: $i,SV302: $i] :
( ( ( c_Finite__Set_Ofinite @ SV302 @ t_a )
= $true )
| ( ( ~ ( c_Wellfounded_Omax__extp @ SV886 @ SV302 @ SV1430 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3881,plain,
! [SV1826: $i,SV1431: $i,SV887: $i,SV303: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SV1431 ) @ SV1826 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV887 @ SV1431 @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(3882,plain,
! [SV1827: $i,SV1432: $i,SV888: $i,SV304: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV304 )
| ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SV1432 ) @ SV1827 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV888 @ SV1827 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3883,plain,
! [SV1828: $i,SV1433: $i,SV889: $i,SV305: $i] :
( ( ! [SY5664: $i] :
( ( c_Set_Ovimage @ SV305 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV889 @ tc_bool ) ) @ SV1433 ) @ SV1828 ) @ SY5664 @ SV889 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SY5664 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV305 @ SV1433 @ SY5664 @ SV889 ) ) @ ( c_Set_Ovimage @ SV305 @ SV1828 @ SY5664 @ SV889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3884,plain,
! [SV1434: $i,SV890: $i,SV306: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV306 @ tc_bool ) ) @ SV890 ) @ SV1434 ) @ SV306 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1434 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3885,plain,
! [SV1435: $i,SV891: $i,SV307: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV307 @ tc_bool ) ) @ SV891 ) @ SV1435 ) @ SV307 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV891 @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(3886,plain,
! [SV1829: $i,SV1436: $i,SV892: $i,SV308: $i] :
( ( ! [SY5665: $i] :
( ~ ( class_HOL_Oord @ SV308 )
| ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SV1829 @ SV1436 ) @ SV308 )
| ~ ( c_lessequals @ SV892 @ SV1829 @ ( tc_fun @ SY5665 @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3887,plain,
! [SV1830: $i,SV1437: $i,SV893: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV1437 ) @ SV1830 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1830 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3888,plain,
! [SV1831: $i,SV1438: $i,SV894: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SV1438 ) @ SV1831 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1831 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3889,plain,
! [SV1832: $i,SV1439: $i,SV895: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ ( c_Set_Oinsert @ SV1439 @ SV1832 @ SV311 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ SV1832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3890,plain,
! [SV1833: $i,SV1440: $i,SV896: $i,SV312: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ ( c_Set_Oinsert @ SV1440 @ SV1833 @ SV312 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ SV1833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(3891,plain,
! [SV1834: $i,SV1441: $i,SV897: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1441 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1834 ) )
| ~ ( c_lessequals @ SV1834 @ SV1441 @ ( tc_fun @ SV313 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3892,plain,
! [SV1835: $i,SV1442: $i,SV898: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1442 ) )
| ~ ( c_lessequals @ SV1835 @ SV1442 @ ( tc_fun @ SV314 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3893,plain,
! [SV1836: $i,SV1443: $i,SV899: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1443 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1836 ) )
| ~ ( c_lessequals @ SV1836 @ SV1443 @ ( tc_fun @ SV315 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3894,plain,
! [SV1837: $i,SV1444: $i,SV900: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1444 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1837 ) )
| ~ ( c_lessequals @ SV1837 @ SV1444 @ ( tc_fun @ SV316 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3895,plain,
! [SV1838: $i,SV1445: $i,SV901: $i,SV317: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV317 @ tc_bool ) ) @ SV1445 ) @ SV1838 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(3896,plain,
! [SV1839: $i,SV1446: $i,SV902: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV1446 ) @ SV1839 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ SV1839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3897,plain,
! [SV1840: $i,SV1447: $i,SV903: $i,SV319: $i] :
( ( ! [SY5666: $i] :
( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SV903 @ SV1447 @ SV1840 ) @ SY5666 )
= ( hAPP @ SV319 @ SY5666 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1447 ) @ SY5666 ) @ SV903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3898,plain,
! [SV1841: $i,SV1448: $i,SV904: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ SV1448 ) )
| ( SV904 = SV1841 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ ( c_Set_Oinsert @ SV1841 @ SV1448 @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3899,plain,
! [SV1842: $i,SV1449: $i,SV905: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1449 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV1842 ) @ SV1449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3900,plain,
! [SV1843: $i,SV1450: $i,SV906: $i,SV322: $i] :
( ( ! [SY5667: $i,SY5668: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SV1450 @ SV1843 @ SY5667 ) @ SY5668 )
= ( hAPP @ SV906 @ SY5668 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1843 ) @ SY5668 ) @ SV1450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3901,plain,
! [SV1844: $i,SV1451: $i,SV908: $i,SV324: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ SV1451 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ ( c_HOL_Ominus__class_Ominus @ SV1844 @ SV1451 @ ( tc_fun @ SV324 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3902,plain,
! [SV1845: $i,SV1452: $i,SV909: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ SV1452 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ ( c_HOL_Ominus__class_Ominus @ SV1452 @ SV1845 @ ( tc_fun @ SV325 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3903,plain,
! [SV1846: $i,SV1453: $i,SV910: $i,SV326: $i] :
( ( ! [SY5669: $i,SY5670: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SV910 @ SV1453 @ SV1846 @ SY5669 ) @ SY5670 )
= ( hAPP @ SV326 @ SY5670 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1846 ) @ SY5670 ) @ SV1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3904,plain,
! [SV1847: $i,SV1454: $i,SV911: $i,SV327: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1454 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1847 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1847 @ SV1454 @ ( tc_fun @ SV327 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3905,plain,
! [SV1848: $i,SV1458: $i,SV915: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ SV1458 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV331 @ tc_bool ) ) @ SV1848 ) @ SV1458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(3906,plain,
! [SV1849: $i,SV1459: $i,SV916: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ SV1459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV332 @ tc_bool ) ) @ SV1459 ) @ SV1849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3907,plain,
! [SV1460: $i,SV917: $i,SV333: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV333 ) @ SV917 ) @ ( c_Collect @ SV1460 @ SV333 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1460 @ SV917 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3908,plain,
! [SV1461: $i,SV918: $i,SV334: $i] :
( ( ( hBOOL @ ( hAPP @ SV334 @ SV918 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1461 ) @ SV918 ) @ ( c_Collect @ SV334 @ SV1461 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3909,plain,
! [SV1850: $i,SV1462: $i,SV919: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ ( c_HOL_Ominus__class_Ominus @ SV1462 @ SV1850 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1850 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3910,plain,
! [SV1851: $i,SV1463: $i,SV920: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ ( c_HOL_Ominus__class_Ominus @ SV1463 @ SV1851 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1851 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3911,plain,
! [SV1852: $i,SV1464: $i,SV921: $i,SV337: $i] :
( ( ! [SY5671: $i,SY5672: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SY5671 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SY5672 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5671 ) @ SY5672 ) @ SV1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(3912,plain,
! [SV1853: $i,SV1465: $i,SV922: $i,SV338: $i] :
( ( ! [SY5673: $i,SY5674: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SY5673 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SY5674 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5673 ) @ SY5674 ) @ SV1465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3913,plain,
! [SV1854: $i,SV1466: $i,SV923: $i,SV339: $i] :
( ( ! [SY5675: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SV923 ) @ ( c_Set_Ovimage @ SV1466 @ SV1854 @ SV339 @ SY5675 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5675 ) @ ( hAPP @ SV1466 @ SV923 ) ) @ SV1854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(3914,plain,
! [SV1855: $i,SV1467: $i,SV924: $i,SV340: $i] :
( ( ! [SY5676: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SV924 ) @ ( c_Set_Ovimage @ SV1467 @ SV1855 @ SV340 @ SY5676 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5676 ) @ ( hAPP @ SV1467 @ SV924 ) ) @ SV1855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3915,plain,
! [SV1856: $i,SV1468: $i,SV925: $i,SV341: $i] :
( ( ! [SY5677: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SV925 ) @ ( c_Set_Ovimage @ SV1468 @ SV1856 @ SV341 @ SY5677 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5677 ) @ ( hAPP @ SV1468 @ SV925 ) ) @ SV1856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(3916,plain,
! [SV1857: $i,SV1469: $i,SV926: $i,SV342: $i] :
( ( ! [SY5678: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SV926 @ SV1469 ) ) @ SV1857 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5678 ) @ SV1469 ) @ ( c_Set_Ovimage @ SV926 @ SV1857 @ SY5678 @ SV342 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3917,plain,
! [SV1858: $i,SV1470: $i,SV927: $i,SV343: $i] :
( ( ! [SY5679: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SV927 @ SV1470 ) ) @ SV1858 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5679 ) @ SV1470 ) @ ( c_Set_Ovimage @ SV927 @ SV1858 @ SY5679 @ SV343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3918,plain,
! [SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY5680: $i,SY5681: $i,SY5682: $i,SY5683: $i,SY5684: $i,SY5685: $i,SY5686: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5680 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SY5681 @ SV344 @ SY5682 @ SY5683 @ SY5684 @ SY5685 @ SY5686 @ SY5680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(3919,plain,
! [SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY5687: $i,SY5688: $i,SY5689: $i,SY5690: $i,SY5691: $i,SY5692: $i,SY5693: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5687 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5688 @ SV1472 @ SV345 @ SY5689 @ SY5690 @ SY5691 @ SY5692 @ SY5693 @ SY5687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3920,plain,
! [SV1473: $i,SV930: $i,SV346: $i] :
( ( ( ( c_Set_Oinsert @ SV346 @ SV930 @ SV1473 )
= SV930 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1473 ) @ SV346 ) @ SV930 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3405]) ).
thf(3921,plain,
! [SV1861: $i,SV1474: $i,SV931: $i,SV347: $i] :
( ( ! [SY5694: $i,SY5695: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SY5694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SY5695 ) @ SY5694 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SY5695 ) @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3922,plain,
! [SV1862: $i,SV1475: $i,SV932: $i,SV348: $i] :
( ( ! [SY5696: $i,SY5697: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SY5696 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SY5697 ) @ SY5696 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SY5697 ) @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(3923,plain,
! [SV1863: $i,SV1476: $i,SV933: $i,SV349: $i] :
( ( ! [SY5698: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SV933 ) @ SV1476 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1863 ) @ ( hAPP @ SY5698 @ SV933 ) ) @ ( c_Set_Oimage @ SY5698 @ SV1476 @ SV349 @ SV1863 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(3924,plain,
! [SV1864: $i,SV1477: $i,SV934: $i,SV350: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV1477 ) @ SV1864 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV350 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ SV1477 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV350 @ tc_bool ) ) @ SV934 ) @ SV1864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(3925,plain,
! [SV1865: $i,SV1478: $i,SV935: $i,SV351: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV935 ) @ SV1478 ) ) @ SV1865 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV351 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV935 ) @ SV1865 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV351 @ tc_bool ) ) @ SV1478 ) @ SV1865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3926,plain,
! [SV1866: $i,SV1480: $i,SV937: $i,SV353: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SV1480 ) @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
| ~ ( c_lessequals @ SV937 @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1480 ) @ SV353 ) @ SV1866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3927,plain,
! [SV1481: $i,SV938: $i,SV354: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV354 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SV1481 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SV1481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3413]) ).
thf(3928,plain,
! [SV1482: $i,SV939: $i,SV355: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV355 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SV1482 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SV1482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3414]) ).
thf(3929,plain,
! [SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY5699: $i,SY5700: $i,SY5701: $i,SY5702: $i,SY5703: $i,SY5704: $i,SY5705: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SY5699 @ SY5699 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SY5699 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5700 @ SV1484 @ SY5701 @ SY5702 @ SY5703 @ SV357 @ SY5704 @ SY5705 @ SY5699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(3930,plain,
! [SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY5706: $i,SY5707: $i,SY5708: $i,SY5709: $i,SY5710: $i,SY5711: $i,SY5712: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SY5706 @ SY5706 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SY5706 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SY5707 @ SY5708 @ SY5709 @ SV358 @ SY5710 @ SY5711 @ SY5712 @ SY5706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3931,plain,
! [SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY5713: $i,SY5714: $i,SY5715: $i,SY5716: $i,SY5717: $i,SY5718: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SY5713 @ SY5713 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SY5713 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5714 @ SV359 @ SY5715 @ SY5716 @ SY5717 @ SV1486 @ SV1869 @ SY5718 @ SY5713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(3932,plain,
! [SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY5719: $i,SY5720: $i,SY5721: $i,SY5722: $i,SY5723: $i,SY5724: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SY5719 @ SY5719 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SY5719 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SY5720 @ SY5721 @ SY5722 @ SV1487 @ SY5723 @ SY5724 @ SV1870 @ SY5719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3933,plain,
! [SV1871: $i,SV1488: $i,SV945: $i,SV361: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV945 @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV1871 @ SV945 @ SV1488 ) @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3934,plain,
! [SV1872: $i,SV1489: $i,SV946: $i,SV362: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ ( c_Set_Oinsert @ SV946 @ SV1489 @ SV1872 ) @ ( tc_fun @ SV1872 @ tc_bool ) ) @ SV1872 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ SV1489 @ ( tc_fun @ SV1872 @ tc_bool ) ) @ SV1872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3935,plain,
! [SV1873: $i,SV1492: $i,SV949: $i,SV365: $i] :
( ( ! [SY5725: $i,SY5726: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV365 @ SV949 @ SV1492 @ SV1873 @ SY5725 ) @ SY5726 @ SY5725 @ SV1873 )
= ( c_Set_Oimage @ SV365 @ ( c_Set_Oimage @ SV949 @ SY5726 @ SY5725 @ SV1492 ) @ SV1492 @ SV1873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3936,plain,
! [SV1493: $i,SV950: $i,SV367: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV367 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1493 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 @ SV1493 @ SV367 @ SV367 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1493 @ SV367 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(3937,plain,
! [SV951: $i,SV368: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV368 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV368 ) @ SV951 ) @ SV951 )
= SV951 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3938,plain,
! [SV1874: $i,SV1494: $i,SV953: $i,SV370: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV370 )
| ( c_lessequals @ SV953 @ SV1494 @ SV370 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SV1874 ) @ SV953 ) @ SV1494 @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3939,plain,
! [SV1875: $i,SV1495: $i,SV954: $i,SV371: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV371 )
| ( c_lessequals @ SV954 @ SV1495 @ SV371 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SV1875 ) @ SV1495 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3940,plain,
! [SV1876: $i,SV1496: $i,SV955: $i,SV372: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV372 )
| ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SV1496 ) @ SV1876 ) @ SV372 )
| ~ ( c_lessequals @ SV955 @ SV1876 @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3941,plain,
! [SV1877: $i,SV1497: $i,SV956: $i,SV373: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV373 )
| ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SV1497 ) @ SV1877 ) @ SV373 )
| ~ ( c_lessequals @ SV956 @ SV1497 @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(3942,plain,
! [SV1878: $i,SV1498: $i,SV957: $i,SV374: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV374 )
| ( c_lessequals @ SV957 @ SV1498 @ SV374 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SV1878 ) @ SV957 ) @ SV1498 @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(3943,plain,
! [SV1879: $i,SV1499: $i,SV958: $i,SV375: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV375 )
| ( c_lessequals @ SV958 @ SV1499 @ SV375 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SV1879 ) @ SV1499 @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3944,plain,
! [SV1880: $i,SV1500: $i,SV959: $i,SV376: $i] :
( ( ( c_lessequals @ SV376 @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1500 @ tc_bool ) ) @ SV376 ) @ SV1880 ) @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3945,plain,
! [SV1881: $i,SV1501: $i,SV960: $i,SV377: $i] :
( ( ( c_lessequals @ SV377 @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1501 @ tc_bool ) ) @ SV1881 ) @ SV377 ) @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3946,plain,
! [SV1502: $i,SV961: $i,SV378: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV378 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ SV378 ) ) @ SV961 ) @ SV1502 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 ) @ ( hAPP @ SV961 @ v_x ) ) @ ( hAPP @ SV1502 @ v_x ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3436]) ).
thf(3947,plain,
! [SV1882: $i,SV1503: $i,SV962: $i,SV379: $i] :
( ( ~ ( class_Orderings_Oorder @ SV379 )
| ( c_lessequals @ SV962 @ SV1503 @ SV379 )
| ~ ( c_lessequals @ SV962 @ SV1882 @ SV379 )
| ~ ( c_lessequals @ SV1882 @ SV1503 @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(3948,plain,
! [SV1883: $i,SV1504: $i,SV963: $i,SV380: $i] :
( ( ~ ( class_Orderings_Oorder @ SV380 )
| ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
| ~ ( c_lessequals @ SV963 @ SV1883 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(3949,plain,
! [SV1884: $i,SV1505: $i,SV964: $i,SV381: $i] :
( ( ~ ( class_Orderings_Oorder @ SV381 )
| ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
| ~ ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 )
| ~ ( c_lessequals @ SV1884 @ SV1505 @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(3950,plain,
! [SV1885: $i,SV1506: $i,SV965: $i,SV382: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV382 )
| ( c_lessequals @ SV965 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV1885 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV965 @ SV1885 @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(3951,plain,
! [SV1886: $i,SV1507: $i,SV968: $i,SV385: $i] :
( ( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
| ~ ( c_lessequals @ SV1886 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
| ~ ( c_lessequals @ SV385 @ SV1886 @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3952,plain,
! [SV1887: $i,SV1508: $i,SV969: $i,SV386: $i] :
( ( ! [SY5727: $i] :
( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SV1887 )
| ~ ( c_lessequals @ SV969 @ SY5727 @ ( tc_fun @ SV1508 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV386 @ SY5727 @ SV1508 @ SV1887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(3953,plain,
! [SV1888: $i,SV1509: $i,SV970: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
| ~ ( hBOOL @ ( hAPP @ SV1509 @ SV970 ) )
| ~ ( c_lessequals @ SV1509 @ SV387 @ ( tc_fun @ SV1888 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(3954,plain,
! [SV971: $i,SV388: $i] :
( ( ( class_Orderings_Oorder @ SV388 )
= $false )
| ( ( c_lessequals @ SV971 @ SV971 @ SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3955,plain,
! [SV972: $i,SV389: $i] :
( ( ( class_Orderings_Opreorder @ SV389 )
= $false )
| ( ( c_lessequals @ SV972 @ SV972 @ SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3956,plain,
! [SV1510: $i,SV973: $i,SV390: $i] :
( ( ( c_Finite__Set_Ofinite @ SV390 @ SV973 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1510 @ SV973 )
| ~ ( c_lessequals @ SV390 @ SV1510 @ ( tc_fun @ SV973 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(3957,plain,
! [SV1889: $i,SV1511: $i,SV974: $i,SV391: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
| ~ ( c_lessequals @ SV1889 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV391 @ SV1889 @ ( tc_fun @ SV1511 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(3958,plain,
! [SV1890: $i,SV1512: $i,SV975: $i,SV392: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1890 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
| ~ ( c_lessequals @ SV392 @ SV1890 @ ( tc_fun @ SV1512 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(3959,plain,
! [SV1891: $i,SV1513: $i,SV976: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
| ~ ( c_lessequals @ SV1513 @ SV393 @ ( tc_fun @ SV1891 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1513 @ SV976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(3960,plain,
! [SV1514: $i,SV977: $i,SV394: $i] :
( ( ( c_Finite__Set_Ofinite @ SV394 @ SV977 )
= $true )
| ( ( ~ ( c_lessequals @ SV394 @ SV1514 @ ( tc_fun @ SV977 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1514 @ SV977 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(3961,plain,
! [SV1892: $i,SV1515: $i,SV978: $i,SV395: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV395 )
| ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
| ~ ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 )
| ~ ( c_lessequals @ SV978 @ SV1892 @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(3962,plain,
! [SV1893: $i,SV1516: $i,SV979: $i,SV396: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV396 )
| ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
| ~ ( c_lessequals @ SV1893 @ SV1516 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(3963,plain,
! [SV980: $i,SV397: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV397 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV980 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV397 @ tc_bool ) ) @ SV397 ) @ SV397 )
= SV980 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3453]) ).
thf(3964,plain,
! [SV1894: $i,SV1517: $i,SV981: $i,SV398: $i] :
( ( ! [SY5728: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV1894 ) @ SY5728 ) @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV1517 @ SY5728 @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV981 @ SV1894 @ ( tc_fun @ SV398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(3965,plain,
! [SV1895: $i,SV1518: $i,SV982: $i,SV399: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV399 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV982 @ tc_bool ) ) @ SV1518 ) @ SV1895 ) @ ( tc_fun @ SV982 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV982 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SV1518 @ ( tc_fun @ SV982 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV399 @ SV1895 @ ( tc_fun @ SV982 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(3966,plain,
! [SV1896: $i,SV1519: $i,SV984: $i,SV401: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SV984 ) @ SV1519 ) @ SV1896 @ ( tc_fun @ SV401 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV401 @ tc_bool ) ) @ SV984 ) @ ( c_HOL_Ominus__class_Ominus @ SV1519 @ SV1896 @ ( tc_fun @ SV401 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(3967,plain,
! [SV1897: $i,SV1520: $i,SV985: $i,SV402: $i] :
( ( ! [SY5729: $i,SY5730: $i] :
( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SY5729 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SY5729 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SY5729 ) @ ( tc_fun @ SY5729 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1520 @ SY5730 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_lessequals @ SV985 @ SY5730 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SY5730 @ SV1897 @ SY5729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(3968,plain,
! [SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY5731: $i,SY5732: $i,SY5733: $i,SY5734: $i,SY5735: $i,SY5736: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SY5731 @ SY5732 @ SY5733 @ SY5734 @ SY5735 @ SY5736 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(3969,plain,
! [SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY5737: $i,SY5738: $i,SY5739: $i,SY5740: $i,SY5741: $i,SY5742: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SY5737 @ SY5738 @ SY5739 @ SY5740 @ SY5741 @ SY5742 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3970,plain,
! [SV1900: $i,SV1523: $i,SV988: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SV1523 ) @ ( c_Collect @ SV1900 @ SV405 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV1900 @ SV988 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SV1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3971,plain,
! [SV1524: $i,SV989: $i,SV406: $i] :
( ( ( SV406
= ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) )
= $true )
| ( ( ( SV406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV406 @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) @ ( tc_fun @ SV1524 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3461]) ).
thf(3972,plain,
! [SV1901: $i,SV1525: $i,SV990: $i,SV407: $i] :
( ( ! [SY5743: $i] :
( ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ SV1525 @ SV1901 ) @ SY5743 @ SV1901 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5743 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1901 @ tc_bool ) ) @ SV1901 ) @ SY5743 @ SV1901 ) ) @ ( c_Set_Ovimage @ SV407 @ SV1525 @ SY5743 @ SV1901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(3973,plain,
! [SV1902: $i,SV1526: $i,SV991: $i,SV408: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV408 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV991 @ tc_bool ) ) @ SV1526 ) @ SV1902 ) @ ( tc_fun @ SV991 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV991 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SV1526 @ ( tc_fun @ SV991 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV408 @ SV1902 @ ( tc_fun @ SV991 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(3974,plain,
! [SV1903: $i,SV1527: $i,SV992: $i,SV409: $i] :
( ( ! [SY5744: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV409 @ tc_bool ) ) @ SV992 ) @ SV1527 ) @ SV1903 @ SV409 @ ( tc_fun @ SY5744 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5744 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV992 @ SV1903 @ SV409 @ ( tc_fun @ SY5744 @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1527 @ SV1903 @ SV409 @ ( tc_fun @ SY5744 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(3975,plain,
! [SV1904: $i,SV1528: $i,SV993: $i,SV410: $i] :
( ( ! [SY5745: $i] :
( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SV993 @ SV1528 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV993 @ SV410 @ SV1904 @ SY5745 ) @ SV1528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3976,plain,
! [SV1905: $i,SV1529: $i,SV994: $i,SV411: $i] :
( ( ! [SY5746: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SV994 @ SV1529 @ SV1905 ) @ SY5746 ) )
| ~ ( hBOOL @ ( hAPP @ SV994 @ ( hAPP @ SV411 @ SY5746 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(3977,plain,
! [SV1530: $i,SV995: $i,SV412: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV412 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) )
| ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3467]) ).
thf(3978,plain,
! [SV1906: $i,SV1531: $i,SV996: $i,SV413: $i] :
( ( ! [SY5747: $i,SY5748: $i,SY5749: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SY5747 @ SY5748 ) @ SY5749 @ SY5748 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SY5747 @ SY5749 @ SY5748 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5748 ) @ SV1906 ) @ SY5747 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5747 @ SY5748 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SY5749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3979,plain,
! [SV1907: $i,SV1532: $i,SV997: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SV1532 ) @ SV1907 ) )
| ~ ( hBOOL @ ( hAPP @ SV1532 @ SV1907 ) )
| ~ ( hBOOL @ ( hAPP @ SV997 @ SV1907 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(3980,plain,
! [SV1908: $i,SV1533: $i,SV998: $i,SV415: $i] :
( ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV415 @ SV998 @ SV1533 ) @ SV1908 @ SV1533 @ SV998 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1533 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV998 ) @ SV415 ) @ SV1908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(3981,plain,
! [SV1909: $i,SV1534: $i,SV999: $i,SV416: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SV1534 @ ( tc_fun @ SV1909 @ tc_bool ) ) @ ( tc_fun @ SV1909 @ tc_bool ) )
= SV1534 )
| ~ ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SV1909 @ tc_bool ) )
| ~ ( c_lessequals @ SV1534 @ SV416 @ ( tc_fun @ SV1909 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(3982,plain,
! [SV1910: $i,SV1535: $i,SV1000: $i,SV417: $i] :
( ( ! [SY5750: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SV1000 @ SV1535 @ SV1910 ) @ ( c_Set_Oimage @ SV417 @ SY5750 @ SV1535 @ SV1910 ) @ ( tc_fun @ SV1910 @ tc_bool ) )
| ~ ( c_lessequals @ SV1000 @ SY5750 @ ( tc_fun @ SV1535 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(3983,plain,
! [SV1911: $i,SV1536: $i,SV1001: $i,SV418: $i] :
( ( ! [SY5751: $i] :
( ~ ( c_lessequals @ SV418 @ SV1001 @ ( tc_fun @ SV1536 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SV1911 @ SV418 @ SV1536 @ SY5751 ) @ ( c_Set_Oimage @ SV1911 @ SV1001 @ SV1536 @ SY5751 ) @ ( tc_fun @ SY5751 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(3984,plain,
! [SV1912: $i,SV1537: $i,SV1003: $i,SV420: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV420 @ SV1003 @ SV1537 ) @ ( c_Set_Oinsert @ SV420 @ SV1912 @ SV1537 ) @ ( tc_fun @ SV1537 @ tc_bool ) )
| ~ ( c_lessequals @ SV1003 @ SV1912 @ ( tc_fun @ SV1537 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3985,plain,
! [SV1913: $i,SV1538: $i,SV1004: $i,SV421: $i] :
( ( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
| ~ ( c_Fun_Oinj__on @ SV1538 @ SV421 @ SV1004 @ SV1913 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV1538 @ SV421 @ SV1004 @ SV1913 ) @ SV1913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(3986,plain,
! [SV1539: $i,SV1005: $i,SV422: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV422 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1005 @ SV1539 @ SV422 )
| ( SV1539 = SV1005 )
| ~ ( c_lessequals @ SV1005 @ SV1539 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3476]) ).
thf(3987,plain,
! [SV1540: $i,SV1006: $i,SV423: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV423 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1006 @ SV1540 @ SV423 )
| ~ ( c_lessequals @ SV1006 @ SV1540 @ SV423 )
| ( SV1540 = SV1006 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3477]) ).
thf(3988,plain,
! [SV1541: $i,SV1007: $i,SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) )
= $true )
| ( ( ( SV424 = SV1007 )
| ~ ( c_lessequals @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3478]) ).
thf(3989,plain,
! [SV1542: $i,SV1008: $i,SV425: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV425 ) )
= $true )
| ( ( ( SV1008 = SV1542 )
| ( c_HOL_Oord__class_Oless @ SV1008 @ SV1542 @ SV425 )
| ~ ( c_lessequals @ SV1008 @ SV1542 @ SV425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3479]) ).
thf(3990,plain,
! [SV1543: $i,SV1009: $i,SV426: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV426 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV1543 @ SV426 )
| ( SV1009 = SV1543 )
| ~ ( c_lessequals @ SV1009 @ SV1543 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3480]) ).
thf(3991,plain,
! [SV1544: $i,SV1010: $i,SV427: $i] :
( ( ( SV427 = SV1010 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) )
| ~ ( c_lessequals @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3481]) ).
thf(3992,plain,
! [SV1545: $i,SV1011: $i,SV428: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV428 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1545 @ SV428 )
| ( SV1011 = SV1545 )
| ~ ( c_lessequals @ SV1011 @ SV1545 @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3482]) ).
thf(3993,plain,
! [SV1546: $i,SV1012: $i,SV429: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV429 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1012 @ SV1546 @ SV429 )
| ~ ( c_lessequals @ SV1012 @ SV1546 @ SV429 )
| ( SV1012 = SV1546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3483]) ).
thf(3994,plain,
! [SV1547: $i,SV1013: $i,SV430: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV430 ) )
= $true )
| ( ( ( SV1013 = SV1547 )
| ~ ( c_lessequals @ SV1013 @ SV1547 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1013 @ SV1547 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3995,plain,
! [SV1548: $i,SV1014: $i,SV431: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV431 ) )
= $true )
| ( ( ( SV1014 = SV1548 )
| ( c_HOL_Oord__class_Oless @ SV1014 @ SV1548 @ SV431 )
| ~ ( c_lessequals @ SV1014 @ SV1548 @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3485]) ).
thf(3996,plain,
! [SV1549: $i,SV1015: $i,SV432: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV432 ) )
= $true )
| ( ( ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1549 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3486]) ).
thf(3997,plain,
! [SV1914: $i,SV1550: $i,SV1016: $i,SV433: $i] :
( ( ! [SY5752: $i] :
( ( c_Set_Oimage @ SV433 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1016 @ tc_bool ) ) @ SV1550 ) @ SV1914 ) @ SV1016 @ SY5752 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5752 @ tc_bool ) ) @ ( c_Set_Oimage @ SV433 @ SV1550 @ SV1016 @ SY5752 ) ) @ ( c_Set_Oimage @ SV433 @ SV1914 @ SV1016 @ SY5752 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(3998,plain,
! [SV1551: $i,SV1018: $i,SV435: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV435 ) )
= $true )
| ( ( ( c_lessequals @ SV1018 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1551 @ SV435 ) @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SV1018 ) @ SV1551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3999,plain,
! [SV1915: $i,SV1552: $i,SV1019: $i,SV436: $i] :
( ( ! [SY5753: $i,SY5754: $i,SY5755: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SV1019 @ SV1552 @ SV1915 @ SY5753 ) @ SY5754 @ SV1552 @ SY5753 @ SY5755 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SV1019 @ SY5754 @ SV1915 @ SY5753 @ SY5755 ) @ SV1552 @ SV1915 @ SY5755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4000,plain,
! [SV1553: $i,SV1020: $i,SV437: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV437 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1020 @ SV1553 @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SV1553 @ SV1020 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3490]) ).
thf(4001,plain,
! [SV1554: $i,SV1021: $i,SV438: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV438 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SV1554 @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1021 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(4002,plain,
! [SV1555: $i,SV1022: $i,SV439: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV439 ) )
= $true )
| ( ( ( c_lessequals @ SV1022 @ SV1555 @ SV439 )
| ( c_lessequals @ SV1555 @ SV1022 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(4003,plain,
! [SV1556: $i,SV1023: $i,SV440: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV440 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1023 @ SV1556 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1023 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(4004,plain,
! [SV1557: $i,SV1024: $i,SV441: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV441 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1024 @ SV1557 @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV1024 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3494]) ).
thf(4005,plain,
! [SV1916: $i,SV1558: $i,SV1025: $i,SV442: $i] :
( ( ! [SY5756: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SV1025 ) @ SV1558 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1916 ) @ ( hAPP @ SY5756 @ SV1025 ) ) @ ( c_Set_Oimage @ SY5756 @ SV1558 @ SV442 @ SV1916 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4006,plain,
! [SV1917: $i,SV1559: $i,SV1026: $i,SV443: $i] :
( ( ! [SY5757: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SV1026 @ SV1559 ) ) @ ( c_Set_Oimage @ SV1026 @ SV1917 @ SY5757 @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5757 ) @ SV1559 ) @ SV1917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4007,plain,
! [SV1918: $i,SV1560: $i,SV1027: $i,SV444: $i] :
( ( ! [SY5758: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SV1027 @ SV1560 ) ) @ ( c_Set_Oimage @ SV1027 @ SV1918 @ SY5758 @ SV444 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5758 ) @ SV1560 ) @ SV1918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4008,plain,
! [SV1028: $i,SV445: $i] :
( ( ( class_Orderings_Olinorder @ SV445 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1028 @ SV445 ) ) @ SV1028 ) )
| ( SV1028
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1028 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(4009,plain,
! [SV1029: $i,SV446: $i] :
( ( ( class_Orderings_Olinorder @ SV446 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1029 @ SV446 ) ) @ SV1029 ) )
| ( SV1029
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1029 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3499]) ).
thf(4010,plain,
! [SV1561: $i,SV1030: $i,SV447: $i] :
( ( ( ( c_Set_Oinsert @ SV447 @ ( c_HOL_Ominus__class_Ominus @ SV1030 @ ( c_Set_Oinsert @ SV447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1561 @ tc_bool ) ) @ SV1561 ) @ ( tc_fun @ SV1561 @ tc_bool ) ) @ SV1561 )
= SV1030 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV447 ) @ SV1030 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(4011,plain,
! [SV1919: $i,SV1562: $i,SV1031: $i,SV448: $i] :
( ( ! [SY5759: $i] :
( ( ( hAPP @ SV448 @ SV1031 )
= SV1562 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1919 ) @ SV1031 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SV1562 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5759 @ tc_bool ) ) @ SY5759 ) @ SV1919 @ SY5759 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4012,plain,
! [SV1920: $i,SV1563: $i,SV1032: $i,SV449: $i] :
( ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV449 @ SV1032 @ SV1563 ) @ SV1920 @ SV1563 @ SV1032 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1563 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1032 ) @ SV449 ) @ SV1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4013,plain,
! [SV1921: $i,SV1564: $i,SV1033: $i,SV450: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV450 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1033 @ SV1564 @ SV1921 @ ( tc_fun @ SV450 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1921 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1033 @ SV1564 @ SV1921 @ SV450 ) ) @ SV1033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4014,plain,
! [SV1922: $i,SV1565: $i,SV1034: $i,SV451: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1034 ) @ ( c_Set_Ovimage @ SV1565 @ ( c_Set_Oinsert @ ( hAPP @ SV1565 @ SV1034 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1922 @ tc_bool ) ) @ SV1922 ) @ SV451 @ SV1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4015,plain,
! [SV1035: $i,SV452: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__1 @ SV1035 @ SV452 ) ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xab__semigroup__mult__class__Xnonempty__iff__1__2 @ SV1035 @ SV452 ) ) )
= $false )
| ( ( SV1035
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV452 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(4016,plain,
! [SV1923: $i,SV1566: $i,SV1036: $i,SV453: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV453 @ SV1036 @ SV1566 @ ( tc_fun @ SV1923 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1923 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1566 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV453 @ SV1036 @ SV1566 @ SV1923 ) ) @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(4017,plain,
! [SV1567: $i,SV1037: $i,SV454: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV454 @ SV1037 @ SV1567 ) @ ( c_Set_Oinsert @ SV454 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1567 @ tc_bool ) ) @ SV1567 ) @ ( tc_fun @ SV1567 @ tc_bool ) )
= SV1037 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1567 ) @ SV454 ) @ SV1037 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(4018,plain,
! [SV1568: $i,SV1038: $i,SV455: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV455 @ tc_bool ) ) @ SV1038 ) @ SV1568 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV455 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV455 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__2 @ SV1038 @ SV1568 @ SV455 ) ) @ SV1568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(4019,plain,
! [SV1569: $i,SV1039: $i,SV456: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV456 @ tc_bool ) ) @ SV1039 ) @ SV1569 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ ( c_ATP__Linkup_Osko__Set__Xdisjoint__iff__not__equal__1__1 @ SV1039 @ SV1569 @ SV456 ) ) @ SV1039 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(4020,plain,
! [SV1040: $i,SV457: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV457 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV457 ) @ ( c_Orderings_Obot__class_Obot @ SV457 ) ) @ SV1040 )
= SV1040 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(4021,plain,
! [SV1041: $i,SV458: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV458 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV458 ) @ SV1041 ) @ ( c_Orderings_Obot__class_Obot @ SV458 ) )
= SV1041 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(4022,plain,
! [SV1042: $i,SV459: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV459 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV459 ) @ ( c_Orderings_Obot__class_Obot @ SV459 ) ) @ SV1042 )
= ( c_Orderings_Obot__class_Obot @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(4023,plain,
! [SV1043: $i,SV460: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV460 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV460 ) @ SV1043 ) @ ( c_Orderings_Obot__class_Obot @ SV460 ) )
= ( c_Orderings_Obot__class_Obot @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(4024,plain,
! [SV1044: $i,SV461: $i] :
( ( ( class_Orderings_Obot @ SV461 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV461 ) @ SV1044 @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(4025,plain,
! [SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ! [SY5760: $i,SY5761: $i,SY5762: $i,SY5763: $i,SY5764: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SY5760 @ SY5761 @ SY5762 @ SY5763 @ SY5764 @ SV1571 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4026,plain,
! [SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ! [SY5765: $i,SY5766: $i,SY5767: $i,SY5768: $i,SY5769: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SY5765 @ SY5766 @ SY5767 @ SY5768 @ SV1572 @ SY5769 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4027,plain,
! [SV1926: $i,SV1573: $i,SV1049: $i,SV467: $i] :
( ( ! [SY5770: $i] :
( ( c_Finite__Set_Ofold__image @ SV467 @ SV1049 @ SV1573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1926 @ tc_bool ) ) @ SY5770 @ SV1926 )
= SV1573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4028,plain,
! [SV1927: $i,SV1574: $i,SV1050: $i,SV468: $i] :
( ( ( c_Finite__Set_Ofold @ SV468 @ SV1050 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1574 @ tc_bool ) ) @ SV1574 @ SV1927 )
= SV1050 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4029,plain,
! [SV1051: $i,SV470: $i] :
( ( ( c_lessequals @ SV470 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1051 @ tc_bool ) ) @ ( tc_fun @ SV1051 @ tc_bool ) )
= $false )
| ( ( SV470
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1051 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(4030,plain,
! [SV1575: $i,SV1053: $i,SV472: $i] :
( ( c_Finite__Set_Ofold1Set @ SV472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1053 @ tc_bool ) ) @ SV1575 @ SV1053 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(4031,plain,
! [SV1928: $i,SV1576: $i,SV1060: $i,SV480: $i] :
( ( ! [SY5771: $i] :
( ( SV480 = SV1060 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1576 @ SV1060 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1928 @ tc_bool ) ) @ SV480 @ SV1928 @ SY5771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4032,plain,
! [SV1929: $i,SV1581: $i,SV1068: $i,SV488: $i] :
( ( c_Finite__Set_Ofold__graph @ SV488 @ SV1068 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1581 @ tc_bool ) ) @ SV1068 @ SV1581 @ SV1929 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4033,plain,
! [SV1930: $i,SV1582: $i,SV1069: $i,SV489: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV489 @ SV1069 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1582 @ tc_bool ) ) @ SV1069 @ SV1582 @ SV1930 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4034,plain,
! [SV1931: $i,SV1584: $i,SV1071: $i,SV491: $i] :
( ( ( c_Fun_Ooverride__on @ SV491 @ SV1071 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1584 @ tc_bool ) ) @ SV1584 @ SV1931 )
= SV491 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(4035,plain,
! [SV1932: $i,SV1585: $i,SV1075: $i,SV495: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV495 @ SV1075 @ SV1585 @ SV1932 @ t_a ) @ v_x )
= ( hAPP @ SV495 @ ( hAPP @ SV1075 @ v_x ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4036,plain,
! [SV1933: $i,SV1586: $i,SV1076: $i,SV496: $i] :
( ( ( hAPP @ ( c_Fun_Ofcomp @ SV496 @ SV1076 @ t_a @ SV1586 @ SV1933 ) @ v_x )
= ( hAPP @ SV1076 @ ( hAPP @ SV496 @ v_x ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4037,plain,
! [SV1587: $i,SV1078: $i,SV498: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV498 @ SV1078 @ SV1587 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV498 ) @ SV1078 @ SV1587 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3535]) ).
thf(4038,plain,
! [SV1934: $i,SV1588: $i,SV1079: $i,SV499: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1934 @ SV499 ) ) @ SV1934 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1934 @ SV1588 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(4039,plain,
! [SV1589: $i,SV1080: $i,SV500: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SV1080 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1080 ) @ SV1589 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SV1589 ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3537]) ).
thf(4040,plain,
! [SV1590: $i,SV1081: $i,SV501: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV501 @ SV1081 @ t_a )
= $true )
| ( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ SV501 @ SV1081 ) @ SV1590 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1590 ) @ SV501 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(4041,plain,
! [SV1935: $i,SV1591: $i,SV1082: $i,SV502: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4042,plain,
! [SV1592: $i,SV1087: $i,SV507: $i] :
( ( ( SV507 = SV1087 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1592 ) @ SV507 ) @ ( c_Set_Oinsert @ SV1087 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(4043,plain,
! [SV1593: $i,SV1088: $i,SV509: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV509 @ SV1088 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1088 ) @ SV1593 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV509 @ SV1593 ) ) @ SV1593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3545]) ).
thf(4044,plain,
! [SV1594: $i,SV1090: $i,SV511: $i] :
( ( ( hBOOL @ ( hAPP @ SV511 @ SV1090 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1594 ) @ SV1090 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1594 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3547]) ).
thf(4045,plain,
! [SV1595: $i,SV1094: $i,SV516: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV516 ) @ SV1094 ) @ SV1595 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1595 @ SV1094 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(4046,plain,
! [SV1596: $i,SV1095: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ SV517 @ SV1095 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1596 ) @ SV1095 ) @ SV517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(4047,plain,
! [SV1597: $i,SV1096: $i,SV518: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV518 @ SV1096 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1597 ) @ SV1096 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1597 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(4048,plain,
! [SV519: $i,SV1097: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV1097 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV519 @ SV1097 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(4049,plain,
! [SV520: $i,SV1098: $i] :
( ( ( class_Lattices_Olattice @ SV1098 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV520 @ SV1098 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(4050,plain,
! [SV521: $i,SV1099: $i] :
( ( ( class_Lattices_Olattice @ SV1099 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV521 @ SV1099 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(4051,plain,
! [SV522: $i,SV1100: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV1100 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV522 @ SV1100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(4052,plain,
! [SV523: $i,SV1101: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV1101 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV523 @ SV1101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(4053,plain,
! [SV524: $i,SV1102: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1102 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV524 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV524 @ SV1102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(4054,plain,
! [SV525: $i,SV1103: $i] :
( ( ( class_Orderings_Opreorder @ SV1103 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV525 @ SV1103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3561]) ).
thf(4055,plain,
! [SV526: $i,SV1104: $i] :
( ( ( class_Lattices_Olattice @ SV1104 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV526 @ SV1104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(4056,plain,
! [SV527: $i,SV1105: $i] :
( ( ( class_Orderings_Oorder @ SV1105 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV527 @ SV1105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(4057,plain,
! [SV528: $i,SV1106: $i] :
( ( ( class_Orderings_Otop @ SV1106 )
= $false )
| ( ( class_Orderings_Otop @ ( tc_fun @ SV528 @ SV1106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3564]) ).
thf(4058,plain,
! [SV529: $i,SV1107: $i] :
( ( ( class_Orderings_Obot @ SV1107 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV529 @ SV1107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(4059,plain,
! [SV530: $i,SV1108: $i] :
( ( ( class_HOL_Ominus @ SV1108 )
= $false )
| ( ( class_HOL_Ominus @ ( tc_fun @ SV530 @ SV1108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3566]) ).
thf(4060,plain,
! [SV531: $i,SV1109: $i] :
( ( ( class_HOL_Oord @ SV1109 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV531 @ SV1109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(4061,plain,
! [SV1598: $i,SV1111: $i,SV534: $i] :
( ( ( SV534 = SV1111 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1598 ) @ SV534 ) @ SV1111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(4062,plain,
! [SV1936: $i,SV1599: $i,SV1112: $i,SV535: $i] :
( ( ! [SY5772: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SY5772 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SV1936 @ SY5772 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(4063,plain,
! [SV1937: $i,SV1600: $i,SV1113: $i,SV536: $i] :
( ( ! [SY5773: $i] :
( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 )
!= ( c_Set_Oinsert @ SV1937 @ ( c_Set_Oinsert @ SY5773 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 ) )
| ( SV536 = SY5773 )
| ( SV536 = SV1937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4064,plain,
! [SV1938: $i,SV1601: $i,SV1114: $i,SV537: $i] :
( ( ! [SY5774: $i] :
( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 )
!= ( c_Set_Oinsert @ SV1938 @ ( c_Set_Oinsert @ SY5774 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 ) )
| ( SV1114 = SV1938 )
| ( SV1114 = SY5774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(4065,plain,
! [SV1939: $i,SV1602: $i,SV1115: $i,SV538: $i] :
( ( ! [SY5775: $i] :
( ( ( hAPP @ SV538 @ SV1115 )
!= ( hAPP @ SV538 @ SV1602 ) )
| ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 @ SY5775 )
| ( SV1115 = SV1602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(4066,plain,
! [SV1940: $i,SV1603: $i,SV1116: $i,SV539: $i] :
( ( ! [SY5776: $i] :
( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 )
!= ( c_Set_Oinsert @ SV1940 @ ( c_Set_Oinsert @ SY5776 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 ) )
| ( SV539 = SY5776 )
| ( SV1116 = SY5776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4067,plain,
! [SV1941: $i,SV1604: $i,SV1117: $i,SV540: $i] :
( ( ! [SY5777: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SV1941 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
| ( ( hAPP @ SV1117 @ SY5777 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SY5777 ) @ SV540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4068,plain,
! [SV1942: $i,SV1605: $i,SV1118: $i,SV541: $i] :
( ( ! [SY5778: $i] :
( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 )
!= ( c_Set_Oinsert @ SV1942 @ ( c_Set_Oinsert @ SY5778 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 ) )
| ( SV1118 = SV1942 )
| ( SV541 = SV1942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4069,plain,
! [SV1943: $i,SV1606: $i,SV1119: $i,SV542: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV542 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SV1606 @ SV1943 @ SV542 ) )
| ( SV1606 = SV1943 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4070,plain,
! [SV1944: $i,SV1607: $i,SV1120: $i,SV543: $i] :
( ( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SV1607 )
!= ( c_Set_Oinsert @ SV543 @ SV1944 @ SV1607 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1944 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1120 ) )
| ( SV1120 = SV1944 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4071,plain,
! [SV1608: $i,SV1121: $i,SV544: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV544 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SV1121 ) @ SV1608 )
!= ( c_Orderings_Obot__class_Obot @ SV544 ) )
| ( SV1608
= ( c_Orderings_Obot__class_Obot @ SV544 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(4072,plain,
! [SV1945: $i,SV1609: $i,SV1122: $i,SV545: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1945 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SV1945 ) @ SV1609 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(4073,plain,
! [SV1610: $i,SV1123: $i,SV546: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV546 @ tc_bool ) ) @ SV1123 ) @ SV1610 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
= $true )
| ( ( SV1123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(4074,plain,
! [SV1946: $i,SV1611: $i,SV1124: $i,SV547: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ SV1611 ) ) @ SV1946 )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1611 ) @ SV1946 ) ) )
| ( c_lessequals @ SV1946 @ SV1124 @ ( tc_fun @ SV547 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4075,plain,
! [SV1612: $i,SV1125: $i,SV548: $i] :
( ( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1125 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1612 ) )
= $true )
| ( ( SV1125 = SV1612 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(4076,plain,
! [SV1947: $i,SV1613: $i,SV1126: $i,SV549: $i] :
( ( ! [SY5779: $i] :
( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SV1947 )
!= ( c_Set_Oimage @ SV549 @ SY5779 @ SV1613 @ SV1947 ) )
| ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SV1947 )
| ( SV1126 = SY5779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4077,plain,
! [SV1948: $i,SV1614: $i,SV1127: $i,SV550: $i] :
( ( ! [SY5780: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SY5780 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SY5780 @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4078,plain,
! [SV1615: $i,SV1128: $i,SV551: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV551 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SV1128 ) @ SV1615 )
!= ( c_Orderings_Otop__class_Otop @ SV551 ) )
| ( SV1128
= ( c_Orderings_Otop__class_Otop @ SV551 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3586]) ).
thf(4079,plain,
! [SV1616: $i,SV1129: $i,SV552: $i] :
( ( ( ( c_Set_Oinsert @ SV552 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 )
!= ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 ) )
= $true )
| ( ( SV552 = SV1616 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(4080,plain,
! [SV1617: $i,SV1130: $i,SV553: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV553 @ tc_bool ) ) @ SV1130 ) @ SV1617 )
!= SV1617 )
= $true )
| ( ( c_lessequals @ SV1130 @ SV1617 @ ( tc_fun @ SV553 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(4081,plain,
! [SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY5781: $i,SY5782: $i,SY5783: $i,SY5784: $i,SY5785: $i,SY5786: $i,SY5787: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SY5781 @ SY5782 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SY5783 @ SY5784 @ SY5785 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SY5781 @ SY5786 @ SY5784 @ SY5787 ) @ SY5782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(4082,plain,
! [SV1950: $i,SV1619: $i,SV1132: $i,SV555: $i] :
( ( ! [SY5788: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SY5788 @ tc_bool ) ) @ SY5788 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SY5788 @ tc_bool ) ) @ SY5788 @ SV555 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SY5788 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SY5788 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SY5788 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SY5788 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4083,plain,
! [SV1620: $i,SV1133: $i,SV556: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV556 @ tc_bool ) ) @ SV1133 ) @ SV1620 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV556 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1133 @ SV1620 @ ( tc_fun @ SV556 @ tc_bool ) )
= SV1133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(4084,plain,
! [SV1951: $i,SV1621: $i,SV1134: $i,SV558: $i] :
( ( ( ( hAPP @ SV558 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1134 @ SV558 @ SV1621 @ SV1951 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1134 @ SV558 @ SV1621 @ ( tc_fun @ SV1951 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(4085,plain,
! [SV1952: $i,SV1622: $i,SV1135: $i,SV559: $i] :
( ( ! [SY5789: $i] :
( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV1952 @ SY5789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4086,plain,
! [SV1623: $i,SV1136: $i,SV560: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV560 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SV1136 ) @ SV1623 )
!= SV1136 )
| ( c_lessequals @ SV1136 @ SV1623 @ SV560 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4087,plain,
! [SV1624: $i,SV1137: $i,SV561: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV561 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SV1137 ) @ SV1624 )
!= ( c_Orderings_Obot__class_Obot @ SV561 ) )
| ( SV1137
= ( c_Orderings_Obot__class_Obot @ SV561 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4088,plain,
! [SV1953: $i,SV1625: $i,SV1138: $i,SV562: $i] :
( ( ! [SY5790: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SY5790 @ SV562 ) )
| ( c_lessequals @ SY5790 @ SV1953 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(4089,plain,
! [SV1954: $i,SV1626: $i,SV1139: $i,SV563: $i] :
( ( ! [SY5791: $i,SY5792: $i] :
( ( ( hAPP @ SV563 @ SV1139 )
!= ( hAPP @ SV563 @ SV1626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SY5791 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SY5791 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SY5791 @ SV1954 @ SY5792 )
| ( SV1139 = SV1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(4090,plain,
! [SV1955: $i,SV1627: $i,SV1140: $i,SV564: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV564 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SV1627 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SV1955 @ SV1955 @ SV564 ) )
| ( SV1140 = SV1627 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(4091,plain,
! [SV1956: $i,SV1628: $i,SV1141: $i,SV565: $i] :
( ( ! [SY5793: $i,SY5794: $i] :
( ( ( hAPP @ SV565 @ SV1141 )
!= ( hAPP @ SV565 @ SV1628 ) )
| ~ ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SY5793 @ SY5794 )
| ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5793 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5793 ) @ SV1141 ) @ SV1956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4092,plain,
! [SV1629: $i,SV1142: $i,SV566: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV566 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SV1142 ) @ SV1629 )
!= SV1629 )
| ( c_lessequals @ SV1142 @ SV1629 @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3600]) ).
thf(4093,plain,
! [SV1957: $i,SV1630: $i,SV1143: $i,SV567: $i] :
( ( ! [SY5795: $i] :
( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SV1957 )
!= ( c_Set_Oimage @ SV567 @ SY5795 @ SV1630 @ SV1957 ) )
| ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SY5795 ) @ SV1630 @ SV1957 )
| ( SV1143 = SY5795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4094,plain,
! [SV1144: $i,SV568: $i] :
( ( ( ( c_Suc @ SV568 )
= ( c_Suc @ SV1144 ) )
= $false )
| ( ( SV568 = SV1144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3602]) ).
thf(4095,plain,
! [SV1631: $i,SV1145: $i,SV569: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV569 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1145 @ SV1631 @ SV569 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(4096,plain,
! [SV1632: $i,SV1146: $i,SV570: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) )
!= ( c_Collect @ SV1146 @ SV570 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1146 @ SV1632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3604]) ).
thf(4097,plain,
! [SV1633: $i,SV1147: $i,SV571: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV571 @ tc_bool ) ) @ SV1147 ) @ SV1633 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= $true )
| ( ( SV1633
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3605]) ).
thf(4098,plain,
! [SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ! [SY5796: $i,SY5797: $i,SY5798: $i,SY5799: $i,SY5800: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SY5796 )
!= ( c_Fun_Ocomp @ SY5797 @ SY5798 @ SY5799 @ SV1958 @ SY5796 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY5800 ) )
= ( hAPP @ SY5797 @ ( hAPP @ SY5798 @ SY5800 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4099,plain,
! [SV1635: $i,SV1149: $i,SV573: $i] :
( ( ( ( c_Set_Oinsert @ SV573 @ SV1149 @ SV1635 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1635 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1635 ) @ SV573 ) @ SV1149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(4100,plain,
! [SV1150: $i,SV574: $i] :
( ( ( ( c_Suc @ SV574 )
= ( c_Suc @ SV1150 ) )
= $false )
| ( ( SV574 = SV1150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(4101,plain,
! [SV1959: $i,SV1636: $i,SV1151: $i,SV575: $i] :
( ( ! [SY5801: $i,SY5802: $i,SY5803: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SV1959 @ SY5801 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV1959 ) @ SY5802 @ SV1959 @ SV1959 @ SY5801 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SY5803 ) )
= ( hAPP @ SY5802 @ SY5803 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4102,plain,
! [SV1960: $i,SV1637: $i,SV1152: $i,SV576: $i] :
( ( ! [SY5804: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SV1960 @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ( ( hAPP @ SV1637 @ SY5804 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1960 ) @ SY5804 ) @ SV1152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4103,plain,
! [SV1961: $i,SV1638: $i,SV1153: $i,SV578: $i] :
( ( ( ( c_Set_Oimage @ SV578 @ SV1153 @ SV1638 @ SV1961 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1961 @ tc_bool ) ) )
| ( SV1153
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1638 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4104,plain,
! [SV1639: $i,SV1154: $i,SV580: $i] :
( ( ( c_Set_Oinsert @ SV580 @ SV1154 @ SV1639 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1639 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(4105,plain,
! [SV1962: $i,SV1640: $i,SV1155: $i,SV581: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) )
!= ( c_Set_Oimage @ SV1155 @ SV1640 @ SV1962 @ SV581 ) )
| ( SV1640
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1962 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4106,plain,
! [SV1641: $i,SV1156: $i,SV582: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV582 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SV1156 ) @ SV1641 )
!= ( c_Orderings_Otop__class_Otop @ SV582 ) )
| ( SV1641
= ( c_Orderings_Otop__class_Otop @ SV582 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3614]) ).
thf(4107,plain,
! [SV1642: $i,SV1157: $i,SV583: $i] :
( ( ( ( c_Collect @ SV583 @ SV1157 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1157 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV583 @ SV1642 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(4108,plain,
! [SV1963: $i,SV1643: $i,SV1158: $i,SV584: $i] :
( ( ! [SY5805: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SY5805 @ SV584 ) )
| ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SY5805 @ SV1963 @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4109,plain,
! [SV1964: $i,SV1644: $i,SV1159: $i,SV585: $i] :
( ( ( ( hAPP @ SV585 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV1159 @ SV585 @ SV1644 @ SV1964 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1964 @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1159 @ SV585 @ SV1644 @ ( tc_fun @ SV1964 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1964 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4110,plain,
! [SV1965: $i,SV1645: $i,SV1160: $i,SV586: $i] :
( ( ! [SY5806: $i,SY5807: $i] :
( ( ( hAPP @ SV586 @ SV1160 )
!= ( hAPP @ SV586 @ SV1645 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SY5806 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SY5806 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SY5806 @ SV1965 @ SY5807 )
| ( SV1160 = SV1645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4111,plain,
! [SV1966: $i,SV1646: $i,SV1161: $i,SV587: $i] :
( ( ! [SY5808: $i,SY5809: $i] :
( ( ( hAPP @ SV587 @ SV1161 )
!= ( hAPP @ SV587 @ SV1646 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SY5808 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SY5808 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SY5808 @ SV1966 @ SY5809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4112,plain,
! [SV1967: $i,SV1647: $i,SV1162: $i,SV588: $i,SV2: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SV1647 ) @ ( c_Set_Oimage @ SV2 @ SV1967 @ SV1162 @ SV1647 ) @ ( tc_fun @ SV1647 @ tc_bool ) )
| ~ ( c_lessequals @ SV588 @ SV1967 @ ( tc_fun @ SV1162 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SV1647 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4113,plain,
! [SV1968: $i,SV1648: $i,SV1163: $i,SV589: $i,SV3: $i] :
( ( ( c_Fun_Oinj__on @ SV3 @ SV589 @ SV1163 @ SV1648 )
| ~ ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SV1968 @ SV589 @ SV1163 ) @ SV1163 @ SV1648 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4114,plain,
! [SV1969: $i,SV1649: $i,SV1164: $i,SV590: $i,SV4: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
| ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1649 @ SV590 @ SV1969 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1164 ) @ SV1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4115,plain,
! [SV1970: $i,SV1650: $i,SV1165: $i,SV591: $i,SV5: $i] :
( ( ( c_lessequals @ ( hAPP @ SV5 @ SV591 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1165 @ SV5 @ SV1650 @ ( tc_fun @ SV1970 @ tc_bool ) ) @ ( tc_fun @ SV1970 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV591 ) @ SV1165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4116,plain,
! [SV1651: $i,SV1166: $i,SV592: $i,SV6: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV6 @ SV592 @ SV1166 ) @ SV1651 @ ( tc_fun @ SV1166 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV592 @ SV1651 @ ( tc_fun @ SV1166 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1166 ) @ SV6 ) @ SV1651 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(4117,plain,
! [SV1652: $i,SV1167: $i,SV593: $i,SV7: $i] :
( ( ( c_lessequals @ SV7 @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1652 @ SV7 @ SV1167 ) @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3625]) ).
thf(4118,plain,
! [SV1653: $i,SV1168: $i,SV594: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ ( c_Set_Oinsert @ SV594 @ SV1168 @ SV1653 ) @ ( tc_fun @ SV1653 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV8 @ SV1168 @ ( tc_fun @ SV1653 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(4119,plain,
! [SV1971: $i,SV1654: $i,SV1169: $i,SV595: $i,SV9: $i] :
( ( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SV1169 @ SV1654 ) @ SV1971 @ SV1654 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1654 ) @ SV595 ) @ SV1169 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SV1169 @ SV1971 @ SV1654 @ SV1654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4120,plain,
! [SV1972: $i,SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ! [SY5810: $i,SY5811: $i,SY5812: $i,SY5813: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SY5810 @ SY5811 @ SY5812 @ SY5813 @ SV1170 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3628]) ).
thf(4121,plain,
! [SV1973: $i,SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ! [SY5814: $i,SY5815: $i,SY5816: $i,SY5817: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SY5814 @ SY5815 @ SY5816 @ SV1171 @ SY5817 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(4122,plain,
! [SV1657: $i,SV1172: $i,SV598: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1657 @ ( tc_fun @ SV1172 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV1657 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SV1657 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3630]) ).
thf(4123,plain,
! [SV1658: $i,SV1173: $i,SV599: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV13 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SV1658 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV1173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(4124,plain,
! [SV1974: $i,SV1659: $i,SV1174: $i,SV600: $i,SV14: $i] :
( ( ! [SY5818: $i,SY5819: $i,SY5820: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SY5818 @ SY5819 ) @ SY5820 @ SY5819 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SY5819 @ SY5820 @ SY5818 ) @ SV1174 @ SV1974 @ SY5820 @ SY5818 ) )
| ~ ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SY5818 @ SY5819 )
| ~ ( c_Finite__Set_Ofinite @ SV1974 @ SY5818 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY5820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4125,plain,
! [SV601: $i,SV1175: $i,SV15: $i] :
( ( ( c_Finite__Set_Ofinite @ SV15 @ SV1175 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV601 @ ( tc_fun @ SV1175 @ tc_bool ) ) @ SV1175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3633]) ).
thf(4126,plain,
! [SV1660: $i,SV1176: $i,SV602: $i,SV16: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV16 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1660 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3634]) ).
thf(4127,plain,
! [SV1975: $i,SV1661: $i,SV1177: $i,SV603: $i,SV17: $i] :
( ( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SV603 @ SV1177 @ ( tc_fun @ SV1661 @ tc_bool ) ) @ SV1661 @ SV1975 )
| ~ ( c_Fun_Oinj__on @ SV17 @ SV603 @ SV1661 @ SV1975 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(4128,plain,
! [SV1976: $i,SV1664: $i,SV1180: $i,SV606: $i,SV20: $i] :
( ( ( c_Set_Ovimage @ SV20 @ ( c_HOL_Ominus__class_Ominus @ SV606 @ SV1180 @ ( tc_fun @ SV1664 @ tc_bool ) ) @ SV1976 @ SV1664 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV20 @ SV606 @ SV1976 @ SV1664 ) @ ( c_Set_Ovimage @ SV20 @ SV1180 @ SV1976 @ SV1664 ) @ ( tc_fun @ SV1976 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4129,plain,
! [SV1665: $i,SV1181: $i,SV607: $i,SV21: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(4130,plain,
! [SV1667: $i,SV1183: $i,SV609: $i,SV23: $i] :
( ( ( ( c_Set_Ovimage @ SV23 @ ( c_Set_Oimage @ SV23 @ SV609 @ SV1183 @ SV1667 ) @ SV1183 @ SV1667 )
= SV609 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV23 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1183 @ SV1667 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3641]) ).
thf(4131,plain,
! [SV1668: $i,SV1184: $i,SV611: $i,SV25: $i] :
( ( ( SV25 = SV611 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold1Set @ SV1184 @ ( c_Set_Oinsert @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1668 @ tc_bool ) ) @ SV1668 ) @ SV611 @ SV1668 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3642]) ).
thf(4132,plain,
! [SV1186: $i,SV613: $i,SV27: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV27 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV613 @ SV1186 @ SV27 ) @ SV27 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV27 ) @ SV613 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1186 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3643]) ).
thf(4133,plain,
! [SV620: $i,SV1189: $i,SV34: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV1189 @ ( tc_fun @ SV620 @ tc_bool ) ) @ SV620 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1189 @ SV620 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV34 @ SV620 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(4134,plain,
! [SV621: $i,SV1190: $i,SV35: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV35 @ SV1190 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV621 @ SV1190 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SV621 @ ( tc_fun @ SV1190 @ tc_bool ) ) @ SV1190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(4135,plain,
! [SV1977: $i,SV1672: $i,SV1193: $i,SV624: $i,SV38: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
| ~ ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3651]) ).
thf(4136,plain,
! [SV1673: $i,SV1194: $i,SV625: $i,SV39: $i] :
( ( ( hBOOL @ ( hAPP @ SV39 @ SV625 ) )
= $true )
| ( ( ( SV1194 = SV625 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1194 @ SV39 @ SV1673 ) @ SV625 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3652]) ).
thf(4137,plain,
! [SV1978: $i,SV1674: $i,SV1195: $i,SV627: $i,SV41: $i] :
( ( ! [SY5821: $i] :
( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1978 ) @ SV627 ) @ SY5821 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5821 @ SV41 @ SV1978 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4138,plain,
! [SV630: $i,SV44: $i,SV1198: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1198 @ SV44 @ SV630 ) @ SV630 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV44 @ SV630 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(4139,plain,
! [SV45: $i,SV1199: $i,SV631: $i] :
( ( ( c_Finite__Set_Ofinite @ SV631 @ SV1199 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV45 @ SV631 @ SV1199 ) @ SV1199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(4140,plain,
! [SV1979: $i,SV1676: $i,SV1200: $i,SV632: $i,SV46: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SV632 @ SV1200 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SV1979 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SV1979 @ ( tc_fun @ SV46 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1979 ) @ SV1200 ) @ SV1676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(4141,plain,
! [SV1980: $i,SV1677: $i,SV1201: $i,SV633: $i,SV47: $i] :
( ( ! [SY5822: $i,SY5823: $i] :
( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SY5822 @ SY5823 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5822 ) @ SV1677 ) @ SV1201 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5822 @ tc_bool ) ) @ SY5822 ) @ ( tc_fun @ SY5822 @ tc_bool ) ) @ SV1980 @ SY5822 @ SY5823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4142,plain,
! [SV1981: $i,SV1678: $i,SV1202: $i,SV634: $i,SV48: $i] :
( ( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV1202 ) @ SV1678 ) @ SV634 @ SV1981 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1981 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SV1202 @ SV634 @ SV1981 ) ) @ ( c_Set_Oimage @ SV48 @ SV1678 @ SV634 @ SV1981 ) ) )
| ~ ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV634 @ SV1981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4143,plain,
! [SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY5824: $i,SY5825: $i,SY5826: $i,SY5827: $i,SY5828: $i,SY5829: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5824 @ SV49 @ SY5825 @ SY5826 @ SY5827 @ SV1982 @ SY5828 @ SY5829 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(4144,plain,
! [SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY5830: $i,SY5831: $i,SY5832: $i,SY5833: $i,SY5834: $i,SY5835: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SY5830 @ SY5831 @ SY5832 @ SV1983 @ SY5833 @ SY5834 @ SY5835 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4145,plain,
! [SV1984: $i,SV1681: $i,SV1205: $i,SV637: $i,SV51: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV51 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV637 @ tc_bool ) ) @ SV1205 ) @ SV1681 ) @ SV637 @ SV1984 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1984 @ tc_bool ) ) @ ( c_Set_Oimage @ SV51 @ SV1205 @ SV637 @ SV1984 ) ) @ ( c_Set_Oimage @ SV51 @ SV1681 @ SV637 @ SV1984 ) ) @ ( tc_fun @ SV1984 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4146,plain,
! [SV638: $i,SV52: $i,SV1206: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1206 @ SV52 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV638 @ SV52 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SV638 ) @ SV1206 ) @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3663]) ).
thf(4147,plain,
! [SV639: $i,SV53: $i,SV1207: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1207 @ SV53 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV639 @ SV53 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SV639 ) @ SV1207 ) @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(4148,plain,
! [SV1985: $i,SV1682: $i,SV1208: $i,SV640: $i,SV54: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ SV54 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV640 @ tc_bool ) ) @ SV1208 ) @ SV1682 ) @ SV640 @ SV1985 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1985 @ tc_bool ) ) @ ( c_Relation_OImage @ SV54 @ SV1208 @ SV640 @ SV1985 ) ) @ ( c_Relation_OImage @ SV54 @ SV1682 @ SV640 @ SV1985 ) ) @ ( tc_fun @ SV1985 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(4149,plain,
! [SV1683: $i,SV1209: $i,SV641: $i,SV55: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ SV1209 ) ) @ SV1683 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV1209 ) @ SV1683 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1683 @ SV641 @ ( tc_fun @ SV55 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(4150,plain,
! [SV1986: $i,SV1684: $i,SV1210: $i,SV642: $i,SV56: $i] :
( ( ( ( hAPP @ ( c_Map_Orestrict__map @ SV56 @ SV642 @ SV1210 @ SV1684 ) @ SV1986 )
= ( c_Option_Ooption_ONone @ SV1684 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1210 ) @ SV1986 ) @ SV642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4151,plain,
! [SV1987: $i,SV1685: $i,SV1212: $i,SV644: $i,SV58: $i] :
( ( ! [SY5836: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV58 @ SV644 @ SV1212 @ SV1685 @ SV1987 ) @ SY5836 )
= ( hAPP @ SV58 @ ( hAPP @ SV644 @ SY5836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(4152,plain,
! [SV1988: $i,SV1686: $i,SV1213: $i,SV645: $i,SV59: $i] :
( ( ! [SY5837: $i] :
( ( hAPP @ SV59 @ ( hAPP @ SV645 @ SV1213 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV59 @ SV645 @ SV1686 @ SV1988 @ SY5837 ) @ SV1213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4153,plain,
! [SV1989: $i,SV1687: $i,SV1214: $i,SV646: $i,SV60: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ ( hAPP @ SV1989 @ SV646 ) ) @ ( c_Set_Oimage @ SV1989 @ SV1214 @ SV60 @ SV1687 ) ) )
| ~ ( c_Fun_Oinj__on @ SV1989 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SV1687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4154,plain,
! [SV1990: $i,SV1688: $i,SV1215: $i,SV647: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SV1688 @ SV1990 @ SV61 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1990 ) @ SV1215 ) @ SV1688 ) )
| ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1990 @ tc_bool ) ) @ SV1990 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4155,plain,
! [SV1991: $i,SV1689: $i,SV1216: $i,SV648: $i,SV62: $i] :
( ( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ SV1216 ) ) @ SV1689 )
= ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ ( hAPP @ ( hAPP @ SV62 @ SV1216 ) @ SV1689 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SV1991 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4156,plain,
! [SV1992: $i,SV1690: $i,SV1217: $i,SV649: $i,SV63: $i] :
( ( ( ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ SV1690 ) )
= ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ SV1690 ) ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SV1992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(4157,plain,
! [SV1691: $i,SV1218: $i,SV650: $i,SV64: $i] :
( ( ( ( hAPP @ ( hAPP @ SV64 @ SV650 ) @ SV1218 )
= ( hAPP @ ( hAPP @ SV64 @ SV1218 ) @ SV650 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV64 @ SV1691 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(4158,plain,
! [SV1692: $i,SV1219: $i,SV651: $i,SV65: $i] :
( ( ( hBOOL @ ( hAPP @ SV65 @ SV651 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV1219 @ SV651 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1692 @ tc_bool ) ) @ SV1219 ) @ SV65 ) @ SV651 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(4159,plain,
! [SV1693: $i,SV1220: $i,SV652: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV66 @ tc_bool ) ) @ SV652 ) @ SV1220 ) @ SV1693 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1220 @ SV1693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(4160,plain,
! [SV1694: $i,SV1221: $i,SV653: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV67 @ tc_bool ) ) @ SV653 ) @ SV1221 ) @ SV1694 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV653 @ SV1694 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(4161,plain,
! [SV1993: $i,SV1695: $i,SV1222: $i,SV654: $i,SV68: $i] :
( ( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV1695 @ SV68 @ SV1222 @ SV1993 ) @ ( c_Set_Oimage @ SV1695 @ SV654 @ SV1222 @ SV1993 ) @ ( tc_fun @ SV1993 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV1695 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SV1993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(4162,plain,
! [SV1696: $i,SV1223: $i,SV655: $i,SV69: $i] :
( ( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SV1223 @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1696 ) @ SV655 ) @ SV69 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1223 @ ( tc_fun @ SV1696 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(4163,plain,
! [SV1697: $i,SV1224: $i,SV656: $i,SV70: $i] :
( ( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SV1224 @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV656 ) @ SV70 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1224 @ ( tc_fun @ SV1697 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(4164,plain,
! [SV1698: $i,SV1225: $i,SV657: $i,SV71: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1698 @ ( tc_fun @ SV1225 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1225 ) @ SV657 ) @ SV71 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SV1698 @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(4165,plain,
! [SV1994: $i,SV1699: $i,SV1226: $i,SV658: $i,SV72: $i] :
( ( ! [SY5838: $i] :
( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
| ~ ( c_lessequals @ SV1699 @ SY5838 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_lessequals @ SV1226 @ SY5838 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SY5838 @ SV658 @ SV1994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4166,plain,
! [SV1995: $i,SV1700: $i,SV1227: $i,SV659: $i,SV73: $i] :
( ( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
| ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SV1700 @ SV1995 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1700 @ SV1995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(4167,plain,
! [SV1996: $i,SV1701: $i,SV1228: $i,SV660: $i,SV74: $i] :
( ( ! [SY5839: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1996 ) @ SV1228 ) @ SY5839 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SY5839 @ SV1996 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(4168,plain,
! [SV1997: $i,SV1702: $i,SV1229: $i,SV661: $i,SV75: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SV661 @ SV1229 ) @ SV1702 @ SV1229 @ SV661 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV661 @ tc_bool ) ) @ SV661 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1229 ) @ SV1997 ) @ SV1702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(4169,plain,
! [SV1998: $i,SV1703: $i,SV1230: $i,SV662: $i,SV76: $i] :
( ( ! [SY5840: $i] :
( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1230 @ SV1703 @ SV76 @ SV1998 @ SV662 @ SY5840 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4170,plain,
! [SV1231: $i,SV663: $i,SV77: $i] :
( ( ( class_Lattices_Olattice @ SV77 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ SV77 ) ) @ SV663 ) @ SV1231 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV77 ) @ ( hAPP @ SV663 @ v_x ) ) @ ( hAPP @ SV1231 @ v_x ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(4171,plain,
! [SV1999: $i,SV1704: $i,SV1232: $i,SV664: $i,SV78: $i] :
( ( ! [SY5841: $i] :
( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SV1232 @ SV1704 @ SV1999 ) @ SV1999 @ SY5841 )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SV1999 @ SY5841 @ SV1704 ) @ SV1232 @ SV1704 @ SY5841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(4172,plain,
! [SV1707: $i,SV1235: $i,SV667: $i,SV81: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV81 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ SV1235 ) @ SV1707 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1235 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1707 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(4173,plain,
! [SV1708: $i,SV1236: $i,SV668: $i,SV82: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV82 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ SV668 ) @ SV1236 ) ) @ SV1708 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV668 ) @ SV1708 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV1236 ) @ SV1708 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(4174,plain,
! [SV1709: $i,SV1237: $i,SV669: $i,SV83: $i] :
( ( ( hBOOL @ ( hAPP @ SV83 @ SV669 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1237 ) @ SV669 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1237 @ tc_bool ) ) @ SV1709 ) @ ( c_Collect @ SV83 @ SV1237 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3694]) ).
thf(4175,plain,
! [SV1710: $i,SV1240: $i,SV672: $i,SV86: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SV1240 @ SV1710 ) @ SV1240 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1240 @ tc_bool ) ) @ SV1240 @ SV1710 )
| ~ ( c_Finite__Set_Ofinite @ SV672 @ SV1710 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(4176,plain,
! [SV1711: $i,SV1241: $i,SV675: $i,SV89: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3697]) ).
thf(4177,plain,
! [SV1712: $i,SV1242: $i,SV676: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1712 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV90 @ SV1712 @ ( tc_fun @ SV1242 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3698]) ).
thf(4178,plain,
! [SV1713: $i,SV1243: $i,SV677: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV91 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(4179,plain,
! [SV2000: $i,SV1714: $i,SV1244: $i,SV678: $i,SV92: $i] :
( ( ( c_Relation_OImage @ SV92 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV678 @ tc_bool ) ) @ SV1244 ) @ SV1714 ) @ SV678 @ SV2000 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2000 @ tc_bool ) ) @ ( c_Relation_OImage @ SV92 @ SV1244 @ SV678 @ SV2000 ) ) @ ( c_Relation_OImage @ SV92 @ SV1714 @ SV678 @ SV2000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3700]) ).
thf(4180,plain,
! [SV2001: $i,SV1715: $i,SV1245: $i,SV679: $i,SV93: $i] :
( ( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SV1245 @ SV1715 ) @ SV1715 @ SV2001 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 ) @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 @ SV2001 ) ) )
| ~ ( c_Fun_Oinj__on @ SV93 @ SV1245 @ SV1715 @ SV2001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(4181,plain,
! [SV2002: $i,SV1718: $i,SV1248: $i,SV683: $i,SV97: $i] :
( ( ! [SY5842: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV97 @ SV683 @ SV1248 @ SV1718 ) @ SV2002 ) @ SY5842 )
= ( hAPP @ ( hAPP @ SV97 @ SY5842 ) @ SV2002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4182,plain,
! [SV2003: $i,SV1720: $i,SV1250: $i,SV685: $i,SV99: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1720 @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV2003 @ SV99 ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1720 @ SV1250 @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV2003 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV685 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV1250 ) @ SV1720 ) @ SV2003 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(4183,plain,
! [SV1252: $i,SV687: $i,SV101: $i] :
( ( ( class_Orderings_Olinorder @ SV101 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV687 @ SV1252 @ SV101 )
| ( c_lessequals @ SV1252 @ SV687 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4184,plain,
! [SV102: $i,SV688: $i] :
( ( ( ~ ( c_lessequals @ SV688 @ SV688 @ SV102 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV688 @ SV688 @ SV102 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3708]) ).
thf(4185,plain,
! [SV103: $i,SV689: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV689 @ SV689 @ SV103 )
= $true )
| ( ( c_lessequals @ SV689 @ SV689 @ SV103 )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(4186,plain,
! [SV1253: $i,SV690: $i,SV104: $i] :
( ( ( class_Orderings_Olinorder @ SV104 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV690 @ SV1253 @ SV104 )
| ~ ( c_lessequals @ SV1253 @ SV690 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(4187,plain,
! [SV1254: $i,SV691: $i,SV105: $i] :
( ( ( class_Orderings_Olinorder @ SV105 )
= $false )
| ( ( ( c_lessequals @ SV691 @ SV1254 @ SV105 )
| ( c_HOL_Oord__class_Oless @ SV1254 @ SV691 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(4188,plain,
! [SV1255: $i,SV692: $i,SV106: $i] :
( ( ( class_Orderings_Olinorder @ SV106 )
= $false )
| ( ( ~ ( c_lessequals @ SV692 @ SV1255 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ SV1255 @ SV692 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(4189,plain,
! [SV1256: $i,SV693: $i,SV107: $i] :
( ( ( class_Orderings_Olinorder @ SV107 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1256 @ SV107 )
| ( c_lessequals @ SV1256 @ SV693 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(4190,plain,
! [SV1721: $i,SV1257: $i,SV694: $i,SV108: $i] :
( ( ( ~ ( class_HOL_Oord @ SV108 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SV1721 @ SV108 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SV1721 @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(4191,plain,
! [SV1258: $i,SV695: $i,SV109: $i] :
( ( ( class_Orderings_Opreorder @ SV109 )
= $false )
| ( ( ~ ( c_lessequals @ SV695 @ SV1258 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV1258 @ SV695 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3715]) ).
thf(4192,plain,
! [SV111: $i,SV697: $i] :
( ( ( ( c_Complete__Lattice_OSup__class_OSup @ SV697 @ SV111 )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 ) @ ( c_Orderings_Obot__class_Obot @ SV111 ) @ SV697 @ SV111 @ SV111 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV697 @ SV111 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(4193,plain,
! [SV1260: $i,SV698: $i,SV112: $i] :
( ( ( class_Orderings_Olinorder @ SV112 )
= $false )
| ( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
| ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(4194,plain,
! [SV2004: $i,SV1723: $i,SV1261: $i,SV700: $i,SV114: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV114 @ SV700 @ SV1261 @ SV1723 ) @ ( c_Set_Oimage @ SV114 @ SV2004 @ SV1261 @ SV1723 ) @ ( tc_fun @ SV1723 @ tc_bool ) ) @ ( c_Set_Oimage @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV700 @ SV2004 @ ( tc_fun @ SV1261 @ tc_bool ) ) @ SV1261 @ SV1723 ) @ ( tc_fun @ SV1723 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(4195,plain,
! [SV1726: $i,SV1264: $i,SV703: $i,SV117: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV117 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ SV1264 ) ) @ SV1726 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV1264 ) @ SV1726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(4196,plain,
! [SV1727: $i,SV1265: $i,SV704: $i,SV118: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV118 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ SV1727 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ SV1727 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(4197,plain,
! [SV1728: $i,SV1266: $i,SV705: $i,SV119: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV119 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ SV1728 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ SV1728 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(4198,plain,
! [SV1729: $i,SV1267: $i,SV706: $i,SV120: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV120 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ SV1267 ) ) @ SV1729 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV1267 ) @ SV1729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(4199,plain,
! [SV121: $i,SV1268: $i,SV707: $i] :
( ( ( c_lessequals @ SV707 @ SV1268 @ ( tc_fun @ SV121 @ tc_bool ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV121 @ tc_bool ) ) @ SV707 ) @ SV1268 )
= SV707 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(4200,plain,
! [SV122: $i,SV708: $i,SV1269: $i] :
( ( ( c_lessequals @ SV1269 @ SV708 @ ( tc_fun @ SV122 @ tc_bool ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV122 @ tc_bool ) ) @ SV708 ) @ SV1269 )
= SV1269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(4201,plain,
! [SV1270: $i,SV709: $i,SV123: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV123 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SV709 ) @ SV1270 )
= SV709 )
| ~ ( c_lessequals @ SV709 @ SV1270 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3729]) ).
thf(4202,plain,
! [SV1271: $i,SV710: $i,SV124: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV124 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SV710 ) @ SV1271 )
= SV1271 )
| ~ ( c_lessequals @ SV1271 @ SV710 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(4203,plain,
! [SV1730: $i,SV1272: $i,SV711: $i,SV125: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SV1272 ) @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1272 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
| ~ ( c_lessequals @ SV711 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(4204,plain,
! [SV1731: $i,SV1275: $i,SV714: $i,SV128: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SV1275 ) @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1275 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
| ~ ( c_lessequals @ SV714 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3732]) ).
thf(4205,plain,
! [SV1732: $i,SV1276: $i,SV715: $i,SV129: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV129 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV1276 @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV715 @ SV1732 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(4206,plain,
! [SV1277: $i,SV716: $i,SV130: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV130 )
= $false )
| ( ( c_lessequals @ SV716 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 ) @ SV716 ) @ SV1277 ) @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3734]) ).
thf(4207,plain,
! [SV1278: $i,SV717: $i,SV131: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV131 )
= $false )
| ( ( c_lessequals @ SV717 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV131 ) @ SV1278 ) @ SV717 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(4208,plain,
! [SV1733: $i,SV1279: $i,SV718: $i,SV132: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV132 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV1279 @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV718 @ SV1733 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3736]) ).
thf(4209,plain,
! [SV1734: $i,SV1280: $i,SV719: $i,SV133: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV133 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV1280 @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV719 @ SV1734 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(4210,plain,
! [SV1281: $i,SV720: $i,SV134: $i] :
( ( ( class_Lattices_Olattice @ SV134 )
= $false )
| ( ( c_lessequals @ SV720 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV134 ) @ SV1281 ) @ SV720 ) @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3738]) ).
thf(4211,plain,
! [SV1282: $i,SV721: $i,SV135: $i] :
( ( ( class_Lattices_Olattice @ SV135 )
= $false )
| ( ( c_lessequals @ SV721 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV135 ) @ SV721 ) @ SV1282 ) @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(4212,plain,
! [SV1284: $i,SV723: $i,SV137: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV137 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV723 ) @ SV1284 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV137 ) @ SV1284 ) @ SV723 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(4213,plain,
! [SV1285: $i,SV724: $i,SV138: $i] :
( ( ( class_Lattices_Olattice @ SV138 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV724 ) @ SV1285 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV138 ) @ SV1285 ) @ SV724 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(4214,plain,
! [SV2005: $i,SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ! [SY5843: $i,SY5844: $i,SY5845: $i,SY5846: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SY5843 @ SY5844 @ SY5845 @ SY5846 @ SV1735 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SY5844 @ SY5843 @ SY5846 @ SY5845 @ SV1735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(4215,plain,
! [SV140: $i,SV1287: $i,SV726: $i] :
( ( ( c_lessequals @ SV726 @ SV1287 @ ( tc_fun @ SV140 @ tc_bool ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV140 @ tc_bool ) ) @ SV726 ) @ ( c_HOL_Ominus__class_Ominus @ SV1287 @ SV726 @ ( tc_fun @ SV140 @ tc_bool ) ) )
= SV1287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(4216,plain,
! [SV1736: $i,SV1288: $i,SV727: $i,SV141: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV141 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1288 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1736 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ SV1288 ) @ SV1736 ) ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4217,plain,
! [SV1737: $i,SV1291: $i,SV730: $i,SV144: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1737 ) @ SV730 ) @ SV1291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(4218,plain,
! [SV2006: $i,SV1739: $i,SV1294: $i,SV733: $i,SV147: $i] :
( ( ! [SY5847: $i] :
( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SY5847 ) @ SV2006 @ SV2006 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SY5847 @ SV2006 @ SV2006 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(4219,plain,
! [SV2007: $i,SV1740: $i,SV1295: $i,SV734: $i,SV148: $i] :
( ( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SV734 @ SV1295 @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SV2007 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SV734 @ SV1740 @ SV2007 ) @ ( c_Set_Oimage @ SV148 @ SV1295 @ SV1740 @ SV2007 ) @ ( tc_fun @ SV2007 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SV2007 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(4220,plain,
! [SV1741: $i,SV1296: $i,SV735: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV149 ) @ SV735 ) @ SV1296 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV735 @ SV1741 @ SV149 ) @ SV1296 @ ( tc_fun @ SV149 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3749]) ).
thf(4221,plain,
! [SV1742: $i,SV1297: $i,SV736: $i,SV150: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV150 ) )
= $true )
| ( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV736 @ ( c_COMBK @ SV1297 @ SV150 @ SV1742 ) @ SV1742 @ SV150 )
= SV1297 )
| ( SV736
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1742 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3750]) ).
thf(4222,plain,
! [SV1743: $i,SV1298: $i,SV737: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV151 @ SV737 @ SV1298 ) @ SV1743 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV737 @ SV1743 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3751]) ).
thf(4223,plain,
! [SV2008: $i,SV1744: $i,SV1299: $i,SV738: $i,SV152: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SV738 ) @ ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SV2008 ) @ SV2008 )
= ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SV2008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1744 ) @ SV738 ) @ SV1299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3752]) ).
thf(4224,plain,
! [SV1745: $i,SV1300: $i,SV739: $i,SV153: $i] :
( ( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SV739 @ SV1300 @ SV1745 ) @ ( tc_fun @ SV1745 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV153 @ SV1300 @ ( tc_fun @ SV1745 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1745 ) @ SV739 ) @ SV153 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(4225,plain,
! [SV1746: $i,SV1301: $i,SV740: $i,SV154: $i] :
( ( ( c_lessequals @ SV154 @ SV740 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1301 ) @ SV1746 ) @ SV154 ) )
| ~ ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SV1746 @ SV740 @ SV1301 ) @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(4226,plain,
! [SV1747: $i,SV1302: $i,SV741: $i,SV155: $i] :
( ( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SV741 @ SV1302 @ SV1747 ) @ ( tc_fun @ SV1747 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV155 @ SV1302 @ ( tc_fun @ SV1747 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1747 ) @ SV741 ) @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3755]) ).
thf(4227,plain,
! [SV1748: $i,SV1303: $i,SV742: $i,SV156: $i] :
( ( ( c_lessequals @ SV156 @ SV742 @ ( tc_fun @ SV1303 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SV1748 @ SV742 @ SV1303 ) @ ( tc_fun @ SV1303 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1303 ) @ SV1748 ) @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(4228,plain,
! [SV2009: $i,SV1749: $i,SV1304: $i,SV743: $i,SV157: $i] :
( ( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SV743 @ SV1304 @ SV1749 ) @ ( c_Set_Ovimage @ SV157 @ SV2009 @ SV1304 @ SV1749 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
| ~ ( c_lessequals @ SV743 @ SV2009 @ ( tc_fun @ SV1749 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(4229,plain,
! [SV1750: $i,SV1305: $i,SV744: $i,SV158: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1305 @ SV1750 @ SV158 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV158 @ tc_bool ) ) @ SV744 ) @ SV1750 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV158 ) @ SV1305 ) @ SV744 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(4230,plain,
! [SV1751: $i,SV1306: $i,SV745: $i,SV159: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV745 @ SV1306 @ SV159 ) ) @ SV1751 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV159 @ tc_bool ) ) @ SV1306 ) @ SV1751 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV159 ) @ SV745 ) @ SV1751 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3759]) ).
thf(4231,plain,
! [SV1309: $i,SV748: $i,SV162: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV748 @ SV1309 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3760]) ).
thf(4232,plain,
! [SV1752: $i,SV1310: $i,SV749: $i,SV163: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV163 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ SV1310 ) ) @ SV1752 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV1310 ) @ SV1752 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3761]) ).
thf(4233,plain,
! [SV1753: $i,SV1311: $i,SV750: $i,SV164: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV164 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ SV1753 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ SV1753 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(4234,plain,
! [SV1754: $i,SV1312: $i,SV751: $i,SV165: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV165 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ SV1754 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ SV1754 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(4235,plain,
! [SV1755: $i,SV1313: $i,SV752: $i,SV166: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV166 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ SV1313 ) ) @ SV1755 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV1313 ) @ SV1755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3764]) ).
thf(4236,plain,
! [SV1316: $i,SV170: $i,SV756: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV756 @ tc_bool ) ) @ SV170 ) @ SV1316 ) @ SV756 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV170 @ SV756 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(4237,plain,
! [SV171: $i,SV1317: $i,SV757: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV757 @ tc_bool ) ) @ SV1317 ) @ SV171 ) @ SV757 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV171 @ SV757 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(4238,plain,
! [SV2010: $i,SV1758: $i,SV1318: $i,SV758: $i,SV172: $i] :
( ( ( c_Map_Orestrict__map @ ( c_Map_Orestrict__map @ SV172 @ SV758 @ SV1318 @ SV1758 ) @ SV2010 @ SV1318 @ SV1758 )
= ( c_Map_Orestrict__map @ SV172 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1318 @ tc_bool ) ) @ SV758 ) @ SV2010 ) @ SV1318 @ SV1758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(4239,plain,
! [SV1761: $i,SV1321: $i,SV761: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SV1321 @ tc_bool ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV175 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV761 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SV1761 @ SV761 @ SV1321 ) @ ( tc_fun @ SV1321 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(4240,plain,
! [SV1762: $i,SV1322: $i,SV762: $i,SV176: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SV1322 @ SV1762 ) @ ( tc_fun @ SV1762 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV176 @ SV1322 @ ( tc_fun @ SV1762 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV1322 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(4241,plain,
! [SV1765: $i,SV1325: $i,SV765: $i,SV179: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV179 @ SV765 @ SV1325 ) @ SV1765 @ SV1325 @ SV765 )
= ( c_Set_Oinsert @ SV179 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV765 @ tc_bool ) ) @ SV765 ) )
= $true )
| ( ( SV1765
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(4242,plain,
! [SV1766: $i,SV1326: $i,SV766: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SV1326 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1326 ) @ SV1766 ) @ SV766 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SV1766 @ SV766 @ SV1326 ) @ ( tc_fun @ SV1326 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(4243,plain,
! [SV1767: $i,SV1327: $i,SV767: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SV1327 @ SV1767 ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1767 ) @ SV767 ) @ SV1327 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1327 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3779]) ).
thf(4244,plain,
! [SV1768: $i,SV1328: $i,SV768: $i,SV182: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV182 ) )
= $true )
| ( ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SV1328 @ SV1768 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV1328 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SV1768 @ SV182 @ SV182 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1768 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(4245,plain,
! [SV2011: $i,SV1769: $i,SV1329: $i,SV769: $i,SV183: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1769 @ SV2011 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SV2011 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SV183 @ SV1769 @ ( tc_fun @ SV1329 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4246,plain,
! [SV1771: $i,SV1331: $i,SV775: $i,SV189: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV189 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ SV1331 ) @ SV1771 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1331 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1771 ) ) @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(4247,plain,
! [SV1333: $i,SV777: $i,SV191: $i] :
( ( ( class_Orderings_Opreorder @ SV191 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV777 @ SV1333 @ SV191 )
| ( c_lessequals @ SV1333 @ SV777 @ SV191 )
| ~ ( c_lessequals @ SV777 @ SV1333 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(4248,plain,
! [SV1773: $i,SV1334: $i,SV779: $i,SV193: $i] :
( ( ( ~ ( class_HOL_Oord @ SV193 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
| ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SV1773 @ SV193 ) )
| ~ ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3788]) ).
thf(4249,plain,
! [SV194: $i,SV780: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV780 @ SV780 @ SV194 )
= $false )
| ( ( class_Orderings_Oorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(4250,plain,
! [SV195: $i,SV781: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV781 @ SV781 @ SV195 )
= $false )
| ( ( class_Orderings_Olinorder @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3790]) ).
thf(4251,plain,
! [SV196: $i,SV782: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV196 )
= $false )
| ( ( class_Orderings_Opreorder @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(4252,plain,
! [SV1335: $i,SV783: $i,SV197: $i] :
( ( ( class_Lattices_Olattice @ SV197 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 ) @ SV783 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV197 ) @ SV783 ) @ SV1335 ) )
= SV783 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3792]) ).
thf(4253,plain,
! [SV785: $i,SV200: $i,SV1336: $i] :
( ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1336 ) @ SV1336 @ ( tc_fun @ SV1336 @ tc_bool ) @ tc_bool ) @ SV200 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1336 ) @ SV1336 @ ( tc_fun @ SV1336 @ tc_bool ) @ tc_bool ) @ SV785 ) @ ( tc_fun @ SV1336 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV200 @ SV785 @ ( tc_fun @ SV1336 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(4254,plain,
! [SV201: $i,SV1337: $i,SV786: $i] :
( ( ( c_lessequals @ SV786 @ SV1337 @ ( tc_fun @ SV201 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV786 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV201 ) @ SV201 @ ( tc_fun @ SV201 @ tc_bool ) @ tc_bool ) @ SV1337 ) @ ( tc_fun @ SV201 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3794]) ).
thf(4255,plain,
! [SV1774: $i,SV1338: $i,SV787: $i,SV202: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV202 ) )
= $true )
| ( ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SV1338 @ SV1774 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV1338 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SV1774 @ SV202 @ SV202 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1774 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3795]) ).
thf(4256,plain,
! [SV1339: $i,SV788: $i,SV203: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV203 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1339 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ SV788 @ SV203 )
| ( SV1339 = SV788 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3796]) ).
thf(4257,plain,
! [SV1340: $i,SV789: $i,SV204: $i] :
( ( ( class_Orderings_Olinorder @ SV204 )
= $false )
| ( ( ( SV789 = SV1340 )
| ( c_HOL_Oord__class_Oless @ SV1340 @ SV789 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SV1340 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3797]) ).
thf(4258,plain,
! [SV1341: $i,SV205: $i,SV790: $i] :
( ( ( ~ ( c_lessequals @ SV790 @ SV205 @ ( tc_fun @ SV1341 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV205 @ SV790 @ ( tc_fun @ SV1341 @ tc_bool ) ) )
= $true )
| ( ( SV205 = SV790 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(4259,plain,
! [SV1342: $i,SV206: $i,SV791: $i] :
( ( ( ~ ( c_lessequals @ SV791 @ SV206 @ ( tc_fun @ SV1342 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV206 @ SV791 @ ( tc_fun @ SV1342 @ tc_bool ) ) )
= $true )
| ( ( SV206 = SV791 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3799]) ).
thf(4260,plain,
! [SV1343: $i,SV792: $i,SV207: $i] :
( ( ( class_Orderings_Oorder @ SV207 )
= $false )
| ( ( ( SV792 = SV1343 )
| ~ ( c_lessequals @ SV1343 @ SV792 @ SV207 )
| ~ ( c_lessequals @ SV792 @ SV1343 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(4261,plain,
! [SV1344: $i,SV793: $i,SV208: $i] :
( ( ( class_Orderings_Olinorder @ SV208 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV793 @ SV1344 @ SV208 )
| ( c_HOL_Oord__class_Oless @ SV1344 @ SV793 @ SV208 )
| ( SV1344 = SV793 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(4262,plain,
! [SV1345: $i,SV794: $i,SV209: $i] :
( ( ( class_Orderings_Oorder @ SV209 )
= $false )
| ( ( ( SV794 = SV1345 )
| ~ ( c_lessequals @ SV1345 @ SV794 @ SV209 )
| ~ ( c_lessequals @ SV794 @ SV1345 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(4263,plain,
! [SV1346: $i,SV795: $i,SV210: $i] :
( ( ( class_Orderings_Oorder @ SV210 )
= $false )
| ( ( ( SV795 = SV1346 )
| ~ ( c_lessequals @ SV795 @ SV1346 @ SV210 )
| ~ ( c_lessequals @ SV1346 @ SV795 @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(4264,plain,
! [SV1347: $i,SV796: $i,SV211: $i] :
( ( ( class_Orderings_Olinorder @ SV211 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV796 @ SV1347 @ SV211 )
| ( SV1347 = SV796 )
| ( c_HOL_Oord__class_Oless @ SV1347 @ SV796 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(4265,plain,
! [SV1348: $i,SV797: $i,SV212: $i] :
( ( ( class_Orderings_Olinorder @ SV212 )
= $false )
| ( ( ( SV797 = SV1348 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SV1348 @ SV212 )
| ( c_HOL_Oord__class_Oless @ SV1348 @ SV797 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(4266,plain,
! [SV1349: $i,SV798: $i,SV213: $i] :
( ( ( class_Lattices_Olattice @ SV213 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV213 ) @ SV798 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV213 ) @ SV798 ) @ SV1349 ) )
= SV798 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(4267,plain,
! [SV1775: $i,SV1350: $i,SV799: $i,SV214: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV214 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SV1350 ) @ SV1775 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV1775 @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(4268,plain,
! [SV1776: $i,SV1351: $i,SV800: $i,SV215: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV215 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SV1351 ) @ SV1776 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ SV800 @ SV1776 @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3808]) ).
thf(4269,plain,
! [SV1353: $i,SV802: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV217 @ SV802 @ ( tc_fun @ SV1353 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV217 @ SV802 @ ( tc_fun @ SV1353 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(4270,plain,
! [SV1777: $i,SV1354: $i,SV803: $i,SV218: $i] :
( ( ( ~ ( class_HOL_Oord @ SV218 ) )
= $true )
| ( ( ( c_lessequals @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3810]) ).
thf(4271,plain,
! [SV1355: $i,SV804: $i,SV219: $i] :
( ( ( class_Orderings_Oorder @ SV219 )
= $false )
| ( ( ( c_lessequals @ SV804 @ SV1355 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1355 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(4272,plain,
! [SV1356: $i,SV805: $i,SV220: $i] :
( ( ( class_Orderings_Opreorder @ SV220 )
= $false )
| ( ( ( c_lessequals @ SV805 @ SV1356 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV805 @ SV1356 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(4273,plain,
! [SV1357: $i,SV806: $i,SV221: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV221 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SV806 ) @ SV1357 )
= SV806 )
| ~ ( c_lessequals @ SV1357 @ SV806 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(4274,plain,
! [SV1358: $i,SV807: $i,SV222: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV222 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SV807 ) @ SV1358 )
= SV1358 )
| ~ ( c_lessequals @ SV807 @ SV1358 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(4275,plain,
! [SV223: $i,SV1359: $i,SV808: $i] :
( ( ( c_lessequals @ SV808 @ SV1359 @ ( tc_fun @ SV223 @ tc_bool ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV223 @ tc_bool ) ) @ SV808 ) @ SV1359 )
= SV1359 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(4276,plain,
! [SV224: $i,SV809: $i,SV1360: $i] :
( ( ( c_lessequals @ SV1360 @ SV809 @ ( tc_fun @ SV224 @ tc_bool ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV224 @ tc_bool ) ) @ SV809 ) @ SV1360 )
= SV809 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3816]) ).
thf(4277,plain,
! [SV1778: $i,SV1361: $i,SV810: $i,SV225: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV225 @ SV810 @ SV1361 @ SV1778 ) @ SV1778 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV810 @ SV1361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(4278,plain,
! [SV1779: $i,SV1362: $i,SV811: $i,SV226: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SV1779 ) @ ( tc_fun @ SV1779 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1779 ) @ SV811 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(4279,plain,
! [SV1363: $i,SV812: $i,SV227: $i] :
( ( ( class_Orderings_Olinorder @ SV227 )
= $false )
| ( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
| ~ ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
| ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(4280,plain,
! [SV2012: $i,SV1780: $i,SV1364: $i,SV813: $i,SV228: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV228 @ SV813 @ SV1364 ) @ SV1780 @ SV1364 @ ( tc_fun @ SV2012 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2012 @ tc_bool ) ) @ ( hAPP @ SV1780 @ SV228 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV813 @ SV1780 @ SV1364 @ ( tc_fun @ SV2012 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(4281,plain,
! [SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY5848: $i,SY5849: $i,SY5850: $i,SY5851: $i,SY5852: $i,SY5853: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5848 @ SV229 @ SY5849 @ SY5850 @ SY5851 @ SV2013 @ SY5852 @ SY5853 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3821]) ).
thf(4282,plain,
! [SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY5854: $i,SY5855: $i,SY5856: $i,SY5857: $i,SY5858: $i,SY5859: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SY5854 @ SY5855 @ SY5856 @ SV2014 @ SY5857 @ SY5858 @ SY5859 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(4283,plain,
! [SV1783: $i,SV1368: $i,SV817: $i,SV232: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SV1368 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV1783 @ SV1368 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1783 @ SV817 @ SV1368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(4284,plain,
! [SV1784: $i,SV1369: $i,SV818: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV818 @ SV1369 @ SV233 ) ) @ SV1784 )
= ( c_Set_Oinsert @ SV818 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ SV1369 ) @ SV1784 ) @ SV233 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV233 ) @ SV818 ) @ SV1784 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4285,plain,
! [SV1785: $i,SV1370: $i,SV819: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ ( c_Set_Oinsert @ SV1370 @ SV1785 @ SV234 ) )
= ( c_Set_Oinsert @ SV1370 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ SV1785 ) @ SV234 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV234 ) @ SV1370 ) @ SV819 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(4286,plain,
! [SV2015: $i,SV1786: $i,SV1371: $i,SV820: $i,SV235: $i] :
( ( ( c_Set_Oimage @ SV235 @ ( c_Set_Oinsert @ SV820 @ SV1371 @ SV1786 ) @ SV1786 @ SV2015 )
= ( c_Set_Oinsert @ ( hAPP @ SV235 @ SV820 ) @ ( c_Set_Oimage @ SV235 @ SV1371 @ SV1786 @ SV2015 ) @ SV2015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4287,plain,
! [SV2016: $i,SV1787: $i,SV1372: $i,SV822: $i,SV237: $i] :
( ( ! [SY5860: $i] :
( ( hAPP @ ( c_Fun_Ofcomp @ SV237 @ SV822 @ SV1372 @ SV1787 @ SV2016 ) @ SY5860 )
= ( hAPP @ SV822 @ ( hAPP @ SV237 @ SY5860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4288,plain,
! [SV2017: $i,SV1788: $i,SV1373: $i,SV823: $i,SV238: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV1788 ) @ SV2017 ) @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV1373 @ SV2017 @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV823 @ SV1788 @ ( tc_fun @ SV238 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(4289,plain,
! [SV1374: $i,SV824: $i,SV239: $i] :
( ( ( class_Lattices_Olattice @ SV239 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV239 ) @ SV824 ) @ SV1374 ) @ SV824 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(4290,plain,
! [SV1375: $i,SV825: $i,SV240: $i] :
( ( ( class_Lattices_Olattice @ SV240 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV240 ) @ SV825 ) @ SV1375 ) @ SV1375 @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(4291,plain,
! [SV1789: $i,SV1376: $i,SV826: $i,SV241: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV241 ) )
= $true )
| ( ( ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1789 @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(4292,plain,
! [SV1790: $i,SV1377: $i,SV827: $i,SV242: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV242 ) )
= $true )
| ( ( ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1790 @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(4293,plain,
! [SV1791: $i,SV1378: $i,SV828: $i,SV243: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV243 ) )
= $true )
| ( ( ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1791 @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(4294,plain,
! [SV1379: $i,SV829: $i,SV244: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV244 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV244 ) @ SV829 ) @ SV1379 ) @ SV1379 @ SV244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4295,plain,
! [SV1380: $i,SV830: $i,SV245: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV245 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV245 ) @ SV830 ) @ SV1380 ) @ SV830 @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3835]) ).
thf(4296,plain,
! [SV1792: $i,SV1383: $i,SV833: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SV1383 ) @ SV1792 ) @ ( tc_fun @ SV833 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV248 @ SV1792 @ ( tc_fun @ SV833 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV1383 @ ( tc_fun @ SV833 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(4297,plain,
! [SV1793: $i,SV1384: $i,SV834: $i,SV249: $i] :
( ( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV1384 ) @ SV1793 ) @ ( tc_fun @ SV834 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV249 @ SV1793 @ ( tc_fun @ SV834 @ tc_bool ) )
| ~ ( c_lessequals @ SV249 @ SV1384 @ ( tc_fun @ SV834 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4298,plain,
! [SV2018: $i,SV1794: $i,SV1385: $i,SV837: $i,SV252: $i] :
( ( ! [SY5861: $i,SY5862: $i] :
( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SV837 @ SV1385 @ SV1794 @ SV2018 @ SY5861 ) @ SV2018 @ SY5862 @ SY5861 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SV837 @ SV2018 @ SY5862 @ SV1794 ) @ SV1385 @ SV1794 @ SY5862 @ SY5861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4299,plain,
! [SV1796: $i,SV1387: $i,SV839: $i,SV254: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV254 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ SV839 ) @ SV1387 ) ) @ SV1796 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV839 ) @ SV1796 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV1387 ) @ SV1796 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3841]) ).
thf(4300,plain,
! [SV1797: $i,SV1388: $i,SV840: $i,SV255: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV255 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ SV1388 ) @ SV1797 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1388 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1797 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4301,plain,
! [SV1389: $i,SV841: $i,SV256: $i] :
( ( ( class_HOL_Ominus @ SV256 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV841 @ SV1389 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV841 @ v_x ) @ ( hAPP @ SV1389 @ v_x ) @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(4302,plain,
! [SV1798: $i,SV1390: $i,SV842: $i,SV257: $i] :
( ( ( c_lessequals @ SV257 @ SV842 @ ( tc_fun @ SV1390 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV257 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1390 @ tc_bool ) ) @ SV1798 ) @ SV842 ) @ ( tc_fun @ SV1390 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3844]) ).
thf(4303,plain,
! [SV1799: $i,SV1391: $i,SV843: $i,SV258: $i] :
( ( ( c_lessequals @ SV258 @ SV843 @ ( tc_fun @ SV1391 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV258 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1391 @ tc_bool ) ) @ SV843 ) @ SV1799 ) @ ( tc_fun @ SV1391 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3845]) ).
thf(4304,plain,
! [SV1800: $i,SV1392: $i,SV844: $i,SV259: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV259 ) )
= $true )
| ( ( ( c_lessequals @ SV844 @ SV1392 @ SV259 )
| ~ ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SV1392 ) @ SV1800 ) @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(4305,plain,
! [SV1801: $i,SV1393: $i,SV845: $i,SV260: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV260 ) )
= $true )
| ( ( ( c_lessequals @ SV845 @ SV1393 @ SV260 )
| ~ ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SV1801 ) @ SV1393 ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3847]) ).
thf(4306,plain,
! [SV1802: $i,SV1394: $i,SV846: $i,SV261: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV261 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SV1394 ) @ SV1802 @ SV261 )
| ~ ( c_lessequals @ SV846 @ SV1802 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4307,plain,
! [SV1803: $i,SV1395: $i,SV847: $i,SV262: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV262 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SV1395 ) @ SV1803 @ SV262 )
| ~ ( c_lessequals @ SV1395 @ SV1803 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(4308,plain,
! [SV1804: $i,SV1396: $i,SV848: $i,SV263: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV263 ) )
= $true )
| ( ( ( c_lessequals @ SV848 @ SV1396 @ SV263 )
| ~ ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SV1396 ) @ SV1804 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(4309,plain,
! [SV1805: $i,SV1397: $i,SV849: $i,SV264: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV264 ) )
= $true )
| ( ( ( c_lessequals @ SV849 @ SV1397 @ SV264 )
| ~ ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SV1805 ) @ SV1397 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4310,plain,
! [SV1807: $i,SV1399: $i,SV852: $i,SV267: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV267 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(4311,plain,
! [SV2019: $i,SV1808: $i,SV1400: $i,SV853: $i,SV268: $i] :
( ( ! [SY5863: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ SV268 @ SV853 @ SV1400 @ SV1808 @ SV2019 ) @ SY5863 @ SV2019 @ SV1808 )
= ( c_Set_Ovimage @ SV853 @ ( c_Set_Ovimage @ SV268 @ SY5863 @ SV1400 @ SV1808 ) @ SV2019 @ SV1400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4312,plain,
! [SV1809: $i,SV1402: $i,SV855: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4313,plain,
! [SV1404: $i,SV857: $i,SV272: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV272 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV857 ) @ SV1404 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 ) @ SV1404 ) @ SV857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(4314,plain,
! [SV1405: $i,SV858: $i,SV273: $i] :
( ( ( class_Lattices_Olattice @ SV273 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV858 ) @ SV1405 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV273 ) @ SV1405 ) @ SV858 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3857]) ).
thf(4315,plain,
! [SV1408: $i,SV862: $i,SV277: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV277 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SV1408 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV277 ) @ SV862 ) @ SV1408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(4316,plain,
! [SV1409: $i,SV863: $i,SV278: $i] :
( ( ( class_Lattices_Olattice @ SV278 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SV1409 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV278 ) @ SV863 ) @ SV1409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(4317,plain,
! [SV2020: $i,SV1810: $i,SV1410: $i,SV864: $i,SV279: $i] :
( ( ! [SY5864: $i] :
( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SY5864 @ SV2020 @ SV2020 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SY5864 @ SV2020 @ SV2020 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3860]) ).
thf(4318,plain,
! [SV2021: $i,SV1811: $i,SV1411: $i,SV865: $i,SV280: $i] :
( ( ! [SY5865: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SV2021 ) @ SY5865 @ SV2021 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SY5865 @ SV2021 @ SV1411 ) @ SV1411 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV865 @ SY5865 @ SV2021 @ SV1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3861]) ).
thf(4319,plain,
! [SV2022: $i,SV1812: $i,SV1413: $i,SV868: $i,SV283: $i] :
( ( ! [SY5866: $i,SY5867: $i] :
( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SV2022 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SY5866 ) @ SV2022 @ SY5867 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SY5866 @ SV2022 @ SY5867 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2022 ) @ SV1413 ) @ SV1812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4320,plain,
! [SV1813: $i,SV1414: $i,SV869: $i,SV284: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ SV1414 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV284 @ tc_bool ) ) @ SV1414 ) @ ( c_Collect @ SV1813 @ SV284 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4321,plain,
! [SV2023: $i,SV1814: $i,SV1415: $i,SV870: $i,SV285: $i] :
( ( ( c_Set_Ovimage @ SV285 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV870 @ tc_bool ) ) @ SV1415 ) @ SV1814 ) @ SV2023 @ SV870 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2023 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV285 @ SV1415 @ SV2023 @ SV870 ) ) @ ( c_Set_Ovimage @ SV285 @ SV1814 @ SV2023 @ SV870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4322,plain,
! [SV1416: $i,SV871: $i,SV286: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV871 @ ( c_Set_Oinsert @ SV1416 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV286 @ tc_bool ) ) @ SV286 ) @ SV286 ) @ SV286 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV286 ) @ SV871 ) @ SV1416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3866]) ).
thf(4323,plain,
! [SV2024: $i,SV1815: $i,SV1417: $i,SV872: $i,SV287: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SV1417 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Set_Oinsert @ SV1417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 ) @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 @ SV287 ) ) )
| ~ ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SV1417 @ SV1815 @ SV2024 ) @ SV2024 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4324,plain,
! [SV1816: $i,SV1418: $i,SV873: $i,SV288: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV288 @ SV873 @ SV1418 ) @ SV1816 @ ( tc_fun @ SV1418 @ tc_bool ) )
= ( c_Set_Oinsert @ SV288 @ ( c_HOL_Ominus__class_Ominus @ SV873 @ SV1816 @ ( tc_fun @ SV1418 @ tc_bool ) ) @ SV1418 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV288 ) @ SV1816 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(4325,plain,
! [SV2025: $i,SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ! [SY5868: $i,SY5869: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SY5868 @ SY5869 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5868 @ tc_bool ) ) @ SY5868 ) @ ( tc_fun @ SY5868 @ tc_bool ) ) @ SV2025 @ SY5868 @ SY5869 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5868 ) @ SV1817 ) @ SV1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4326,plain,
! [SV1818: $i,SV1420: $i,SV875: $i,SV290: $i] :
( ( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SV1420 @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV290 @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3870]) ).
thf(4327,plain,
! [SV1819: $i,SV1421: $i,SV876: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ SV876 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1819 ) @ SV291 ) @ SV876 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3871]) ).
thf(4328,plain,
! [SV1820: $i,SV1422: $i,SV877: $i,SV292: $i] :
( ( ( hBOOL @ ( hAPP @ SV292 @ SV877 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1422 @ tc_bool ) ) @ SV292 ) @ SV1820 ) @ SV877 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4329,plain,
! [SV1423: $i,SV293: $i,SV878: $i] :
( ( ( ~ ( c_lessequals @ SV878 @ ( c_Set_Oimage @ SV293 @ SV878 @ SV1423 @ SV1423 ) @ ( tc_fun @ SV1423 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV878 @ SV1423 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV293 @ SV878 @ SV1423 @ SV1423 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3873]) ).
thf(4330,plain,
! [SV2026: $i,SV1821: $i,SV1424: $i,SV879: $i,SV294: $i] :
( ( ( c_Fun_Oinj__on @ SV294 @ SV879 @ SV1424 @ SV1821 )
| ~ ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV2026 ) @ SV879 ) @ SV1424 @ SV1821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4331,plain,
! [SV2027: $i,SV1822: $i,SV1425: $i,SV880: $i,SV295: $i] :
( ( ( c_Fun_Oinj__on @ SV295 @ SV880 @ SV1425 @ SV1822 )
| ~ ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1425 @ tc_bool ) ) @ SV880 ) @ SV2027 ) @ SV1425 @ SV1822 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(4332,plain,
! [SV2028: $i,SV1823: $i,SV1426: $i,SV881: $i,SV296: $i] :
( ( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SV1823 ) @ SV2028 @ ( tc_fun @ SV1426 @ tc_bool ) )
| ~ ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SV2028 @ SV1426 @ SV1823 ) @ ( tc_fun @ SV1823 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SV1823 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(4333,plain,
! [SV1824: $i,SV1427: $i,SV883: $i,SV299: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV299 @ SV883 @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV1824 @ ( tc_fun @ SV1427 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV883 ) @ SV1824 ) @ ( tc_fun @ SV1427 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(4334,plain,
! [SV1825: $i,SV1428: $i,SV884: $i,SV300: $i] :
( ( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1428 ) @ SV1825 ) @ ( tc_fun @ SV884 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV300 @ SV1428 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1825 @ ( tc_fun @ SV884 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4335,plain,
! [SV301: $i,SV1429: $i,SV885: $i] :
( ( ( c_Wellfounded_Omax__extp @ SV885 @ SV1429 @ SV301 @ t_a )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV301 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(4336,plain,
! [SV1430: $i,SV302: $i,SV886: $i] :
( ( ( c_Wellfounded_Omax__extp @ SV886 @ SV302 @ SV1430 @ t_a )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV302 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(4337,plain,
! [SV1826: $i,SV1431: $i,SV887: $i,SV303: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV303 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SV1431 ) @ SV1826 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV887 @ SV1431 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4338,plain,
! [SV1827: $i,SV1432: $i,SV888: $i,SV304: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV304 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SV1432 ) @ SV1827 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV888 @ SV1827 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(4339,plain,
! [SV2029: $i,SV1828: $i,SV1433: $i,SV889: $i,SV305: $i] :
( ( ( c_Set_Ovimage @ SV305 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV889 @ tc_bool ) ) @ SV1433 ) @ SV1828 ) @ SV2029 @ SV889 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV2029 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV305 @ SV1433 @ SV2029 @ SV889 ) ) @ ( c_Set_Ovimage @ SV305 @ SV1828 @ SV2029 @ SV889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(4340,plain,
! [SV890: $i,SV306: $i,SV1434: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1434 @ SV306 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV306 @ tc_bool ) ) @ SV890 ) @ SV1434 ) @ SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(4341,plain,
! [SV1435: $i,SV307: $i,SV891: $i] :
( ( ( c_Finite__Set_Ofinite @ SV891 @ SV307 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV307 @ tc_bool ) ) @ SV891 ) @ SV1435 ) @ SV307 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4342,plain,
! [SV2030: $i,SV1829: $i,SV1436: $i,SV892: $i,SV308: $i] :
( ( ~ ( class_HOL_Oord @ SV308 )
| ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SV1829 @ SV1436 ) @ SV308 )
| ~ ( c_lessequals @ SV892 @ SV1829 @ ( tc_fun @ SV2030 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(4343,plain,
! [SV1830: $i,SV1437: $i,SV893: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV1437 ) @ SV1830 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1830 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1437 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3887]) ).
thf(4344,plain,
! [SV1831: $i,SV1438: $i,SV894: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SV1438 ) @ SV1831 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1831 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(4345,plain,
! [SV1832: $i,SV1439: $i,SV895: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ ( c_Set_Oinsert @ SV1439 @ SV1832 @ SV311 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ SV1832 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(4346,plain,
! [SV1833: $i,SV1440: $i,SV896: $i,SV312: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ ( c_Set_Oinsert @ SV1440 @ SV1833 @ SV312 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ SV1833 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4347,plain,
! [SV1834: $i,SV1441: $i,SV897: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1441 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1834 ) )
| ~ ( c_lessequals @ SV1834 @ SV1441 @ ( tc_fun @ SV313 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3891]) ).
thf(4348,plain,
! [SV1835: $i,SV1442: $i,SV898: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1442 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1835 @ SV1442 @ ( tc_fun @ SV314 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1835 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3892]) ).
thf(4349,plain,
! [SV1836: $i,SV1443: $i,SV899: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1443 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1836 ) )
| ~ ( c_lessequals @ SV1836 @ SV1443 @ ( tc_fun @ SV315 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(4350,plain,
! [SV1837: $i,SV1444: $i,SV900: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1444 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1837 ) )
| ~ ( c_lessequals @ SV1837 @ SV1444 @ ( tc_fun @ SV316 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3894]) ).
thf(4351,plain,
! [SV1838: $i,SV1445: $i,SV901: $i,SV317: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV317 @ tc_bool ) ) @ SV1445 ) @ SV1838 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ SV1445 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3895]) ).
thf(4352,plain,
! [SV1839: $i,SV1446: $i,SV902: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV1446 ) @ SV1839 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ SV1839 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3896]) ).
thf(4353,plain,
! [SV2031: $i,SV1840: $i,SV1447: $i,SV903: $i,SV319: $i] :
( ( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SV903 @ SV1447 @ SV1840 ) @ SV2031 )
= ( hAPP @ SV319 @ SV2031 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1447 ) @ SV2031 ) @ SV903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4354,plain,
! [SV1841: $i,SV1448: $i,SV904: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ SV1448 ) )
= $true )
| ( ( ( SV904 = SV1841 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ ( c_Set_Oinsert @ SV1841 @ SV1448 @ SV320 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3898]) ).
thf(4355,plain,
! [SV1842: $i,SV1449: $i,SV905: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1449 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV1842 ) @ SV1449 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(4356,plain,
! [SV2032: $i,SV1843: $i,SV1450: $i,SV906: $i,SV322: $i] :
( ( ! [SY5870: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SV1450 @ SV1843 @ SV2032 ) @ SY5870 )
= ( hAPP @ SV906 @ SY5870 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1843 ) @ SY5870 ) @ SV1450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4357,plain,
! [SV1844: $i,SV1451: $i,SV908: $i,SV324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ SV1451 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ ( c_HOL_Ominus__class_Ominus @ SV1844 @ SV1451 @ ( tc_fun @ SV324 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4358,plain,
! [SV1845: $i,SV1452: $i,SV909: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ SV1452 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ ( c_HOL_Ominus__class_Ominus @ SV1452 @ SV1845 @ ( tc_fun @ SV325 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4359,plain,
! [SV2033: $i,SV1846: $i,SV1453: $i,SV910: $i,SV326: $i] :
( ( ! [SY5871: $i] :
( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SV910 @ SV1453 @ SV1846 @ SV2033 ) @ SY5871 )
= ( hAPP @ SV326 @ SY5871 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1846 ) @ SY5871 ) @ SV1453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4360,plain,
! [SV1847: $i,SV1454: $i,SV911: $i,SV327: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1454 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1847 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1847 @ SV1454 @ ( tc_fun @ SV327 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4361,plain,
! [SV1848: $i,SV1458: $i,SV915: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ SV1458 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV331 @ tc_bool ) ) @ SV1848 ) @ SV1458 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4362,plain,
! [SV1849: $i,SV1459: $i,SV916: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ SV1459 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV332 @ tc_bool ) ) @ SV1459 ) @ SV1849 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(4363,plain,
! [SV333: $i,SV917: $i,SV1460: $i] :
( ( ( hBOOL @ ( hAPP @ SV1460 @ SV917 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV333 ) @ SV917 ) @ ( c_Collect @ SV1460 @ SV333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(4364,plain,
! [SV334: $i,SV918: $i,SV1461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1461 ) @ SV918 ) @ ( c_Collect @ SV334 @ SV1461 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV334 @ SV918 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4365,plain,
! [SV1850: $i,SV1462: $i,SV919: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ ( c_HOL_Ominus__class_Ominus @ SV1462 @ SV1850 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1850 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3909]) ).
thf(4366,plain,
! [SV1851: $i,SV1463: $i,SV920: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ ( c_HOL_Ominus__class_Ominus @ SV1463 @ SV1851 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1851 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1463 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3910]) ).
thf(4367,plain,
! [SV2034: $i,SV1852: $i,SV1464: $i,SV921: $i,SV337: $i] :
( ( ! [SY5872: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SV2034 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SY5872 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2034 ) @ SY5872 ) @ SV1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4368,plain,
! [SV2035: $i,SV1853: $i,SV1465: $i,SV922: $i,SV338: $i] :
( ( ! [SY5873: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SV2035 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SY5873 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2035 ) @ SY5873 ) @ SV1465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4369,plain,
! [SV2036: $i,SV1854: $i,SV1466: $i,SV923: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SV923 ) @ ( c_Set_Ovimage @ SV1466 @ SV1854 @ SV339 @ SV2036 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2036 ) @ ( hAPP @ SV1466 @ SV923 ) ) @ SV1854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4370,plain,
! [SV2037: $i,SV1855: $i,SV1467: $i,SV924: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SV924 ) @ ( c_Set_Ovimage @ SV1467 @ SV1855 @ SV340 @ SV2037 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2037 ) @ ( hAPP @ SV1467 @ SV924 ) ) @ SV1855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4371,plain,
! [SV2038: $i,SV1856: $i,SV1468: $i,SV925: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SV925 ) @ ( c_Set_Ovimage @ SV1468 @ SV1856 @ SV341 @ SV2038 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2038 ) @ ( hAPP @ SV1468 @ SV925 ) ) @ SV1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4372,plain,
! [SV2039: $i,SV1857: $i,SV1469: $i,SV926: $i,SV342: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SV926 @ SV1469 ) ) @ SV1857 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2039 ) @ SV1469 ) @ ( c_Set_Ovimage @ SV926 @ SV1857 @ SV2039 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4373,plain,
! [SV2040: $i,SV1858: $i,SV1470: $i,SV927: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SV927 @ SV1470 ) ) @ SV1858 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2040 ) @ SV1470 ) @ ( c_Set_Ovimage @ SV927 @ SV1858 @ SV2040 @ SV343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4374,plain,
! [SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY5874: $i,SY5875: $i,SY5876: $i,SY5877: $i,SY5878: $i,SY5879: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SY5874 @ SV344 @ SY5875 @ SY5876 @ SY5877 @ SY5878 @ SY5879 @ SV2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4375,plain,
! [SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY5880: $i,SY5881: $i,SY5882: $i,SY5883: $i,SY5884: $i,SY5885: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5880 @ SV1472 @ SV345 @ SY5881 @ SY5882 @ SY5883 @ SY5884 @ SY5885 @ SV2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4376,plain,
! [SV930: $i,SV346: $i,SV1473: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1473 ) @ SV346 ) @ SV930 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV346 @ SV930 @ SV1473 )
= SV930 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3920]) ).
thf(4377,plain,
! [SV2043: $i,SV1861: $i,SV1474: $i,SV931: $i,SV347: $i] :
( ( ! [SY5886: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SV2043 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SY5886 ) @ SV2043 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SY5886 ) @ SV347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3921]) ).
thf(4378,plain,
! [SV2044: $i,SV1862: $i,SV1475: $i,SV932: $i,SV348: $i] :
( ( ! [SY5887: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SV2044 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SY5887 ) @ SV2044 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SY5887 ) @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4379,plain,
! [SV2045: $i,SV1863: $i,SV1476: $i,SV933: $i,SV349: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SV933 ) @ SV1476 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1863 ) @ ( hAPP @ SV2045 @ SV933 ) ) @ ( c_Set_Oimage @ SV2045 @ SV1476 @ SV349 @ SV1863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4380,plain,
! [SV1866: $i,SV1480: $i,SV937: $i,SV353: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SV1480 ) @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV937 @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1480 ) @ SV353 ) @ SV1866 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4381,plain,
! [SV1481: $i,SV938: $i,SV354: $i] :
( ( ( class_Lattices_Olattice @ SV354 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SV1481 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV354 ) @ SV938 ) @ SV1481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4382,plain,
! [SV1482: $i,SV939: $i,SV355: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV355 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SV1482 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV355 ) @ SV939 ) @ SV1482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(4383,plain,
! [SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY5888: $i,SY5889: $i,SY5890: $i,SY5891: $i,SY5892: $i,SY5893: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5888 @ SV1484 @ SY5889 @ SY5890 @ SY5891 @ SV357 @ SY5892 @ SY5893 @ SV2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4384,plain,
! [SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY5894: $i,SY5895: $i,SY5896: $i,SY5897: $i,SY5898: $i,SY5899: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SY5894 @ SY5895 @ SY5896 @ SV358 @ SY5897 @ SY5898 @ SY5899 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(4385,plain,
! [SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY5900: $i,SY5901: $i,SY5902: $i,SY5903: $i,SY5904: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5900 @ SV359 @ SY5901 @ SY5902 @ SY5903 @ SV1486 @ SV1869 @ SY5904 @ SV2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(4386,plain,
! [SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY5905: $i,SY5906: $i,SY5907: $i,SY5908: $i,SY5909: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SY5905 @ SY5906 @ SY5907 @ SV1487 @ SY5908 @ SY5909 @ SV1870 @ SV2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4387,plain,
! [SV1871: $i,SV1488: $i,SV945: $i,SV361: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV945 @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV1871 @ SV945 @ SV1488 ) @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3933]) ).
thf(4388,plain,
! [SV1872: $i,SV1489: $i,SV946: $i,SV362: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ ( c_Set_Oinsert @ SV946 @ SV1489 @ SV1872 ) @ ( tc_fun @ SV1872 @ tc_bool ) ) @ SV1872 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ SV1489 @ ( tc_fun @ SV1872 @ tc_bool ) ) @ SV1872 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3934]) ).
thf(4389,plain,
! [SV2050: $i,SV1873: $i,SV1492: $i,SV949: $i,SV365: $i] :
( ( ! [SY5910: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV365 @ SV949 @ SV1492 @ SV1873 @ SV2050 ) @ SY5910 @ SV2050 @ SV1873 )
= ( c_Set_Oimage @ SV365 @ ( c_Set_Oimage @ SV949 @ SY5910 @ SV2050 @ SV1492 ) @ SV1492 @ SV1873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4390,plain,
! [SV1493: $i,SV950: $i,SV367: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV367 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1493 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 @ SV1493 @ SV367 @ SV367 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1493 @ SV367 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(4391,plain,
! [SV1874: $i,SV1494: $i,SV953: $i,SV370: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV370 ) )
= $true )
| ( ( ( c_lessequals @ SV953 @ SV1494 @ SV370 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SV1874 ) @ SV953 ) @ SV1494 @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3938]) ).
thf(4392,plain,
! [SV1875: $i,SV1495: $i,SV954: $i,SV371: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV371 ) )
= $true )
| ( ( ( c_lessequals @ SV954 @ SV1495 @ SV371 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SV1875 ) @ SV1495 @ SV371 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3939]) ).
thf(4393,plain,
! [SV1876: $i,SV1496: $i,SV955: $i,SV372: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV372 ) )
= $true )
| ( ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SV1496 ) @ SV1876 ) @ SV372 )
| ~ ( c_lessequals @ SV955 @ SV1876 @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4394,plain,
! [SV1877: $i,SV1497: $i,SV956: $i,SV373: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV373 ) )
= $true )
| ( ( ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SV1497 ) @ SV1877 ) @ SV373 )
| ~ ( c_lessequals @ SV956 @ SV1497 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4395,plain,
! [SV1878: $i,SV1498: $i,SV957: $i,SV374: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV374 ) )
= $true )
| ( ( ( c_lessequals @ SV957 @ SV1498 @ SV374 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SV1878 ) @ SV957 ) @ SV1498 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3942]) ).
thf(4396,plain,
! [SV1879: $i,SV1499: $i,SV958: $i,SV375: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV375 ) )
= $true )
| ( ( ( c_lessequals @ SV958 @ SV1499 @ SV375 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SV1879 ) @ SV1499 @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3943]) ).
thf(4397,plain,
! [SV1880: $i,SV1500: $i,SV959: $i,SV376: $i] :
( ( ( c_lessequals @ SV376 @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1500 @ tc_bool ) ) @ SV376 ) @ SV1880 ) @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3944]) ).
thf(4398,plain,
! [SV1881: $i,SV1501: $i,SV960: $i,SV377: $i] :
( ( ( c_lessequals @ SV377 @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1501 @ tc_bool ) ) @ SV1881 ) @ SV377 ) @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3945]) ).
thf(4399,plain,
! [SV1502: $i,SV961: $i,SV378: $i] :
( ( ( class_Lattices_Olattice @ SV378 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ SV378 ) ) @ SV961 ) @ SV1502 ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV378 ) @ ( hAPP @ SV961 @ v_x ) ) @ ( hAPP @ SV1502 @ v_x ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4400,plain,
! [SV1882: $i,SV1503: $i,SV962: $i,SV379: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV379 ) )
= $true )
| ( ( ( c_lessequals @ SV962 @ SV1503 @ SV379 )
| ~ ( c_lessequals @ SV962 @ SV1882 @ SV379 )
| ~ ( c_lessequals @ SV1882 @ SV1503 @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(4401,plain,
! [SV1883: $i,SV1504: $i,SV963: $i,SV380: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV380 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
| ~ ( c_lessequals @ SV963 @ SV1883 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4402,plain,
! [SV1884: $i,SV1505: $i,SV964: $i,SV381: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV381 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
| ~ ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 )
| ~ ( c_lessequals @ SV1884 @ SV1505 @ SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3949]) ).
thf(4403,plain,
! [SV1885: $i,SV1506: $i,SV965: $i,SV382: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV382 ) )
= $true )
| ( ( ( c_lessequals @ SV965 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV1885 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV965 @ SV1885 @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4404,plain,
! [SV1886: $i,SV1507: $i,SV968: $i,SV385: $i] :
( ( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1886 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
| ~ ( c_lessequals @ SV385 @ SV1886 @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4405,plain,
! [SV2051: $i,SV1887: $i,SV1508: $i,SV969: $i,SV386: $i] :
( ( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SV1887 )
| ~ ( c_lessequals @ SV969 @ SV2051 @ ( tc_fun @ SV1508 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV386 @ SV2051 @ SV1508 @ SV1887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4406,plain,
! [SV1888: $i,SV1509: $i,SV970: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1509 @ SV970 ) )
| ~ ( c_lessequals @ SV1509 @ SV387 @ ( tc_fun @ SV1888 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3953]) ).
thf(4407,plain,
! [SV390: $i,SV973: $i,SV1510: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1510 @ SV973 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV390 @ SV1510 @ ( tc_fun @ SV973 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV390 @ SV973 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3956]) ).
thf(4408,plain,
! [SV1889: $i,SV1511: $i,SV974: $i,SV391: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1889 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV391 @ SV1889 @ ( tc_fun @ SV1511 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4409,plain,
! [SV1890: $i,SV1512: $i,SV975: $i,SV392: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1890 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
| ~ ( c_lessequals @ SV392 @ SV1890 @ ( tc_fun @ SV1512 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3958]) ).
thf(4410,plain,
! [SV1891: $i,SV1513: $i,SV976: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1513 @ SV393 @ ( tc_fun @ SV1891 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1513 @ SV976 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4411,plain,
! [SV977: $i,SV1514: $i,SV394: $i] :
( ( ( ~ ( c_lessequals @ SV394 @ SV1514 @ ( tc_fun @ SV977 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1514 @ SV977 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV394 @ SV977 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3960]) ).
thf(4412,plain,
! [SV1892: $i,SV1515: $i,SV978: $i,SV395: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV395 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
| ~ ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 )
| ~ ( c_lessequals @ SV978 @ SV1892 @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3961]) ).
thf(4413,plain,
! [SV1893: $i,SV1516: $i,SV979: $i,SV396: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV396 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
| ~ ( c_lessequals @ SV1893 @ SV1516 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(4414,plain,
! [SV2052: $i,SV1894: $i,SV1517: $i,SV981: $i,SV398: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV1894 ) @ SV2052 ) @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV1517 @ SV2052 @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV981 @ SV1894 @ ( tc_fun @ SV398 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4415,plain,
! [SV2053: $i,SV1897: $i,SV1520: $i,SV985: $i,SV402: $i] :
( ( ! [SY5911: $i] :
( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1520 @ SY5911 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_lessequals @ SV985 @ SY5911 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SY5911 @ SV1897 @ SV2053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3967]) ).
thf(4416,plain,
! [SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY5912: $i,SY5913: $i,SY5914: $i,SY5915: $i,SY5916: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SY5912 @ SY5913 @ SY5914 @ SY5915 @ SY5916 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3968]) ).
thf(4417,plain,
! [SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY5917: $i,SY5918: $i,SY5919: $i,SY5920: $i,SY5921: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SY5917 @ SY5918 @ SY5919 @ SY5920 @ SY5921 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3969]) ).
thf(4418,plain,
! [SV1900: $i,SV1523: $i,SV988: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SV1523 ) @ ( c_Collect @ SV1900 @ SV405 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1900 @ SV988 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SV1523 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4419,plain,
! [SV989: $i,SV1524: $i,SV406: $i] :
( ( ( SV406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV406 @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) @ ( tc_fun @ SV1524 @ tc_bool ) ) )
= $true )
| ( ( SV406
= ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(4420,plain,
! [SV2056: $i,SV1901: $i,SV1525: $i,SV990: $i,SV407: $i] :
( ( ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ SV1525 @ SV1901 ) @ SV2056 @ SV1901 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2056 @ tc_bool ) ) @ ( c_Set_Ovimage @ SV407 @ ( c_Set_Oinsert @ SV990 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1901 @ tc_bool ) ) @ SV1901 ) @ SV2056 @ SV1901 ) ) @ ( c_Set_Ovimage @ SV407 @ SV1525 @ SV2056 @ SV1901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4421,plain,
! [SV2057: $i,SV1903: $i,SV1527: $i,SV992: $i,SV409: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV409 @ tc_bool ) ) @ SV992 ) @ SV1527 ) @ SV1903 @ SV409 @ ( tc_fun @ SV2057 @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2057 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV992 @ SV1903 @ SV409 @ ( tc_fun @ SV2057 @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1527 @ SV1903 @ SV409 @ ( tc_fun @ SV2057 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4422,plain,
! [SV2058: $i,SV1904: $i,SV1528: $i,SV993: $i,SV410: $i] :
( ( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SV993 @ SV1528 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV993 @ SV410 @ SV1904 @ SV2058 ) @ SV1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4423,plain,
! [SV2059: $i,SV1905: $i,SV1529: $i,SV994: $i,SV411: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SV994 @ SV1529 @ SV1905 ) @ SV2059 ) )
| ~ ( hBOOL @ ( hAPP @ SV994 @ ( hAPP @ SV411 @ SV2059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4424,plain,
! [SV1530: $i,SV995: $i,SV412: $i] :
( ( ( class_Orderings_Olinorder @ SV412 )
= $false )
| ( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) )
| ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4425,plain,
! [SV2060: $i,SV1906: $i,SV1531: $i,SV996: $i,SV413: $i] :
( ( ! [SY5922: $i,SY5923: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SY5922 ) @ SY5923 @ SY5922 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SY5923 @ SY5922 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5922 ) @ SV1906 ) @ SV2060 ) )
| ~ ( c_Finite__Set_Ofinite @ SV2060 @ SY5922 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SY5923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4426,plain,
! [SV1907: $i,SV1532: $i,SV997: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SV1532 ) @ SV1907 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1532 @ SV1907 ) )
| ~ ( hBOOL @ ( hAPP @ SV997 @ SV1907 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4427,plain,
! [SV1908: $i,SV1533: $i,SV998: $i,SV415: $i] :
( ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV415 @ SV998 @ SV1533 ) @ SV1908 @ SV1533 @ SV998 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1533 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV998 ) @ SV415 ) @ SV1908 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3980]) ).
thf(4428,plain,
! [SV1909: $i,SV1534: $i,SV999: $i,SV416: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SV1534 @ ( tc_fun @ SV1909 @ tc_bool ) ) @ ( tc_fun @ SV1909 @ tc_bool ) )
= SV1534 )
= $true )
| ( ( ~ ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SV1909 @ tc_bool ) )
| ~ ( c_lessequals @ SV1534 @ SV416 @ ( tc_fun @ SV1909 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3981]) ).
thf(4429,plain,
! [SV2061: $i,SV1910: $i,SV1535: $i,SV1000: $i,SV417: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SV1000 @ SV1535 @ SV1910 ) @ ( c_Set_Oimage @ SV417 @ SV2061 @ SV1535 @ SV1910 ) @ ( tc_fun @ SV1910 @ tc_bool ) )
| ~ ( c_lessequals @ SV1000 @ SV2061 @ ( tc_fun @ SV1535 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4430,plain,
! [SV2062: $i,SV1911: $i,SV1536: $i,SV1001: $i,SV418: $i] :
( ( ~ ( c_lessequals @ SV418 @ SV1001 @ ( tc_fun @ SV1536 @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ SV1911 @ SV418 @ SV1536 @ SV2062 ) @ ( c_Set_Oimage @ SV1911 @ SV1001 @ SV1536 @ SV2062 ) @ ( tc_fun @ SV2062 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(4431,plain,
! [SV1912: $i,SV1537: $i,SV1003: $i,SV420: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV420 @ SV1003 @ SV1537 ) @ ( c_Set_Oinsert @ SV420 @ SV1912 @ SV1537 ) @ ( tc_fun @ SV1537 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1003 @ SV1912 @ ( tc_fun @ SV1537 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4432,plain,
! [SV1913: $i,SV1538: $i,SV1004: $i,SV421: $i] :
( ( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1538 @ SV421 @ SV1004 @ SV1913 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV1538 @ SV421 @ SV1004 @ SV1913 ) @ SV1913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3985]) ).
thf(4433,plain,
! [SV1539: $i,SV1005: $i,SV422: $i] :
( ( ( class_Orderings_Oorder @ SV422 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1005 @ SV1539 @ SV422 )
| ( SV1539 = SV1005 )
| ~ ( c_lessequals @ SV1005 @ SV1539 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3986]) ).
thf(4434,plain,
! [SV1540: $i,SV1006: $i,SV423: $i] :
( ( ( class_Orderings_Oorder @ SV423 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1006 @ SV1540 @ SV423 )
| ~ ( c_lessequals @ SV1006 @ SV1540 @ SV423 )
| ( SV1540 = SV1006 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3987]) ).
thf(4435,plain,
! [SV1541: $i,SV1007: $i,SV424: $i] :
( ( ( SV424 = SV1007 )
= $true )
| ( ( ~ ( c_lessequals @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3988]) ).
thf(4436,plain,
! [SV1542: $i,SV1008: $i,SV425: $i] :
( ( ( class_Orderings_Oorder @ SV425 )
= $false )
| ( ( ( SV1008 = SV1542 )
| ( c_HOL_Oord__class_Oless @ SV1008 @ SV1542 @ SV425 )
| ~ ( c_lessequals @ SV1008 @ SV1542 @ SV425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4437,plain,
! [SV1543: $i,SV1009: $i,SV426: $i] :
( ( ( class_Orderings_Oorder @ SV426 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV1543 @ SV426 )
| ( SV1009 = SV1543 )
| ~ ( c_lessequals @ SV1009 @ SV1543 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4438,plain,
! [SV1544: $i,SV1010: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) ) )
= $true )
| ( ( SV427 = SV1010 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3991]) ).
thf(4439,plain,
! [SV1545: $i,SV1011: $i,SV428: $i] :
( ( ( class_Orderings_Oorder @ SV428 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1545 @ SV428 )
| ( SV1011 = SV1545 )
| ~ ( c_lessequals @ SV1011 @ SV1545 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4440,plain,
! [SV1546: $i,SV1012: $i,SV429: $i] :
( ( ( class_Orderings_Oorder @ SV429 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1012 @ SV1546 @ SV429 )
| ~ ( c_lessequals @ SV1012 @ SV1546 @ SV429 )
| ( SV1012 = SV1546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4441,plain,
! [SV1547: $i,SV1013: $i,SV430: $i] :
( ( ( class_Orderings_Olinorder @ SV430 )
= $false )
| ( ( ( SV1013 = SV1547 )
| ~ ( c_lessequals @ SV1013 @ SV1547 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1013 @ SV1547 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3994]) ).
thf(4442,plain,
! [SV1548: $i,SV1014: $i,SV431: $i] :
( ( ( class_Orderings_Olinorder @ SV431 )
= $false )
| ( ( ( SV1014 = SV1548 )
| ( c_HOL_Oord__class_Oless @ SV1014 @ SV1548 @ SV431 )
| ~ ( c_lessequals @ SV1014 @ SV1548 @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4443,plain,
! [SV1549: $i,SV1015: $i,SV432: $i] :
( ( ( class_Orderings_Olinorder @ SV432 )
= $false )
| ( ( ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1549 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4444,plain,
! [SV2063: $i,SV1914: $i,SV1550: $i,SV1016: $i,SV433: $i] :
( ( ( c_Set_Oimage @ SV433 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1016 @ tc_bool ) ) @ SV1550 ) @ SV1914 ) @ SV1016 @ SV2063 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2063 @ tc_bool ) ) @ ( c_Set_Oimage @ SV433 @ SV1550 @ SV1016 @ SV2063 ) ) @ ( c_Set_Oimage @ SV433 @ SV1914 @ SV1016 @ SV2063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4445,plain,
! [SV1551: $i,SV1018: $i,SV435: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV435 )
= $false )
| ( ( ( c_lessequals @ SV1018 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1551 @ SV435 ) @ SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SV1018 ) @ SV1551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3998]) ).
thf(4446,plain,
! [SV2064: $i,SV1915: $i,SV1552: $i,SV1019: $i,SV436: $i] :
( ( ! [SY5924: $i,SY5925: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SV1019 @ SV1552 @ SV1915 @ SV2064 ) @ SY5924 @ SV1552 @ SV2064 @ SY5925 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SV1019 @ SY5924 @ SV1915 @ SV2064 @ SY5925 ) @ SV1552 @ SV1915 @ SY5925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4447,plain,
! [SV1553: $i,SV1020: $i,SV437: $i] :
( ( ( class_Orderings_Oorder @ SV437 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1020 @ SV1553 @ SV437 )
| ~ ( c_HOL_Oord__class_Oless @ SV1553 @ SV1020 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4448,plain,
! [SV1554: $i,SV1021: $i,SV438: $i] :
( ( ( class_Orderings_Olinorder @ SV438 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SV1554 @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1021 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4449,plain,
! [SV1555: $i,SV1022: $i,SV439: $i] :
( ( ( class_Orderings_Olinorder @ SV439 )
= $false )
| ( ( ( c_lessequals @ SV1022 @ SV1555 @ SV439 )
| ( c_lessequals @ SV1555 @ SV1022 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4002]) ).
thf(4450,plain,
! [SV1556: $i,SV1023: $i,SV440: $i] :
( ( ( class_Orderings_Opreorder @ SV440 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1023 @ SV1556 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1023 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4451,plain,
! [SV1557: $i,SV1024: $i,SV441: $i] :
( ( ( class_Orderings_Opreorder @ SV441 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1024 @ SV1557 @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV1024 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4004]) ).
thf(4452,plain,
! [SV2065: $i,SV1916: $i,SV1558: $i,SV1025: $i,SV442: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SV1025 ) @ SV1558 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1916 ) @ ( hAPP @ SV2065 @ SV1025 ) ) @ ( c_Set_Oimage @ SV2065 @ SV1558 @ SV442 @ SV1916 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4453,plain,
! [SV2066: $i,SV1917: $i,SV1559: $i,SV1026: $i,SV443: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SV1026 @ SV1559 ) ) @ ( c_Set_Oimage @ SV1026 @ SV1917 @ SV2066 @ SV443 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2066 ) @ SV1559 ) @ SV1917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4454,plain,
! [SV2067: $i,SV1918: $i,SV1560: $i,SV1027: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SV1027 @ SV1560 ) ) @ ( c_Set_Oimage @ SV1027 @ SV1918 @ SV2067 @ SV444 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV1560 ) @ SV1918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4455,plain,
! [SV1028: $i,SV445: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1028 @ SV445 ) ) @ SV1028 ) )
= $true )
| ( ( ( SV1028
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1028 @ SV445 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4456,plain,
! [SV1029: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1029 @ SV446 ) ) @ SV1029 ) )
= $true )
| ( ( ( SV1029
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1029 @ SV446 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4457,plain,
! [SV1030: $i,SV447: $i,SV1561: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV447 ) @ SV1030 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV447 @ ( c_HOL_Ominus__class_Ominus @ SV1030 @ ( c_Set_Oinsert @ SV447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1561 @ tc_bool ) ) @ SV1561 ) @ ( tc_fun @ SV1561 @ tc_bool ) ) @ SV1561 )
= SV1030 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4010]) ).
thf(4458,plain,
! [SV2068: $i,SV1919: $i,SV1562: $i,SV1031: $i,SV448: $i] :
( ( ( ( hAPP @ SV448 @ SV1031 )
= SV1562 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1919 ) @ SV1031 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SV1562 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2068 @ tc_bool ) ) @ SV2068 ) @ SV1919 @ SV2068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4459,plain,
! [SV1920: $i,SV1563: $i,SV1032: $i,SV449: $i] :
( ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV449 @ SV1032 @ SV1563 ) @ SV1920 @ SV1563 @ SV1032 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1563 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1032 ) @ SV449 ) @ SV1920 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4460,plain,
! [SV1921: $i,SV1564: $i,SV1033: $i,SV450: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV450 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1033 @ SV1564 @ SV1921 @ ( tc_fun @ SV450 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1921 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1033 @ SV1564 @ SV1921 @ SV450 ) ) @ SV1033 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4461,plain,
! [SV1923: $i,SV1566: $i,SV1036: $i,SV453: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV453 @ SV1036 @ SV1566 @ ( tc_fun @ SV1923 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1923 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1566 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV453 @ SV1036 @ SV1566 @ SV1923 ) ) @ SV453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4462,plain,
! [SV2069: $i,SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ! [SY5926: $i,SY5927: $i,SY5928: $i,SY5929: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SY5926 @ SY5927 @ SY5928 @ SY5929 @ SV1571 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4463,plain,
! [SV2070: $i,SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ! [SY5930: $i,SY5931: $i,SY5932: $i,SY5933: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SY5930 @ SY5931 @ SY5932 @ SV1572 @ SY5933 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(4464,plain,
! [SV2071: $i,SV1926: $i,SV1573: $i,SV1049: $i,SV467: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV467 @ SV1049 @ SV1573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1926 @ tc_bool ) ) @ SV2071 @ SV1926 )
= SV1573 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4465,plain,
! [SV2072: $i,SV1928: $i,SV1576: $i,SV1060: $i,SV480: $i] :
( ( ( SV480 = SV1060 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1576 @ SV1060 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1928 @ tc_bool ) ) @ SV480 @ SV1928 @ SV2072 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4031]) ).
thf(4466,plain,
! [SV1587: $i,SV1078: $i,SV498: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV498 ) @ SV1078 @ SV1587 )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV498 @ SV1078 @ SV1587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4467,plain,
! [SV1934: $i,SV1588: $i,SV1079: $i,SV499: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1934 @ SV499 ) ) @ SV1934 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1934 @ SV1588 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4468,plain,
! [SV500: $i,SV1589: $i,SV1080: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1080 ) @ SV1589 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SV1589 ) @ t_a ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SV1080 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4039]) ).
thf(4469,plain,
! [SV1590: $i,SV1081: $i,SV501: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ SV501 @ SV1081 ) @ SV1590 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1590 ) @ SV501 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV501 @ SV1081 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4470,plain,
! [SV1935: $i,SV1591: $i,SV1082: $i,SV502: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4471,plain,
! [SV1087: $i,SV507: $i,SV1592: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1592 ) @ SV507 ) @ ( c_Set_Oinsert @ SV1087 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) ) )
= $false )
| ( ( SV507 = SV1087 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4472,plain,
! [SV509: $i,SV1593: $i,SV1088: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1088 ) @ SV1593 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV509 @ SV1593 ) ) @ SV1593 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV509 @ SV1088 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4043]) ).
thf(4473,plain,
! [SV511: $i,SV1090: $i,SV1594: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1594 ) @ SV1090 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1594 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV511 @ SV1090 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4474,plain,
! [SV516: $i,SV1094: $i,SV1595: $i] :
( ( ( hBOOL @ ( hAPP @ SV1595 @ SV1094 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV516 ) @ SV1094 ) @ SV1595 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4045]) ).
thf(4475,plain,
! [SV517: $i,SV1095: $i,SV1596: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1596 ) @ SV1095 ) @ SV517 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV517 @ SV1095 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4046]) ).
thf(4476,plain,
! [SV1597: $i,SV1096: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP @ SV518 @ SV1096 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1597 ) @ SV1096 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1597 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4477,plain,
! [SV524: $i,SV1102: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV1102 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV524 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV524 @ SV1102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4478,plain,
! [SV1111: $i,SV534: $i,SV1598: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1598 ) @ SV534 ) @ SV1111 ) )
= $false )
| ( ( SV534 = SV1111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4479,plain,
! [SV2073: $i,SV1936: $i,SV1599: $i,SV1112: $i,SV535: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4480,plain,
! [SV2074: $i,SV1937: $i,SV1600: $i,SV1113: $i,SV536: $i] :
( ( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 )
!= ( c_Set_Oinsert @ SV1937 @ ( c_Set_Oinsert @ SV2074 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 ) )
| ( SV536 = SV2074 )
| ( SV536 = SV1937 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4481,plain,
! [SV2075: $i,SV1938: $i,SV1601: $i,SV1114: $i,SV537: $i] :
( ( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 )
!= ( c_Set_Oinsert @ SV1938 @ ( c_Set_Oinsert @ SV2075 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 ) )
| ( SV1114 = SV1938 )
| ( SV1114 = SV2075 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4482,plain,
! [SV2076: $i,SV1939: $i,SV1602: $i,SV1115: $i,SV538: $i] :
( ( ( ( hAPP @ SV538 @ SV1115 )
!= ( hAPP @ SV538 @ SV1602 ) )
| ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 @ SV2076 )
| ( SV1115 = SV1602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4483,plain,
! [SV2077: $i,SV1940: $i,SV1603: $i,SV1116: $i,SV539: $i] :
( ( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 )
!= ( c_Set_Oinsert @ SV1940 @ ( c_Set_Oinsert @ SV2077 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 ) )
| ( SV539 = SV2077 )
| ( SV1116 = SV2077 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(4484,plain,
! [SV2078: $i,SV1941: $i,SV1604: $i,SV1117: $i,SV540: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SV1941 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
| ( ( hAPP @ SV1117 @ SV2078 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SV2078 ) @ SV540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4485,plain,
! [SV2079: $i,SV1942: $i,SV1605: $i,SV1118: $i,SV541: $i] :
( ( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 )
!= ( c_Set_Oinsert @ SV1942 @ ( c_Set_Oinsert @ SV2079 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 ) )
| ( SV1118 = SV1942 )
| ( SV541 = SV1942 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4486,plain,
! [SV1943: $i,SV1606: $i,SV1119: $i,SV542: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV542 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SV1606 @ SV1943 @ SV542 ) )
| ( SV1606 = SV1943 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4487,plain,
! [SV1944: $i,SV1607: $i,SV1120: $i,SV543: $i] :
( ( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SV1607 )
!= ( c_Set_Oinsert @ SV543 @ SV1944 @ SV1607 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1944 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1120 ) )
| ( SV1120 = SV1944 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4070]) ).
thf(4488,plain,
! [SV1608: $i,SV1121: $i,SV544: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV544 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SV1121 ) @ SV1608 )
!= ( c_Orderings_Obot__class_Obot @ SV544 ) )
| ( SV1608
= ( c_Orderings_Obot__class_Obot @ SV544 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4489,plain,
! [SV1945: $i,SV1609: $i,SV1122: $i,SV545: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1945 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SV1945 ) @ SV1609 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4490,plain,
! [SV1610: $i,SV1123: $i,SV546: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV546 @ tc_bool ) ) @ SV1123 ) @ SV1610 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
= $false )
| ( ( SV1123
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV546 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4491,plain,
! [SV1946: $i,SV1611: $i,SV1124: $i,SV547: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ SV1611 ) ) @ SV1946 )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1611 ) @ SV1946 ) ) )
= $true )
| ( ( c_lessequals @ SV1946 @ SV1124 @ ( tc_fun @ SV547 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4492,plain,
! [SV1612: $i,SV1125: $i,SV548: $i] :
( ( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1125 )
= ( hAPP @ ( c_COMBC @ ( c_in @ SV548 ) @ SV548 @ ( tc_fun @ SV548 @ tc_bool ) @ tc_bool ) @ SV1612 ) )
= $false )
| ( ( SV1125 = SV1612 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4075]) ).
thf(4493,plain,
! [SV2080: $i,SV1947: $i,SV1613: $i,SV1126: $i,SV549: $i] :
( ( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SV1947 )
!= ( c_Set_Oimage @ SV549 @ SV2080 @ SV1613 @ SV1947 ) )
| ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SV1947 )
| ( SV1126 = SV2080 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4494,plain,
! [SV2081: $i,SV1948: $i,SV1614: $i,SV1127: $i,SV550: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(4495,plain,
! [SV1615: $i,SV1128: $i,SV551: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV551 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SV1128 ) @ SV1615 )
!= ( c_Orderings_Otop__class_Otop @ SV551 ) )
| ( SV1128
= ( c_Orderings_Otop__class_Otop @ SV551 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4496,plain,
! [SV1616: $i,SV1129: $i,SV552: $i] :
( ( ( ( c_Set_Oinsert @ SV552 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 )
= ( c_Set_Oinsert @ SV1616 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1129 @ tc_bool ) ) @ SV1129 ) )
= $false )
| ( ( SV552 = SV1616 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4497,plain,
! [SV1617: $i,SV1130: $i,SV553: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV553 @ tc_bool ) ) @ SV1130 ) @ SV1617 )
= SV1617 )
= $false )
| ( ( c_lessequals @ SV1130 @ SV1617 @ ( tc_fun @ SV553 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4080]) ).
thf(4498,plain,
! [SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY5934: $i,SY5935: $i,SY5936: $i,SY5937: $i,SY5938: $i,SY5939: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SY5934 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SY5935 @ SY5936 @ SY5937 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SY5938 @ SY5936 @ SY5939 ) @ SY5934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4081]) ).
thf(4499,plain,
! [SV2083: $i,SV1950: $i,SV1619: $i,SV1132: $i,SV555: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4500,plain,
! [SV1620: $i,SV1133: $i,SV556: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV556 @ tc_bool ) ) @ SV1133 ) @ SV1620 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV556 @ tc_bool ) ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1133 @ SV1620 @ ( tc_fun @ SV556 @ tc_bool ) )
= SV1133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4501,plain,
! [SV1951: $i,SV1621: $i,SV1134: $i,SV558: $i] :
( ( ( ( hAPP @ SV558 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1134 @ SV558 @ SV1621 @ SV1951 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1134 @ SV558 @ SV1621 @ ( tc_fun @ SV1951 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4502,plain,
! [SV2084: $i,SV1952: $i,SV1622: $i,SV1135: $i,SV559: $i] :
( ( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV1952 @ SV2084 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4503,plain,
! [SV1623: $i,SV1136: $i,SV560: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV560 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SV1136 ) @ SV1623 )
!= SV1136 )
| ( c_lessequals @ SV1136 @ SV1623 @ SV560 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4086]) ).
thf(4504,plain,
! [SV1624: $i,SV1137: $i,SV561: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV561 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SV1137 ) @ SV1624 )
!= ( c_Orderings_Obot__class_Obot @ SV561 ) )
| ( SV1137
= ( c_Orderings_Obot__class_Obot @ SV561 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4087]) ).
thf(4505,plain,
! [SV2085: $i,SV1953: $i,SV1625: $i,SV1138: $i,SV562: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
| ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4506,plain,
! [SV2086: $i,SV1954: $i,SV1626: $i,SV1139: $i,SV563: $i] :
( ( ! [SY5940: $i] :
( ( ( hAPP @ SV563 @ SV1139 )
!= ( hAPP @ SV563 @ SV1626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SY5940 )
| ( SV1139 = SV1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(4507,plain,
! [SV1955: $i,SV1627: $i,SV1140: $i,SV564: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV564 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SV1627 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SV1955 @ SV1955 @ SV564 ) )
| ( SV1140 = SV1627 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4508,plain,
! [SV2087: $i,SV1956: $i,SV1628: $i,SV1141: $i,SV565: $i] :
( ( ! [SY5941: $i] :
( ( ( hAPP @ SV565 @ SV1141 )
!= ( hAPP @ SV565 @ SV1628 ) )
| ~ ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SY5941 )
| ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(4509,plain,
! [SV1629: $i,SV1142: $i,SV566: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV566 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SV1142 ) @ SV1629 )
!= SV1629 )
| ( c_lessequals @ SV1142 @ SV1629 @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4510,plain,
! [SV2088: $i,SV1957: $i,SV1630: $i,SV1143: $i,SV567: $i] :
( ( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SV1957 )
!= ( c_Set_Oimage @ SV567 @ SV2088 @ SV1630 @ SV1957 ) )
| ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SV2088 ) @ SV1630 @ SV1957 )
| ( SV1143 = SV2088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4511,plain,
! [SV1632: $i,SV1146: $i,SV570: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) )
= ( c_Collect @ SV1146 @ SV570 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1146 @ SV1632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4512,plain,
! [SV1633: $i,SV1147: $i,SV571: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV571 @ tc_bool ) ) @ SV1147 ) @ SV1633 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= $false )
| ( ( SV1633
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4513,plain,
! [SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ! [SY5942: $i,SY5943: $i,SY5944: $i,SY5945: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
!= ( c_Fun_Ocomp @ SY5942 @ SY5943 @ SY5944 @ SV1958 @ SV2089 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY5945 ) )
= ( hAPP @ SY5942 @ ( hAPP @ SY5943 @ SY5945 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4514,plain,
! [SV1635: $i,SV1149: $i,SV573: $i] :
( ( ( ( c_Set_Oinsert @ SV573 @ SV1149 @ SV1635 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1635 @ tc_bool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1635 ) @ SV573 ) @ SV1149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4099]) ).
thf(4515,plain,
! [SV2090: $i,SV1959: $i,SV1636: $i,SV1151: $i,SV575: $i] :
( ( ! [SY5946: $i,SY5947: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SV1959 @ SV2090 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV1959 ) @ SY5946 @ SV1959 @ SV1959 @ SV2090 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SY5947 ) )
= ( hAPP @ SY5946 @ SY5947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4516,plain,
! [SV2091: $i,SV1960: $i,SV1637: $i,SV1152: $i,SV576: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SV1960 @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ( ( hAPP @ SV1637 @ SV2091 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1960 ) @ SV2091 ) @ SV1152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4517,plain,
! [SV1961: $i,SV1638: $i,SV1153: $i,SV578: $i] :
( ( ( ( c_Set_Oimage @ SV578 @ SV1153 @ SV1638 @ SV1961 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1961 @ tc_bool ) ) )
= $true )
| ( ( SV1153
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1638 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4518,plain,
! [SV1962: $i,SV1640: $i,SV1155: $i,SV581: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) )
!= ( c_Set_Oimage @ SV1155 @ SV1640 @ SV1962 @ SV581 ) )
= $true )
| ( ( SV1640
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1962 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4519,plain,
! [SV1641: $i,SV1156: $i,SV582: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV582 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SV1156 ) @ SV1641 )
!= ( c_Orderings_Otop__class_Otop @ SV582 ) )
| ( SV1641
= ( c_Orderings_Otop__class_Otop @ SV582 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4520,plain,
! [SV1642: $i,SV1157: $i,SV583: $i] :
( ( ( ( c_Collect @ SV583 @ SV1157 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1157 @ tc_bool ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV583 @ SV1642 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4521,plain,
! [SV2092: $i,SV1963: $i,SV1643: $i,SV1158: $i,SV584: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
| ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SV2092 @ SV1963 @ SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(4522,plain,
! [SV1964: $i,SV1644: $i,SV1159: $i,SV585: $i] :
( ( ( ( hAPP @ SV585 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV1159 @ SV585 @ SV1644 @ SV1964 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1964 @ tc_bool ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1159 @ SV585 @ SV1644 @ ( tc_fun @ SV1964 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1964 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4109]) ).
thf(4523,plain,
! [SV2093: $i,SV1965: $i,SV1645: $i,SV1160: $i,SV586: $i] :
( ( ! [SY5948: $i] :
( ( ( hAPP @ SV586 @ SV1160 )
!= ( hAPP @ SV586 @ SV1645 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SY5948 )
| ( SV1160 = SV1645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4524,plain,
! [SV2094: $i,SV1966: $i,SV1646: $i,SV1161: $i,SV587: $i] :
( ( ! [SY5949: $i] :
( ( ( hAPP @ SV587 @ SV1161 )
!= ( hAPP @ SV587 @ SV1646 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SY5949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4111]) ).
thf(4525,plain,
! [SV1967: $i,SV1647: $i,SV1162: $i,SV588: $i,SV2: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SV1647 ) @ ( c_Set_Oimage @ SV2 @ SV1967 @ SV1162 @ SV1647 ) @ ( tc_fun @ SV1647 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV588 @ SV1967 @ ( tc_fun @ SV1162 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SV1647 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4526,plain,
! [SV1968: $i,SV1648: $i,SV1163: $i,SV589: $i,SV3: $i] :
( ( ( c_Fun_Oinj__on @ SV3 @ SV589 @ SV1163 @ SV1648 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SV1968 @ SV589 @ SV1163 ) @ SV1163 @ SV1648 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4527,plain,
! [SV1969: $i,SV1649: $i,SV1164: $i,SV590: $i,SV4: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV4 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1649 @ SV590 @ SV1969 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1164 ) @ SV1649 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4528,plain,
! [SV1970: $i,SV1650: $i,SV1165: $i,SV591: $i,SV5: $i] :
( ( ( c_lessequals @ ( hAPP @ SV5 @ SV591 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1165 @ SV5 @ SV1650 @ ( tc_fun @ SV1970 @ tc_bool ) ) @ ( tc_fun @ SV1970 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV591 ) @ SV1165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4529,plain,
! [SV592: $i,SV1651: $i,SV6: $i,SV1166: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1166 ) @ SV6 ) @ SV1651 ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV6 @ SV592 @ SV1166 ) @ SV1651 @ ( tc_fun @ SV1166 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV592 @ SV1651 @ ( tc_fun @ SV1166 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4530,plain,
! [SV593: $i,SV1167: $i,SV7: $i,SV1652: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV1652 @ SV7 @ SV1167 ) @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV7 @ SV593 @ ( tc_fun @ SV1167 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4117]) ).
thf(4531,plain,
! [SV594: $i,SV1653: $i,SV1168: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV1168 @ ( tc_fun @ SV1653 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV8 @ ( c_Set_Oinsert @ SV594 @ SV1168 @ SV1653 ) @ ( tc_fun @ SV1653 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4118]) ).
thf(4532,plain,
! [SV1971: $i,SV1654: $i,SV1169: $i,SV595: $i,SV9: $i] :
( ( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SV1169 @ SV1654 ) @ SV1971 @ SV1654 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1654 ) @ SV595 ) @ SV1169 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SV1169 @ SV1971 @ SV1654 @ SV1654 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4533,plain,
! [SV2095: $i,SV1972: $i,SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ! [SY5950: $i,SY5951: $i,SY5952: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SV2095 @ SY5950 @ SY5951 @ SY5952 @ SV1170 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4534,plain,
! [SV2096: $i,SV1973: $i,SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ! [SY5953: $i,SY5954: $i,SY5955: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SV2096 @ SY5953 @ SY5954 @ SV1171 @ SY5955 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4121]) ).
thf(4535,plain,
! [SV1657: $i,SV12: $i,SV598: $i,SV1172: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV1657 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SV1657 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1657 @ ( tc_fun @ SV1172 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4536,plain,
! [SV1173: $i,SV13: $i,SV599: $i,SV1658: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV13 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SV1658 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV1173 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4537,plain,
! [SV2097: $i,SV1974: $i,SV1659: $i,SV1174: $i,SV600: $i,SV14: $i] :
( ( ! [SY5956: $i,SY5957: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SY5956 ) @ SY5957 @ SY5956 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SY5956 @ SY5957 @ SV2097 ) @ SV1174 @ SV1974 @ SY5957 @ SV2097 ) )
| ~ ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SY5956 )
| ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY5957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(4538,plain,
! [SV1660: $i,SV1176: $i,SV602: $i,SV16: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV16 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1660 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4126]) ).
thf(4539,plain,
! [SV1975: $i,SV1661: $i,SV1177: $i,SV603: $i,SV17: $i] :
( ( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SV603 @ SV1177 @ ( tc_fun @ SV1661 @ tc_bool ) ) @ SV1661 @ SV1975 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV17 @ SV603 @ SV1661 @ SV1975 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4540,plain,
! [SV1181: $i,SV21: $i,SV607: $i,SV1665: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4129]) ).
thf(4541,plain,
! [SV609: $i,SV1667: $i,SV1183: $i,SV23: $i] :
( ( ( c_Fun_Oinj__on @ SV23 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1183 @ tc_bool ) ) @ SV1183 @ SV1667 )
= $false )
| ( ( ( c_Set_Ovimage @ SV23 @ ( c_Set_Oimage @ SV23 @ SV609 @ SV1183 @ SV1667 ) @ SV1183 @ SV1667 )
= SV609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4130]) ).
thf(4542,plain,
! [SV611: $i,SV1668: $i,SV25: $i,SV1184: $i] :
( ( ( c_Finite__Set_Ofold1Set @ SV1184 @ ( c_Set_Oinsert @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1668 @ tc_bool ) ) @ SV1668 ) @ SV611 @ SV1668 )
= $false )
| ( ( SV25 = SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4131]) ).
thf(4543,plain,
! [SV620: $i,SV1189: $i,SV34: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV1189 @ ( tc_fun @ SV620 @ tc_bool ) ) @ SV620 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1189 @ SV620 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV34 @ SV620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4133]) ).
thf(4544,plain,
! [SV621: $i,SV1190: $i,SV35: $i] :
( ( ( c_Finite__Set_Ofinite @ SV35 @ SV1190 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV621 @ SV1190 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SV621 @ ( tc_fun @ SV1190 @ tc_bool ) ) @ SV1190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4545,plain,
! [SV1977: $i,SV1672: $i,SV1193: $i,SV624: $i,SV38: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
| ~ ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4135]) ).
thf(4546,plain,
! [SV1673: $i,SV39: $i,SV625: $i,SV1194: $i] :
( ( ( SV1194 = SV625 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1194 @ SV39 @ SV1673 ) @ SV625 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV39 @ SV625 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4547,plain,
! [SV2098: $i,SV1978: $i,SV1674: $i,SV1195: $i,SV627: $i,SV41: $i] :
( ( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1978 ) @ SV627 ) @ SV2098 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2098 @ SV41 @ SV1978 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4548,plain,
! [SV1979: $i,SV1676: $i,SV1200: $i,SV632: $i,SV46: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SV632 @ SV1200 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SV1979 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SV1979 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1979 ) @ SV1200 ) @ SV1676 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4140]) ).
thf(4549,plain,
! [SV2099: $i,SV1980: $i,SV1677: $i,SV1201: $i,SV633: $i,SV47: $i] :
( ( ! [SY5958: $i] :
( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SV2099 @ SY5958 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2099 ) @ SV1677 ) @ SV1201 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV2099 ) @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV1980 @ SV2099 @ SY5958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4550,plain,
! [SV1981: $i,SV1678: $i,SV1202: $i,SV634: $i,SV48: $i] :
( ( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV1202 ) @ SV1678 ) @ SV634 @ SV1981 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1981 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SV1202 @ SV634 @ SV1981 ) ) @ ( c_Set_Oimage @ SV48 @ SV1678 @ SV634 @ SV1981 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV634 @ SV1981 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4142]) ).
thf(4551,plain,
! [SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY5959: $i,SY5960: $i,SY5961: $i,SY5962: $i,SY5963: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SY5959 @ SY5960 @ SY5961 @ SV1982 @ SY5962 @ SY5963 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(4552,plain,
! [SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY5964: $i,SY5965: $i,SY5966: $i,SY5967: $i,SY5968: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SY5964 @ SY5965 @ SV1983 @ SY5966 @ SY5967 @ SY5968 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(4553,plain,
! [SV638: $i,SV52: $i,SV1206: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1206 @ SV52 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV638 @ SV52 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SV638 ) @ SV1206 ) @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4146]) ).
thf(4554,plain,
! [SV639: $i,SV53: $i,SV1207: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1207 @ SV53 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV639 @ SV53 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SV639 ) @ SV1207 ) @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4555,plain,
! [SV1209: $i,SV55: $i,SV641: $i,SV1683: $i] :
( ( ( c_lessequals @ SV1683 @ SV641 @ ( tc_fun @ SV55 @ tc_bool ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ SV1209 ) ) @ SV1683 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV641 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV55 @ tc_bool ) ) @ SV1209 ) @ SV1683 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4556,plain,
! [SV1986: $i,SV1684: $i,SV1210: $i,SV642: $i,SV56: $i] :
( ( ( ( hAPP @ ( c_Map_Orestrict__map @ SV56 @ SV642 @ SV1210 @ SV1684 ) @ SV1986 )
= ( c_Option_Ooption_ONone @ SV1684 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1210 ) @ SV1986 ) @ SV642 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4557,plain,
! [SV2102: $i,SV1987: $i,SV1685: $i,SV1212: $i,SV644: $i,SV58: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV58 @ SV644 @ SV1212 @ SV1685 @ SV1987 ) @ SV2102 )
= ( hAPP @ SV58 @ ( hAPP @ SV644 @ SV2102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(4558,plain,
! [SV2103: $i,SV1988: $i,SV1686: $i,SV1213: $i,SV645: $i,SV59: $i] :
( ( ( hAPP @ SV59 @ ( hAPP @ SV645 @ SV1213 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV59 @ SV645 @ SV1686 @ SV1988 @ SV2103 ) @ SV1213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4559,plain,
! [SV1989: $i,SV1687: $i,SV1214: $i,SV646: $i,SV60: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ ( hAPP @ SV1989 @ SV646 ) ) @ ( c_Set_Oimage @ SV1989 @ SV1214 @ SV60 @ SV1687 ) ) )
| ~ ( c_Fun_Oinj__on @ SV1989 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SV1687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4560,plain,
! [SV1990: $i,SV1688: $i,SV1215: $i,SV647: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SV1688 @ SV1990 @ SV61 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1990 ) @ SV1215 ) @ SV1688 ) )
| ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1990 @ tc_bool ) ) @ SV1990 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4561,plain,
! [SV1991: $i,SV1689: $i,SV1216: $i,SV648: $i,SV62: $i] :
( ( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ SV1216 ) ) @ SV1689 )
= ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ ( hAPP @ ( hAPP @ SV62 @ SV1216 ) @ SV1689 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SV1991 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4562,plain,
! [SV1992: $i,SV1690: $i,SV1217: $i,SV649: $i,SV63: $i] :
( ( ( ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ SV1690 ) )
= ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ SV1690 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SV1992 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4563,plain,
! [SV1218: $i,SV650: $i,SV1691: $i,SV64: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV64 @ SV1691 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV64 @ SV650 ) @ SV1218 )
= ( hAPP @ ( hAPP @ SV64 @ SV1218 ) @ SV650 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4157]) ).
thf(4564,plain,
! [SV65: $i,SV1692: $i,SV651: $i,SV1219: $i] :
( ( ( hBOOL @ ( hAPP @ SV1219 @ SV651 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1692 @ tc_bool ) ) @ SV1219 ) @ SV65 ) @ SV651 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV65 @ SV651 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4158]) ).
thf(4565,plain,
! [SV652: $i,SV66: $i,SV1693: $i,SV1220: $i] :
( ( ( hBOOL @ ( hAPP @ SV1220 @ SV1693 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV66 @ tc_bool ) ) @ SV652 ) @ SV1220 ) @ SV1693 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4566,plain,
! [SV1221: $i,SV67: $i,SV1694: $i,SV653: $i] :
( ( ( hBOOL @ ( hAPP @ SV653 @ SV1694 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV67 @ tc_bool ) ) @ SV653 ) @ SV1221 ) @ SV1694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4567,plain,
! [SV1993: $i,SV1695: $i,SV1222: $i,SV654: $i,SV68: $i] :
( ( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV1695 @ SV68 @ SV1222 @ SV1993 ) @ ( c_Set_Oimage @ SV1695 @ SV654 @ SV1222 @ SV1993 ) @ ( tc_fun @ SV1993 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV1695 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SV1993 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4568,plain,
! [SV1223: $i,SV69: $i,SV655: $i,SV1696: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1696 ) @ SV655 ) @ SV69 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1223 @ ( tc_fun @ SV1696 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SV1223 @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4569,plain,
! [SV1224: $i,SV70: $i,SV656: $i,SV1697: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV656 ) @ SV70 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1224 @ ( tc_fun @ SV1697 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SV1224 @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4163]) ).
thf(4570,plain,
! [SV1698: $i,SV71: $i,SV657: $i,SV1225: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1225 ) @ SV657 ) @ SV71 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SV1698 @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1698 @ ( tc_fun @ SV1225 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4571,plain,
! [SV2104: $i,SV1994: $i,SV1699: $i,SV1226: $i,SV658: $i,SV72: $i] :
( ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
| ~ ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4165]) ).
thf(4572,plain,
! [SV1995: $i,SV1700: $i,SV1227: $i,SV659: $i,SV73: $i] :
( ( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
= $true )
| ( ( ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SV1700 @ SV1995 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1700 @ SV1995 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4573,plain,
! [SV2105: $i,SV1996: $i,SV1701: $i,SV1228: $i,SV660: $i,SV74: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1996 ) @ SV1228 ) @ SV2105 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SV2105 @ SV1996 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4167]) ).
thf(4574,plain,
! [SV1997: $i,SV1702: $i,SV1229: $i,SV661: $i,SV75: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SV661 @ SV1229 ) @ SV1702 @ SV1229 @ SV661 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV661 @ tc_bool ) ) @ SV661 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1229 ) @ SV1997 ) @ SV1702 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4575,plain,
! [SV2106: $i,SV1998: $i,SV1703: $i,SV1230: $i,SV662: $i,SV76: $i] :
( ( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
| ~ ( c_Finite__Set_Ofold__graph @ SV1230 @ SV1703 @ SV76 @ SV1998 @ SV662 @ SV2106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4576,plain,
! [SV2107: $i,SV1999: $i,SV1704: $i,SV1232: $i,SV664: $i,SV78: $i] :
( ( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SV1232 @ SV1704 @ SV1999 ) @ SV1999 @ SV2107 )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SV1999 @ SV2107 @ SV1704 ) @ SV1232 @ SV1704 @ SV2107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4577,plain,
! [SV1707: $i,SV1235: $i,SV667: $i,SV81: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV81 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ SV1235 ) @ SV1707 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV81 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1235 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV81 ) @ SV667 ) @ SV1707 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4172]) ).
thf(4578,plain,
! [SV1708: $i,SV1236: $i,SV668: $i,SV82: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV82 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ SV668 ) @ SV1236 ) ) @ SV1708 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV82 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV668 ) @ SV1708 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV82 ) @ SV1236 ) @ SV1708 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4173]) ).
thf(4579,plain,
! [SV83: $i,SV1709: $i,SV669: $i,SV1237: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1237 ) @ SV669 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1237 @ tc_bool ) ) @ SV1709 ) @ ( c_Collect @ SV83 @ SV1237 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV83 @ SV669 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4580,plain,
! [SV672: $i,SV1710: $i,SV1240: $i,SV86: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1240 @ tc_bool ) ) @ SV1240 @ SV1710 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV672 @ SV1710 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SV1240 @ SV1710 ) @ SV1240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4175]) ).
thf(4581,plain,
! [SV1711: $i,SV1241: $i,SV675: $i,SV89: $i] :
( ( ( class_Orderings_Opreorder @ SV89 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4582,plain,
! [SV90: $i,SV1242: $i,SV676: $i,SV1712: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1712 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV90 @ SV1712 @ ( tc_fun @ SV1242 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4177]) ).
thf(4583,plain,
! [SV1713: $i,SV1243: $i,SV677: $i,SV91: $i] :
( ( ( class_Orderings_Oorder @ SV91 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4584,plain,
! [SV2001: $i,SV1715: $i,SV1245: $i,SV679: $i,SV93: $i] :
( ( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SV1245 @ SV1715 ) @ SV1715 @ SV2001 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 ) @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 @ SV2001 ) ) )
| ~ ( c_Fun_Oinj__on @ SV93 @ SV1245 @ SV1715 @ SV2001 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4180]) ).
thf(4585,plain,
! [SV2108: $i,SV2002: $i,SV1718: $i,SV1248: $i,SV683: $i,SV97: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV97 @ SV683 @ SV1248 @ SV1718 ) @ SV2002 ) @ SV2108 )
= ( hAPP @ ( hAPP @ SV97 @ SV2108 ) @ SV2002 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4586,plain,
! [SV2003: $i,SV1720: $i,SV1250: $i,SV685: $i,SV99: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1720 @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV2003 @ SV99 ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1720 @ SV1250 @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV2003 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV685 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV1250 ) @ SV1720 ) @ SV2003 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4182]) ).
thf(4587,plain,
! [SV101: $i,SV1252: $i,SV687: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV687 @ SV1252 @ SV101 )
= $true )
| ( ( c_lessequals @ SV1252 @ SV687 @ SV101 )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4183]) ).
thf(4588,plain,
! [SV102: $i,SV688: $i] :
( ( ( c_lessequals @ SV688 @ SV688 @ SV102 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV688 @ SV688 @ SV102 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4184]) ).
thf(4589,plain,
! [SV104: $i,SV1253: $i,SV690: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV690 @ SV1253 @ SV104 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1253 @ SV690 @ SV104 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4590,plain,
! [SV105: $i,SV1254: $i,SV691: $i] :
( ( ( c_lessequals @ SV691 @ SV1254 @ SV105 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1254 @ SV691 @ SV105 )
= $true )
| ( ( class_Orderings_Olinorder @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4187]) ).
thf(4591,plain,
! [SV106: $i,SV1255: $i,SV692: $i] :
( ( ( ~ ( c_lessequals @ SV692 @ SV1255 @ SV106 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1255 @ SV692 @ SV106 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4592,plain,
! [SV107: $i,SV1256: $i,SV693: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1256 @ SV107 )
= $true )
| ( ( c_lessequals @ SV1256 @ SV693 @ SV107 )
= $true )
| ( ( class_Orderings_Olinorder @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4189]) ).
thf(4593,plain,
! [SV1721: $i,SV1257: $i,SV694: $i,SV108: $i] :
( ( ( class_HOL_Oord @ SV108 )
= $false )
| ( ( ~ ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SV1721 @ SV108 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SV1721 @ SV108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4190]) ).
thf(4594,plain,
! [SV109: $i,SV1258: $i,SV695: $i] :
( ( ( ~ ( c_lessequals @ SV695 @ SV1258 @ SV109 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1258 @ SV695 @ SV109 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4595,plain,
! [SV111: $i,SV697: $i] :
( ( ( c_Finite__Set_Ofinite @ SV697 @ SV111 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ SV697 @ SV111 )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 ) @ ( c_Orderings_Obot__class_Obot @ SV111 ) @ SV697 @ SV111 @ SV111 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4596,plain,
! [SV1260: $i,SV112: $i,SV698: $i] :
( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
| ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4193]) ).
thf(4597,plain,
! [SV1726: $i,SV1264: $i,SV703: $i,SV117: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV117 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ SV1264 ) ) @ SV1726 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV703 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV117 ) @ SV1264 ) @ SV1726 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4195]) ).
thf(4598,plain,
! [SV1727: $i,SV1265: $i,SV704: $i,SV118: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV118 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ SV1727 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV1265 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV118 ) @ SV704 ) @ SV1727 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4599,plain,
! [SV1728: $i,SV1266: $i,SV705: $i,SV119: $i] :
( ( ( class_Lattices_Olattice @ SV119 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ SV1728 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV1266 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV119 ) @ SV705 ) @ SV1728 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4600,plain,
! [SV1729: $i,SV1267: $i,SV706: $i,SV120: $i] :
( ( ( class_Lattices_Olattice @ SV120 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ SV1267 ) ) @ SV1729 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV706 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV120 ) @ SV1267 ) @ SV1729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4198]) ).
thf(4601,plain,
! [SV1270: $i,SV709: $i,SV123: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SV709 ) @ SV1270 )
= SV709 )
= $true )
| ( ( ~ ( c_lessequals @ SV709 @ SV1270 @ SV123 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4201]) ).
thf(4602,plain,
! [SV1271: $i,SV710: $i,SV124: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SV710 ) @ SV1271 )
= SV1271 )
= $true )
| ( ( ~ ( c_lessequals @ SV1271 @ SV710 @ SV124 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4202]) ).
thf(4603,plain,
! [SV711: $i,SV125: $i,SV1730: $i,SV1272: $i] :
( ( ( ~ ( c_lessequals @ SV1272 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV711 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SV1272 ) @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4604,plain,
! [SV714: $i,SV128: $i,SV1731: $i,SV1275: $i] :
( ( ( ~ ( c_lessequals @ SV1275 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV714 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SV1275 ) @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4605,plain,
! [SV1732: $i,SV1276: $i,SV715: $i,SV129: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV129 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV1276 @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV715 @ SV1732 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4606,plain,
! [SV1733: $i,SV1279: $i,SV718: $i,SV132: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV1279 @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV718 @ SV1733 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4208]) ).
thf(4607,plain,
! [SV1734: $i,SV1280: $i,SV719: $i,SV133: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV133 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV1280 @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV719 @ SV1734 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4209]) ).
thf(4608,plain,
! [SV2109: $i,SV2005: $i,SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ! [SY5969: $i,SY5970: $i,SY5971: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SV2109 @ SY5969 @ SY5970 @ SY5971 @ SV1735 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SY5969 @ SV2109 @ SY5971 @ SY5970 @ SV1735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4214]) ).
thf(4609,plain,
! [SV1736: $i,SV1288: $i,SV727: $i,SV141: $i] :
( ( ( class_Lattices_Olattice @ SV141 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1288 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ SV1736 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV141 ) @ SV727 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 ) @ SV1288 ) @ SV1736 ) ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4610,plain,
! [SV730: $i,SV1737: $i,SV1291: $i,SV144: $i] :
( ( ( ~ ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1737 ) @ SV730 ) @ SV1291 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4217]) ).
thf(4611,plain,
! [SV2110: $i,SV2006: $i,SV1739: $i,SV1294: $i,SV733: $i,SV147: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SV2110 ) @ SV2006 @ SV2006 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SV2110 @ SV2006 @ SV2006 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4612,plain,
! [SV2007: $i,SV1740: $i,SV1295: $i,SV734: $i,SV148: $i] :
( ( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SV734 @ SV1295 @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SV2007 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SV734 @ SV1740 @ SV2007 ) @ ( c_Set_Oimage @ SV148 @ SV1295 @ SV1740 @ SV2007 ) @ ( tc_fun @ SV2007 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SV2007 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4613,plain,
! [SV1296: $i,SV149: $i,SV1741: $i,SV735: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV735 @ SV1741 @ SV149 ) @ SV1296 @ ( tc_fun @ SV149 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV149 ) @ SV735 ) @ SV1296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4220]) ).
thf(4614,plain,
! [SV1742: $i,SV1297: $i,SV736: $i,SV150: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV150 )
= $false )
| ( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV736 @ ( c_COMBK @ SV1297 @ SV150 @ SV1742 ) @ SV1742 @ SV150 )
= SV1297 )
| ( SV736
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1742 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4615,plain,
! [SV1298: $i,SV151: $i,SV1743: $i,SV737: $i] :
( ( ( hBOOL @ ( hAPP @ SV737 @ SV1743 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV151 @ SV737 @ SV1298 ) @ SV1743 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4616,plain,
! [SV2008: $i,SV1744: $i,SV1299: $i,SV738: $i,SV152: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SV738 ) @ ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SV2008 ) @ SV2008 )
= ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SV2008 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1744 ) @ SV738 ) @ SV1299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4617,plain,
! [SV739: $i,SV1745: $i,SV1300: $i,SV153: $i] :
( ( ( ~ ( c_lessequals @ SV153 @ SV1300 @ ( tc_fun @ SV1745 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1745 ) @ SV739 ) @ SV153 ) )
= $true )
| ( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SV739 @ SV1300 @ SV1745 ) @ ( tc_fun @ SV1745 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4618,plain,
! [SV740: $i,SV154: $i,SV1746: $i,SV1301: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1301 ) @ SV1746 ) @ SV154 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SV1746 @ SV740 @ SV1301 ) @ ( tc_fun @ SV1301 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV154 @ SV740 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4225]) ).
thf(4619,plain,
! [SV741: $i,SV1747: $i,SV1302: $i,SV155: $i] :
( ( ( ~ ( c_lessequals @ SV155 @ SV1302 @ ( tc_fun @ SV1747 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1747 ) @ SV741 ) @ SV155 ) )
= $true )
| ( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SV741 @ SV1302 @ SV1747 ) @ ( tc_fun @ SV1747 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4226]) ).
thf(4620,plain,
! [SV1303: $i,SV742: $i,SV1748: $i,SV156: $i] :
( ( ( ~ ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SV1748 @ SV742 @ SV1303 ) @ ( tc_fun @ SV1303 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1303 ) @ SV1748 ) @ SV156 ) )
= $true )
| ( ( c_lessequals @ SV156 @ SV742 @ ( tc_fun @ SV1303 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4227]) ).
thf(4621,plain,
! [SV2009: $i,SV1749: $i,SV1304: $i,SV743: $i,SV157: $i] :
( ( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SV743 @ SV1304 @ SV1749 ) @ ( c_Set_Ovimage @ SV157 @ SV2009 @ SV1304 @ SV1749 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV743 @ SV2009 @ ( tc_fun @ SV1749 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4228]) ).
thf(4622,plain,
! [SV1309: $i,SV748: $i,SV162: $i] :
( ( ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV748 @ SV1309 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4623,plain,
! [SV1752: $i,SV1310: $i,SV749: $i,SV163: $i] :
( ( ( class_Lattices_Olattice @ SV163 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ SV1310 ) ) @ SV1752 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV749 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV163 ) @ SV1310 ) @ SV1752 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4624,plain,
! [SV1753: $i,SV1311: $i,SV750: $i,SV164: $i] :
( ( ( class_Lattices_Olattice @ SV164 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ SV1753 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV1311 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV164 ) @ SV750 ) @ SV1753 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4625,plain,
! [SV1754: $i,SV1312: $i,SV751: $i,SV165: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV165 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ SV1754 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV1312 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 ) @ SV751 ) @ SV1754 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4234]) ).
thf(4626,plain,
! [SV1755: $i,SV1313: $i,SV752: $i,SV166: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV166 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ SV1313 ) ) @ SV1755 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV752 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV166 ) @ SV1313 ) @ SV1755 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4627,plain,
! [SV761: $i,SV175: $i,SV1761: $i,SV1321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV175 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV761 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SV1761 @ SV761 @ SV1321 ) @ ( tc_fun @ SV1321 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SV1321 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4239]) ).
thf(4628,plain,
! [SV762: $i,SV1762: $i,SV1322: $i,SV176: $i] :
( ( ( ~ ( c_lessequals @ SV176 @ SV1322 @ ( tc_fun @ SV1762 @ tc_bool ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV1322 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SV1322 @ SV1762 ) @ ( tc_fun @ SV1762 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4240]) ).
thf(4629,plain,
! [SV180: $i,SV766: $i,SV1766: $i,SV1326: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1326 ) @ SV1766 ) @ SV766 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SV1766 @ SV766 @ SV1326 ) @ ( tc_fun @ SV1326 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SV1326 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4242]) ).
thf(4630,plain,
! [SV181: $i,SV1327: $i,SV767: $i,SV1767: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1767 ) @ SV767 ) @ SV1327 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1327 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SV1327 @ SV1767 ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4631,plain,
! [SV1768: $i,SV1328: $i,SV768: $i,SV182: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV182 )
= $false )
| ( ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SV1328 @ SV1768 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV1328 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SV1768 @ SV182 @ SV182 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1768 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4632,plain,
! [SV2011: $i,SV1769: $i,SV1329: $i,SV769: $i,SV183: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1769 @ SV2011 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2011 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) )
| ~ ( c_lessequals @ SV183 @ SV1769 @ ( tc_fun @ SV1329 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4633,plain,
! [SV1771: $i,SV1331: $i,SV775: $i,SV189: $i] :
( ( ( class_Lattices_Olattice @ SV189 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ SV1331 ) @ SV1771 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV189 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1331 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV189 ) @ SV775 ) @ SV1771 ) ) @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4634,plain,
! [SV191: $i,SV1333: $i,SV777: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV777 @ SV1333 @ SV191 )
= $true )
| ( ( ( c_lessequals @ SV1333 @ SV777 @ SV191 )
| ~ ( c_lessequals @ SV777 @ SV1333 @ SV191 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4247]) ).
thf(4635,plain,
! [SV1773: $i,SV1334: $i,SV779: $i,SV193: $i] :
( ( ( class_HOL_Oord @ SV193 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
| ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SV1773 @ SV193 ) )
| ~ ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4636,plain,
! [SV1774: $i,SV1338: $i,SV787: $i,SV202: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false )
| ( ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SV1338 @ SV1774 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV1338 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SV1774 @ SV202 @ SV202 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV1774 @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4637,plain,
! [SV203: $i,SV1339: $i,SV788: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1339 @ SV203 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1339 @ SV788 @ SV203 )
| ( SV1339 = SV788 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4256]) ).
thf(4638,plain,
! [SV204: $i,SV1340: $i,SV789: $i] :
( ( ( SV789 = SV1340 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV789 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SV1340 @ SV204 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4257]) ).
thf(4639,plain,
! [SV1341: $i,SV205: $i,SV790: $i] :
( ( ( c_lessequals @ SV790 @ SV205 @ ( tc_fun @ SV1341 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV205 @ SV790 @ ( tc_fun @ SV1341 @ tc_bool ) ) )
= $true )
| ( ( SV205 = SV790 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4640,plain,
! [SV1342: $i,SV206: $i,SV791: $i] :
( ( ( c_lessequals @ SV791 @ SV206 @ ( tc_fun @ SV1342 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV206 @ SV791 @ ( tc_fun @ SV1342 @ tc_bool ) ) )
= $true )
| ( ( SV206 = SV791 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4641,plain,
! [SV207: $i,SV1343: $i,SV792: $i] :
( ( ( SV792 = SV1343 )
= $true )
| ( ( ~ ( c_lessequals @ SV1343 @ SV792 @ SV207 )
| ~ ( c_lessequals @ SV792 @ SV1343 @ SV207 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4642,plain,
! [SV208: $i,SV1344: $i,SV793: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV793 @ SV1344 @ SV208 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1344 @ SV793 @ SV208 )
| ( SV1344 = SV793 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4643,plain,
! [SV209: $i,SV1345: $i,SV794: $i] :
( ( ( SV794 = SV1345 )
= $true )
| ( ( ~ ( c_lessequals @ SV1345 @ SV794 @ SV209 )
| ~ ( c_lessequals @ SV794 @ SV1345 @ SV209 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4262]) ).
thf(4644,plain,
! [SV210: $i,SV1346: $i,SV795: $i] :
( ( ( SV795 = SV1346 )
= $true )
| ( ( ~ ( c_lessequals @ SV795 @ SV1346 @ SV210 )
| ~ ( c_lessequals @ SV1346 @ SV795 @ SV210 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4263]) ).
thf(4645,plain,
! [SV211: $i,SV1347: $i,SV796: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV796 @ SV1347 @ SV211 )
= $true )
| ( ( ( SV1347 = SV796 )
| ( c_HOL_Oord__class_Oless @ SV1347 @ SV796 @ SV211 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4264]) ).
thf(4646,plain,
! [SV212: $i,SV1348: $i,SV797: $i] :
( ( ( SV797 = SV1348 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1348 @ SV212 )
| ( c_HOL_Oord__class_Oless @ SV1348 @ SV797 @ SV212 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4647,plain,
! [SV1775: $i,SV1350: $i,SV799: $i,SV214: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV214 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SV1350 ) @ SV1775 @ SV214 )
| ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV1775 @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4267]) ).
thf(4648,plain,
! [SV1776: $i,SV1351: $i,SV800: $i,SV215: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SV1351 ) @ SV1776 @ SV215 )
| ~ ( c_HOL_Oord__class_Oless @ SV800 @ SV1776 @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4268]) ).
thf(4649,plain,
! [SV1777: $i,SV1354: $i,SV803: $i,SV218: $i] :
( ( ( class_HOL_Oord @ SV218 )
= $false )
| ( ( ( c_lessequals @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4650,plain,
! [SV219: $i,SV1355: $i,SV804: $i] :
( ( ( c_lessequals @ SV804 @ SV1355 @ SV219 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1355 @ SV219 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4651,plain,
! [SV220: $i,SV1356: $i,SV805: $i] :
( ( ( c_lessequals @ SV805 @ SV1356 @ SV220 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV805 @ SV1356 @ SV220 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4272]) ).
thf(4652,plain,
! [SV1357: $i,SV806: $i,SV221: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SV806 ) @ SV1357 )
= SV806 )
= $true )
| ( ( ~ ( c_lessequals @ SV1357 @ SV806 @ SV221 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4273]) ).
thf(4653,plain,
! [SV1358: $i,SV807: $i,SV222: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SV807 ) @ SV1358 )
= SV1358 )
= $true )
| ( ( ~ ( c_lessequals @ SV807 @ SV1358 @ SV222 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4274]) ).
thf(4654,plain,
! [SV1778: $i,SV225: $i,SV1361: $i,SV810: $i] :
( ( ( c_Finite__Set_Ofinite @ SV810 @ SV1361 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV225 @ SV810 @ SV1361 @ SV1778 ) @ SV1778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4655,plain,
! [SV811: $i,SV1779: $i,SV1362: $i,SV226: $i] :
( ( ( ~ ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1779 ) @ SV811 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SV1779 ) @ ( tc_fun @ SV1779 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4278]) ).
thf(4656,plain,
! [SV1363: $i,SV227: $i,SV812: $i] :
( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
| ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4657,plain,
! [SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY5972: $i,SY5973: $i,SY5974: $i,SY5975: $i,SY5976: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SY5972 @ SY5973 @ SY5974 @ SV2013 @ SY5975 @ SY5976 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(4658,plain,
! [SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY5977: $i,SY5978: $i,SY5979: $i,SY5980: $i,SY5981: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SY5977 @ SY5978 @ SV2014 @ SY5979 @ SY5980 @ SY5981 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4282]) ).
thf(4659,plain,
! [SV817: $i,SV1368: $i,SV1783: $i,SV232: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV1783 @ SV1368 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1783 @ SV817 @ SV1368 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SV1368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4660,plain,
! [SV1369: $i,SV1784: $i,SV818: $i,SV233: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV233 ) @ SV818 ) @ SV1784 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV818 @ SV1369 @ SV233 ) ) @ SV1784 )
= ( c_Set_Oinsert @ SV818 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV233 @ tc_bool ) ) @ SV1369 ) @ SV1784 ) @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4284]) ).
thf(4661,plain,
! [SV1785: $i,SV819: $i,SV1370: $i,SV234: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV234 ) @ SV1370 ) @ SV819 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ ( c_Set_Oinsert @ SV1370 @ SV1785 @ SV234 ) )
= ( c_Set_Oinsert @ SV1370 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV234 @ tc_bool ) ) @ SV819 ) @ SV1785 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4662,plain,
! [SV2113: $i,SV2016: $i,SV1787: $i,SV1372: $i,SV822: $i,SV237: $i] :
( ( ( hAPP @ ( c_Fun_Ofcomp @ SV237 @ SV822 @ SV1372 @ SV1787 @ SV2016 ) @ SV2113 )
= ( hAPP @ SV822 @ ( hAPP @ SV237 @ SV2113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(4663,plain,
! [SV2017: $i,SV1788: $i,SV1373: $i,SV823: $i,SV238: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV1788 ) @ SV2017 ) @ ( tc_fun @ SV238 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1373 @ SV2017 @ ( tc_fun @ SV238 @ tc_bool ) )
| ~ ( c_lessequals @ SV823 @ SV1788 @ ( tc_fun @ SV238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4288]) ).
thf(4664,plain,
! [SV1789: $i,SV1376: $i,SV826: $i,SV241: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV241 )
= $false )
| ( ( ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1789 @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4665,plain,
! [SV1790: $i,SV1377: $i,SV827: $i,SV242: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV242 )
= $false )
| ( ( ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1790 @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4666,plain,
! [SV1791: $i,SV1378: $i,SV828: $i,SV243: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV243 )
= $false )
| ( ( ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1791 @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4293]) ).
thf(4667,plain,
! [SV1383: $i,SV833: $i,SV1792: $i,SV248: $i] :
( ( ( ~ ( c_lessequals @ SV248 @ SV1792 @ ( tc_fun @ SV833 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV248 @ SV1383 @ ( tc_fun @ SV833 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SV1383 ) @ SV1792 ) @ ( tc_fun @ SV833 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4296]) ).
thf(4668,plain,
! [SV1384: $i,SV834: $i,SV1793: $i,SV249: $i] :
( ( ( ~ ( c_lessequals @ SV249 @ SV1793 @ ( tc_fun @ SV834 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV249 @ SV1384 @ ( tc_fun @ SV834 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV1384 ) @ SV1793 ) @ ( tc_fun @ SV834 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4297]) ).
thf(4669,plain,
! [SV2114: $i,SV2018: $i,SV1794: $i,SV1385: $i,SV837: $i,SV252: $i] :
( ( ! [SY5982: $i] :
( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SV837 @ SV1385 @ SV1794 @ SV2018 @ SV2114 ) @ SV2018 @ SY5982 @ SV2114 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SV837 @ SV2018 @ SY5982 @ SV1794 ) @ SV1385 @ SV1794 @ SY5982 @ SV2114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4298]) ).
thf(4670,plain,
! [SV1796: $i,SV1387: $i,SV839: $i,SV254: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV254 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ SV839 ) @ SV1387 ) ) @ SV1796 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV254 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV839 ) @ SV1796 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV254 ) @ SV1387 ) @ SV1796 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4299]) ).
thf(4671,plain,
! [SV1797: $i,SV1388: $i,SV840: $i,SV255: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV255 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ SV1388 ) @ SV1797 ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV255 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1388 ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 ) @ SV840 ) @ SV1797 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4672,plain,
! [SV842: $i,SV1798: $i,SV1390: $i,SV257: $i] :
( ( ( c_lessequals @ SV257 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1390 @ tc_bool ) ) @ SV1798 ) @ SV842 ) @ ( tc_fun @ SV1390 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV257 @ SV842 @ ( tc_fun @ SV1390 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4673,plain,
! [SV1799: $i,SV843: $i,SV1391: $i,SV258: $i] :
( ( ( c_lessequals @ SV258 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1391 @ tc_bool ) ) @ SV843 ) @ SV1799 ) @ ( tc_fun @ SV1391 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV258 @ SV843 @ ( tc_fun @ SV1391 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4303]) ).
thf(4674,plain,
! [SV1800: $i,SV1392: $i,SV844: $i,SV259: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV259 )
= $false )
| ( ( ( c_lessequals @ SV844 @ SV1392 @ SV259 )
| ~ ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SV1392 ) @ SV1800 ) @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4675,plain,
! [SV1801: $i,SV1393: $i,SV845: $i,SV260: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV260 )
= $false )
| ( ( ( c_lessequals @ SV845 @ SV1393 @ SV260 )
| ~ ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SV1801 ) @ SV1393 ) @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4305]) ).
thf(4676,plain,
! [SV1802: $i,SV1394: $i,SV846: $i,SV261: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV261 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SV1394 ) @ SV1802 @ SV261 )
| ~ ( c_lessequals @ SV846 @ SV1802 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4306]) ).
thf(4677,plain,
! [SV1803: $i,SV1395: $i,SV847: $i,SV262: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV262 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SV1395 ) @ SV1803 @ SV262 )
| ~ ( c_lessequals @ SV1395 @ SV1803 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4678,plain,
! [SV1804: $i,SV1396: $i,SV848: $i,SV263: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV263 )
= $false )
| ( ( ( c_lessequals @ SV848 @ SV1396 @ SV263 )
| ~ ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SV1396 ) @ SV1804 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4308]) ).
thf(4679,plain,
! [SV1805: $i,SV1397: $i,SV849: $i,SV264: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV264 )
= $false )
| ( ( ( c_lessequals @ SV849 @ SV1397 @ SV264 )
| ~ ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SV1805 ) @ SV1397 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4309]) ).
thf(4680,plain,
! [SV1807: $i,SV1399: $i,SV852: $i,SV267: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV267 )
= $false )
| ( ( ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4310]) ).
thf(4681,plain,
! [SV2115: $i,SV2019: $i,SV1808: $i,SV1400: $i,SV853: $i,SV268: $i] :
( ( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ SV268 @ SV853 @ SV1400 @ SV1808 @ SV2019 ) @ SV2115 @ SV2019 @ SV1808 )
= ( c_Set_Ovimage @ SV853 @ ( c_Set_Ovimage @ SV268 @ SV2115 @ SV1400 @ SV1808 ) @ SV2019 @ SV1400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(4682,plain,
! [SV855: $i,SV1809: $i,SV1402: $i,SV270: $i] :
( ( ( ~ ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4683,plain,
! [SV2116: $i,SV2020: $i,SV1810: $i,SV1410: $i,SV864: $i,SV279: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(4684,plain,
! [SV2117: $i,SV2021: $i,SV1811: $i,SV1411: $i,SV865: $i,SV280: $i] :
( ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SV2021 ) @ SV2117 @ SV2021 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SV2117 @ SV2021 @ SV1411 ) @ SV1411 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV865 @ SV2117 @ SV2021 @ SV1411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4685,plain,
! [SV2118: $i,SV2022: $i,SV1812: $i,SV1413: $i,SV868: $i,SV283: $i] :
( ( ! [SY5983: $i] :
( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SV2022 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SV2118 ) @ SV2022 @ SY5983 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SV2118 @ SV2022 @ SY5983 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2022 ) @ SV1413 ) @ SV1812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4319]) ).
thf(4686,plain,
! [SV1813: $i,SV1414: $i,SV869: $i,SV284: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV284 @ tc_bool ) ) @ SV1414 ) @ ( c_Collect @ SV1813 @ SV284 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV284 ) @ SV869 ) @ SV1414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4687,plain,
! [SV2024: $i,SV1815: $i,SV1417: $i,SV872: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SV1417 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Set_Oinsert @ SV1417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 ) @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 @ SV287 ) ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SV1417 @ SV1815 @ SV2024 ) @ SV2024 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4323]) ).
thf(4688,plain,
! [SV2119: $i,SV2025: $i,SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ! [SY5984: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SV2119 @ SY5984 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2025 @ SV2119 @ SY5984 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2119 ) @ SV1817 ) @ SV1419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4689,plain,
! [SV875: $i,SV1818: $i,SV1420: $i,SV290: $i] :
( ( ( ~ ( c_lessequals @ SV290 @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SV1420 @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4326]) ).
thf(4690,plain,
! [SV876: $i,SV291: $i,SV1819: $i,SV1421: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1819 ) @ SV291 ) @ SV876 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV291 @ SV876 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4691,plain,
! [SV877: $i,SV1820: $i,SV292: $i,SV1422: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1422 @ tc_bool ) ) @ SV292 ) @ SV1820 ) @ SV877 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV292 @ SV877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4328]) ).
thf(4692,plain,
! [SV1423: $i,SV293: $i,SV878: $i] :
( ( ( c_lessequals @ SV878 @ ( c_Set_Oimage @ SV293 @ SV878 @ SV1423 @ SV1423 ) @ ( tc_fun @ SV1423 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV878 @ SV1423 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV293 @ SV878 @ SV1423 @ SV1423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4329]) ).
thf(4693,plain,
! [SV2026: $i,SV1821: $i,SV1424: $i,SV879: $i,SV294: $i] :
( ( ( c_Fun_Oinj__on @ SV294 @ SV879 @ SV1424 @ SV1821 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV2026 ) @ SV879 ) @ SV1424 @ SV1821 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4694,plain,
! [SV2027: $i,SV1822: $i,SV1425: $i,SV880: $i,SV295: $i] :
( ( ( c_Fun_Oinj__on @ SV295 @ SV880 @ SV1425 @ SV1822 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1425 @ tc_bool ) ) @ SV880 ) @ SV2027 ) @ SV1425 @ SV1822 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4331]) ).
thf(4695,plain,
! [SV2028: $i,SV1823: $i,SV1426: $i,SV881: $i,SV296: $i] :
( ( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SV1823 ) @ SV2028 @ ( tc_fun @ SV1426 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SV2028 @ SV1426 @ SV1823 ) @ ( tc_fun @ SV1823 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SV1823 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4332]) ).
thf(4696,plain,
! [SV1824: $i,SV883: $i,SV1427: $i,SV299: $i] :
( ( ( c_lessequals @ SV299 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV883 ) @ SV1824 ) @ ( tc_fun @ SV1427 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV299 @ SV883 @ ( tc_fun @ SV1427 @ tc_bool ) ) @ SV1824 @ ( tc_fun @ SV1427 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4333]) ).
thf(4697,plain,
! [SV1825: $i,SV884: $i,SV1428: $i,SV300: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV300 @ SV1428 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1825 @ ( tc_fun @ SV884 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV300 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV1428 ) @ SV1825 ) @ ( tc_fun @ SV884 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4698,plain,
! [SV1826: $i,SV1431: $i,SV887: $i,SV303: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SV1431 ) @ SV1826 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV887 @ SV1431 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4337]) ).
thf(4699,plain,
! [SV1827: $i,SV1432: $i,SV888: $i,SV304: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SV1432 ) @ SV1827 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV888 @ SV1827 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4700,plain,
! [SV2030: $i,SV1829: $i,SV1436: $i,SV892: $i,SV308: $i] :
( ( ( ~ ( class_HOL_Oord @ SV308 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SV1829 @ SV1436 ) @ SV308 )
| ~ ( c_lessequals @ SV892 @ SV1829 @ ( tc_fun @ SV2030 @ SV308 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4342]) ).
thf(4701,plain,
! [SV1437: $i,SV1830: $i,SV893: $i,SV309: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1830 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1437 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV1437 ) @ SV1830 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4343]) ).
thf(4702,plain,
! [SV1438: $i,SV1831: $i,SV894: $i,SV310: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1831 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SV1438 ) @ SV1831 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4344]) ).
thf(4703,plain,
! [SV1439: $i,SV1832: $i,SV895: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ SV1832 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV311 ) @ SV895 ) @ ( c_Set_Oinsert @ SV1439 @ SV1832 @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4345]) ).
thf(4704,plain,
! [SV1440: $i,SV1833: $i,SV896: $i,SV312: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ SV1833 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV312 ) @ SV896 ) @ ( c_Set_Oinsert @ SV1440 @ SV1833 @ SV312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4346]) ).
thf(4705,plain,
! [SV1441: $i,SV1834: $i,SV897: $i,SV313: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1834 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1834 @ SV1441 @ ( tc_fun @ SV313 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4347]) ).
thf(4706,plain,
! [SV898: $i,SV314: $i,SV1442: $i,SV1835: $i] :
( ( ( ~ ( c_lessequals @ SV1835 @ SV1442 @ ( tc_fun @ SV314 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1835 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4348]) ).
thf(4707,plain,
! [SV1443: $i,SV1836: $i,SV899: $i,SV315: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1836 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1836 @ SV1443 @ ( tc_fun @ SV315 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(4708,plain,
! [SV1444: $i,SV1837: $i,SV900: $i,SV316: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1837 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1837 @ SV1444 @ ( tc_fun @ SV316 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4709,plain,
! [SV1838: $i,SV1445: $i,SV901: $i,SV317: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ SV1445 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV317 ) @ SV901 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV317 @ tc_bool ) ) @ SV1445 ) @ SV1838 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4351]) ).
thf(4710,plain,
! [SV1446: $i,SV1839: $i,SV902: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ SV1839 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV318 ) @ SV902 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV1446 ) @ SV1839 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4352]) ).
thf(4711,plain,
! [SV2031: $i,SV1840: $i,SV1447: $i,SV903: $i,SV319: $i] :
( ( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SV903 @ SV1447 @ SV1840 ) @ SV2031 )
= ( hAPP @ SV319 @ SV2031 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1447 ) @ SV2031 ) @ SV903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4353]) ).
thf(4712,plain,
! [SV1448: $i,SV320: $i,SV1841: $i,SV904: $i] :
( ( ( SV904 = SV1841 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ ( c_Set_Oinsert @ SV1841 @ SV1448 @ SV320 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4354]) ).
thf(4713,plain,
! [SV1449: $i,SV1842: $i,SV905: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1842 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV1842 ) @ SV1449 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4355]) ).
thf(4714,plain,
! [SV2120: $i,SV2032: $i,SV1843: $i,SV1450: $i,SV906: $i,SV322: $i] :
( ( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SV1450 @ SV1843 @ SV2032 ) @ SV2120 )
= ( hAPP @ SV906 @ SV2120 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1843 ) @ SV2120 ) @ SV1450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4356]) ).
thf(4715,plain,
! [SV1844: $i,SV1451: $i,SV908: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ SV1451 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ ( c_HOL_Ominus__class_Ominus @ SV1844 @ SV1451 @ ( tc_fun @ SV324 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4357]) ).
thf(4716,plain,
! [SV1845: $i,SV1452: $i,SV909: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ ( c_HOL_Ominus__class_Ominus @ SV1452 @ SV1845 @ ( tc_fun @ SV325 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV325 ) @ SV909 ) @ SV1452 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4358]) ).
thf(4717,plain,
! [SV2121: $i,SV2033: $i,SV1846: $i,SV1453: $i,SV910: $i,SV326: $i] :
( ( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SV910 @ SV1453 @ SV1846 @ SV2033 ) @ SV2121 )
= ( hAPP @ SV326 @ SV2121 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1846 ) @ SV2121 ) @ SV1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(4718,plain,
! [SV1454: $i,SV1847: $i,SV911: $i,SV327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1847 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1847 @ SV1454 @ ( tc_fun @ SV327 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4360]) ).
thf(4719,plain,
! [SV1458: $i,SV1848: $i,SV915: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV331 @ tc_bool ) ) @ SV1848 ) @ SV1458 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV331 ) @ SV915 ) @ SV1458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4361]) ).
thf(4720,plain,
! [SV1849: $i,SV1459: $i,SV916: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV332 @ tc_bool ) ) @ SV1459 ) @ SV1849 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV332 ) @ SV916 ) @ SV1459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4362]) ).
thf(4721,plain,
! [SV1462: $i,SV1850: $i,SV919: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1850 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1462 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ ( c_HOL_Ominus__class_Ominus @ SV1462 @ SV1850 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(4722,plain,
! [SV1463: $i,SV1851: $i,SV920: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1851 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1463 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ ( c_HOL_Ominus__class_Ominus @ SV1463 @ SV1851 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(4723,plain,
! [SV2122: $i,SV2034: $i,SV1852: $i,SV1464: $i,SV921: $i,SV337: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SV2034 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SV2122 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2034 ) @ SV2122 ) @ SV1464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(4724,plain,
! [SV2123: $i,SV2035: $i,SV1853: $i,SV1465: $i,SV922: $i,SV338: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SV2035 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SV2123 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2035 ) @ SV2123 ) @ SV1465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(4725,plain,
! [SV2036: $i,SV1854: $i,SV1466: $i,SV923: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SV923 ) @ ( c_Set_Ovimage @ SV1466 @ SV1854 @ SV339 @ SV2036 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2036 ) @ ( hAPP @ SV1466 @ SV923 ) ) @ SV1854 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4369]) ).
thf(4726,plain,
! [SV2037: $i,SV1855: $i,SV1467: $i,SV924: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SV924 ) @ ( c_Set_Ovimage @ SV1467 @ SV1855 @ SV340 @ SV2037 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2037 ) @ ( hAPP @ SV1467 @ SV924 ) ) @ SV1855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4370]) ).
thf(4727,plain,
! [SV2038: $i,SV1856: $i,SV1468: $i,SV925: $i,SV341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SV925 ) @ ( c_Set_Ovimage @ SV1468 @ SV1856 @ SV341 @ SV2038 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2038 ) @ ( hAPP @ SV1468 @ SV925 ) ) @ SV1856 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4371]) ).
thf(4728,plain,
! [SV2039: $i,SV1857: $i,SV1469: $i,SV926: $i,SV342: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SV926 @ SV1469 ) ) @ SV1857 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2039 ) @ SV1469 ) @ ( c_Set_Ovimage @ SV926 @ SV1857 @ SV2039 @ SV342 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4372]) ).
thf(4729,plain,
! [SV2040: $i,SV1858: $i,SV1470: $i,SV927: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SV927 @ SV1470 ) ) @ SV1858 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2040 ) @ SV1470 ) @ ( c_Set_Ovimage @ SV927 @ SV1858 @ SV2040 @ SV343 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(4730,plain,
! [SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY5985: $i,SY5986: $i,SY5987: $i,SY5988: $i,SY5989: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SY5985 @ SY5986 @ SY5987 @ SY5988 @ SY5989 @ SV2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4731,plain,
! [SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY5990: $i,SY5991: $i,SY5992: $i,SY5993: $i,SY5994: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SY5990 @ SY5991 @ SY5992 @ SY5993 @ SY5994 @ SV2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4375]) ).
thf(4732,plain,
! [SV2126: $i,SV2043: $i,SV1861: $i,SV1474: $i,SV931: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SV2043 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SV2126 ) @ SV2043 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SV2126 ) @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4733,plain,
! [SV2127: $i,SV2044: $i,SV1862: $i,SV1475: $i,SV932: $i,SV348: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SV2044 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SV2127 ) @ SV2044 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SV2127 ) @ SV348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4378]) ).
thf(4734,plain,
! [SV2045: $i,SV1863: $i,SV1476: $i,SV933: $i,SV349: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SV933 ) @ SV1476 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1863 ) @ ( hAPP @ SV2045 @ SV933 ) ) @ ( c_Set_Oimage @ SV2045 @ SV1476 @ SV349 @ SV1863 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4379]) ).
thf(4735,plain,
! [SV353: $i,SV1480: $i,SV1866: $i,SV937: $i] :
( ( ( ~ ( c_lessequals @ SV937 @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1480 ) @ SV353 ) @ SV1866 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SV1480 ) @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4380]) ).
thf(4736,plain,
! [SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY5995: $i,SY5996: $i,SY5997: $i,SY5998: $i,SY5999: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SY5995 @ SY5996 @ SY5997 @ SV357 @ SY5998 @ SY5999 @ SV2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(4737,plain,
! [SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY6000: $i,SY6001: $i,SY6002: $i,SY6003: $i,SY6004: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SY6000 @ SY6001 @ SV358 @ SY6002 @ SY6003 @ SY6004 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(4738,plain,
! [SV2130: $i,SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY6005: $i,SY6006: $i,SY6007: $i,SY6008: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SY6005 @ SY6006 @ SY6007 @ SV1486 @ SV1869 @ SY6008 @ SV2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4739,plain,
! [SV2131: $i,SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY6009: $i,SY6010: $i,SY6011: $i,SY6012: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SY6009 @ SY6010 @ SV1487 @ SY6011 @ SY6012 @ SV1870 @ SV2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(4740,plain,
! [SV1488: $i,SV945: $i,SV1871: $i,SV361: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV1871 @ SV945 @ SV1488 ) @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV945 @ ( tc_fun @ SV1488 @ tc_bool ) ) @ SV1488 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4387]) ).
thf(4741,plain,
! [SV946: $i,SV1872: $i,SV1489: $i,SV362: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ SV1489 @ ( tc_fun @ SV1872 @ tc_bool ) ) @ SV1872 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV362 @ ( c_Set_Oinsert @ SV946 @ SV1489 @ SV1872 ) @ ( tc_fun @ SV1872 @ tc_bool ) ) @ SV1872 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4742,plain,
! [SV2132: $i,SV2050: $i,SV1873: $i,SV1492: $i,SV949: $i,SV365: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV365 @ SV949 @ SV1492 @ SV1873 @ SV2050 ) @ SV2132 @ SV2050 @ SV1873 )
= ( c_Set_Oimage @ SV365 @ ( c_Set_Oimage @ SV949 @ SV2132 @ SV2050 @ SV1492 ) @ SV1492 @ SV1873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4389]) ).
thf(4743,plain,
! [SV1493: $i,SV950: $i,SV367: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1493 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 @ SV1493 @ SV367 @ SV367 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1493 @ SV367 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4744,plain,
! [SV1874: $i,SV1494: $i,SV953: $i,SV370: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV370 )
= $false )
| ( ( ( c_lessequals @ SV953 @ SV1494 @ SV370 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SV1874 ) @ SV953 ) @ SV1494 @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(4745,plain,
! [SV1875: $i,SV1495: $i,SV954: $i,SV371: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV371 )
= $false )
| ( ( ( c_lessequals @ SV954 @ SV1495 @ SV371 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SV1875 ) @ SV1495 @ SV371 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(4746,plain,
! [SV1876: $i,SV1496: $i,SV955: $i,SV372: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV372 )
= $false )
| ( ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SV1496 ) @ SV1876 ) @ SV372 )
| ~ ( c_lessequals @ SV955 @ SV1876 @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4393]) ).
thf(4747,plain,
! [SV1877: $i,SV1497: $i,SV956: $i,SV373: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV373 )
= $false )
| ( ( ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SV1497 ) @ SV1877 ) @ SV373 )
| ~ ( c_lessequals @ SV956 @ SV1497 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4394]) ).
thf(4748,plain,
! [SV1878: $i,SV1498: $i,SV957: $i,SV374: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV374 )
= $false )
| ( ( ( c_lessequals @ SV957 @ SV1498 @ SV374 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SV1878 ) @ SV957 ) @ SV1498 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4395]) ).
thf(4749,plain,
! [SV1879: $i,SV1499: $i,SV958: $i,SV375: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV375 )
= $false )
| ( ( ( c_lessequals @ SV958 @ SV1499 @ SV375 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SV1879 ) @ SV1499 @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4750,plain,
! [SV959: $i,SV1880: $i,SV376: $i,SV1500: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1500 @ tc_bool ) ) @ SV376 ) @ SV1880 ) @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV376 @ SV959 @ ( tc_fun @ SV1500 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4397]) ).
thf(4751,plain,
! [SV960: $i,SV377: $i,SV1881: $i,SV1501: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1501 @ tc_bool ) ) @ SV1881 ) @ SV377 ) @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV377 @ SV960 @ ( tc_fun @ SV1501 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4398]) ).
thf(4752,plain,
! [SV1882: $i,SV1503: $i,SV962: $i,SV379: $i] :
( ( ( class_Orderings_Oorder @ SV379 )
= $false )
| ( ( ( c_lessequals @ SV962 @ SV1503 @ SV379 )
| ~ ( c_lessequals @ SV962 @ SV1882 @ SV379 )
| ~ ( c_lessequals @ SV1882 @ SV1503 @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4753,plain,
! [SV1883: $i,SV1504: $i,SV963: $i,SV380: $i] :
( ( ( class_Orderings_Oorder @ SV380 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
| ~ ( c_lessequals @ SV963 @ SV1883 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(4754,plain,
! [SV1884: $i,SV1505: $i,SV964: $i,SV381: $i] :
( ( ( class_Orderings_Oorder @ SV381 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
| ~ ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 )
| ~ ( c_lessequals @ SV1884 @ SV1505 @ SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(4755,plain,
! [SV1885: $i,SV1506: $i,SV965: $i,SV382: $i] :
( ( ( class_Orderings_Opreorder @ SV382 )
= $false )
| ( ( ( c_lessequals @ SV965 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV1885 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV965 @ SV1885 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4756,plain,
! [SV385: $i,SV1507: $i,SV968: $i,SV1886: $i] :
( ( ( ~ ( c_lessequals @ SV1886 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV385 @ SV1886 @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4404]) ).
thf(4757,plain,
! [SV2051: $i,SV1887: $i,SV1508: $i,SV969: $i,SV386: $i] :
( ( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SV1887 )
= $true )
| ( ( ~ ( c_lessequals @ SV969 @ SV2051 @ ( tc_fun @ SV1508 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV386 @ SV2051 @ SV1508 @ SV1887 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4405]) ).
thf(4758,plain,
! [SV1888: $i,SV387: $i,SV970: $i,SV1509: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1509 @ SV970 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1509 @ SV387 @ ( tc_fun @ SV1888 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4759,plain,
! [SV390: $i,SV973: $i,SV1510: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1510 @ SV973 )
= $false )
| ( ( ~ ( c_lessequals @ SV390 @ SV1510 @ ( tc_fun @ SV973 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV390 @ SV973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4760,plain,
! [SV391: $i,SV1511: $i,SV974: $i,SV1889: $i] :
( ( ( ~ ( c_lessequals @ SV1889 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV391 @ SV1889 @ ( tc_fun @ SV1511 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4408]) ).
thf(4761,plain,
! [SV392: $i,SV1512: $i,SV975: $i,SV1890: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1890 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV392 @ SV1890 @ ( tc_fun @ SV1512 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(4762,plain,
! [SV976: $i,SV1891: $i,SV393: $i,SV1513: $i] :
( ( ( ~ ( c_lessequals @ SV1513 @ SV393 @ ( tc_fun @ SV1891 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1513 @ SV976 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4410]) ).
thf(4763,plain,
! [SV977: $i,SV1514: $i,SV394: $i] :
( ( ( c_lessequals @ SV394 @ SV1514 @ ( tc_fun @ SV977 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1514 @ SV977 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV394 @ SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4764,plain,
! [SV1892: $i,SV1515: $i,SV978: $i,SV395: $i] :
( ( ( class_Orderings_Opreorder @ SV395 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
| ~ ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 )
| ~ ( c_lessequals @ SV978 @ SV1892 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4412]) ).
thf(4765,plain,
! [SV1893: $i,SV1516: $i,SV979: $i,SV396: $i] :
( ( ( class_Orderings_Opreorder @ SV396 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
| ~ ( c_lessequals @ SV1893 @ SV1516 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4413]) ).
thf(4766,plain,
! [SV2052: $i,SV1894: $i,SV1517: $i,SV981: $i,SV398: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV1894 ) @ SV2052 ) @ ( tc_fun @ SV398 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1517 @ SV2052 @ ( tc_fun @ SV398 @ tc_bool ) )
| ~ ( c_lessequals @ SV981 @ SV1894 @ ( tc_fun @ SV398 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4414]) ).
thf(4767,plain,
! [SV2133: $i,SV2053: $i,SV1897: $i,SV1520: $i,SV985: $i,SV402: $i] :
( ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4415]) ).
thf(4768,plain,
! [SV2134: $i,SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY6013: $i,SY6014: $i,SY6015: $i,SY6016: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SY6013 @ SY6014 @ SY6015 @ SY6016 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4416]) ).
thf(4769,plain,
! [SV2135: $i,SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY6017: $i,SY6018: $i,SY6019: $i,SY6020: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SY6017 @ SY6018 @ SY6019 @ SY6020 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4417]) ).
thf(4770,plain,
! [SV1523: $i,SV405: $i,SV988: $i,SV1900: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1900 @ SV988 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SV1523 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SV1523 ) @ ( c_Collect @ SV1900 @ SV405 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4418]) ).
thf(4771,plain,
! [SV1524: $i,SV989: $i,SV406: $i] :
( ( ( c_lessequals @ SV406 @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) @ ( tc_fun @ SV1524 @ tc_bool ) )
= $false )
| ( ( SV406
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) )
= $true )
| ( ( SV406
= ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1524 @ tc_bool ) ) @ SV1524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4419]) ).
thf(4772,plain,
! [SV2058: $i,SV1904: $i,SV1528: $i,SV993: $i,SV410: $i] :
( ( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SV993 @ SV1528 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV993 @ SV410 @ SV1904 @ SV2058 ) @ SV1528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4422]) ).
thf(4773,plain,
! [SV2059: $i,SV1905: $i,SV1529: $i,SV994: $i,SV411: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SV994 @ SV1529 @ SV1905 ) @ SV2059 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV994 @ ( hAPP @ SV411 @ SV2059 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4423]) ).
thf(4774,plain,
! [SV1530: $i,SV412: $i,SV995: $i] :
( ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) )
| ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4424]) ).
thf(4775,plain,
! [SV2136: $i,SV2060: $i,SV1906: $i,SV1531: $i,SV996: $i,SV413: $i] :
( ( ! [SY6021: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SY6021 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SY6021 @ SV2136 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
| ~ ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SY6021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4425]) ).
thf(4776,plain,
! [SV414: $i,SV997: $i,SV1907: $i,SV1532: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1532 @ SV1907 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV997 @ SV1907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SV1532 ) @ SV1907 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4426]) ).
thf(4777,plain,
! [SV1533: $i,SV1908: $i,SV415: $i,SV998: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV998 ) @ SV415 ) @ SV1908 ) )
= $false )
| ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV415 @ SV998 @ SV1533 ) @ SV1908 @ SV1533 @ SV998 )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1533 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(4778,plain,
! [SV1534: $i,SV1909: $i,SV999: $i,SV416: $i] :
( ( ( ~ ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SV1909 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1534 @ SV416 @ ( tc_fun @ SV1909 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SV1534 @ ( tc_fun @ SV1909 @ tc_bool ) ) @ ( tc_fun @ SV1909 @ tc_bool ) )
= SV1534 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4428]) ).
thf(4779,plain,
! [SV2061: $i,SV1910: $i,SV1535: $i,SV1000: $i,SV417: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SV1000 @ SV1535 @ SV1910 ) @ ( c_Set_Oimage @ SV417 @ SV2061 @ SV1535 @ SV1910 ) @ ( tc_fun @ SV1910 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1000 @ SV2061 @ ( tc_fun @ SV1535 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4429]) ).
thf(4780,plain,
! [SV2062: $i,SV1911: $i,SV1536: $i,SV1001: $i,SV418: $i] :
( ( ( ~ ( c_lessequals @ SV418 @ SV1001 @ ( tc_fun @ SV1536 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV1911 @ SV418 @ SV1536 @ SV2062 ) @ ( c_Set_Oimage @ SV1911 @ SV1001 @ SV1536 @ SV2062 ) @ ( tc_fun @ SV2062 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(4781,plain,
! [SV420: $i,SV1537: $i,SV1912: $i,SV1003: $i] :
( ( ( c_lessequals @ SV1003 @ SV1912 @ ( tc_fun @ SV1537 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV420 @ SV1003 @ SV1537 ) @ ( c_Set_Oinsert @ SV420 @ SV1912 @ SV1537 ) @ ( tc_fun @ SV1537 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4431]) ).
thf(4782,plain,
! [SV1913: $i,SV1004: $i,SV421: $i,SV1538: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV1538 @ SV421 @ SV1004 @ SV1913 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV1538 @ SV421 @ SV1004 @ SV1913 ) @ SV1913 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4432]) ).
thf(4783,plain,
! [SV422: $i,SV1539: $i,SV1005: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1005 @ SV1539 @ SV422 )
= $true )
| ( ( ( SV1539 = SV1005 )
| ~ ( c_lessequals @ SV1005 @ SV1539 @ SV422 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV422 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4784,plain,
! [SV423: $i,SV1540: $i,SV1006: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1006 @ SV1540 @ SV423 )
= $true )
| ( ( ~ ( c_lessequals @ SV1006 @ SV1540 @ SV423 )
| ( SV1540 = SV1006 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4434]) ).
thf(4785,plain,
! [SV1541: $i,SV1007: $i,SV424: $i] :
( ( ( c_lessequals @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) )
= $false )
| ( ( SV424 = SV1007 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV424 @ SV1007 @ ( tc_fun @ SV1541 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4435]) ).
thf(4786,plain,
! [SV425: $i,SV1542: $i,SV1008: $i] :
( ( ( SV1008 = SV1542 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1008 @ SV1542 @ SV425 )
| ~ ( c_lessequals @ SV1008 @ SV1542 @ SV425 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4436]) ).
thf(4787,plain,
! [SV426: $i,SV1543: $i,SV1009: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV1543 @ SV426 )
= $true )
| ( ( ( SV1009 = SV1543 )
| ~ ( c_lessequals @ SV1009 @ SV1543 @ SV426 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV426 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(4788,plain,
! [SV1544: $i,SV1010: $i,SV427: $i] :
( ( ( c_lessequals @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1010 @ ( tc_fun @ SV1544 @ tc_bool ) )
= $true )
| ( ( SV427 = SV1010 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4438]) ).
thf(4789,plain,
! [SV428: $i,SV1545: $i,SV1011: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1545 @ SV428 )
= $true )
| ( ( ( SV1011 = SV1545 )
| ~ ( c_lessequals @ SV1011 @ SV1545 @ SV428 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(4790,plain,
! [SV429: $i,SV1546: $i,SV1012: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1012 @ SV1546 @ SV429 )
= $true )
| ( ( ~ ( c_lessequals @ SV1012 @ SV1546 @ SV429 )
| ( SV1012 = SV1546 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(4791,plain,
! [SV430: $i,SV1547: $i,SV1013: $i] :
( ( ( SV1013 = SV1547 )
= $true )
| ( ( ~ ( c_lessequals @ SV1013 @ SV1547 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1013 @ SV1547 @ SV430 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4441]) ).
thf(4792,plain,
! [SV431: $i,SV1548: $i,SV1014: $i] :
( ( ( SV1014 = SV1548 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1548 @ SV431 )
| ~ ( c_lessequals @ SV1014 @ SV1548 @ SV431 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4442]) ).
thf(4793,plain,
! [SV432: $i,SV1549: $i,SV1015: $i] :
( ( ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1549 @ SV432 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(4794,plain,
! [SV435: $i,SV1551: $i,SV1018: $i] :
( ( ( c_lessequals @ SV1018 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1551 @ SV435 ) @ SV435 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SV1018 ) @ SV1551 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(4795,plain,
! [SV2137: $i,SV2064: $i,SV1915: $i,SV1552: $i,SV1019: $i,SV436: $i] :
( ( ! [SY6022: $i] :
( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SV1019 @ SV1552 @ SV1915 @ SV2064 ) @ SV2137 @ SV1552 @ SV2064 @ SY6022 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SV1019 @ SV2137 @ SV1915 @ SV2064 @ SY6022 ) @ SV1552 @ SV1915 @ SY6022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4446]) ).
thf(4796,plain,
! [SV437: $i,SV1553: $i,SV1020: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1020 @ SV1553 @ SV437 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1553 @ SV1020 @ SV437 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV437 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(4797,plain,
! [SV438: $i,SV1554: $i,SV1021: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1021 @ SV1554 @ SV438 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1021 @ SV438 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4448]) ).
thf(4798,plain,
! [SV439: $i,SV1555: $i,SV1022: $i] :
( ( ( c_lessequals @ SV1022 @ SV1555 @ SV439 )
= $true )
| ( ( c_lessequals @ SV1555 @ SV1022 @ SV439 )
= $true )
| ( ( class_Orderings_Olinorder @ SV439 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4799,plain,
! [SV440: $i,SV1556: $i,SV1023: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1023 @ SV1556 @ SV440 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1023 @ SV440 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4450]) ).
thf(4800,plain,
! [SV441: $i,SV1557: $i,SV1024: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1024 @ SV1557 @ SV441 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV1024 @ SV441 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(4801,plain,
! [SV2065: $i,SV1916: $i,SV1558: $i,SV1025: $i,SV442: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SV1025 ) @ SV1558 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1916 ) @ ( hAPP @ SV2065 @ SV1025 ) ) @ ( c_Set_Oimage @ SV2065 @ SV1558 @ SV442 @ SV1916 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4452]) ).
thf(4802,plain,
! [SV2066: $i,SV1917: $i,SV1559: $i,SV1026: $i,SV443: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SV1026 @ SV1559 ) ) @ ( c_Set_Oimage @ SV1026 @ SV1917 @ SV2066 @ SV443 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2066 ) @ SV1559 ) @ SV1917 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4453]) ).
thf(4803,plain,
! [SV2067: $i,SV1918: $i,SV1560: $i,SV1027: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SV1027 @ SV1560 ) ) @ ( c_Set_Oimage @ SV1027 @ SV1918 @ SV2067 @ SV444 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV1560 ) @ SV1918 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(4804,plain,
! [SV445: $i,SV1028: $i] :
( ( ( SV1028
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1028 @ SV445 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1028 @ SV445 ) ) @ SV1028 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(4805,plain,
! [SV446: $i,SV1029: $i] :
( ( ( SV1029
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1029 @ SV446 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1029 @ SV446 ) ) @ SV1029 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4456]) ).
thf(4806,plain,
! [SV2068: $i,SV1919: $i,SV1562: $i,SV1031: $i,SV448: $i] :
( ( ( ( hAPP @ SV448 @ SV1031 )
= SV1562 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1919 ) @ SV1031 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SV1562 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2068 @ tc_bool ) ) @ SV2068 ) @ SV1919 @ SV2068 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4807,plain,
! [SV2138: $i,SV2069: $i,SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ! [SY6023: $i,SY6024: $i,SY6025: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SV2138 @ SY6023 @ SY6024 @ SY6025 @ SV1571 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4462]) ).
thf(4808,plain,
! [SV2139: $i,SV2070: $i,SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ! [SY6026: $i,SY6027: $i,SY6028: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SV2139 @ SY6026 @ SY6027 @ SV1572 @ SY6028 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4463]) ).
thf(4809,plain,
! [SV2072: $i,SV1928: $i,SV1576: $i,SV1060: $i,SV480: $i] :
( ( ( SV480 = SV1060 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV1576 @ SV1060 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1928 @ tc_bool ) ) @ SV480 @ SV1928 @ SV2072 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(4810,plain,
! [SV499: $i,SV1934: $i,SV1588: $i,SV1079: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1934 @ SV499 ) ) @ SV1934 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1934 @ SV1588 @ t_a ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4811,plain,
! [SV500: $i,SV1589: $i,SV1080: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1080 ) @ SV1589 ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SV1589 ) @ t_a ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SV1080 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4812,plain,
! [SV1081: $i,SV501: $i,SV1590: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1590 ) @ SV501 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 @ SV501 @ SV1081 ) @ SV1590 @ t_a )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV501 @ SV1081 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4813,plain,
! [SV1935: $i,SV502: $i,SV1591: $i,SV1082: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4470]) ).
thf(4814,plain,
! [SV509: $i,SV1593: $i,SV1088: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1088 ) @ SV1593 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV509 @ SV1593 ) ) @ SV1593 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV509 @ SV1088 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4472]) ).
thf(4815,plain,
! [SV518: $i,SV1096: $i,SV1597: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1597 ) @ SV1096 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1597 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV518 @ SV1096 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4476]) ).
thf(4816,plain,
! [SV1102: $i,SV524: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV524 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ SV1102 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV524 @ SV1102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4817,plain,
! [SV2073: $i,SV1936: $i,SV1599: $i,SV1112: $i,SV535: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV535 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4479]) ).
thf(4818,plain,
! [SV2074: $i,SV1937: $i,SV1600: $i,SV1113: $i,SV536: $i] :
( ( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 )
!= ( c_Set_Oinsert @ SV1937 @ ( c_Set_Oinsert @ SV2074 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 ) )
= $true )
| ( ( ( SV536 = SV2074 )
| ( SV536 = SV1937 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4480]) ).
thf(4819,plain,
! [SV2075: $i,SV1938: $i,SV1601: $i,SV1114: $i,SV537: $i] :
( ( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 )
!= ( c_Set_Oinsert @ SV1938 @ ( c_Set_Oinsert @ SV2075 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 ) )
= $true )
| ( ( ( SV1114 = SV1938 )
| ( SV1114 = SV2075 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4481]) ).
thf(4820,plain,
! [SV2076: $i,SV1939: $i,SV1602: $i,SV1115: $i,SV538: $i] :
( ( ( ( hAPP @ SV538 @ SV1115 )
!= ( hAPP @ SV538 @ SV1602 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 @ SV2076 )
| ( SV1115 = SV1602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(4821,plain,
! [SV2077: $i,SV1940: $i,SV1603: $i,SV1116: $i,SV539: $i] :
( ( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 )
!= ( c_Set_Oinsert @ SV1940 @ ( c_Set_Oinsert @ SV2077 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 ) )
= $true )
| ( ( ( SV539 = SV2077 )
| ( SV1116 = SV2077 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(4822,plain,
! [SV2078: $i,SV1941: $i,SV1604: $i,SV1117: $i,SV540: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SV1941 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
= $true )
| ( ( ( ( hAPP @ SV1117 @ SV2078 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SV2078 ) @ SV540 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4484]) ).
thf(4823,plain,
! [SV2079: $i,SV1942: $i,SV1605: $i,SV1118: $i,SV541: $i] :
( ( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 )
!= ( c_Set_Oinsert @ SV1942 @ ( c_Set_Oinsert @ SV2079 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 ) )
= $true )
| ( ( ( SV1118 = SV1942 )
| ( SV541 = SV1942 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4485]) ).
thf(4824,plain,
! [SV1943: $i,SV1606: $i,SV1119: $i,SV542: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV542 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SV1606 @ SV1943 @ SV542 ) )
| ( SV1606 = SV1943 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4825,plain,
! [SV1944: $i,SV1607: $i,SV1120: $i,SV543: $i] :
( ( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SV1607 )
= ( c_Set_Oinsert @ SV543 @ SV1944 @ SV1607 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1944 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1120 ) )
| ( SV1120 = SV1944 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4487]) ).
thf(4826,plain,
! [SV1608: $i,SV1121: $i,SV544: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SV1121 ) @ SV1608 )
!= ( c_Orderings_Obot__class_Obot @ SV544 ) )
= $true )
| ( ( SV1608
= ( c_Orderings_Obot__class_Obot @ SV544 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV544 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(4827,plain,
! [SV1945: $i,SV1609: $i,SV1122: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1945 ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SV1945 ) @ SV1609 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4828,plain,
! [SV1946: $i,SV1611: $i,SV1124: $i,SV547: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ SV1611 ) ) @ SV1946 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1124 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV547 @ tc_bool ) ) @ SV1611 ) @ SV1946 ) ) )
= $false )
| ( ( c_lessequals @ SV1946 @ SV1124 @ ( tc_fun @ SV547 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4829,plain,
! [SV2080: $i,SV1947: $i,SV1613: $i,SV1126: $i,SV549: $i] :
( ( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SV1947 )
!= ( c_Set_Oimage @ SV549 @ SV2080 @ SV1613 @ SV1947 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SV1947 )
| ( SV1126 = SV2080 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4493]) ).
thf(4830,plain,
! [SV2081: $i,SV1948: $i,SV1614: $i,SV1127: $i,SV550: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV550 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(4831,plain,
! [SV1615: $i,SV1128: $i,SV551: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SV1128 ) @ SV1615 )
!= ( c_Orderings_Otop__class_Otop @ SV551 ) )
= $true )
| ( ( SV1128
= ( c_Orderings_Otop__class_Otop @ SV551 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV551 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(4832,plain,
! [SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY6029: $i,SY6030: $i,SY6031: $i,SY6032: $i,SY6033: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SY6029 @ SY6030 @ SY6031 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SY6032 @ SY6030 @ SY6033 ) @ SV2140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4498]) ).
thf(4833,plain,
! [SV2083: $i,SV1950: $i,SV1619: $i,SV1132: $i,SV555: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4834,plain,
! [SV1951: $i,SV1621: $i,SV1134: $i,SV558: $i] :
( ( ( ( hAPP @ SV558 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__1__1 @ SV1134 @ SV558 @ SV1621 @ SV1951 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1134 @ SV558 @ SV1621 @ ( tc_fun @ SV1951 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4501]) ).
thf(4835,plain,
! [SV2084: $i,SV1952: $i,SV1622: $i,SV1135: $i,SV559: $i] :
( ( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV1952 @ SV2084 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4502]) ).
thf(4836,plain,
! [SV1623: $i,SV1136: $i,SV560: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SV1136 ) @ SV1623 )
!= SV1136 )
= $true )
| ( ( c_lessequals @ SV1136 @ SV1623 @ SV560 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV560 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4503]) ).
thf(4837,plain,
! [SV1624: $i,SV1137: $i,SV561: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SV1137 ) @ SV1624 )
!= ( c_Orderings_Obot__class_Obot @ SV561 ) )
= $true )
| ( ( SV1137
= ( c_Orderings_Obot__class_Obot @ SV561 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV561 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4838,plain,
! [SV2085: $i,SV1953: $i,SV1625: $i,SV1138: $i,SV562: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV562 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
| ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4839,plain,
! [SV2141: $i,SV2086: $i,SV1954: $i,SV1626: $i,SV1139: $i,SV563: $i] :
( ( ( ( hAPP @ SV563 @ SV1139 )
!= ( hAPP @ SV563 @ SV1626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4506]) ).
thf(4840,plain,
! [SV1955: $i,SV1627: $i,SV1140: $i,SV564: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV564 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SV1627 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SV1955 @ SV1955 @ SV564 ) )
| ( SV1140 = SV1627 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(4841,plain,
! [SV2142: $i,SV2087: $i,SV1956: $i,SV1628: $i,SV1141: $i,SV565: $i] :
( ( ( ( hAPP @ SV565 @ SV1141 )
!= ( hAPP @ SV565 @ SV1628 ) )
| ~ ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
| ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4508]) ).
thf(4842,plain,
! [SV1629: $i,SV1142: $i,SV566: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SV1142 ) @ SV1629 )
!= SV1629 )
= $true )
| ( ( c_lessequals @ SV1142 @ SV1629 @ SV566 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV566 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4843,plain,
! [SV2088: $i,SV1957: $i,SV1630: $i,SV1143: $i,SV567: $i] :
( ( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SV1957 )
!= ( c_Set_Oimage @ SV567 @ SV2088 @ SV1630 @ SV1957 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SV2088 ) @ SV1630 @ SV1957 )
| ( SV1143 = SV2088 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(4844,plain,
! [SV570: $i,SV1632: $i,SV1146: $i] :
( ( ( hBOOL @ ( hAPP @ SV1146 @ SV1632 ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) )
= ( c_Collect @ SV1146 @ SV570 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(4845,plain,
! [SV2143: $i,SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ! [SY6034: $i,SY6035: $i,SY6036: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
!= ( c_Fun_Ocomp @ SV2143 @ SY6034 @ SY6035 @ SV1958 @ SV2089 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY6036 ) )
= ( hAPP @ SV2143 @ ( hAPP @ SY6034 @ SY6036 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4513]) ).
thf(4846,plain,
! [SV2144: $i,SV2090: $i,SV1959: $i,SV1636: $i,SV1151: $i,SV575: $i] :
( ( ! [SY6037: $i] :
( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SV1959 @ SV2090 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV1959 ) @ SV2144 @ SV1959 @ SV1959 @ SV2090 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SY6037 ) )
= ( hAPP @ SV2144 @ SY6037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4515]) ).
thf(4847,plain,
! [SV2091: $i,SV1960: $i,SV1637: $i,SV1152: $i,SV576: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SV1960 @ ( tc_fun @ SV576 @ tc_bool ) ) )
= $true )
| ( ( ( ( hAPP @ SV1637 @ SV2091 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1960 ) @ SV2091 ) @ SV1152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4516]) ).
thf(4848,plain,
! [SV1961: $i,SV1638: $i,SV1153: $i,SV578: $i] :
( ( ( ( c_Set_Oimage @ SV578 @ SV1153 @ SV1638 @ SV1961 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1961 @ tc_bool ) ) )
= $false )
| ( ( SV1153
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1638 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(4849,plain,
! [SV1962: $i,SV1640: $i,SV1155: $i,SV581: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) )
= ( c_Set_Oimage @ SV1155 @ SV1640 @ SV1962 @ SV581 ) )
= $false )
| ( ( SV1640
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1962 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4518]) ).
thf(4850,plain,
! [SV1641: $i,SV1156: $i,SV582: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SV1156 ) @ SV1641 )
!= ( c_Orderings_Otop__class_Otop @ SV582 ) )
= $true )
| ( ( SV1641
= ( c_Orderings_Otop__class_Otop @ SV582 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV582 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(4851,plain,
! [SV1157: $i,SV1642: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ SV583 @ SV1642 ) )
= $false )
| ( ( ( c_Collect @ SV583 @ SV1157 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1157 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(4852,plain,
! [SV2092: $i,SV1963: $i,SV1643: $i,SV1158: $i,SV584: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV584 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
| ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SV2092 @ SV1963 @ SV584 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(4853,plain,
! [SV1964: $i,SV1644: $i,SV1159: $i,SV585: $i] :
( ( ( ( hAPP @ SV585 @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUNION__empty__conv__2__1 @ SV1159 @ SV585 @ SV1644 @ SV1964 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1964 @ tc_bool ) ) )
= $false )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1159 @ SV585 @ SV1644 @ ( tc_fun @ SV1964 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1964 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(4854,plain,
! [SV2145: $i,SV2093: $i,SV1965: $i,SV1645: $i,SV1160: $i,SV586: $i] :
( ( ( ( hAPP @ SV586 @ SV1160 )
!= ( hAPP @ SV586 @ SV1645 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4523]) ).
thf(4855,plain,
! [SV2146: $i,SV2094: $i,SV1966: $i,SV1646: $i,SV1161: $i,SV587: $i] :
( ( ( ( hAPP @ SV587 @ SV1161 )
!= ( hAPP @ SV587 @ SV1646 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4524]) ).
thf(4856,plain,
! [SV1647: $i,SV2: $i,SV1162: $i,SV1967: $i,SV588: $i] :
( ( ( ~ ( c_lessequals @ SV588 @ SV1967 @ ( tc_fun @ SV1162 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SV1647 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SV1647 ) @ ( c_Set_Oimage @ SV2 @ SV1967 @ SV1162 @ SV1647 ) @ ( tc_fun @ SV1647 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4857,plain,
! [SV1648: $i,SV1163: $i,SV589: $i,SV1968: $i,SV3: $i] :
( ( ( c_Fun_Oinj__on @ SV3 @ ( c_Set_Oinsert @ SV1968 @ SV589 @ SV1163 ) @ SV1163 @ SV1648 )
= $false )
| ( ( c_Fun_Oinj__on @ SV3 @ SV589 @ SV1163 @ SV1648 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(4858,plain,
! [SV1969: $i,SV1649: $i,SV1164: $i,SV590: $i,SV4: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1649 @ SV590 @ SV1969 @ SV4 ) @ SV4 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1164 ) @ SV1649 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(4859,plain,
! [SV1970: $i,SV5: $i,SV1165: $i,SV591: $i,SV1650: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV591 ) @ SV1165 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV5 @ SV591 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1165 @ SV5 @ SV1650 @ ( tc_fun @ SV1970 @ tc_bool ) ) @ ( tc_fun @ SV1970 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4528]) ).
thf(4860,plain,
! [SV1971: $i,SV9: $i,SV1169: $i,SV595: $i,SV1654: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1654 ) @ SV595 ) @ SV1169 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SV1169 @ SV1971 @ SV1654 @ SV1654 ) )
= $true )
| ( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SV1169 @ SV1654 ) @ SV1971 @ SV1654 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(4861,plain,
! [SV2147: $i,SV2095: $i,SV1972: $i,SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ! [SY6038: $i,SY6039: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SV2095 @ SV2147 @ SY6038 @ SY6039 @ SV1170 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4533]) ).
thf(4862,plain,
! [SV2148: $i,SV2096: $i,SV1973: $i,SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ! [SY6040: $i,SY6041: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SV2096 @ SV2148 @ SY6040 @ SV1171 @ SY6041 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4534]) ).
thf(4863,plain,
! [SV1657: $i,SV12: $i,SV598: $i,SV1172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV1657 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SV1657 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1657 @ ( tc_fun @ SV1172 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4864,plain,
! [SV1173: $i,SV13: $i,SV599: $i,SV1658: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV13 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SV1658 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV1173 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4536]) ).
thf(4865,plain,
! [SV2149: $i,SV2097: $i,SV1974: $i,SV1659: $i,SV1174: $i,SV600: $i,SV14: $i] :
( ( ! [SY6042: $i] :
( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SY6042 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SY6042 @ SV2097 ) @ SV1174 @ SV1974 @ SY6042 @ SV2097 ) )
| ~ ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
| ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SY6042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4537]) ).
thf(4866,plain,
! [SV1660: $i,SV1176: $i,SV602: $i,SV16: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1660 @ SV16 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4538]) ).
thf(4867,plain,
! [SV1177: $i,SV1975: $i,SV1661: $i,SV603: $i,SV17: $i] :
( ( ( c_Fun_Oinj__on @ SV17 @ SV603 @ SV1661 @ SV1975 )
= $false )
| ( ( c_Fun_Oinj__on @ SV17 @ ( c_HOL_Ominus__class_Ominus @ SV603 @ SV1177 @ ( tc_fun @ SV1661 @ tc_bool ) ) @ SV1661 @ SV1975 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4868,plain,
! [SV1181: $i,SV21: $i,SV607: $i,SV1665: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4869,plain,
! [SV34: $i,SV620: $i,SV1189: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1189 @ SV620 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV34 @ SV1189 @ ( tc_fun @ SV620 @ tc_bool ) ) @ SV620 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV34 @ SV620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4543]) ).
thf(4870,plain,
! [SV35: $i,SV1190: $i,SV621: $i] :
( ( ( c_Finite__Set_Ofinite @ SV621 @ SV1190 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV35 @ SV1190 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV35 @ SV621 @ ( tc_fun @ SV1190 @ tc_bool ) ) @ SV1190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4544]) ).
thf(4871,plain,
! [SV1193: $i,SV38: $i,SV1977: $i,SV624: $i,SV1672: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
| ~ ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(4872,plain,
! [SV625: $i,SV1673: $i,SV39: $i,SV1194: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1194 @ SV39 @ SV1673 ) @ SV625 ) )
= $false )
| ( ( SV1194 = SV625 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV39 @ SV625 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4873,plain,
! [SV2098: $i,SV1978: $i,SV1674: $i,SV1195: $i,SV627: $i,SV41: $i] :
( ( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1978 ) @ SV627 ) @ SV2098 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2098 @ SV41 @ SV1978 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(4874,plain,
! [SV632: $i,SV46: $i,SV1676: $i,SV1200: $i,SV1979: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1979 ) @ SV1200 ) @ SV1676 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV46 @ tc_bool ) ) @ ( hAPP @ SV632 @ SV1200 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SV1979 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1676 @ SV632 @ SV1979 @ ( tc_fun @ SV46 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4548]) ).
thf(4875,plain,
! [SV2150: $i,SV2099: $i,SV1980: $i,SV1677: $i,SV1201: $i,SV633: $i,SV47: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SV2099 @ SV2150 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2099 ) @ SV1677 ) @ SV1201 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV2099 ) @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV1980 @ SV2099 @ SV2150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4549]) ).
thf(4876,plain,
! [SV1678: $i,SV1202: $i,SV1981: $i,SV634: $i,SV48: $i] :
( ( ( c_Fun_Oinj__on @ SV48 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV634 @ SV1981 )
= $false )
| ( ( ( c_Set_Oimage @ SV48 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV634 @ tc_bool ) ) @ SV1202 ) @ SV1678 ) @ SV634 @ SV1981 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1981 @ tc_bool ) ) @ ( c_Set_Oimage @ SV48 @ SV1202 @ SV634 @ SV1981 ) ) @ ( c_Set_Oimage @ SV48 @ SV1678 @ SV634 @ SV1981 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4877,plain,
! [SV2151: $i,SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY6043: $i,SY6044: $i,SY6045: $i,SY6046: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SY6043 @ SY6044 @ SV1982 @ SY6045 @ SY6046 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4551]) ).
thf(4878,plain,
! [SV2152: $i,SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY6047: $i,SY6048: $i,SY6049: $i,SY6050: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SY6047 @ SV1983 @ SY6048 @ SY6049 @ SY6050 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4552]) ).
thf(4879,plain,
! [SV1206: $i,SV52: $i,SV638: $i] :
( ( ( c_Finite__Set_Ofinite @ SV638 @ SV52 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1206 @ SV52 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV52 @ tc_bool ) ) @ SV638 ) @ SV1206 ) @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4553]) ).
thf(4880,plain,
! [SV1207: $i,SV53: $i,SV639: $i] :
( ( ( c_Finite__Set_Ofinite @ SV639 @ SV53 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1207 @ SV53 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV53 @ tc_bool ) ) @ SV639 ) @ SV1207 ) @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4881,plain,
! [SV60: $i,SV1214: $i,SV646: $i,SV1989: $i,SV1687: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ ( hAPP @ SV1989 @ SV646 ) ) @ ( c_Set_Oimage @ SV1989 @ SV1214 @ SV60 @ SV1687 ) ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1989 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SV1687 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4882,plain,
! [SV61: $i,SV647: $i,SV1688: $i,SV1215: $i,SV1990: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1990 ) @ SV1215 ) @ SV1688 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1990 @ tc_bool ) ) @ SV1990 @ SV61 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SV1688 @ SV1990 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(4883,plain,
! [SV1689: $i,SV1216: $i,SV648: $i,SV1991: $i,SV62: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV62 @ SV1991 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV62 @ ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ SV1216 ) ) @ SV1689 )
= ( hAPP @ ( hAPP @ SV62 @ SV648 ) @ ( hAPP @ ( hAPP @ SV62 @ SV1216 ) @ SV1689 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4884,plain,
! [SV1690: $i,SV1217: $i,SV649: $i,SV1992: $i,SV63: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV63 @ SV1992 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ SV1690 ) )
= ( hAPP @ ( hAPP @ SV63 @ SV1217 ) @ ( hAPP @ ( hAPP @ SV63 @ SV649 ) @ SV1690 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4885,plain,
! [SV651: $i,SV65: $i,SV1219: $i,SV1692: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1692 @ tc_bool ) ) @ SV1219 ) @ SV65 ) @ SV651 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1219 @ SV651 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV65 @ SV651 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4564]) ).
thf(4886,plain,
! [SV654: $i,SV1993: $i,SV1222: $i,SV68: $i,SV1695: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV1695 @ SV68 @ SV1222 @ SV1993 ) @ ( c_Set_Oimage @ SV1695 @ SV654 @ SV1222 @ SV1993 ) @ ( tc_fun @ SV1993 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1695 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SV1993 ) )
= $true )
| ( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4567]) ).
thf(4887,plain,
! [SV1223: $i,SV69: $i,SV655: $i,SV1696: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1696 ) @ SV655 ) @ SV69 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1223 @ ( tc_fun @ SV1696 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SV1223 @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(4888,plain,
! [SV1224: $i,SV70: $i,SV656: $i,SV1697: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV656 ) @ SV70 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1224 @ ( tc_fun @ SV1697 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SV1224 @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4569]) ).
thf(4889,plain,
! [SV1698: $i,SV71: $i,SV657: $i,SV1225: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1225 ) @ SV657 ) @ SV71 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SV1698 @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1698 @ ( tc_fun @ SV1225 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(4890,plain,
! [SV2104: $i,SV1994: $i,SV1699: $i,SV1226: $i,SV658: $i,SV72: $i] :
( ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(4891,plain,
! [SV659: $i,SV1995: $i,SV1700: $i,SV1227: $i,SV73: $i] :
( ( ( ~ ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SV1700 @ SV1995 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1700 @ SV1995 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(4892,plain,
! [SV2105: $i,SV1996: $i,SV1701: $i,SV1228: $i,SV660: $i,SV74: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1996 ) @ SV1228 ) @ SV2105 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SV2105 @ SV1996 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(4893,plain,
! [SV661: $i,SV75: $i,SV1702: $i,SV1997: $i,SV1229: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1229 ) @ SV1997 ) @ SV1702 ) )
= $false )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV75 @ SV661 @ SV1229 ) @ SV1702 @ SV1229 @ SV661 )
= ( c_Set_Oinsert @ SV75 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV661 @ tc_bool ) ) @ SV661 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4894,plain,
! [SV2106: $i,SV1998: $i,SV1703: $i,SV1230: $i,SV662: $i,SV76: $i] :
( ( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV1230 @ SV1703 @ SV76 @ SV1998 @ SV662 @ SV2106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4575]) ).
thf(4895,plain,
! [SV2107: $i,SV1999: $i,SV1704: $i,SV1232: $i,SV664: $i,SV78: $i] :
( ( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SV1232 @ SV1704 @ SV1999 ) @ SV1999 @ SV2107 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SV1999 @ SV2107 @ SV1704 ) @ SV1232 @ SV1704 @ SV2107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4576]) ).
thf(4896,plain,
! [SV672: $i,SV1710: $i,SV1240: $i,SV86: $i] :
( ( ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1240 @ tc_bool ) ) @ SV1240 @ SV1710 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV672 @ SV1710 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SV1240 @ SV1710 ) @ SV1240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(4897,plain,
! [SV1711: $i,SV89: $i,SV1241: $i,SV675: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(4898,plain,
! [SV90: $i,SV1242: $i,SV676: $i,SV1712: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1712 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV90 @ SV1712 @ ( tc_fun @ SV1242 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4899,plain,
! [SV1713: $i,SV91: $i,SV1243: $i,SV677: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(4900,plain,
! [SV1715: $i,SV1245: $i,SV679: $i,SV93: $i,SV2001: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 ) @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 @ SV2001 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV93 @ SV1245 @ SV1715 @ SV2001 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SV1245 @ SV1715 ) @ SV1715 @ SV2001 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4584]) ).
thf(4901,plain,
! [SV99: $i,SV1720: $i,SV1250: $i,SV2003: $i,SV685: $i] :
( ( ( c_Fun_Oinj__on @ SV685 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV1250 ) @ SV1720 ) @ SV2003 @ SV99 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV99 @ tc_bool ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1720 @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV2003 @ SV99 ) ) @ ( c_Set_Oimage @ SV685 @ ( c_HOL_Ominus__class_Ominus @ SV1720 @ SV1250 @ ( tc_fun @ SV2003 @ tc_bool ) ) @ SV2003 @ SV99 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV99 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4902,plain,
! [SV102: $i,SV688: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV688 @ SV688 @ SV102 )
= $false )
| ( ( c_lessequals @ SV688 @ SV688 @ SV102 )
= $false )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(4903,plain,
! [SV104: $i,SV1253: $i,SV690: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV690 @ SV1253 @ SV104 )
= $false )
| ( ( ~ ( c_lessequals @ SV1253 @ SV690 @ SV104 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4904,plain,
! [SV106: $i,SV1255: $i,SV692: $i] :
( ( ( c_lessequals @ SV692 @ SV1255 @ SV106 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1255 @ SV692 @ SV106 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(4905,plain,
! [SV108: $i,SV1721: $i,SV1257: $i,SV694: $i] :
( ( ( ~ ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SV1721 @ SV108 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SV1721 @ SV108 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4593]) ).
thf(4906,plain,
! [SV109: $i,SV1258: $i,SV695: $i] :
( ( ( c_lessequals @ SV695 @ SV1258 @ SV109 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1258 @ SV695 @ SV109 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4594]) ).
thf(4907,plain,
! [SV698: $i,SV112: $i,SV1260: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1260 @ SV112 ) )
= $true )
| ( ( ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4596]) ).
thf(4908,plain,
! [SV123: $i,SV1270: $i,SV709: $i] :
( ( ( c_lessequals @ SV709 @ SV1270 @ SV123 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV123 ) @ SV709 ) @ SV1270 )
= SV709 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(4909,plain,
! [SV124: $i,SV710: $i,SV1271: $i] :
( ( ( c_lessequals @ SV1271 @ SV710 @ SV124 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV124 ) @ SV710 ) @ SV1271 )
= SV1271 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4602]) ).
thf(4910,plain,
! [SV711: $i,SV125: $i,SV1730: $i,SV1272: $i] :
( ( ( c_lessequals @ SV1272 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV711 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SV1272 ) @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4603]) ).
thf(4911,plain,
! [SV714: $i,SV128: $i,SV1731: $i,SV1275: $i] :
( ( ( c_lessequals @ SV1275 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV714 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SV1275 ) @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(4912,plain,
! [SV1732: $i,SV1276: $i,SV715: $i,SV129: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
= $true )
| ( ( ~ ( c_lessequals @ SV1276 @ SV1732 @ SV129 )
| ~ ( c_lessequals @ SV715 @ SV1732 @ SV129 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4605]) ).
thf(4913,plain,
! [SV1733: $i,SV1279: $i,SV718: $i,SV132: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
= $true )
| ( ( ~ ( c_lessequals @ SV1279 @ SV1733 @ SV132 )
| ~ ( c_lessequals @ SV718 @ SV1733 @ SV132 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4606]) ).
thf(4914,plain,
! [SV1734: $i,SV1280: $i,SV719: $i,SV133: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
= $true )
| ( ( ~ ( c_lessequals @ SV1280 @ SV1734 @ SV133 )
| ~ ( c_lessequals @ SV719 @ SV1734 @ SV133 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(4915,plain,
! [SV2153: $i,SV2109: $i,SV2005: $i,SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ! [SY6051: $i,SY6052: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SV2109 @ SV2153 @ SY6051 @ SY6052 @ SV1735 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SV2153 @ SV2109 @ SY6052 @ SY6051 @ SV1735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4608]) ).
thf(4916,plain,
! [SV730: $i,SV1737: $i,SV1291: $i,SV144: $i] :
( ( ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1737 ) @ SV730 ) @ SV1291 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4610]) ).
thf(4917,plain,
! [SV2110: $i,SV2006: $i,SV1739: $i,SV1294: $i,SV733: $i,SV147: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SV2110 ) @ SV2006 @ SV2006 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SV2110 @ SV2006 @ SV2006 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4611]) ).
thf(4918,plain,
! [SV1295: $i,SV734: $i,SV2007: $i,SV1740: $i,SV148: $i] :
( ( ( c_Fun_Oinj__on @ SV148 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SV2007 )
= $false )
| ( ( ( c_Set_Oimage @ SV148 @ ( c_HOL_Ominus__class_Ominus @ SV734 @ SV1295 @ ( tc_fun @ SV1740 @ tc_bool ) ) @ SV1740 @ SV2007 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV148 @ SV734 @ SV1740 @ SV2007 ) @ ( c_Set_Oimage @ SV148 @ SV1295 @ SV1740 @ SV2007 ) @ ( tc_fun @ SV2007 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4612]) ).
thf(4919,plain,
! [SV1742: $i,SV150: $i,SV1297: $i,SV736: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV736 @ ( c_COMBK @ SV1297 @ SV150 @ SV1742 ) @ SV1742 @ SV150 )
= SV1297 )
= $true )
| ( ( SV736
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1742 @ tc_bool ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(4920,plain,
! [SV2008: $i,SV152: $i,SV1299: $i,SV738: $i,SV1744: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1744 ) @ SV738 ) @ SV1299 ) )
= $false )
| ( ( ( c_Set_Oinsert @ ( hAPP @ SV152 @ SV738 ) @ ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SV2008 ) @ SV2008 )
= ( c_Set_Oimage @ SV152 @ SV1299 @ SV1744 @ SV2008 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4616]) ).
thf(4921,plain,
! [SV739: $i,SV1745: $i,SV1300: $i,SV153: $i] :
( ( ( c_lessequals @ SV153 @ SV1300 @ ( tc_fun @ SV1745 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1745 ) @ SV739 ) @ SV153 ) )
= $true )
| ( ( c_lessequals @ SV153 @ ( c_Set_Oinsert @ SV739 @ SV1300 @ SV1745 ) @ ( tc_fun @ SV1745 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4617]) ).
thf(4922,plain,
! [SV1301: $i,SV740: $i,SV1746: $i,SV154: $i] :
( ( ( c_lessequals @ SV154 @ ( c_Set_Oinsert @ SV1746 @ SV740 @ SV1301 ) @ ( tc_fun @ SV1301 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1301 ) @ SV1746 ) @ SV154 ) )
= $true )
| ( ( c_lessequals @ SV154 @ SV740 @ ( tc_fun @ SV1301 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4618]) ).
thf(4923,plain,
! [SV741: $i,SV1747: $i,SV1302: $i,SV155: $i] :
( ( ( c_lessequals @ SV155 @ SV1302 @ ( tc_fun @ SV1747 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1747 ) @ SV741 ) @ SV155 ) )
= $true )
| ( ( c_lessequals @ SV155 @ ( c_Set_Oinsert @ SV741 @ SV1302 @ SV1747 ) @ ( tc_fun @ SV1747 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4619]) ).
thf(4924,plain,
! [SV1303: $i,SV742: $i,SV1748: $i,SV156: $i] :
( ( ( c_lessequals @ SV156 @ ( c_Set_Oinsert @ SV1748 @ SV742 @ SV1303 ) @ ( tc_fun @ SV1303 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1303 ) @ SV1748 ) @ SV156 ) )
= $true )
| ( ( c_lessequals @ SV156 @ SV742 @ ( tc_fun @ SV1303 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(4925,plain,
! [SV1304: $i,SV157: $i,SV1749: $i,SV2009: $i,SV743: $i] :
( ( ( c_lessequals @ SV743 @ SV2009 @ ( tc_fun @ SV1749 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Ovimage @ SV157 @ SV743 @ SV1304 @ SV1749 ) @ ( c_Set_Ovimage @ SV157 @ SV2009 @ SV1304 @ SV1749 ) @ ( tc_fun @ SV1304 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(4926,plain,
! [SV1309: $i,SV748: $i,SV162: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV748 @ SV1309 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 )
= $false )
| ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(4927,plain,
! [SV175: $i,SV761: $i,SV1761: $i,SV1321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV761 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SV1761 @ SV761 @ SV1321 ) @ ( tc_fun @ SV1321 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV175 ) )
= $true )
| ( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SV1321 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4627]) ).
thf(4928,plain,
! [SV762: $i,SV1762: $i,SV1322: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ SV1322 @ ( tc_fun @ SV1762 @ tc_bool ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV176 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV1322 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SV1322 @ SV1762 ) @ ( tc_fun @ SV1762 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4929,plain,
! [SV180: $i,SV766: $i,SV1766: $i,SV1326: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1326 ) @ SV1766 ) @ SV766 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SV1766 @ SV766 @ SV1326 ) @ ( tc_fun @ SV1326 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SV1326 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4930,plain,
! [SV181: $i,SV1327: $i,SV767: $i,SV1767: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1767 ) @ SV767 ) @ SV1327 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1327 @ ( tc_fun @ SV1767 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SV1327 @ SV1767 ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4931,plain,
! [SV1768: $i,SV1328: $i,SV768: $i,SV182: $i] :
( ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SV1328 @ SV1768 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV1328 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SV1768 @ SV182 @ SV182 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1768 @ SV182 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(4932,plain,
! [SV1769: $i,SV183: $i,SV1329: $i,SV769: $i,SV2011: $i] :
( ( ( ~ ( c_lessequals @ SV2011 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV183 @ SV1769 @ ( tc_fun @ SV1329 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1769 @ SV2011 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(4933,plain,
! [SV191: $i,SV777: $i,SV1333: $i] :
( ( ( c_lessequals @ SV1333 @ SV777 @ SV191 )
= $true )
| ( ( ~ ( c_lessequals @ SV777 @ SV1333 @ SV191 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV777 @ SV1333 @ SV191 )
= $true )
| ( ( class_Orderings_Opreorder @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4634]) ).
thf(4934,plain,
! [SV193: $i,SV1773: $i,SV1334: $i,SV779: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
= $true )
| ( ( ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SV1773 @ SV193 ) )
| ~ ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(4935,plain,
! [SV1774: $i,SV1338: $i,SV787: $i,SV202: $i] :
( ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SV1338 @ SV1774 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV1338 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SV1774 @ SV202 @ SV202 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1774 @ SV202 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4636]) ).
thf(4936,plain,
! [SV203: $i,SV788: $i,SV1339: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1339 @ SV788 @ SV203 )
= $true )
| ( ( SV1339 = SV788 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1339 @ SV203 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4637]) ).
thf(4937,plain,
! [SV204: $i,SV789: $i,SV1340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1340 @ SV789 @ SV204 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1340 @ SV204 )
= $true )
| ( ( SV789 = SV1340 )
= $true )
| ( ( class_Orderings_Olinorder @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(4938,plain,
! [SV1341: $i,SV790: $i,SV205: $i] :
( ( ( c_lessequals @ SV205 @ SV790 @ ( tc_fun @ SV1341 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV790 @ SV205 @ ( tc_fun @ SV1341 @ tc_bool ) )
= $false )
| ( ( SV205 = SV790 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4639]) ).
thf(4939,plain,
! [SV1342: $i,SV791: $i,SV206: $i] :
( ( ( c_lessequals @ SV206 @ SV791 @ ( tc_fun @ SV1342 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV791 @ SV206 @ ( tc_fun @ SV1342 @ tc_bool ) )
= $false )
| ( ( SV206 = SV791 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4640]) ).
thf(4940,plain,
! [SV207: $i,SV792: $i,SV1343: $i] :
( ( ( ~ ( c_lessequals @ SV1343 @ SV792 @ SV207 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV792 @ SV1343 @ SV207 ) )
= $true )
| ( ( SV792 = SV1343 )
= $true )
| ( ( class_Orderings_Oorder @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(4941,plain,
! [SV208: $i,SV793: $i,SV1344: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1344 @ SV793 @ SV208 )
= $true )
| ( ( SV1344 = SV793 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV793 @ SV1344 @ SV208 )
= $true )
| ( ( class_Orderings_Olinorder @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(4942,plain,
! [SV209: $i,SV794: $i,SV1345: $i] :
( ( ( ~ ( c_lessequals @ SV1345 @ SV794 @ SV209 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV794 @ SV1345 @ SV209 ) )
= $true )
| ( ( SV794 = SV1345 )
= $true )
| ( ( class_Orderings_Oorder @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(4943,plain,
! [SV210: $i,SV1346: $i,SV795: $i] :
( ( ( ~ ( c_lessequals @ SV795 @ SV1346 @ SV210 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1346 @ SV795 @ SV210 ) )
= $true )
| ( ( SV795 = SV1346 )
= $true )
| ( ( class_Orderings_Oorder @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4644]) ).
thf(4944,plain,
! [SV211: $i,SV796: $i,SV1347: $i] :
( ( ( SV1347 = SV796 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1347 @ SV796 @ SV211 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV796 @ SV1347 @ SV211 )
= $true )
| ( ( class_Orderings_Olinorder @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4645]) ).
thf(4945,plain,
! [SV212: $i,SV1348: $i,SV797: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1348 @ SV212 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1348 @ SV797 @ SV212 )
= $true )
| ( ( SV797 = SV1348 )
= $true )
| ( ( class_Orderings_Olinorder @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4646]) ).
thf(4946,plain,
! [SV1775: $i,SV1350: $i,SV799: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SV1350 ) @ SV1775 @ SV214 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1350 @ SV1775 @ SV214 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(4947,plain,
! [SV1776: $i,SV1351: $i,SV800: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SV1351 ) @ SV1776 @ SV215 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV800 @ SV1776 @ SV215 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(4948,plain,
! [SV218: $i,SV1777: $i,SV1354: $i,SV803: $i] :
( ( ( c_lessequals @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(4949,plain,
! [SV219: $i,SV1355: $i,SV804: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1355 @ SV219 )
= $false )
| ( ( c_lessequals @ SV804 @ SV1355 @ SV219 )
= $true )
| ( ( class_Orderings_Oorder @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4650]) ).
thf(4950,plain,
! [SV220: $i,SV1356: $i,SV805: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV805 @ SV1356 @ SV220 )
= $false )
| ( ( c_lessequals @ SV805 @ SV1356 @ SV220 )
= $true )
| ( ( class_Orderings_Opreorder @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(4951,plain,
! [SV221: $i,SV806: $i,SV1357: $i] :
( ( ( c_lessequals @ SV1357 @ SV806 @ SV221 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV221 ) @ SV806 ) @ SV1357 )
= SV806 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4652]) ).
thf(4952,plain,
! [SV222: $i,SV1358: $i,SV807: $i] :
( ( ( c_lessequals @ SV807 @ SV1358 @ SV222 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV222 ) @ SV807 ) @ SV1358 )
= SV1358 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(4953,plain,
! [SV811: $i,SV1779: $i,SV1362: $i,SV226: $i] :
( ( ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1779 ) @ SV811 ) @ SV226 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SV1779 ) @ ( tc_fun @ SV1779 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4954,plain,
! [SV1363: $i,SV227: $i,SV812: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV812 @ SV227 ) )
= $true )
| ( ( ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
= $true )
| ( ( class_Orderings_Olinorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(4955,plain,
! [SV2154: $i,SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY6053: $i,SY6054: $i,SY6055: $i,SY6056: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SY6053 @ SY6054 @ SV2013 @ SY6055 @ SY6056 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4657]) ).
thf(4956,plain,
! [SV2155: $i,SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY6057: $i,SY6058: $i,SY6059: $i,SY6060: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SY6057 @ SV2014 @ SY6058 @ SY6059 @ SY6060 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4658]) ).
thf(4957,plain,
! [SV817: $i,SV1368: $i,SV1783: $i,SV232: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV1783 @ SV1368 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1783 @ SV817 @ SV1368 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SV1368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4659]) ).
thf(4958,plain,
! [SV1788: $i,SV823: $i,SV238: $i,SV2017: $i,SV1373: $i] :
( ( ( ~ ( c_lessequals @ SV1373 @ SV2017 @ ( tc_fun @ SV238 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV823 @ SV1788 @ ( tc_fun @ SV238 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV1788 ) @ SV2017 ) @ ( tc_fun @ SV238 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(4959,plain,
! [SV1789: $i,SV1376: $i,SV241: $i,SV826: $i] :
( ( ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
= $true )
| ( ( ~ ( c_lessequals @ SV826 @ SV1789 @ SV241 )
| ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4664]) ).
thf(4960,plain,
! [SV1790: $i,SV1377: $i,SV242: $i,SV827: $i] :
( ( ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
= $true )
| ( ( ~ ( c_lessequals @ SV827 @ SV1790 @ SV242 )
| ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4665]) ).
thf(4961,plain,
! [SV1791: $i,SV1378: $i,SV243: $i,SV828: $i] :
( ( ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
= $true )
| ( ( ~ ( c_lessequals @ SV828 @ SV1791 @ SV243 )
| ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4666]) ).
thf(4962,plain,
! [SV1383: $i,SV833: $i,SV1792: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ SV1792 @ ( tc_fun @ SV833 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV248 @ SV1383 @ ( tc_fun @ SV833 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SV1383 ) @ SV1792 ) @ ( tc_fun @ SV833 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4667]) ).
thf(4963,plain,
! [SV1384: $i,SV834: $i,SV1793: $i,SV249: $i] :
( ( ( c_lessequals @ SV249 @ SV1793 @ ( tc_fun @ SV834 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV249 @ SV1384 @ ( tc_fun @ SV834 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV1384 ) @ SV1793 ) @ ( tc_fun @ SV834 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(4964,plain,
! [SV2156: $i,SV2114: $i,SV2018: $i,SV1794: $i,SV1385: $i,SV837: $i,SV252: $i] :
( ( ( c_Fun_Ocomp @ SV252 @ ( c_Fun_Ocomp @ SV837 @ SV1385 @ SV1794 @ SV2018 @ SV2114 ) @ SV2018 @ SV2156 @ SV2114 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV252 @ SV837 @ SV2018 @ SV2156 @ SV1794 ) @ SV1385 @ SV1794 @ SV2156 @ SV2114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4669]) ).
thf(4965,plain,
! [SV1800: $i,SV259: $i,SV1392: $i,SV844: $i] :
( ( ( c_lessequals @ SV844 @ SV1392 @ SV259 )
= $true )
| ( ( ~ ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SV1392 ) @ SV1800 ) @ SV259 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(4966,plain,
! [SV1801: $i,SV260: $i,SV1393: $i,SV845: $i] :
( ( ( c_lessequals @ SV845 @ SV1393 @ SV260 )
= $true )
| ( ( ~ ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SV1801 ) @ SV1393 ) @ SV260 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(4967,plain,
! [SV1802: $i,SV1394: $i,SV846: $i,SV261: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SV1394 ) @ SV1802 @ SV261 )
= $true )
| ( ( ~ ( c_lessequals @ SV846 @ SV1802 @ SV261 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(4968,plain,
! [SV1803: $i,SV1395: $i,SV847: $i,SV262: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SV1395 ) @ SV1803 @ SV262 )
= $true )
| ( ( ~ ( c_lessequals @ SV1395 @ SV1803 @ SV262 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(4969,plain,
! [SV1804: $i,SV263: $i,SV1396: $i,SV848: $i] :
( ( ( c_lessequals @ SV848 @ SV1396 @ SV263 )
= $true )
| ( ( ~ ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SV1396 ) @ SV1804 ) @ SV263 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(4970,plain,
! [SV1805: $i,SV264: $i,SV1397: $i,SV849: $i] :
( ( ( c_lessequals @ SV849 @ SV1397 @ SV264 )
= $true )
| ( ( ~ ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SV1805 ) @ SV1397 ) @ SV264 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4679]) ).
thf(4971,plain,
! [SV1807: $i,SV1399: $i,SV852: $i,SV267: $i] :
( ( ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4680]) ).
thf(4972,plain,
! [SV855: $i,SV1809: $i,SV1402: $i,SV270: $i] :
( ( ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(4973,plain,
! [SV2116: $i,SV2020: $i,SV1810: $i,SV1410: $i,SV864: $i,SV279: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(4974,plain,
! [SV2117: $i,SV2021: $i,SV1811: $i,SV1411: $i,SV865: $i,SV280: $i] :
( ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SV2021 ) @ SV2117 @ SV2021 @ SV1811 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SV2117 @ SV2021 @ SV1411 ) @ SV1411 @ SV1811 )
| ~ ( c_Fun_Oinj__on @ SV865 @ SV2117 @ SV2021 @ SV1411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4684]) ).
thf(4975,plain,
! [SV2157: $i,SV2118: $i,SV2022: $i,SV1812: $i,SV1413: $i,SV868: $i,SV283: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SV2022 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SV2118 ) @ SV2022 @ SV2157 )
| ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SV2118 @ SV2022 @ SV2157 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2022 ) @ SV1413 ) @ SV1812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4685]) ).
thf(4976,plain,
! [SV2024: $i,SV1815: $i,SV1417: $i,SV872: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SV1417 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Set_Oinsert @ SV1417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 ) @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 @ SV287 ) ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SV1417 @ SV1815 @ SV2024 ) @ SV2024 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4687]) ).
thf(4977,plain,
! [SV2158: $i,SV2119: $i,SV2025: $i,SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SV2119 @ SV2158 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2025 @ SV2119 @ SV2158 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2119 ) @ SV1817 ) @ SV1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4688]) ).
thf(4978,plain,
! [SV875: $i,SV1818: $i,SV1420: $i,SV290: $i] :
( ( ( c_lessequals @ SV290 @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SV1420 @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(4979,plain,
! [SV293: $i,SV1423: $i,SV878: $i] :
( ( ( c_Finite__Set_Ofinite @ SV878 @ SV1423 )
= $false )
| ( ( c_lessequals @ SV878 @ ( c_Set_Oimage @ SV293 @ SV878 @ SV1423 @ SV1423 ) @ ( tc_fun @ SV1423 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV293 @ SV878 @ SV1423 @ SV1423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(4980,plain,
! [SV1821: $i,SV879: $i,SV2026: $i,SV1424: $i,SV294: $i] :
( ( ( c_Fun_Oinj__on @ SV294 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1424 @ tc_bool ) ) @ SV2026 ) @ SV879 ) @ SV1424 @ SV1821 )
= $false )
| ( ( c_Fun_Oinj__on @ SV294 @ SV879 @ SV1424 @ SV1821 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(4981,plain,
! [SV1822: $i,SV2027: $i,SV880: $i,SV1425: $i,SV295: $i] :
( ( ( c_Fun_Oinj__on @ SV295 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1425 @ tc_bool ) ) @ SV880 ) @ SV2027 ) @ SV1425 @ SV1822 )
= $false )
| ( ( c_Fun_Oinj__on @ SV295 @ SV880 @ SV1425 @ SV1822 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(4982,plain,
! [SV1823: $i,SV1426: $i,SV2028: $i,SV296: $i,SV881: $i] :
( ( ( ~ ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SV2028 @ SV1426 @ SV1823 ) @ ( tc_fun @ SV1823 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SV1823 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SV1823 ) @ SV2028 @ ( tc_fun @ SV1426 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4695]) ).
thf(4983,plain,
! [SV1826: $i,SV1431: $i,SV303: $i,SV887: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SV1431 ) @ SV1826 ) @ SV303 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV887 @ SV1431 @ SV303 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4698]) ).
thf(4984,plain,
! [SV1827: $i,SV1432: $i,SV304: $i,SV888: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SV1432 ) @ SV1827 ) @ SV304 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV888 @ SV1827 @ SV304 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(4985,plain,
! [SV2030: $i,SV1829: $i,SV1436: $i,SV892: $i,SV308: $i] :
( ( ( class_HOL_Oord @ SV308 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SV1829 @ SV1436 ) @ SV308 )
| ~ ( c_lessequals @ SV892 @ SV1829 @ ( tc_fun @ SV2030 @ SV308 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4700]) ).
thf(4986,plain,
! [SV1437: $i,SV1830: $i,SV893: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1830 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1437 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV1437 ) @ SV1830 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4701]) ).
thf(4987,plain,
! [SV1438: $i,SV1831: $i,SV894: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1831 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SV1438 ) @ SV1831 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4702]) ).
thf(4988,plain,
! [SV1441: $i,SV1834: $i,SV897: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1834 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1834 @ SV1441 @ ( tc_fun @ SV313 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4705]) ).
thf(4989,plain,
! [SV898: $i,SV314: $i,SV1442: $i,SV1835: $i] :
( ( ( c_lessequals @ SV1835 @ SV1442 @ ( tc_fun @ SV314 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1835 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(4990,plain,
! [SV1443: $i,SV1836: $i,SV899: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1836 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1836 @ SV1443 @ ( tc_fun @ SV315 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(4991,plain,
! [SV1444: $i,SV1837: $i,SV900: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1837 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1837 @ SV1444 @ ( tc_fun @ SV316 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4708]) ).
thf(4992,plain,
! [SV1840: $i,SV319: $i,SV903: $i,SV2031: $i,SV1447: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1447 ) @ SV2031 ) @ SV903 ) )
= $false )
| ( ( ( hAPP @ ( c_Map_Orestrict__map @ SV319 @ SV903 @ SV1447 @ SV1840 ) @ SV2031 )
= ( hAPP @ SV319 @ SV2031 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4993,plain,
! [SV1448: $i,SV1841: $i,SV904: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ ( c_Set_Oinsert @ SV1841 @ SV1448 @ SV320 ) ) )
= $false )
| ( ( SV904 = SV1841 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV320 ) @ SV904 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4712]) ).
thf(4994,plain,
! [SV1449: $i,SV1842: $i,SV905: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV1842 ) @ SV1449 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1842 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV321 ) @ SV905 ) @ SV1449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4713]) ).
thf(4995,plain,
! [SV2120: $i,SV2032: $i,SV1843: $i,SV1450: $i,SV906: $i,SV322: $i] :
( ( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SV1450 @ SV1843 @ SV2032 ) @ SV2120 )
= ( hAPP @ SV906 @ SV2120 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1843 ) @ SV2120 ) @ SV1450 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4714]) ).
thf(4996,plain,
! [SV1451: $i,SV1844: $i,SV908: $i,SV324: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ ( c_HOL_Ominus__class_Ominus @ SV1844 @ SV1451 @ ( tc_fun @ SV324 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV324 ) @ SV908 ) @ SV1451 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4715]) ).
thf(4997,plain,
! [SV2121: $i,SV2033: $i,SV1846: $i,SV1453: $i,SV910: $i,SV326: $i] :
( ( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV326 @ SV910 @ SV1453 @ SV1846 @ SV2033 ) @ SV2121 )
= ( hAPP @ SV326 @ SV2121 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1846 ) @ SV2121 ) @ SV1453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(4998,plain,
! [SV1454: $i,SV1847: $i,SV911: $i,SV327: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1847 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1847 @ SV1454 @ ( tc_fun @ SV327 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4718]) ).
thf(4999,plain,
! [SV1850: $i,SV1462: $i,SV919: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1462 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ SV1850 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV335 ) @ SV919 ) @ ( c_HOL_Ominus__class_Ominus @ SV1462 @ SV1850 @ ( tc_fun @ SV335 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4721]) ).
thf(5000,plain,
! [SV1851: $i,SV1463: $i,SV920: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1463 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ SV1851 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV336 ) @ SV920 ) @ ( c_HOL_Ominus__class_Ominus @ SV1463 @ SV1851 @ ( tc_fun @ SV336 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(5001,plain,
! [SV2122: $i,SV2034: $i,SV1852: $i,SV1464: $i,SV921: $i,SV337: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SV2034 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SV2122 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2034 ) @ SV2122 ) @ SV1464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4723]) ).
thf(5002,plain,
! [SV2123: $i,SV2035: $i,SV1853: $i,SV1465: $i,SV922: $i,SV338: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SV2035 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SV2123 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2035 ) @ SV2123 ) @ SV1465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(5003,plain,
! [SV339: $i,SV1854: $i,SV923: $i,SV1466: $i,SV2036: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2036 ) @ ( hAPP @ SV1466 @ SV923 ) ) @ SV1854 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV339 ) @ SV923 ) @ ( c_Set_Ovimage @ SV1466 @ SV1854 @ SV339 @ SV2036 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(5004,plain,
! [SV340: $i,SV1855: $i,SV924: $i,SV1467: $i,SV2037: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2037 ) @ ( hAPP @ SV1467 @ SV924 ) ) @ SV1855 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV340 ) @ SV924 ) @ ( c_Set_Ovimage @ SV1467 @ SV1855 @ SV340 @ SV2037 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4726]) ).
thf(5005,plain,
! [SV341: $i,SV1856: $i,SV925: $i,SV1468: $i,SV2038: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2038 ) @ ( hAPP @ SV1468 @ SV925 ) ) @ SV1856 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV341 ) @ SV925 ) @ ( c_Set_Ovimage @ SV1468 @ SV1856 @ SV341 @ SV2038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(5006,plain,
! [SV342: $i,SV1857: $i,SV926: $i,SV1469: $i,SV2039: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2039 ) @ SV1469 ) @ ( c_Set_Ovimage @ SV926 @ SV1857 @ SV2039 @ SV342 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV342 ) @ ( hAPP @ SV926 @ SV1469 ) ) @ SV1857 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(5007,plain,
! [SV343: $i,SV1858: $i,SV927: $i,SV1470: $i,SV2040: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2040 ) @ SV1470 ) @ ( c_Set_Ovimage @ SV927 @ SV1858 @ SV2040 @ SV343 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV343 ) @ ( hAPP @ SV927 @ SV1470 ) ) @ SV1858 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4729]) ).
thf(5008,plain,
! [SV2159: $i,SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY6061: $i,SY6062: $i,SY6063: $i,SY6064: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SY6061 @ SY6062 @ SY6063 @ SY6064 @ SV2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4730]) ).
thf(5009,plain,
! [SV2160: $i,SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY6065: $i,SY6066: $i,SY6067: $i,SY6068: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SY6065 @ SY6066 @ SY6067 @ SY6068 @ SV2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4731]) ).
thf(5010,plain,
! [SV2126: $i,SV2043: $i,SV1861: $i,SV1474: $i,SV931: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SV2043 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SV2126 ) @ SV2043 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SV2126 ) @ SV347 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(5011,plain,
! [SV2127: $i,SV2044: $i,SV1862: $i,SV1475: $i,SV932: $i,SV348: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SV2044 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SV2127 ) @ SV2044 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SV2127 ) @ SV348 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4733]) ).
thf(5012,plain,
! [SV2045: $i,SV1863: $i,SV1476: $i,SV933: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV349 ) @ SV933 ) @ SV1476 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1863 ) @ ( hAPP @ SV2045 @ SV933 ) ) @ ( c_Set_Oimage @ SV2045 @ SV1476 @ SV349 @ SV1863 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4734]) ).
thf(5013,plain,
! [SV353: $i,SV1480: $i,SV1866: $i,SV937: $i] :
( ( ( c_lessequals @ SV937 @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1480 ) @ SV353 ) @ SV1866 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SV1480 ) @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4735]) ).
thf(5014,plain,
! [SV2161: $i,SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY6069: $i,SY6070: $i,SY6071: $i,SY6072: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SY6069 @ SY6070 @ SV357 @ SY6071 @ SY6072 @ SV2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4736]) ).
thf(5015,plain,
! [SV2162: $i,SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY6073: $i,SY6074: $i,SY6075: $i,SY6076: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SY6073 @ SV358 @ SY6074 @ SY6075 @ SY6076 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4737]) ).
thf(5016,plain,
! [SV2163: $i,SV2130: $i,SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY6077: $i,SY6078: $i,SY6079: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SY6077 @ SY6078 @ SV1486 @ SV1869 @ SY6079 @ SV2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4738]) ).
thf(5017,plain,
! [SV2164: $i,SV2131: $i,SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY6080: $i,SY6081: $i,SY6082: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SY6080 @ SV1487 @ SY6081 @ SY6082 @ SV1870 @ SV2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4739]) ).
thf(5018,plain,
! [SV950: $i,SV367: $i,SV1493: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1493 @ SV367 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV1493 @ SV367 ) )
= ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV367 ) @ SV950 @ SV1493 @ SV367 @ SV367 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4743]) ).
thf(5019,plain,
! [SV1874: $i,SV370: $i,SV1494: $i,SV953: $i] :
( ( ( c_lessequals @ SV953 @ SV1494 @ SV370 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SV1874 ) @ SV953 ) @ SV1494 @ SV370 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV370 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(5020,plain,
! [SV1875: $i,SV371: $i,SV1495: $i,SV954: $i] :
( ( ( c_lessequals @ SV954 @ SV1495 @ SV371 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SV1875 ) @ SV1495 @ SV371 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV371 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4745]) ).
thf(5021,plain,
! [SV1876: $i,SV1496: $i,SV372: $i,SV955: $i] :
( ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SV1496 ) @ SV1876 ) @ SV372 )
= $true )
| ( ( ~ ( c_lessequals @ SV955 @ SV1876 @ SV372 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV372 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(5022,plain,
! [SV1877: $i,SV1497: $i,SV373: $i,SV956: $i] :
( ( ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SV1497 ) @ SV1877 ) @ SV373 )
= $true )
| ( ( ~ ( c_lessequals @ SV956 @ SV1497 @ SV373 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4747]) ).
thf(5023,plain,
! [SV1878: $i,SV374: $i,SV1498: $i,SV957: $i] :
( ( ( c_lessequals @ SV957 @ SV1498 @ SV374 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SV1878 ) @ SV957 ) @ SV1498 @ SV374 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV374 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(5024,plain,
! [SV1879: $i,SV375: $i,SV1499: $i,SV958: $i] :
( ( ( c_lessequals @ SV958 @ SV1499 @ SV375 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SV1879 ) @ SV1499 @ SV375 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4749]) ).
thf(5025,plain,
! [SV1882: $i,SV379: $i,SV1503: $i,SV962: $i] :
( ( ( c_lessequals @ SV962 @ SV1503 @ SV379 )
= $true )
| ( ( ~ ( c_lessequals @ SV962 @ SV1882 @ SV379 )
| ~ ( c_lessequals @ SV1882 @ SV1503 @ SV379 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(5026,plain,
! [SV1883: $i,SV380: $i,SV1504: $i,SV963: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
= $true )
| ( ( ~ ( c_lessequals @ SV963 @ SV1883 @ SV380 )
| ~ ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(5027,plain,
! [SV1884: $i,SV381: $i,SV1505: $i,SV964: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 )
| ~ ( c_lessequals @ SV1884 @ SV1505 @ SV381 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4754]) ).
thf(5028,plain,
! [SV1885: $i,SV382: $i,SV1506: $i,SV965: $i] :
( ( ( c_lessequals @ SV965 @ SV1506 @ SV382 )
= $true )
| ( ( ~ ( c_lessequals @ SV1885 @ SV1506 @ SV382 )
| ~ ( c_lessequals @ SV965 @ SV1885 @ SV382 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(5029,plain,
! [SV385: $i,SV1507: $i,SV968: $i,SV1886: $i] :
( ( ( c_lessequals @ SV1886 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV385 @ SV1886 @ ( tc_fun @ SV1507 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4756]) ).
thf(5030,plain,
! [SV1887: $i,SV386: $i,SV1508: $i,SV2051: $i,SV969: $i] :
( ( ( ~ ( c_lessequals @ SV969 @ SV2051 @ ( tc_fun @ SV1508 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV386 @ SV2051 @ SV1508 @ SV1887 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SV1887 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(5031,plain,
! [SV1888: $i,SV387: $i,SV970: $i,SV1509: $i] :
( ( ( hBOOL @ ( hAPP @ SV1509 @ SV970 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1509 @ SV387 @ ( tc_fun @ SV1888 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(5032,plain,
! [SV973: $i,SV1510: $i,SV390: $i] :
( ( ( c_lessequals @ SV390 @ SV1510 @ ( tc_fun @ SV973 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1510 @ SV973 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV390 @ SV973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(5033,plain,
! [SV391: $i,SV1511: $i,SV974: $i,SV1889: $i] :
( ( ( c_lessequals @ SV1889 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV391 @ SV1889 @ ( tc_fun @ SV1511 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(5034,plain,
! [SV392: $i,SV1512: $i,SV975: $i,SV1890: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1890 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV392 @ SV1890 @ ( tc_fun @ SV1512 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4761]) ).
thf(5035,plain,
! [SV976: $i,SV1891: $i,SV393: $i,SV1513: $i] :
( ( ( c_lessequals @ SV1513 @ SV393 @ ( tc_fun @ SV1891 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1513 @ SV976 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4762]) ).
thf(5036,plain,
! [SV394: $i,SV977: $i,SV1514: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1514 @ SV977 )
= $false )
| ( ( c_lessequals @ SV394 @ SV1514 @ ( tc_fun @ SV977 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV394 @ SV977 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(5037,plain,
! [SV1892: $i,SV395: $i,SV1515: $i,SV978: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 )
| ~ ( c_lessequals @ SV978 @ SV1892 @ SV395 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV395 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(5038,plain,
! [SV1893: $i,SV396: $i,SV1516: $i,SV979: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
= $true )
| ( ( ~ ( c_lessequals @ SV1893 @ SV1516 @ SV396 )
| ~ ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV396 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(5039,plain,
! [SV1894: $i,SV981: $i,SV398: $i,SV2052: $i,SV1517: $i] :
( ( ( ~ ( c_lessequals @ SV1517 @ SV2052 @ ( tc_fun @ SV398 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV981 @ SV1894 @ ( tc_fun @ SV398 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV1894 ) @ SV2052 ) @ ( tc_fun @ SV398 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4766]) ).
thf(5040,plain,
! [SV2133: $i,SV2053: $i,SV1897: $i,SV1520: $i,SV985: $i,SV402: $i] :
( ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4767]) ).
thf(5041,plain,
! [SV2165: $i,SV2134: $i,SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY6083: $i,SY6084: $i,SY6085: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SV2165 @ SY6083 @ SY6084 @ SY6085 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4768]) ).
thf(5042,plain,
! [SV2166: $i,SV2135: $i,SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY6086: $i,SY6087: $i,SY6088: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SV2166 @ SY6086 @ SY6087 @ SY6088 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4769]) ).
thf(5043,plain,
! [SV1523: $i,SV405: $i,SV988: $i,SV1900: $i] :
( ( ( hBOOL @ ( hAPP @ SV1900 @ SV988 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SV1523 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SV1523 ) @ ( c_Collect @ SV1900 @ SV405 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(5044,plain,
! [SV1528: $i,SV2058: $i,SV1904: $i,SV410: $i,SV993: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV993 @ SV410 @ SV1904 @ SV2058 ) @ SV1528 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV410 @ ( hAPP @ SV993 @ SV1528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(5045,plain,
! [SV1905: $i,SV1529: $i,SV2059: $i,SV411: $i,SV994: $i] :
( ( ( hBOOL @ ( hAPP @ SV994 @ ( hAPP @ SV411 @ SV2059 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV411 @ SV994 @ SV1529 @ SV1905 ) @ SV2059 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(5046,plain,
! [SV995: $i,SV1530: $i,SV412: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
= $true )
| ( ( class_Orderings_Olinorder @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(5047,plain,
! [SV2167: $i,SV2136: $i,SV2060: $i,SV1906: $i,SV1531: $i,SV996: $i,SV413: $i] :
( ( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SV2167 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SV2167 @ SV2136 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
| ~ ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SV2167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4775]) ).
thf(5048,plain,
! [SV414: $i,SV997: $i,SV1907: $i,SV1532: $i] :
( ( ( hBOOL @ ( hAPP @ SV1532 @ SV1907 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV997 @ SV1907 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SV1532 ) @ SV1907 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4776]) ).
thf(5049,plain,
! [SV1534: $i,SV1909: $i,SV999: $i,SV416: $i] :
( ( ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SV1909 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1534 @ SV416 @ ( tc_fun @ SV1909 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SV1534 @ ( tc_fun @ SV1909 @ tc_bool ) ) @ ( tc_fun @ SV1909 @ tc_bool ) )
= SV1534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4778]) ).
thf(5050,plain,
! [SV1910: $i,SV417: $i,SV1535: $i,SV2061: $i,SV1000: $i] :
( ( ( c_lessequals @ SV1000 @ SV2061 @ ( tc_fun @ SV1535 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV417 @ SV1000 @ SV1535 @ SV1910 ) @ ( c_Set_Oimage @ SV417 @ SV2061 @ SV1535 @ SV1910 ) @ ( tc_fun @ SV1910 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4779]) ).
thf(5051,plain,
! [SV2062: $i,SV1911: $i,SV1536: $i,SV1001: $i,SV418: $i] :
( ( ( c_lessequals @ SV418 @ SV1001 @ ( tc_fun @ SV1536 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV1911 @ SV418 @ SV1536 @ SV2062 ) @ ( c_Set_Oimage @ SV1911 @ SV1001 @ SV1536 @ SV2062 ) @ ( tc_fun @ SV2062 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4780]) ).
thf(5052,plain,
! [SV1913: $i,SV1004: $i,SV421: $i,SV1538: $i] :
( ( ( c_Fun_Oinj__on @ SV1538 @ SV421 @ SV1004 @ SV1913 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV1538 @ SV421 @ SV1004 @ SV1913 ) @ SV1913 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(5053,plain,
! [SV422: $i,SV1005: $i,SV1539: $i] :
( ( ( SV1539 = SV1005 )
= $true )
| ( ( ~ ( c_lessequals @ SV1005 @ SV1539 @ SV422 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1005 @ SV1539 @ SV422 )
= $true )
| ( ( class_Orderings_Oorder @ SV422 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(5054,plain,
! [SV423: $i,SV1540: $i,SV1006: $i] :
( ( ( ~ ( c_lessequals @ SV1006 @ SV1540 @ SV423 ) )
= $true )
| ( ( SV1540 = SV1006 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1006 @ SV1540 @ SV423 )
= $true )
| ( ( class_Orderings_Oorder @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(5055,plain,
! [SV425: $i,SV1542: $i,SV1008: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1008 @ SV1542 @ SV425 )
= $true )
| ( ( ~ ( c_lessequals @ SV1008 @ SV1542 @ SV425 ) )
= $true )
| ( ( SV1008 = SV1542 )
= $true )
| ( ( class_Orderings_Oorder @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(5056,plain,
! [SV426: $i,SV1543: $i,SV1009: $i] :
( ( ( SV1009 = SV1543 )
= $true )
| ( ( ~ ( c_lessequals @ SV1009 @ SV1543 @ SV426 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV1543 @ SV426 )
= $true )
| ( ( class_Orderings_Oorder @ SV426 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(5057,plain,
! [SV428: $i,SV1545: $i,SV1011: $i] :
( ( ( SV1011 = SV1545 )
= $true )
| ( ( ~ ( c_lessequals @ SV1011 @ SV1545 @ SV428 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1545 @ SV428 )
= $true )
| ( ( class_Orderings_Oorder @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(5058,plain,
! [SV429: $i,SV1546: $i,SV1012: $i] :
( ( ( ~ ( c_lessequals @ SV1012 @ SV1546 @ SV429 ) )
= $true )
| ( ( SV1012 = SV1546 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1012 @ SV1546 @ SV429 )
= $true )
| ( ( class_Orderings_Oorder @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4790]) ).
thf(5059,plain,
! [SV430: $i,SV1547: $i,SV1013: $i] :
( ( ( ~ ( c_lessequals @ SV1013 @ SV1547 @ SV430 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1013 @ SV1547 @ SV430 )
= $true )
| ( ( SV1013 = SV1547 )
= $true )
| ( ( class_Orderings_Olinorder @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(5060,plain,
! [SV431: $i,SV1548: $i,SV1014: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1548 @ SV431 )
= $true )
| ( ( ~ ( c_lessequals @ SV1014 @ SV1548 @ SV431 ) )
= $true )
| ( ( SV1014 = SV1548 )
= $true )
| ( ( class_Orderings_Olinorder @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(5061,plain,
! [SV1549: $i,SV1015: $i,SV432: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1549 @ SV432 ) )
= $true )
| ( ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
= $true )
| ( ( class_Orderings_Olinorder @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4793]) ).
thf(5062,plain,
! [SV1551: $i,SV1018: $i,SV435: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV435 ) @ SV1018 ) @ SV1551 ) )
= $false )
| ( ( c_lessequals @ SV1018 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1551 @ SV435 ) @ SV435 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4794]) ).
thf(5063,plain,
! [SV2168: $i,SV2137: $i,SV2064: $i,SV1915: $i,SV1552: $i,SV1019: $i,SV436: $i] :
( ( ( c_Fun_Ofcomp @ ( c_Fun_Ofcomp @ SV436 @ SV1019 @ SV1552 @ SV1915 @ SV2064 ) @ SV2137 @ SV1552 @ SV2064 @ SV2168 )
= ( c_Fun_Ofcomp @ SV436 @ ( c_Fun_Ofcomp @ SV1019 @ SV2137 @ SV1915 @ SV2064 @ SV2168 ) @ SV1552 @ SV1915 @ SV2168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4795]) ).
thf(5064,plain,
! [SV437: $i,SV1553: $i,SV1020: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1020 @ SV1553 @ SV437 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1553 @ SV1020 @ SV437 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4796]) ).
thf(5065,plain,
! [SV438: $i,SV1554: $i,SV1021: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1021 @ SV1554 @ SV438 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1021 @ SV438 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(5066,plain,
! [SV440: $i,SV1556: $i,SV1023: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1023 @ SV1556 @ SV440 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1023 @ SV440 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4799]) ).
thf(5067,plain,
! [SV441: $i,SV1557: $i,SV1024: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1024 @ SV1557 @ SV441 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV1024 @ SV441 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(5068,plain,
! [SV2065: $i,SV1916: $i,SV1558: $i,SV1025: $i,SV442: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV442 ) @ SV1025 ) @ SV1558 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1916 ) @ ( hAPP @ SV2065 @ SV1025 ) ) @ ( c_Set_Oimage @ SV2065 @ SV1558 @ SV442 @ SV1916 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4801]) ).
thf(5069,plain,
! [SV1026: $i,SV443: $i,SV1917: $i,SV1559: $i,SV2066: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2066 ) @ SV1559 ) @ SV1917 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ ( hAPP @ SV1026 @ SV1559 ) ) @ ( c_Set_Oimage @ SV1026 @ SV1917 @ SV2066 @ SV443 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(5070,plain,
! [SV1027: $i,SV444: $i,SV1918: $i,SV1560: $i,SV2067: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV1560 ) @ SV1918 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ ( hAPP @ SV1027 @ SV1560 ) ) @ ( c_Set_Oimage @ SV1027 @ SV1918 @ SV2067 @ SV444 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(5071,plain,
! [SV445: $i,SV1028: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1028 @ SV445 )
= $false )
| ( ( SV1028
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV445 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV445 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1028 @ SV445 ) ) @ SV1028 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(5072,plain,
! [SV446: $i,SV1029: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1029 @ SV446 )
= $false )
| ( ( SV1029
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV446 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV446 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1029 @ SV446 ) ) @ SV1029 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4805]) ).
thf(5073,plain,
! [SV2068: $i,SV1562: $i,SV448: $i,SV1031: $i,SV1919: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1919 ) @ SV1031 ) @ ( c_Set_Ovimage @ SV448 @ ( c_Set_Oinsert @ SV1562 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2068 @ tc_bool ) ) @ SV2068 ) @ SV1919 @ SV2068 ) ) )
= $false )
| ( ( ( hAPP @ SV448 @ SV1031 )
= SV1562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(5074,plain,
! [SV2169: $i,SV2138: $i,SV2069: $i,SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ! [SY6089: $i,SY6090: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SV2138 @ SV2169 @ SY6089 @ SY6090 @ SV1571 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4807]) ).
thf(5075,plain,
! [SV2170: $i,SV2139: $i,SV2070: $i,SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ! [SY6091: $i,SY6092: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SV2139 @ SV2170 @ SY6091 @ SV1572 @ SY6092 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4808]) ).
thf(5076,plain,
! [SV2072: $i,SV480: $i,SV1928: $i,SV1060: $i,SV1576: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV1576 @ SV1060 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1928 @ tc_bool ) ) @ SV480 @ SV1928 @ SV2072 )
= $false )
| ( ( SV480 = SV1060 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4809]) ).
thf(5077,plain,
! [SV499: $i,SV1934: $i,SV1588: $i,SV1079: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1934 @ SV499 ) ) @ SV1934 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1934 @ SV1588 @ t_a ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4810]) ).
thf(5078,plain,
! [SV1080: $i,SV1589: $i,SV500: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV500 ) @ ( v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 @ SV500 @ SV1589 ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1080 ) @ SV1589 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV500 @ SV1080 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4811]) ).
thf(5079,plain,
! [SV1935: $i,SV502: $i,SV1591: $i,SV1082: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a ) )
= $true )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(5080,plain,
! [SV2073: $i,SV1936: $i,SV1599: $i,SV1112: $i,SV535: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
| ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(5081,plain,
! [SV2074: $i,SV1937: $i,SV1600: $i,SV1113: $i,SV536: $i] :
( ( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 )
= ( c_Set_Oinsert @ SV1937 @ ( c_Set_Oinsert @ SV2074 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 ) )
= $false )
| ( ( ( SV536 = SV2074 )
| ( SV536 = SV1937 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(5082,plain,
! [SV2075: $i,SV1938: $i,SV1601: $i,SV1114: $i,SV537: $i] :
( ( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 )
= ( c_Set_Oinsert @ SV1938 @ ( c_Set_Oinsert @ SV2075 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 ) )
= $false )
| ( ( ( SV1114 = SV1938 )
| ( SV1114 = SV2075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(5083,plain,
! [SV2076: $i,SV1939: $i,SV1602: $i,SV1115: $i,SV538: $i] :
( ( ( ( hAPP @ SV538 @ SV1115 )
= ( hAPP @ SV538 @ SV1602 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 @ SV2076 )
| ( SV1115 = SV1602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4820]) ).
thf(5084,plain,
! [SV2077: $i,SV1940: $i,SV1603: $i,SV1116: $i,SV539: $i] :
( ( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 )
= ( c_Set_Oinsert @ SV1940 @ ( c_Set_Oinsert @ SV2077 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 ) )
= $false )
| ( ( ( SV539 = SV2077 )
| ( SV1116 = SV2077 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4821]) ).
thf(5085,plain,
! [SV2078: $i,SV1941: $i,SV1604: $i,SV1117: $i,SV540: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SV1941 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
= $false )
| ( ( ( ( hAPP @ SV1117 @ SV2078 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SV2078 ) @ SV540 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(5086,plain,
! [SV2079: $i,SV1942: $i,SV1605: $i,SV1118: $i,SV541: $i] :
( ( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 )
= ( c_Set_Oinsert @ SV1942 @ ( c_Set_Oinsert @ SV2079 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 ) )
= $false )
| ( ( ( SV1118 = SV1942 )
| ( SV541 = SV1942 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(5087,plain,
! [SV1943: $i,SV1606: $i,SV542: $i,SV1119: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
!= ( c_HOL_Ominus__class_Ominus @ SV1606 @ SV1943 @ SV542 ) )
= $true )
| ( ( SV1606 = SV1943 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4824]) ).
thf(5088,plain,
! [SV1120: $i,SV1944: $i,SV543: $i,SV1607: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1944 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1120 ) )
| ( SV1120 = SV1944 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SV1607 )
= ( c_Set_Oinsert @ SV543 @ SV1944 @ SV1607 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4825]) ).
thf(5089,plain,
! [SV1608: $i,SV1121: $i,SV544: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV544 ) @ SV1121 ) @ SV1608 )
= ( c_Orderings_Obot__class_Obot @ SV544 ) )
= $false )
| ( ( SV1608
= ( c_Orderings_Obot__class_Obot @ SV544 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV544 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4826]) ).
thf(5090,plain,
! [SV1609: $i,SV1945: $i,SV1122: $i,SV545: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1945 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SV1945 ) @ SV1609 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4827]) ).
thf(5091,plain,
! [SV2080: $i,SV1947: $i,SV1613: $i,SV1126: $i,SV549: $i] :
( ( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SV1947 )
= ( c_Set_Oimage @ SV549 @ SV2080 @ SV1613 @ SV1947 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SV1947 )
| ( SV1126 = SV2080 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(5092,plain,
! [SV2081: $i,SV1948: $i,SV1614: $i,SV1127: $i,SV550: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
| ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(5093,plain,
! [SV1615: $i,SV1128: $i,SV551: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 ) @ SV1128 ) @ SV1615 )
= ( c_Orderings_Otop__class_Otop @ SV551 ) )
= $false )
| ( ( SV1128
= ( c_Orderings_Otop__class_Otop @ SV551 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV551 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(5094,plain,
! [SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY6093: $i,SY6094: $i,SY6095: $i,SY6096: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SY6093 @ SY6094 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SY6095 @ SY6093 @ SY6096 ) @ SV2140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4832]) ).
thf(5095,plain,
! [SV2083: $i,SV1950: $i,SV1619: $i,SV1132: $i,SV555: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 )
| ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4833]) ).
thf(5096,plain,
! [SV2084: $i,SV1952: $i,SV1622: $i,SV1135: $i,SV559: $i] :
( ( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV1952 @ SV2084 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4835]) ).
thf(5097,plain,
! [SV1623: $i,SV1136: $i,SV560: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV560 ) @ SV1136 ) @ SV1623 )
= SV1136 )
= $false )
| ( ( c_lessequals @ SV1136 @ SV1623 @ SV560 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV560 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(5098,plain,
! [SV1624: $i,SV1137: $i,SV561: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV561 ) @ SV1137 ) @ SV1624 )
= ( c_Orderings_Obot__class_Obot @ SV561 ) )
= $false )
| ( ( SV1137
= ( c_Orderings_Obot__class_Obot @ SV561 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(5099,plain,
! [SV2085: $i,SV1953: $i,SV1625: $i,SV1138: $i,SV562: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
| ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(5100,plain,
! [SV2141: $i,SV2086: $i,SV1954: $i,SV1626: $i,SV1139: $i,SV563: $i] :
( ( ( ( hAPP @ SV563 @ SV1139 )
!= ( hAPP @ SV563 @ SV1626 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(5101,plain,
! [SV1955: $i,SV564: $i,SV1627: $i,SV1140: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SV1627 @ SV564 )
!= ( c_HOL_Ominus__class_Ominus @ SV1955 @ SV1955 @ SV564 ) )
= $true )
| ( ( SV1140 = SV1627 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(5102,plain,
! [SV2142: $i,SV2087: $i,SV1956: $i,SV1628: $i,SV1141: $i,SV565: $i] :
( ( ( ( hAPP @ SV565 @ SV1141 )
!= ( hAPP @ SV565 @ SV1628 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
| ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(5103,plain,
! [SV1629: $i,SV1142: $i,SV566: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV566 ) @ SV1142 ) @ SV1629 )
= SV1629 )
= $false )
| ( ( c_lessequals @ SV1142 @ SV1629 @ SV566 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV566 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4842]) ).
thf(5104,plain,
! [SV2088: $i,SV1957: $i,SV1630: $i,SV1143: $i,SV567: $i] :
( ( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SV1957 )
= ( c_Set_Oimage @ SV567 @ SV2088 @ SV1630 @ SV1957 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SV2088 ) @ SV1630 @ SV1957 )
| ( SV1143 = SV2088 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(5105,plain,
! [SV2172: $i,SV2143: $i,SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ! [SY6097: $i,SY6098: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
!= ( c_Fun_Ocomp @ SV2143 @ SV2172 @ SY6097 @ SV1958 @ SV2089 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY6098 ) )
= ( hAPP @ SV2143 @ ( hAPP @ SV2172 @ SY6098 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4845]) ).
thf(5106,plain,
! [SV2173: $i,SV2144: $i,SV2090: $i,SV1959: $i,SV1636: $i,SV1151: $i,SV575: $i] :
( ( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SV1959 @ SV2090 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV1959 ) @ SV2144 @ SV1959 @ SV1959 @ SV2090 ) )
| ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SV2173 ) )
= ( hAPP @ SV2144 @ SV2173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4846]) ).
thf(5107,plain,
! [SV2091: $i,SV1960: $i,SV1637: $i,SV1152: $i,SV576: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SV1960 @ ( tc_fun @ SV576 @ tc_bool ) ) )
= $false )
| ( ( ( ( hAPP @ SV1637 @ SV2091 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1960 ) @ SV2091 ) @ SV1152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(5108,plain,
! [SV1641: $i,SV1156: $i,SV582: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV582 ) @ SV1156 ) @ SV1641 )
= ( c_Orderings_Otop__class_Otop @ SV582 ) )
= $false )
| ( ( SV1641
= ( c_Orderings_Otop__class_Otop @ SV582 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV582 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(5109,plain,
! [SV2092: $i,SV1963: $i,SV1643: $i,SV1158: $i,SV584: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
| ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SV2092 @ SV1963 @ SV584 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(5110,plain,
! [SV2145: $i,SV2093: $i,SV1965: $i,SV1645: $i,SV1160: $i,SV586: $i] :
( ( ( ( hAPP @ SV586 @ SV1160 )
!= ( hAPP @ SV586 @ SV1645 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5111,plain,
! [SV2146: $i,SV2094: $i,SV1966: $i,SV1646: $i,SV1161: $i,SV587: $i] :
( ( ( ( hAPP @ SV587 @ SV1161 )
!= ( hAPP @ SV587 @ SV1646 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(5112,plain,
! [SV1647: $i,SV2: $i,SV1162: $i,SV1967: $i,SV588: $i] :
( ( ( c_lessequals @ SV588 @ SV1967 @ ( tc_fun @ SV1162 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SV1647 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SV1647 ) @ ( c_Set_Oimage @ SV2 @ SV1967 @ SV1162 @ SV1647 ) @ ( tc_fun @ SV1647 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(5113,plain,
! [SV4: $i,SV1969: $i,SV1649: $i,SV1164: $i,SV590: $i] :
( ( ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1649 @ SV590 @ SV1969 @ SV4 ) @ SV4 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1164 ) @ SV1649 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4858]) ).
thf(5114,plain,
! [SV1654: $i,SV1971: $i,SV1169: $i,SV595: $i,SV9: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV9 @ SV595 @ SV1169 @ SV1971 @ SV1654 @ SV1654 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1654 ) @ SV595 ) @ SV1169 ) )
= $true )
| ( ( c_Finite__Set_Ofold1Set @ SV9 @ ( c_Set_Oinsert @ SV595 @ SV1169 @ SV1654 ) @ SV1971 @ SV1654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(5115,plain,
! [SV2174: $i,SV2147: $i,SV2095: $i,SV1972: $i,SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ! [SY6099: $i] :
( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SV2095 @ SV2147 @ SV2174 @ SY6099 @ SV1170 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4861]) ).
thf(5116,plain,
! [SV2175: $i,SV2148: $i,SV2096: $i,SV1973: $i,SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ! [SY6100: $i] :
( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SV2096 @ SV2148 @ SV2175 @ SV1171 @ SY6100 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4862]) ).
thf(5117,plain,
! [SV12: $i,SV1657: $i,SV598: $i,SV1172: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV1657 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SV1657 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1657 @ ( tc_fun @ SV1172 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4863]) ).
thf(5118,plain,
! [SV1173: $i,SV1658: $i,SV599: $i,SV13: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SV1658 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV1173 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV13 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4864]) ).
thf(5119,plain,
! [SV2176: $i,SV2149: $i,SV2097: $i,SV1974: $i,SV1659: $i,SV1174: $i,SV600: $i,SV14: $i] :
( ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
| ~ ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
| ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4865]) ).
thf(5120,plain,
! [SV1176: $i,SV1660: $i,SV602: $i,SV16: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1660 @ SV16 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5121,plain,
! [SV1181: $i,SV1665: $i,SV607: $i,SV21: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(5122,plain,
! [SV1193: $i,SV38: $i,SV1977: $i,SV624: $i,SV1672: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
| ~ ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4871]) ).
thf(5123,plain,
! [SV1195: $i,SV1674: $i,SV41: $i,SV2098: $i,SV627: $i,SV1978: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1978 ) @ SV627 ) @ SV2098 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2098 @ SV41 @ SV1978 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5124,plain,
! [SV2150: $i,SV2099: $i,SV1980: $i,SV1677: $i,SV1201: $i,SV633: $i,SV47: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SV2099 @ SV2150 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2099 ) @ SV1677 ) @ SV1201 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV2099 ) @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV1980 @ SV2099 @ SV2150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(5125,plain,
! [SV2177: $i,SV2151: $i,SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY6101: $i,SY6102: $i,SY6103: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SV2177 @ SY6101 @ SV1982 @ SY6102 @ SY6103 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4877]) ).
thf(5126,plain,
! [SV2178: $i,SV2152: $i,SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY6104: $i,SY6105: $i,SY6106: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SV2178 @ SV1983 @ SY6104 @ SY6105 @ SY6106 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4878]) ).
thf(5127,plain,
! [SV60: $i,SV1214: $i,SV646: $i,SV1989: $i,SV1687: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ ( hAPP @ SV1989 @ SV646 ) ) @ ( c_Set_Oimage @ SV1989 @ SV1214 @ SV60 @ SV1687 ) ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV1989 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SV1687 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4881]) ).
thf(5128,plain,
! [SV61: $i,SV647: $i,SV1688: $i,SV1215: $i,SV1990: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1990 ) @ SV1215 ) @ SV1688 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1990 @ tc_bool ) ) @ SV1990 @ SV61 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SV1688 @ SV1990 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4882]) ).
thf(5129,plain,
! [SV654: $i,SV1993: $i,SV1222: $i,SV68: $i,SV1695: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV1695 @ SV68 @ SV1222 @ SV1993 ) @ ( c_Set_Oimage @ SV1695 @ SV654 @ SV1222 @ SV1993 ) @ ( tc_fun @ SV1993 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV1695 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SV1993 ) )
= $true )
| ( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5130,plain,
! [SV1223: $i,SV1696: $i,SV655: $i,SV69: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV69 @ ( c_Set_Oinsert @ SV655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) ) @ SV1223 @ ( tc_fun @ SV1696 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1696 ) @ SV655 ) @ SV69 ) )
= $false )
| ( ( c_lessequals @ SV69 @ ( c_Set_Oinsert @ SV655 @ SV1223 @ SV1696 ) @ ( tc_fun @ SV1696 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(5131,plain,
! [SV1224: $i,SV1697: $i,SV656: $i,SV70: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV70 @ ( c_Set_Oinsert @ SV656 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) ) @ SV1224 @ ( tc_fun @ SV1697 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV656 ) @ SV70 ) )
= $false )
| ( ( c_lessequals @ SV70 @ ( c_Set_Oinsert @ SV656 @ SV1224 @ SV1697 ) @ ( tc_fun @ SV1697 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(5132,plain,
! [SV1225: $i,SV1698: $i,SV657: $i,SV71: $i] :
( ( ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV657 @ SV1698 @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1225 ) @ SV657 ) @ SV71 ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV657 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1698 @ ( tc_fun @ SV1225 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(5133,plain,
! [SV1994: $i,SV72: $i,SV1226: $i,SV658: $i,SV2104: $i,SV1699: $i] :
( ( ( ~ ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4890]) ).
thf(5134,plain,
! [SV659: $i,SV1995: $i,SV1700: $i,SV1227: $i,SV73: $i] :
( ( ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SV1700 @ SV1995 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1700 @ SV1995 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5135,plain,
! [SV1701: $i,SV74: $i,SV660: $i,SV2105: $i,SV1228: $i,SV1996: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1996 ) @ SV1228 ) @ SV2105 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SV2105 @ SV1996 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4892]) ).
thf(5136,plain,
! [SV2106: $i,SV662: $i,SV1998: $i,SV76: $i,SV1703: $i,SV1230: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV1230 @ SV1703 @ SV76 @ SV1998 @ SV662 @ SV2106 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV76 @ SV662 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4894]) ).
thf(5137,plain,
! [SV1232: $i,SV1704: $i,SV2107: $i,SV1999: $i,SV664: $i,SV78: $i] :
( ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV78 @ SV664 @ SV1999 @ SV2107 @ SV1704 ) @ SV1232 @ SV1704 @ SV2107 )
= $false )
| ( ( c_Fun_Oinj__on @ SV78 @ ( c_Set_Oimage @ SV664 @ SV1232 @ SV1704 @ SV1999 ) @ SV1999 @ SV2107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4895]) ).
thf(5138,plain,
! [SV1240: $i,SV86: $i,SV1710: $i,SV672: $i] :
( ( ( c_Finite__Set_Ofinite @ SV672 @ SV1710 )
= $false )
| ( ( c_Fun_Oinj__on @ SV86 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1240 @ tc_bool ) ) @ SV1240 @ SV1710 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ SV86 @ SV672 @ SV1240 @ SV1710 ) @ SV1240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4896]) ).
thf(5139,plain,
! [SV675: $i,SV89: $i,SV1241: $i,SV1711: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
= $true )
| ( ( class_Orderings_Opreorder @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(5140,plain,
! [SV676: $i,SV1242: $i,SV1712: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ SV1712 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1712 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV676 @ ( tc_fun @ SV1242 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(5141,plain,
! [SV1243: $i,SV91: $i,SV1713: $i,SV677: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4899]) ).
thf(5142,plain,
! [SV679: $i,SV2001: $i,SV1715: $i,SV1245: $i,SV93: $i] :
( ( ( c_Fun_Oinj__on @ SV93 @ SV1245 @ SV1715 @ SV2001 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ ( hAPP @ SV93 @ SV679 ) ) @ ( c_Set_Oimage @ SV93 @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ ( c_Set_Oinsert @ SV679 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 ) @ ( tc_fun @ SV1715 @ tc_bool ) ) @ SV1715 @ SV2001 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV93 @ ( c_Set_Oinsert @ SV679 @ SV1245 @ SV1715 ) @ SV1715 @ SV2001 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(5143,plain,
! [SV104: $i,SV690: $i,SV1253: $i] :
( ( ( c_lessequals @ SV1253 @ SV690 @ SV104 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV690 @ SV1253 @ SV104 )
= $false )
| ( ( class_Orderings_Olinorder @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(5144,plain,
! [SV106: $i,SV692: $i,SV1255: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1255 @ SV692 @ SV106 )
= $false )
| ( ( c_lessequals @ SV692 @ SV1255 @ SV106 )
= $false )
| ( ( class_Orderings_Olinorder @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4904]) ).
thf(5145,plain,
! [SV108: $i,SV1721: $i,SV1257: $i,SV694: $i] :
( ( ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SV1721 @ SV108 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SV1721 @ SV108 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4905]) ).
thf(5146,plain,
! [SV109: $i,SV695: $i,SV1258: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1258 @ SV695 @ SV109 )
= $false )
| ( ( c_lessequals @ SV695 @ SV1258 @ SV109 )
= $false )
| ( ( class_Orderings_Opreorder @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(5147,plain,
! [SV698: $i,SV112: $i,SV1260: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
= $false )
| ( ( ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4907]) ).
thf(5148,plain,
! [SV1272: $i,SV125: $i,SV1730: $i,SV711: $i] :
( ( ( c_lessequals @ SV711 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1272 @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV125 @ tc_bool ) ) @ SV711 ) @ SV1272 ) @ SV1730 @ ( tc_fun @ SV125 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4910]) ).
thf(5149,plain,
! [SV1275: $i,SV128: $i,SV1731: $i,SV714: $i] :
( ( ( c_lessequals @ SV714 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1275 @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV128 @ tc_bool ) ) @ SV714 ) @ SV1275 ) @ SV1731 @ ( tc_fun @ SV128 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4911]) ).
thf(5150,plain,
! [SV715: $i,SV129: $i,SV1732: $i,SV1276: $i] :
( ( ( ~ ( c_lessequals @ SV1276 @ SV1732 @ SV129 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV715 @ SV1732 @ SV129 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4912]) ).
thf(5151,plain,
! [SV718: $i,SV132: $i,SV1733: $i,SV1279: $i] :
( ( ( ~ ( c_lessequals @ SV1279 @ SV1733 @ SV132 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV718 @ SV1733 @ SV132 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(5152,plain,
! [SV719: $i,SV133: $i,SV1734: $i,SV1280: $i] :
( ( ( ~ ( c_lessequals @ SV1280 @ SV1734 @ SV133 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV719 @ SV1734 @ SV133 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5153,plain,
! [SV2179: $i,SV2153: $i,SV2109: $i,SV2005: $i,SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ! [SY6107: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SV2109 @ SV2153 @ SV2179 @ SY6107 @ SV1735 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SV2153 @ SV2109 @ SY6107 @ SV2179 @ SV1735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4915]) ).
thf(5154,plain,
! [SV1291: $i,SV1737: $i,SV730: $i,SV144: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1737 ) @ SV730 ) @ SV1291 ) )
= $true )
| ( ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4916]) ).
thf(5155,plain,
! [SV733: $i,SV2110: $i,SV147: $i,SV1739: $i,SV1294: $i,SV2006: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SV2110 @ SV2006 @ SV2006 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SV2110 ) @ SV2006 @ SV2006 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4917]) ).
thf(5156,plain,
! [SV1309: $i,SV748: $i,SV162: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV748 @ SV1309 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 )
= $false )
| ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4926]) ).
thf(5157,plain,
! [SV1321: $i,SV761: $i,SV1761: $i,SV175: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV175 @ ( c_Set_Oinsert @ SV1761 @ SV761 @ SV1321 ) @ ( tc_fun @ SV1321 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV761 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1321 ) @ SV1761 ) @ SV175 ) )
= $true )
| ( ( c_lessequals @ SV175 @ SV761 @ ( tc_fun @ SV1321 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(5158,plain,
! [SV1322: $i,SV176: $i,SV762: $i,SV1762: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV176 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1762 ) @ SV762 ) @ SV1322 ) )
= $true )
| ( ( c_lessequals @ SV176 @ SV1322 @ ( tc_fun @ SV1762 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV176 @ ( c_Set_Oinsert @ SV762 @ SV1322 @ SV1762 ) @ ( tc_fun @ SV1762 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4928]) ).
thf(5159,plain,
! [SV1326: $i,SV766: $i,SV1766: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ ( c_Set_Oinsert @ SV1766 @ SV766 @ SV1326 ) @ ( tc_fun @ SV1326 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1326 ) @ SV1766 ) @ SV766 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV180 @ SV766 @ ( tc_fun @ SV1326 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4929]) ).
thf(5160,plain,
! [SV767: $i,SV1767: $i,SV1327: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ SV1327 @ ( tc_fun @ SV1767 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1767 ) @ SV767 ) @ SV1327 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV181 @ ( c_Set_Oinsert @ SV767 @ SV1327 @ SV1767 ) @ ( tc_fun @ SV1767 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4930]) ).
thf(5161,plain,
! [SV1328: $i,SV768: $i,SV182: $i,SV1768: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1768 @ SV182 )
= $false )
| ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ ( c_Set_Oinsert @ SV1328 @ SV1768 @ SV182 ) @ SV182 @ SV182 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV1328 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV182 ) @ SV768 @ SV1768 @ SV182 @ SV182 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(5162,plain,
! [SV1769: $i,SV183: $i,SV1329: $i,SV769: $i,SV2011: $i] :
( ( ( c_lessequals @ SV2011 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV183 @ SV1769 @ ( tc_fun @ SV1329 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1769 @ SV2011 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4932]) ).
thf(5163,plain,
! [SV191: $i,SV1333: $i,SV777: $i] :
( ( ( c_lessequals @ SV777 @ SV1333 @ SV191 )
= $false )
| ( ( c_lessequals @ SV1333 @ SV777 @ SV191 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV777 @ SV1333 @ SV191 )
= $true )
| ( ( class_Orderings_Opreorder @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4933]) ).
thf(5164,plain,
! [SV193: $i,SV1773: $i,SV779: $i,SV1334: $i] :
( ( ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SV1773 @ SV193 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
= $true )
| ( ( class_HOL_Oord @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(5165,plain,
! [SV1338: $i,SV787: $i,SV202: $i,SV1774: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1774 @ SV202 )
= $false )
| ( ( ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ ( c_Set_Oinsert @ SV1338 @ SV1774 @ SV202 ) @ SV202 @ SV202 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV1338 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV202 ) @ SV787 @ SV1774 @ SV202 @ SV202 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4935]) ).
thf(5166,plain,
! [SV207: $i,SV792: $i,SV1343: $i] :
( ( ( c_lessequals @ SV1343 @ SV792 @ SV207 )
= $false )
| ( ( ~ ( c_lessequals @ SV792 @ SV1343 @ SV207 ) )
= $true )
| ( ( SV792 = SV1343 )
= $true )
| ( ( class_Orderings_Oorder @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4940]) ).
thf(5167,plain,
! [SV209: $i,SV794: $i,SV1345: $i] :
( ( ( c_lessequals @ SV1345 @ SV794 @ SV209 )
= $false )
| ( ( ~ ( c_lessequals @ SV794 @ SV1345 @ SV209 ) )
= $true )
| ( ( SV794 = SV1345 )
= $true )
| ( ( class_Orderings_Oorder @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(5168,plain,
! [SV210: $i,SV1346: $i,SV795: $i] :
( ( ( c_lessequals @ SV795 @ SV1346 @ SV210 )
= $false )
| ( ( ~ ( c_lessequals @ SV1346 @ SV795 @ SV210 ) )
= $true )
| ( ( SV795 = SV1346 )
= $true )
| ( ( class_Orderings_Oorder @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5169,plain,
! [SV799: $i,SV214: $i,SV1775: $i,SV1350: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1350 @ SV1775 @ SV214 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV214 ) @ SV799 ) @ SV1350 ) @ SV1775 @ SV214 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5170,plain,
! [SV1351: $i,SV215: $i,SV1776: $i,SV800: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV800 @ SV1776 @ SV215 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV215 ) @ SV800 ) @ SV1351 ) @ SV1776 @ SV215 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV215 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4947]) ).
thf(5171,plain,
! [SV218: $i,SV1777: $i,SV1354: $i,SV803: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) )
= $false )
| ( ( c_lessequals @ SV803 @ SV1354 @ ( tc_fun @ SV1777 @ SV218 ) )
= $true )
| ( ( class_HOL_Oord @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4948]) ).
thf(5172,plain,
! [SV1362: $i,SV226: $i,SV811: $i,SV1779: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1779 ) @ SV811 ) @ SV226 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SV1779 ) @ ( tc_fun @ SV1779 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(5173,plain,
! [SV1363: $i,SV227: $i,SV812: $i] :
( ( ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
= $false )
| ( ( ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
= $true )
| ( ( class_Orderings_Olinorder @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4954]) ).
thf(5174,plain,
! [SV2180: $i,SV2154: $i,SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY6108: $i,SY6109: $i,SY6110: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SV2180 @ SY6108 @ SV2013 @ SY6109 @ SY6110 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4955]) ).
thf(5175,plain,
! [SV2181: $i,SV2155: $i,SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY6111: $i,SY6112: $i,SY6113: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SV2181 @ SV2014 @ SY6111 @ SY6112 @ SY6113 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4956]) ).
thf(5176,plain,
! [SV232: $i,SV1368: $i,SV817: $i,SV1783: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1783 @ SV817 @ SV1368 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV1783 @ SV1368 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV232 @ SV817 @ SV1368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4957]) ).
thf(5177,plain,
! [SV1788: $i,SV823: $i,SV238: $i,SV2017: $i,SV1373: $i] :
( ( ( c_lessequals @ SV1373 @ SV2017 @ ( tc_fun @ SV238 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV823 @ SV1788 @ ( tc_fun @ SV238 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV1788 ) @ SV2017 ) @ ( tc_fun @ SV238 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4958]) ).
thf(5178,plain,
! [SV1376: $i,SV241: $i,SV1789: $i,SV826: $i] :
( ( ( ~ ( c_lessequals @ SV826 @ SV1789 @ SV241 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) )
= $true )
| ( ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4959]) ).
thf(5179,plain,
! [SV1377: $i,SV242: $i,SV1790: $i,SV827: $i] :
( ( ( ~ ( c_lessequals @ SV827 @ SV1790 @ SV242 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) )
= $true )
| ( ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(5180,plain,
! [SV1378: $i,SV243: $i,SV1791: $i,SV828: $i] :
( ( ( ~ ( c_lessequals @ SV828 @ SV1791 @ SV243 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) )
= $true )
| ( ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5181,plain,
! [SV1792: $i,SV833: $i,SV1383: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ SV1383 @ ( tc_fun @ SV833 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV248 @ SV1792 @ ( tc_fun @ SV833 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV248 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV833 @ tc_bool ) ) @ SV1383 ) @ SV1792 ) @ ( tc_fun @ SV833 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4962]) ).
thf(5182,plain,
! [SV1793: $i,SV834: $i,SV1384: $i,SV249: $i] :
( ( ( c_lessequals @ SV249 @ SV1384 @ ( tc_fun @ SV834 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV249 @ SV1793 @ ( tc_fun @ SV834 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV249 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV834 @ tc_bool ) ) @ SV1384 ) @ SV1793 ) @ ( tc_fun @ SV834 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4963]) ).
thf(5183,plain,
! [SV1800: $i,SV1392: $i,SV259: $i,SV844: $i] :
( ( ( c_lessequals @ SV844 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV259 ) @ SV1392 ) @ SV1800 ) @ SV259 )
= $false )
| ( ( c_lessequals @ SV844 @ SV1392 @ SV259 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4965]) ).
thf(5184,plain,
! [SV1393: $i,SV1801: $i,SV260: $i,SV845: $i] :
( ( ( c_lessequals @ SV845 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV260 ) @ SV1801 ) @ SV1393 ) @ SV260 )
= $false )
| ( ( c_lessequals @ SV845 @ SV1393 @ SV260 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4966]) ).
thf(5185,plain,
! [SV1394: $i,SV261: $i,SV1802: $i,SV846: $i] :
( ( ( c_lessequals @ SV846 @ SV1802 @ SV261 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV261 ) @ SV846 ) @ SV1394 ) @ SV1802 @ SV261 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4967]) ).
thf(5186,plain,
! [SV847: $i,SV262: $i,SV1803: $i,SV1395: $i] :
( ( ( c_lessequals @ SV1395 @ SV1803 @ SV262 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV262 ) @ SV847 ) @ SV1395 ) @ SV1803 @ SV262 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4968]) ).
thf(5187,plain,
! [SV1804: $i,SV1396: $i,SV263: $i,SV848: $i] :
( ( ( c_lessequals @ SV848 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV263 ) @ SV1396 ) @ SV1804 ) @ SV263 )
= $false )
| ( ( c_lessequals @ SV848 @ SV1396 @ SV263 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5188,plain,
! [SV1397: $i,SV1805: $i,SV264: $i,SV849: $i] :
( ( ( c_lessequals @ SV849 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV264 ) @ SV1805 ) @ SV1397 ) @ SV264 )
= $false )
| ( ( c_lessequals @ SV849 @ SV1397 @ SV264 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4970]) ).
thf(5189,plain,
! [SV852: $i,SV1399: $i,SV1807: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4971]) ).
thf(5190,plain,
! [SV1402: $i,SV1809: $i,SV855: $i,SV270: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4972]) ).
thf(5191,plain,
! [SV2116: $i,SV279: $i,SV864: $i,SV1810: $i,SV1410: $i,SV2020: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(5192,plain,
! [SV1811: $i,SV1411: $i,SV2021: $i,SV2117: $i,SV865: $i,SV280: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SV2117 @ SV2021 @ SV1411 ) @ SV1411 @ SV1811 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV865 @ SV2117 @ SV2021 @ SV1411 ) )
= $true )
| ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SV2021 ) @ SV2117 @ SV2021 @ SV1811 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(5193,plain,
! [SV2157: $i,SV2118: $i,SV2022: $i,SV1812: $i,SV1413: $i,SV868: $i,SV283: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SV2022 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SV2118 ) @ SV2022 @ SV2157 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SV2118 @ SV2022 @ SV2157 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2022 ) @ SV1413 ) @ SV1812 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5194,plain,
! [SV287: $i,SV2024: $i,SV1815: $i,SV1417: $i,SV872: $i] :
( ( ( c_Fun_Oinj__on @ SV872 @ ( c_Set_Oinsert @ SV1417 @ SV1815 @ SV2024 ) @ SV2024 @ SV287 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV287 ) @ ( hAPP @ SV872 @ SV1417 ) ) @ ( c_Set_Oimage @ SV872 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Set_Oinsert @ SV1417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 ) @ ( tc_fun @ SV2024 @ tc_bool ) ) @ SV2024 @ SV287 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4976]) ).
thf(5195,plain,
! [SV2158: $i,SV2119: $i,SV2025: $i,SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SV2119 @ SV2158 )
= $true )
| ( ( ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2025 @ SV2119 @ SV2158 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2119 ) @ SV1817 ) @ SV1419 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(5196,plain,
! [SV1420: $i,SV1818: $i,SV875: $i,SV290: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) ) @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV290 @ SV1420 @ ( tc_fun @ SV1818 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV290 @ ( c_Set_Oinsert @ SV875 @ SV1420 @ SV1818 ) @ ( tc_fun @ SV1818 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5197,plain,
! [SV1823: $i,SV1426: $i,SV2028: $i,SV296: $i,SV881: $i] :
( ( ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SV2028 @ SV1426 @ SV1823 ) @ ( tc_fun @ SV1823 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SV1823 ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SV1823 ) @ SV2028 @ ( tc_fun @ SV1426 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4982]) ).
thf(5198,plain,
! [SV1826: $i,SV303: $i,SV1431: $i,SV887: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV887 @ SV1431 @ SV303 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV887 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV303 ) @ SV1431 ) @ SV1826 ) @ SV303 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4983]) ).
thf(5199,plain,
! [SV1432: $i,SV304: $i,SV1827: $i,SV888: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV888 @ SV1827 @ SV304 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV888 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV304 ) @ SV1432 ) @ SV1827 ) @ SV304 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5200,plain,
! [SV2030: $i,SV308: $i,SV1829: $i,SV1436: $i,SV892: $i] :
( ( ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SV1829 @ SV1436 ) @ SV308 )
= $true )
| ( ( ~ ( c_lessequals @ SV892 @ SV1829 @ ( tc_fun @ SV2030 @ SV308 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5201,plain,
! [SV1830: $i,SV1437: $i,SV893: $i,SV309: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1437 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ SV1830 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV309 ) @ SV893 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV1437 ) @ SV1830 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4986]) ).
thf(5202,plain,
! [SV1831: $i,SV1438: $i,SV894: $i,SV310: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1438 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ SV1831 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV310 ) @ SV894 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV310 @ tc_bool ) ) @ SV1438 ) @ SV1831 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5203,plain,
! [SV897: $i,SV313: $i,SV1441: $i,SV1834: $i] :
( ( ( c_lessequals @ SV1834 @ SV1441 @ ( tc_fun @ SV313 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1834 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV313 ) @ SV897 ) @ SV1441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5204,plain,
! [SV1442: $i,SV1835: $i,SV898: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1835 ) )
= $false )
| ( ( c_lessequals @ SV1835 @ SV1442 @ ( tc_fun @ SV314 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV314 ) @ SV898 ) @ SV1442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5205,plain,
! [SV899: $i,SV315: $i,SV1443: $i,SV1836: $i] :
( ( ( c_lessequals @ SV1836 @ SV1443 @ ( tc_fun @ SV315 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1836 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV315 ) @ SV899 ) @ SV1443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5206,plain,
! [SV900: $i,SV316: $i,SV1444: $i,SV1837: $i] :
( ( ( c_lessequals @ SV1837 @ SV1444 @ ( tc_fun @ SV316 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1837 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV316 ) @ SV900 ) @ SV1444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4991]) ).
thf(5207,plain,
! [SV2032: $i,SV906: $i,SV322: $i,SV1450: $i,SV2120: $i,SV1843: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1843 ) @ SV2120 ) @ SV1450 ) )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ooverride__on @ SV322 @ SV906 @ SV1450 @ SV1843 @ SV2032 ) @ SV2120 )
= ( hAPP @ SV906 @ SV2120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4995]) ).
thf(5208,plain,
! [SV911: $i,SV327: $i,SV1454: $i,SV1847: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1847 @ SV1454 @ ( tc_fun @ SV327 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1847 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV327 ) @ SV911 ) @ SV1454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4998]) ).
thf(5209,plain,
! [SV1464: $i,SV2034: $i,SV2122: $i,SV1852: $i,SV921: $i,SV337: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SV2122 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2034 ) @ SV2122 ) @ SV1464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SV2034 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5001]) ).
thf(5210,plain,
! [SV1465: $i,SV2035: $i,SV2123: $i,SV1853: $i,SV922: $i,SV338: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SV2123 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2035 ) @ SV2123 ) @ SV1465 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SV2035 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5002]) ).
thf(5211,plain,
! [SV2182: $i,SV2159: $i,SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY6114: $i,SY6115: $i,SY6116: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SY6114 @ SY6115 @ SY6116 @ SV2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5008]) ).
thf(5212,plain,
! [SV2183: $i,SV2160: $i,SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY6117: $i,SY6118: $i,SY6119: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SY6117 @ SY6118 @ SY6119 @ SV2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5009]) ).
thf(5213,plain,
! [SV1861: $i,SV347: $i,SV1474: $i,SV2043: $i,SV2126: $i,SV931: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SV2126 ) @ SV2043 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SV2126 ) @ SV347 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SV2043 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5010]) ).
thf(5214,plain,
! [SV1862: $i,SV348: $i,SV1475: $i,SV2044: $i,SV2127: $i,SV932: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SV2127 ) @ SV2044 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SV2127 ) @ SV348 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SV2044 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5215,plain,
! [SV937: $i,SV1866: $i,SV353: $i,SV1480: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1480 ) @ SV353 ) @ SV1866 ) )
= $false )
| ( ( c_lessequals @ SV937 @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV353 @ SV937 @ SV1480 ) @ SV1866 @ ( tc_fun @ SV1480 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5216,plain,
! [SV2184: $i,SV2161: $i,SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY6120: $i,SY6121: $i,SY6122: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SY6120 @ SV357 @ SY6121 @ SY6122 @ SV2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5014]) ).
thf(5217,plain,
! [SV2185: $i,SV2162: $i,SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY6123: $i,SY6124: $i,SY6125: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SY6123 @ SY6124 @ SY6125 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5015]) ).
thf(5218,plain,
! [SV2186: $i,SV2163: $i,SV2130: $i,SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY6126: $i,SY6127: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SY6126 @ SV1486 @ SV1869 @ SY6127 @ SV2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5016]) ).
thf(5219,plain,
! [SV2187: $i,SV2164: $i,SV2131: $i,SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY6128: $i,SY6129: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SY6128 @ SY6129 @ SV1870 @ SV2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5017]) ).
thf(5220,plain,
! [SV1494: $i,SV953: $i,SV1874: $i,SV370: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV370 ) @ SV1874 ) @ SV953 ) @ SV1494 @ SV370 )
= $false )
| ( ( c_lessequals @ SV953 @ SV1494 @ SV370 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV370 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5019]) ).
thf(5221,plain,
! [SV1495: $i,SV1875: $i,SV954: $i,SV371: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV371 ) @ SV954 ) @ SV1875 ) @ SV1495 @ SV371 )
= $false )
| ( ( c_lessequals @ SV954 @ SV1495 @ SV371 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV371 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5020]) ).
thf(5222,plain,
! [SV1496: $i,SV372: $i,SV1876: $i,SV955: $i] :
( ( ( c_lessequals @ SV955 @ SV1876 @ SV372 )
= $false )
| ( ( c_lessequals @ SV955 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV372 ) @ SV1496 ) @ SV1876 ) @ SV372 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5021]) ).
thf(5223,plain,
! [SV1877: $i,SV373: $i,SV1497: $i,SV956: $i] :
( ( ( c_lessequals @ SV956 @ SV1497 @ SV373 )
= $false )
| ( ( c_lessequals @ SV956 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV373 ) @ SV1497 ) @ SV1877 ) @ SV373 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5224,plain,
! [SV1498: $i,SV957: $i,SV1878: $i,SV374: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV374 ) @ SV1878 ) @ SV957 ) @ SV1498 @ SV374 )
= $false )
| ( ( c_lessequals @ SV957 @ SV1498 @ SV374 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5023]) ).
thf(5225,plain,
! [SV1499: $i,SV1879: $i,SV958: $i,SV375: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV375 ) @ SV958 ) @ SV1879 ) @ SV1499 @ SV375 )
= $false )
| ( ( c_lessequals @ SV958 @ SV1499 @ SV375 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5024]) ).
thf(5226,plain,
! [SV1503: $i,SV379: $i,SV1882: $i,SV962: $i] :
( ( ( ~ ( c_lessequals @ SV962 @ SV1882 @ SV379 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1882 @ SV1503 @ SV379 ) )
= $true )
| ( ( c_lessequals @ SV962 @ SV1503 @ SV379 )
= $true )
| ( ( class_Orderings_Oorder @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5227,plain,
! [SV1504: $i,SV380: $i,SV1883: $i,SV963: $i] :
( ( ( ~ ( c_lessequals @ SV963 @ SV1883 @ SV380 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
= $true )
| ( ( class_Orderings_Oorder @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5228,plain,
! [SV1505: $i,SV381: $i,SV1884: $i,SV964: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1884 @ SV1505 @ SV381 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
= $true )
| ( ( class_Orderings_Oorder @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5027]) ).
thf(5229,plain,
! [SV965: $i,SV382: $i,SV1506: $i,SV1885: $i] :
( ( ( ~ ( c_lessequals @ SV1885 @ SV1506 @ SV382 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV965 @ SV1885 @ SV382 ) )
= $true )
| ( ( c_lessequals @ SV965 @ SV1506 @ SV382 )
= $true )
| ( ( class_Orderings_Opreorder @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5028]) ).
thf(5230,plain,
! [SV968: $i,SV1507: $i,SV1886: $i,SV385: $i] :
( ( ( c_lessequals @ SV385 @ SV1886 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1886 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV385 @ SV968 @ ( tc_fun @ SV1507 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5231,plain,
! [SV1887: $i,SV386: $i,SV1508: $i,SV2051: $i,SV969: $i] :
( ( ( c_lessequals @ SV969 @ SV2051 @ ( tc_fun @ SV1508 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV386 @ SV2051 @ SV1508 @ SV1887 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SV1887 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5232,plain,
! [SV970: $i,SV1888: $i,SV387: $i,SV1509: $i] :
( ( ( c_lessequals @ SV1509 @ SV387 @ ( tc_fun @ SV1888 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1509 @ SV970 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV387 @ SV970 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5233,plain,
! [SV974: $i,SV1511: $i,SV1889: $i,SV391: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV391 @ SV1889 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1889 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV391 @ SV974 @ ( tc_fun @ SV1511 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5234,plain,
! [SV975: $i,SV1512: $i,SV1890: $i,SV392: $i] :
( ( ( c_lessequals @ SV392 @ SV1890 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1890 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV975 @ ( tc_fun @ SV1512 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5034]) ).
thf(5235,plain,
! [SV1891: $i,SV393: $i,SV976: $i,SV1513: $i] :
( ( ( hBOOL @ ( hAPP @ SV1513 @ SV976 ) )
= $false )
| ( ( c_lessequals @ SV1513 @ SV393 @ ( tc_fun @ SV1891 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV976 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5236,plain,
! [SV978: $i,SV395: $i,SV1515: $i,SV1892: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV978 @ SV1892 @ SV395 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
= $true )
| ( ( class_Orderings_Opreorder @ SV395 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5037]) ).
thf(5237,plain,
! [SV979: $i,SV396: $i,SV1516: $i,SV1893: $i] :
( ( ( ~ ( c_lessequals @ SV1893 @ SV1516 @ SV396 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
= $true )
| ( ( class_Orderings_Opreorder @ SV396 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5038]) ).
thf(5238,plain,
! [SV1894: $i,SV981: $i,SV398: $i,SV2052: $i,SV1517: $i] :
( ( ( c_lessequals @ SV1517 @ SV2052 @ ( tc_fun @ SV398 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV981 @ SV1894 @ ( tc_fun @ SV398 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV1894 ) @ SV2052 ) @ ( tc_fun @ SV398 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5239,plain,
! [SV2053: $i,SV402: $i,SV985: $i,SV1897: $i,SV2133: $i,SV1520: $i] :
( ( ( ~ ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5040]) ).
thf(5240,plain,
! [SV2188: $i,SV2165: $i,SV2134: $i,SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY6130: $i,SY6131: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SV2165 @ SV2188 @ SY6130 @ SY6131 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5041]) ).
thf(5241,plain,
! [SV2189: $i,SV2166: $i,SV2135: $i,SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY6132: $i,SY6133: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SV2166 @ SV2189 @ SY6132 @ SY6133 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5042]) ).
thf(5242,plain,
! [SV1900: $i,SV1523: $i,SV988: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ SV1523 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1900 @ SV988 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV405 ) @ SV988 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV405 @ tc_bool ) ) @ SV1523 ) @ ( c_Collect @ SV1900 @ SV405 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5243,plain,
! [SV995: $i,SV1530: $i,SV412: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV995 @ SV412 ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
= $true )
| ( ( class_Orderings_Olinorder @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5046]) ).
thf(5244,plain,
! [SV2167: $i,SV2136: $i,SV2060: $i,SV1906: $i,SV1531: $i,SV996: $i,SV413: $i] :
( ( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SV2167 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SV2167 @ SV2136 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
| ~ ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SV2167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5245,plain,
! [SV414: $i,SV1532: $i,SV1907: $i,SV997: $i] :
( ( ( hBOOL @ ( hAPP @ SV997 @ SV1907 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1532 @ SV1907 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV414 @ tc_bool ) ) @ SV997 ) @ SV1532 ) @ SV1907 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5048]) ).
thf(5246,plain,
! [SV999: $i,SV1909: $i,SV416: $i,SV1534: $i] :
( ( ( c_lessequals @ SV1534 @ SV416 @ ( tc_fun @ SV1909 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV416 @ SV999 @ ( tc_fun @ SV1909 @ tc_bool ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV416 @ ( c_HOL_Ominus__class_Ominus @ SV999 @ SV1534 @ ( tc_fun @ SV1909 @ tc_bool ) ) @ ( tc_fun @ SV1909 @ tc_bool ) )
= SV1534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5247,plain,
! [SV1913: $i,SV1004: $i,SV421: $i,SV1538: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV1538 @ SV421 @ SV1004 @ SV1913 ) @ SV1913 )
= $false )
| ( ( c_Fun_Oinj__on @ SV1538 @ SV421 @ SV1004 @ SV1913 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV421 @ SV1004 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5052]) ).
thf(5248,plain,
! [SV422: $i,SV1539: $i,SV1005: $i] :
( ( ( c_lessequals @ SV1005 @ SV1539 @ SV422 )
= $false )
| ( ( SV1539 = SV1005 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1005 @ SV1539 @ SV422 )
= $true )
| ( ( class_Orderings_Oorder @ SV422 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5249,plain,
! [SV423: $i,SV1540: $i,SV1006: $i] :
( ( ( c_lessequals @ SV1006 @ SV1540 @ SV423 )
= $false )
| ( ( SV1540 = SV1006 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1006 @ SV1540 @ SV423 )
= $true )
| ( ( class_Orderings_Oorder @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5054]) ).
thf(5250,plain,
! [SV425: $i,SV1542: $i,SV1008: $i] :
( ( ( c_lessequals @ SV1008 @ SV1542 @ SV425 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1008 @ SV1542 @ SV425 )
= $true )
| ( ( SV1008 = SV1542 )
= $true )
| ( ( class_Orderings_Oorder @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5251,plain,
! [SV426: $i,SV1543: $i,SV1009: $i] :
( ( ( c_lessequals @ SV1009 @ SV1543 @ SV426 )
= $false )
| ( ( SV1009 = SV1543 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV1543 @ SV426 )
= $true )
| ( ( class_Orderings_Oorder @ SV426 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5252,plain,
! [SV428: $i,SV1545: $i,SV1011: $i] :
( ( ( c_lessequals @ SV1011 @ SV1545 @ SV428 )
= $false )
| ( ( SV1011 = SV1545 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1545 @ SV428 )
= $true )
| ( ( class_Orderings_Oorder @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5253,plain,
! [SV429: $i,SV1546: $i,SV1012: $i] :
( ( ( c_lessequals @ SV1012 @ SV1546 @ SV429 )
= $false )
| ( ( SV1012 = SV1546 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1012 @ SV1546 @ SV429 )
= $true )
| ( ( class_Orderings_Oorder @ SV429 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5058]) ).
thf(5254,plain,
! [SV430: $i,SV1547: $i,SV1013: $i] :
( ( ( c_lessequals @ SV1013 @ SV1547 @ SV430 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1013 @ SV1547 @ SV430 )
= $true )
| ( ( SV1013 = SV1547 )
= $true )
| ( ( class_Orderings_Olinorder @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5059]) ).
thf(5255,plain,
! [SV431: $i,SV1548: $i,SV1014: $i] :
( ( ( c_lessequals @ SV1014 @ SV1548 @ SV431 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1548 @ SV431 )
= $true )
| ( ( SV1014 = SV1548 )
= $true )
| ( ( class_Orderings_Olinorder @ SV431 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5060]) ).
thf(5256,plain,
! [SV1549: $i,SV1015: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1549 @ SV432 ) )
= $true )
| ( ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
= $true )
| ( ( class_Orderings_Olinorder @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5257,plain,
! [SV437: $i,SV1020: $i,SV1553: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1553 @ SV1020 @ SV437 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1020 @ SV1553 @ SV437 )
= $false )
| ( ( class_Orderings_Oorder @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5064]) ).
thf(5258,plain,
! [SV438: $i,SV1021: $i,SV1554: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1554 @ SV1021 @ SV438 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1021 @ SV1554 @ SV438 )
= $false )
| ( ( class_Orderings_Olinorder @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5065]) ).
thf(5259,plain,
! [SV440: $i,SV1023: $i,SV1556: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1556 @ SV1023 @ SV440 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1023 @ SV1556 @ SV440 )
= $false )
| ( ( class_Orderings_Opreorder @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5066]) ).
thf(5260,plain,
! [SV441: $i,SV1024: $i,SV1557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1557 @ SV1024 @ SV441 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1024 @ SV1557 @ SV441 )
= $false )
| ( ( class_Orderings_Opreorder @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5067]) ).
thf(5261,plain,
! [SV2190: $i,SV2169: $i,SV2138: $i,SV2069: $i,SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ! [SY6134: $i] :
( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SV2138 @ SV2169 @ SV2190 @ SY6134 @ SV1571 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5074]) ).
thf(5262,plain,
! [SV2191: $i,SV2170: $i,SV2139: $i,SV2070: $i,SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ! [SY6135: $i] :
( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SV2139 @ SV2170 @ SV2191 @ SV1572 @ SY6135 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5075]) ).
thf(5263,plain,
! [SV1079: $i,SV1588: $i,SV499: $i,SV1934: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1934 @ SV499 ) ) @ SV1934 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1934 @ SV1588 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5264,plain,
! [SV1082: $i,SV1591: $i,SV1935: $i,SV502: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(5265,plain,
! [SV2073: $i,SV1936: $i,SV535: $i,SV1599: $i,SV1112: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
!= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(5266,plain,
! [SV1600: $i,SV1113: $i,SV1937: $i,SV2074: $i,SV536: $i] :
( ( ( SV536 = SV2074 )
= $true )
| ( ( SV536 = SV1937 )
= $true )
| ( ( ( c_Set_Oinsert @ SV536 @ ( c_Set_Oinsert @ SV1113 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 )
= ( c_Set_Oinsert @ SV1937 @ ( c_Set_Oinsert @ SV2074 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1600 @ tc_bool ) ) @ SV1600 ) @ SV1600 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5081]) ).
thf(5267,plain,
! [SV1601: $i,SV537: $i,SV2075: $i,SV1938: $i,SV1114: $i] :
( ( ( SV1114 = SV1938 )
= $true )
| ( ( SV1114 = SV2075 )
= $true )
| ( ( ( c_Set_Oinsert @ SV537 @ ( c_Set_Oinsert @ SV1114 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 )
= ( c_Set_Oinsert @ SV1938 @ ( c_Set_Oinsert @ SV2075 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1601 @ tc_bool ) ) @ SV1601 ) @ SV1601 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5082]) ).
thf(5268,plain,
! [SV1602: $i,SV1115: $i,SV2076: $i,SV1939: $i,SV538: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 @ SV2076 ) )
= $true )
| ( ( SV1115 = SV1602 )
= $true )
| ( ( ( hAPP @ SV538 @ SV1115 )
= ( hAPP @ SV538 @ SV1602 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5083]) ).
thf(5269,plain,
! [SV1940: $i,SV1603: $i,SV1116: $i,SV2077: $i,SV539: $i] :
( ( ( SV539 = SV2077 )
= $true )
| ( ( SV1116 = SV2077 )
= $true )
| ( ( ( c_Set_Oinsert @ SV539 @ ( c_Set_Oinsert @ SV1116 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 )
= ( c_Set_Oinsert @ SV1940 @ ( c_Set_Oinsert @ SV2077 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1603 @ tc_bool ) ) @ SV1603 ) @ SV1603 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5084]) ).
thf(5270,plain,
! [SV540: $i,SV1604: $i,SV1941: $i,SV2078: $i,SV1117: $i] :
( ( ( ( hAPP @ SV1117 @ SV2078 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SV2078 ) @ SV540 ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SV1941 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(5271,plain,
! [SV2079: $i,SV1605: $i,SV541: $i,SV1942: $i,SV1118: $i] :
( ( ( SV1118 = SV1942 )
= $true )
| ( ( SV541 = SV1942 )
= $true )
| ( ( ( c_Set_Oinsert @ SV541 @ ( c_Set_Oinsert @ SV1118 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 )
= ( c_Set_Oinsert @ SV1942 @ ( c_Set_Oinsert @ SV2079 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1605 @ tc_bool ) ) @ SV1605 ) @ SV1605 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5272,plain,
! [SV1943: $i,SV1606: $i,SV542: $i,SV1119: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1119 @ SV542 )
= ( c_HOL_Ominus__class_Ominus @ SV1606 @ SV1943 @ SV542 ) )
= $false )
| ( ( SV1606 = SV1943 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5087]) ).
thf(5273,plain,
! [SV1944: $i,SV1120: $i,SV543: $i,SV1607: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1120 ) )
= $true )
| ( ( SV1120 = SV1944 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1607 ) @ SV543 ) @ SV1944 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV543 @ SV1120 @ SV1607 )
= ( c_Set_Oinsert @ SV543 @ SV1944 @ SV1607 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5274,plain,
! [SV1609: $i,SV1945: $i,SV1122: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1945 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SV1945 ) @ SV1609 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5090]) ).
thf(5275,plain,
! [SV2080: $i,SV1126: $i,SV1947: $i,SV1613: $i,SV549: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SV1947 ) )
= $true )
| ( ( SV1126 = SV2080 )
= $true )
| ( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SV1947 )
= ( c_Set_Oimage @ SV549 @ SV2080 @ SV1613 @ SV1947 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5091]) ).
thf(5276,plain,
! [SV2081: $i,SV1948: $i,SV550: $i,SV1614: $i,SV1127: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
!= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5092]) ).
thf(5277,plain,
! [SV2192: $i,SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY6136: $i,SY6137: $i,SY6138: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SV2192 @ SY6136 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SY6137 @ SV2192 @ SY6138 ) @ SV2140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5094]) ).
thf(5278,plain,
! [SV1619: $i,SV555: $i,SV2083: $i,SV1950: $i,SV1132: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5095]) ).
thf(5279,plain,
! [SV2084: $i,SV1952: $i,SV1135: $i,SV559: $i,SV1622: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV1952 @ SV2084 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5096]) ).
thf(5280,plain,
! [SV2085: $i,SV1953: $i,SV562: $i,SV1625: $i,SV1138: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
!= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
= $true )
| ( ( ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5099]) ).
thf(5281,plain,
! [SV2141: $i,SV2086: $i,SV1954: $i,SV1626: $i,SV1139: $i,SV563: $i] :
( ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5100]) ).
thf(5282,plain,
! [SV1955: $i,SV564: $i,SV1627: $i,SV1140: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1140 @ SV1627 @ SV564 )
= ( c_HOL_Ominus__class_Ominus @ SV1955 @ SV1955 @ SV564 ) )
= $false )
| ( ( SV1140 = SV1627 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5101]) ).
thf(5283,plain,
! [SV2142: $i,SV2087: $i,SV1956: $i,SV1628: $i,SV1141: $i,SV565: $i] :
( ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
| ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5102]) ).
thf(5284,plain,
! [SV1957: $i,SV2088: $i,SV1143: $i,SV1630: $i,SV567: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SV2088 ) @ SV1630 @ SV1957 ) )
= $true )
| ( ( SV1143 = SV2088 )
= $true )
| ( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SV1957 )
= ( c_Set_Oimage @ SV567 @ SV2088 @ SV1630 @ SV1957 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(5285,plain,
! [SV2193: $i,SV2172: $i,SV2143: $i,SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ! [SY6139: $i] :
( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
!= ( c_Fun_Ocomp @ SV2143 @ SV2172 @ SV2193 @ SV1958 @ SV2089 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SY6139 ) )
= ( hAPP @ SV2143 @ ( hAPP @ SV2172 @ SY6139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5105]) ).
thf(5286,plain,
! [SV2173: $i,SV2144: $i,SV2090: $i,SV1959: $i,SV1636: $i,SV1151: $i,SV575: $i] :
( ( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SV1959 @ SV2090 )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV1959 ) @ SV2144 @ SV1959 @ SV1959 @ SV2090 ) )
= $true )
| ( ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SV2173 ) )
= ( hAPP @ SV2144 @ SV2173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5106]) ).
thf(5287,plain,
! [SV1152: $i,SV1960: $i,SV576: $i,SV2091: $i,SV1637: $i] :
( ( ( ( hAPP @ SV1637 @ SV2091 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1960 ) @ SV2091 ) @ SV1152 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SV1960 @ ( tc_fun @ SV576 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(5288,plain,
! [SV2092: $i,SV1963: $i,SV584: $i,SV1643: $i,SV1158: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
!= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
= $true )
| ( ( ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SV2092 @ SV1963 @ SV584 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5109]) ).
thf(5289,plain,
! [SV2145: $i,SV2093: $i,SV1965: $i,SV1645: $i,SV1160: $i,SV586: $i] :
( ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5290,plain,
! [SV2146: $i,SV2094: $i,SV1966: $i,SV1646: $i,SV1161: $i,SV587: $i] :
( ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5111]) ).
thf(5291,plain,
! [SV1967: $i,SV588: $i,SV1647: $i,SV1162: $i,SV2: $i] :
( ( ( c_Fun_Oinj__on @ SV2 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1162 @ tc_bool ) ) @ SV1162 @ SV1647 )
= $false )
| ( ( c_lessequals @ SV588 @ SV1967 @ ( tc_fun @ SV1162 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2 @ SV588 @ SV1162 @ SV1647 ) @ ( c_Set_Oimage @ SV2 @ SV1967 @ SV1162 @ SV1647 ) @ ( tc_fun @ SV1647 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5112]) ).
thf(5292,plain,
! [SV4: $i,SV590: $i,SV1649: $i,SV1164: $i,SV1969: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1164 ) @ SV1649 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV590 @ SV1164 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1649 @ SV590 @ SV1969 @ SV4 ) @ SV4 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5293,plain,
! [SV2194: $i,SV2174: $i,SV2147: $i,SV2095: $i,SV1972: $i,SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SV2095 @ SV2147 @ SV2174 @ SV2194 @ SV1170 @ SV596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5115]) ).
thf(5294,plain,
! [SV2195: $i,SV2175: $i,SV2148: $i,SV2096: $i,SV1973: $i,SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SV2096 @ SV2148 @ SV2175 @ SV1171 @ SV2195 @ SV597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5116]) ).
thf(5295,plain,
! [SV1172: $i,SV1657: $i,SV598: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV12 @ ( c_Set_Oinsert @ SV598 @ SV1657 @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV1657 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1172 ) @ SV598 ) @ SV12 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV12 @ ( c_Set_Oinsert @ SV598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1172 ) @ ( tc_fun @ SV1172 @ tc_bool ) ) @ SV1657 @ ( tc_fun @ SV1172 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5117]) ).
thf(5296,plain,
! [SV1173: $i,SV1658: $i,SV599: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV13 @ ( c_Set_Oinsert @ SV599 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) ) @ SV1173 @ ( tc_fun @ SV1658 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV1173 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1658 ) @ SV599 ) @ SV13 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV599 @ SV1173 @ SV1658 ) @ ( tc_fun @ SV1658 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5118]) ).
thf(5297,plain,
! [SV2176: $i,SV2149: $i,SV2097: $i,SV1974: $i,SV1659: $i,SV1174: $i,SV600: $i,SV14: $i] :
( ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
| ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5119]) ).
thf(5298,plain,
! [SV1176: $i,SV1660: $i,SV602: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1660 @ SV16 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5299,plain,
! [SV1181: $i,SV1665: $i,SV607: $i,SV21: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5121]) ).
thf(5300,plain,
! [SV624: $i,SV1193: $i,SV1672: $i,SV38: $i,SV1977: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5301,plain,
! [SV1195: $i,SV1674: $i,SV41: $i,SV2098: $i,SV627: $i,SV1978: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1978 ) @ SV627 ) @ SV2098 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2098 @ SV41 @ SV1978 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5123]) ).
thf(5302,plain,
! [SV2150: $i,SV1980: $i,SV633: $i,SV47: $i,SV1201: $i,SV1677: $i,SV2099: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2099 ) @ SV1677 ) @ SV1201 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV2099 ) @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV1980 @ SV2099 @ SV2150 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SV2099 @ SV2150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5303,plain,
! [SV2196: $i,SV2177: $i,SV2151: $i,SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY6140: $i,SY6141: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SV2177 @ SV2196 @ SV1982 @ SY6140 @ SY6141 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5125]) ).
thf(5304,plain,
! [SV2197: $i,SV2178: $i,SV2152: $i,SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY6142: $i,SY6143: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SV2178 @ SV1983 @ SV2197 @ SY6142 @ SY6143 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5126]) ).
thf(5305,plain,
! [SV1214: $i,SV646: $i,SV1687: $i,SV60: $i,SV1989: $i] :
( ( ( c_Fun_Oinj__on @ SV1989 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV60 @ tc_bool ) ) @ SV60 @ SV1687 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ ( hAPP @ SV1989 @ SV646 ) ) @ ( c_Set_Oimage @ SV1989 @ SV1214 @ SV60 @ SV1687 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV60 ) @ SV646 ) @ SV1214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5127]) ).
thf(5306,plain,
! [SV1688: $i,SV1215: $i,SV61: $i,SV1990: $i,SV647: $i] :
( ( ( c_Fun_Oinj__on @ SV647 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1990 @ tc_bool ) ) @ SV1990 @ SV61 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1990 ) @ SV1215 ) @ SV1688 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV61 ) @ ( hAPP @ SV647 @ SV1215 ) ) @ ( c_Set_Oimage @ SV647 @ SV1688 @ SV1990 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5128]) ).
thf(5307,plain,
! [SV654: $i,SV68: $i,SV1993: $i,SV1222: $i,SV1695: $i] :
( ( ( c_Fun_Oinj__on @ SV1695 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV1222 @ SV1993 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV1695 @ SV68 @ SV1222 @ SV1993 ) @ ( c_Set_Oimage @ SV1695 @ SV654 @ SV1222 @ SV1993 ) @ ( tc_fun @ SV1993 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV68 @ SV654 @ ( tc_fun @ SV1222 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5129]) ).
thf(5308,plain,
! [SV1994: $i,SV72: $i,SV1226: $i,SV658: $i,SV2104: $i,SV1699: $i] :
( ( ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5133]) ).
thf(5309,plain,
! [SV659: $i,SV1227: $i,SV73: $i,SV1995: $i,SV1700: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1700 @ SV1995 )
= $false )
| ( ( c_lessequals @ SV73 @ ( c_Set_Oimage @ SV1227 @ SV1700 @ SV1995 @ SV659 ) @ ( tc_fun @ SV659 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV73 @ SV659 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5134]) ).
thf(5310,plain,
! [SV1701: $i,SV74: $i,SV660: $i,SV2105: $i,SV1228: $i,SV1996: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1996 ) @ SV1228 ) @ SV2105 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SV2105 @ SV1996 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5135]) ).
thf(5311,plain,
! [SV675: $i,SV89: $i,SV1241: $i,SV1711: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
= $true )
| ( ( class_Orderings_Opreorder @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5139]) ).
thf(5312,plain,
! [SV1243: $i,SV91: $i,SV1713: $i,SV677: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5141]) ).
thf(5313,plain,
! [SV108: $i,SV1721: $i,SV694: $i,SV1257: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1257 @ SV694 @ ( tc_fun @ SV1721 @ SV108 ) )
= $false )
| ( ( c_lessequals @ SV694 @ SV1257 @ ( tc_fun @ SV1721 @ SV108 ) )
= $false )
| ( ( class_HOL_Oord @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5314,plain,
! [SV1260: $i,SV112: $i,SV698: $i] :
( ( ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
= $false )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5147]) ).
thf(5315,plain,
! [SV715: $i,SV129: $i,SV1732: $i,SV1276: $i] :
( ( ( c_lessequals @ SV1276 @ SV1732 @ SV129 )
= $false )
| ( ( ~ ( c_lessequals @ SV715 @ SV1732 @ SV129 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5316,plain,
! [SV718: $i,SV132: $i,SV1733: $i,SV1279: $i] :
( ( ( c_lessequals @ SV1279 @ SV1733 @ SV132 )
= $false )
| ( ( ~ ( c_lessequals @ SV718 @ SV1733 @ SV132 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5317,plain,
! [SV719: $i,SV133: $i,SV1734: $i,SV1280: $i] :
( ( ( c_lessequals @ SV1280 @ SV1734 @ SV133 )
= $false )
| ( ( ~ ( c_lessequals @ SV719 @ SV1734 @ SV133 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5152]) ).
thf(5318,plain,
! [SV2198: $i,SV2179: $i,SV2153: $i,SV2109: $i,SV2005: $i,SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SV2109 @ SV2153 @ SV2179 @ SV2198 @ SV1735 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SV2153 @ SV2109 @ SV2198 @ SV2179 @ SV1735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5153]) ).
thf(5319,plain,
! [SV1291: $i,SV1737: $i,SV730: $i,SV144: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV144 @ ( c_Set_Oinsert @ SV730 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) ) @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1737 ) @ SV730 ) @ SV1291 ) )
= $true )
| ( ( c_lessequals @ SV144 @ SV1291 @ ( tc_fun @ SV1737 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ ( c_Set_Oinsert @ SV730 @ SV1291 @ SV1737 ) @ ( tc_fun @ SV1737 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5154]) ).
thf(5320,plain,
! [SV733: $i,SV2006: $i,SV2110: $i,SV1739: $i,SV1294: $i,SV147: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SV2110 @ SV2006 @ SV2006 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SV2110 ) @ SV2006 @ SV2006 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5155]) ).
thf(5321,plain,
! [SV162: $i,SV1309: $i,SV748: $i] :
( ( ( c_Finite__Set_Ofinite @ SV748 @ SV1309 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 ) @ SV748 @ ( tc_fun @ SV1309 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV162 @ SV748 @ SV1309 @ SV1309 )
= $false )
| ( ( ( c_Set_Oimage @ SV162 @ SV748 @ SV1309 @ SV1309 )
= SV748 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5156]) ).
thf(5322,plain,
! [SV769: $i,SV2011: $i,SV1329: $i,SV1769: $i,SV183: $i] :
( ( ( c_lessequals @ SV183 @ SV1769 @ ( tc_fun @ SV1329 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV2011 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV183 @ SV769 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1769 @ SV2011 @ ( tc_fun @ SV1329 @ tc_bool ) ) @ ( tc_fun @ SV1329 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5162]) ).
thf(5323,plain,
! [SV193: $i,SV1773: $i,SV1334: $i,SV779: $i] :
( ( ( c_lessequals @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
= $false )
| ( ( c_lessequals @ SV1334 @ SV779 @ ( tc_fun @ SV1773 @ SV193 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1334 @ ( tc_fun @ SV1773 @ SV193 ) )
= $true )
| ( ( class_HOL_Oord @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5164]) ).
thf(5324,plain,
! [SV207: $i,SV1343: $i,SV792: $i] :
( ( ( c_lessequals @ SV792 @ SV1343 @ SV207 )
= $false )
| ( ( c_lessequals @ SV1343 @ SV792 @ SV207 )
= $false )
| ( ( SV792 = SV1343 )
= $true )
| ( ( class_Orderings_Oorder @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5325,plain,
! [SV209: $i,SV1345: $i,SV794: $i] :
( ( ( c_lessequals @ SV794 @ SV1345 @ SV209 )
= $false )
| ( ( c_lessequals @ SV1345 @ SV794 @ SV209 )
= $false )
| ( ( SV794 = SV1345 )
= $true )
| ( ( class_Orderings_Oorder @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5326,plain,
! [SV210: $i,SV795: $i,SV1346: $i] :
( ( ( c_lessequals @ SV1346 @ SV795 @ SV210 )
= $false )
| ( ( c_lessequals @ SV795 @ SV1346 @ SV210 )
= $false )
| ( ( SV795 = SV1346 )
= $true )
| ( ( class_Orderings_Oorder @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5327,plain,
! [SV811: $i,SV1779: $i,SV1362: $i,SV226: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1779 ) @ SV811 ) @ SV226 ) )
= $true )
| ( ( c_lessequals @ SV226 @ SV1362 @ ( tc_fun @ SV1779 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV226 @ ( c_Set_Oinsert @ SV811 @ SV1362 @ SV1779 ) @ ( tc_fun @ SV1779 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5328,plain,
! [SV812: $i,SV227: $i,SV1363: $i] :
( ( ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
= $false )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
= $true )
| ( ( class_Orderings_Olinorder @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5329,plain,
! [SV2199: $i,SV2180: $i,SV2154: $i,SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY6144: $i,SY6145: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SV2180 @ SV2199 @ SV2013 @ SY6144 @ SY6145 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5174]) ).
thf(5330,plain,
! [SV2200: $i,SV2181: $i,SV2155: $i,SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY6146: $i,SY6147: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SV2181 @ SV2014 @ SV2200 @ SY6146 @ SY6147 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5175]) ).
thf(5331,plain,
! [SV2017: $i,SV1373: $i,SV238: $i,SV1788: $i,SV823: $i] :
( ( ( c_lessequals @ SV823 @ SV1788 @ ( tc_fun @ SV238 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1373 @ SV2017 @ ( tc_fun @ SV238 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV823 ) @ SV1373 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV238 @ tc_bool ) ) @ SV1788 ) @ SV2017 ) @ ( tc_fun @ SV238 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5177]) ).
thf(5332,plain,
! [SV1376: $i,SV241: $i,SV1789: $i,SV826: $i] :
( ( ( c_lessequals @ SV826 @ SV1789 @ SV241 )
= $false )
| ( ( ~ ( c_lessequals @ SV826 @ SV1376 @ SV241 ) )
= $true )
| ( ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5178]) ).
thf(5333,plain,
! [SV1377: $i,SV242: $i,SV1790: $i,SV827: $i] :
( ( ( c_lessequals @ SV827 @ SV1790 @ SV242 )
= $false )
| ( ( ~ ( c_lessequals @ SV827 @ SV1377 @ SV242 ) )
= $true )
| ( ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5334,plain,
! [SV1378: $i,SV243: $i,SV1791: $i,SV828: $i] :
( ( ( c_lessequals @ SV828 @ SV1791 @ SV243 )
= $false )
| ( ( ~ ( c_lessequals @ SV828 @ SV1378 @ SV243 ) )
= $true )
| ( ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5180]) ).
thf(5335,plain,
! [SV852: $i,SV1399: $i,SV1807: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1399 @ SV267 ) )
= $true )
| ( ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5189]) ).
thf(5336,plain,
! [SV1402: $i,SV1809: $i,SV855: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5190]) ).
thf(5337,plain,
! [SV2116: $i,SV1410: $i,SV279: $i,SV1810: $i,SV864: $i,SV2020: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5338,plain,
! [SV1811: $i,SV1411: $i,SV2021: $i,SV2117: $i,SV865: $i,SV280: $i] :
( ( ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SV2117 @ SV2021 @ SV1411 ) @ SV1411 @ SV1811 )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV865 @ SV2117 @ SV2021 @ SV1411 ) )
= $true )
| ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SV2021 ) @ SV2117 @ SV2021 @ SV1811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5339,plain,
! [SV1413: $i,SV2157: $i,SV2022: $i,SV2118: $i,SV1812: $i,SV868: $i,SV283: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SV2118 @ SV2022 @ SV2157 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2022 ) @ SV1413 ) @ SV1812 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SV2022 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SV2118 ) @ SV2022 @ SV2157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5193]) ).
thf(5340,plain,
! [SV2158: $i,SV2025: $i,SV2119: $i,SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ( ~ ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2025 @ SV2119 @ SV2158 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2119 ) @ SV1817 ) @ SV1419 ) ) )
= $true )
| ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SV2119 @ SV2158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5341,plain,
! [SV2028: $i,SV881: $i,SV1823: $i,SV1426: $i,SV296: $i] :
( ( ( c_Fun_Oinj__on @ SV296 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 @ SV1823 )
= $false )
| ( ( c_lessequals @ SV881 @ ( c_Set_Oimage @ SV296 @ SV2028 @ SV1426 @ SV1823 ) @ ( tc_fun @ SV1823 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Ovimage @ SV296 @ SV881 @ SV1426 @ SV1823 ) @ SV2028 @ ( tc_fun @ SV1426 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5197]) ).
thf(5342,plain,
! [SV1436: $i,SV308: $i,SV2030: $i,SV1829: $i,SV892: $i] :
( ( ( c_lessequals @ SV892 @ SV1829 @ ( tc_fun @ SV2030 @ SV308 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV892 @ SV1436 ) @ ( hAPP @ SV1829 @ SV1436 ) @ SV308 )
= $true )
| ( ( class_HOL_Oord @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5200]) ).
thf(5343,plain,
! [SV1464: $i,SV2034: $i,SV2122: $i,SV1852: $i,SV921: $i,SV337: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SV2122 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2034 ) @ SV2122 ) @ SV1464 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SV2034 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5209]) ).
thf(5344,plain,
! [SV1465: $i,SV2035: $i,SV2123: $i,SV1853: $i,SV922: $i,SV338: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SV2123 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2035 ) @ SV2123 ) @ SV1465 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SV2035 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5210]) ).
thf(5345,plain,
! [SV2201: $i,SV2182: $i,SV2159: $i,SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY6148: $i,SY6149: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SY6148 @ SY6149 @ SV2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5211]) ).
thf(5346,plain,
! [SV2202: $i,SV2183: $i,SV2160: $i,SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY6150: $i,SY6151: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SY6150 @ SY6151 @ SV2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5212]) ).
thf(5347,plain,
! [SV1861: $i,SV347: $i,SV1474: $i,SV2043: $i,SV2126: $i,SV931: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SV2126 ) @ SV2043 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SV2126 ) @ SV347 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SV2043 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5213]) ).
thf(5348,plain,
! [SV1862: $i,SV348: $i,SV1475: $i,SV2044: $i,SV2127: $i,SV932: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SV2127 ) @ SV2044 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SV2127 ) @ SV348 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SV2044 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5214]) ).
thf(5349,plain,
! [SV2203: $i,SV2184: $i,SV2161: $i,SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY6152: $i,SY6153: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SY6152 @ SY6153 @ SV2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5216]) ).
thf(5350,plain,
! [SV2204: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY6154: $i,SY6155: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SY6154 @ SY6155 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5217]) ).
thf(5351,plain,
! [SV2205: $i,SV2186: $i,SV2163: $i,SV2130: $i,SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ! [SY6156: $i] :
( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SV2205 @ SV1486 @ SV1869 @ SY6156 @ SV2048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5218]) ).
thf(5352,plain,
! [SV2206: $i,SV2187: $i,SV2164: $i,SV2131: $i,SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ! [SY6157: $i] :
( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SV2206 @ SY6157 @ SV1870 @ SV2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5219]) ).
thf(5353,plain,
! [SV1503: $i,SV379: $i,SV1882: $i,SV962: $i] :
( ( ( c_lessequals @ SV962 @ SV1882 @ SV379 )
= $false )
| ( ( ~ ( c_lessequals @ SV1882 @ SV1503 @ SV379 ) )
= $true )
| ( ( c_lessequals @ SV962 @ SV1503 @ SV379 )
= $true )
| ( ( class_Orderings_Oorder @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5226]) ).
thf(5354,plain,
! [SV1504: $i,SV380: $i,SV1883: $i,SV963: $i] :
( ( ( c_lessequals @ SV963 @ SV1883 @ SV380 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
= $true )
| ( ( class_Orderings_Oorder @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5355,plain,
! [SV1505: $i,SV381: $i,SV1884: $i,SV964: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 )
= $false )
| ( ( ~ ( c_lessequals @ SV1884 @ SV1505 @ SV381 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
= $true )
| ( ( class_Orderings_Oorder @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5228]) ).
thf(5356,plain,
! [SV965: $i,SV382: $i,SV1506: $i,SV1885: $i] :
( ( ( c_lessequals @ SV1885 @ SV1506 @ SV382 )
= $false )
| ( ( ~ ( c_lessequals @ SV965 @ SV1885 @ SV382 ) )
= $true )
| ( ( c_lessequals @ SV965 @ SV1506 @ SV382 )
= $true )
| ( ( class_Orderings_Opreorder @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5229]) ).
thf(5357,plain,
! [SV969: $i,SV1887: $i,SV1508: $i,SV2051: $i,SV386: $i] :
( ( ( c_Fun_Oinj__on @ SV386 @ SV2051 @ SV1508 @ SV1887 )
= $false )
| ( ( c_lessequals @ SV969 @ SV2051 @ ( tc_fun @ SV1508 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV386 @ SV969 @ SV1508 @ SV1887 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5231]) ).
thf(5358,plain,
! [SV978: $i,SV395: $i,SV1515: $i,SV1892: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 )
= $false )
| ( ( ~ ( c_lessequals @ SV978 @ SV1892 @ SV395 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
= $true )
| ( ( class_Orderings_Opreorder @ SV395 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5236]) ).
thf(5359,plain,
! [SV979: $i,SV396: $i,SV1516: $i,SV1893: $i] :
( ( ( c_lessequals @ SV1893 @ SV1516 @ SV396 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
= $true )
| ( ( class_Orderings_Opreorder @ SV396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5237]) ).
thf(5360,plain,
! [SV2052: $i,SV1517: $i,SV398: $i,SV1894: $i,SV981: $i] :
( ( ( c_lessequals @ SV981 @ SV1894 @ ( tc_fun @ SV398 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1517 @ SV2052 @ ( tc_fun @ SV398 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV981 ) @ SV1517 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV398 @ tc_bool ) ) @ SV1894 ) @ SV2052 ) @ ( tc_fun @ SV398 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5361,plain,
! [SV2053: $i,SV402: $i,SV985: $i,SV1897: $i,SV2133: $i,SV1520: $i] :
( ( ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5239]) ).
thf(5362,plain,
! [SV2207: $i,SV2188: $i,SV2165: $i,SV2134: $i,SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ! [SY6158: $i] :
( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SV2165 @ SV2188 @ SV2207 @ SY6158 @ SV1521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5240]) ).
thf(5363,plain,
! [SV2208: $i,SV2189: $i,SV2166: $i,SV2135: $i,SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ! [SY6159: $i] :
( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SV2166 @ SV2189 @ SV2208 @ SY6159 @ SV1522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5241]) ).
thf(5364,plain,
! [SV1530: $i,SV412: $i,SV995: $i] :
( ( ( c_Finite__Set_Ofinite @ SV995 @ SV412 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV412 ) @ SV1530 ) @ SV995 ) )
= $false )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV995 @ SV412 ) @ SV1530 @ SV412 )
= $true )
| ( ( class_Orderings_Olinorder @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5243]) ).
thf(5365,plain,
! [SV1531: $i,SV996: $i,SV2167: $i,SV413: $i,SV2060: $i,SV1906: $i,SV2136: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SV2167 ) )
= $true )
| ( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SV2167 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SV2167 @ SV2136 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5244]) ).
thf(5366,plain,
! [SV1015: $i,SV432: $i,SV1549: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1549 @ SV432 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV432 ) @ SV1015 ) @ SV1549 ) )
= $false )
| ( ( c_lessequals @ SV1015 @ ( c_Finite__Set_Olinorder__class_OMax @ SV1549 @ SV432 ) @ SV432 )
= $true )
| ( ( class_Orderings_Olinorder @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5367,plain,
! [SV2209: $i,SV2190: $i,SV2169: $i,SV2138: $i,SV2069: $i,SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SV2138 @ SV2169 @ SV2190 @ SV2209 @ SV1571 @ SV1046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5261]) ).
thf(5368,plain,
! [SV2210: $i,SV2191: $i,SV2170: $i,SV2139: $i,SV2070: $i,SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SV2139 @ SV2170 @ SV2191 @ SV1572 @ SV2210 @ SV1047 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5262]) ).
thf(5369,plain,
! [SV1079: $i,SV499: $i,SV1588: $i,SV1934: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV1934 @ SV1588 @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1934 @ SV499 ) ) @ SV1934 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1079 ) @ SV1588 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV499 @ SV1079 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5263]) ).
thf(5370,plain,
! [SV1082: $i,SV1591: $i,SV1935: $i,SV502: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5264]) ).
thf(5371,plain,
! [SV2073: $i,SV1936: $i,SV535: $i,SV1599: $i,SV1112: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5265]) ).
thf(5372,plain,
! [SV1602: $i,SV1115: $i,SV2076: $i,SV1939: $i,SV538: $i] :
( ( ( c_Fun_Oinj__on @ SV538 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 @ SV2076 )
= $false )
| ( ( SV1115 = SV1602 )
= $true )
| ( ( ( hAPP @ SV538 @ SV1115 )
= ( hAPP @ SV538 @ SV1602 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(5373,plain,
! [SV1941: $i,SV1117: $i,SV540: $i,SV2078: $i,SV1604: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1604 ) @ SV2078 ) @ SV540 ) )
= $false )
| ( ( ( hAPP @ SV1117 @ SV2078 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV540 @ SV1117 @ SV1604 @ ( tc_fun @ SV1941 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5270]) ).
thf(5374,plain,
! [SV1122: $i,SV1609: $i,SV1945: $i,SV545: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV545 @ tc_bool ) ) @ SV1945 ) @ SV1609 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV545 @ tc_bool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1945 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1122 ) @ SV1609 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5375,plain,
! [SV2080: $i,SV1126: $i,SV1947: $i,SV1613: $i,SV549: $i] :
( ( ( c_Fun_Oinj__on @ SV549 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV1613 @ tc_bool ) ) @ SV1613 @ SV1947 )
= $false )
| ( ( SV1126 = SV2080 )
= $true )
| ( ( ( c_Set_Oimage @ SV549 @ SV1126 @ SV1613 @ SV1947 )
= ( c_Set_Oimage @ SV549 @ SV2080 @ SV1613 @ SV1947 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5376,plain,
! [SV2081: $i,SV1948: $i,SV550: $i,SV1614: $i,SV1127: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
| ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5377,plain,
! [SV2211: $i,SV2192: $i,SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY6160: $i,SY6161: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SV2192 @ SV2211 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SY6160 @ SV2192 @ SY6161 ) @ SV2140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5277]) ).
thf(5378,plain,
! [SV1619: $i,SV555: $i,SV2083: $i,SV1950: $i,SV1132: $i] :
( ( ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 )
| ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5278]) ).
thf(5379,plain,
! [SV1135: $i,SV559: $i,SV1622: $i,SV2084: $i,SV1952: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV1952 @ SV2084 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1622 ) @ SV559 ) @ SV1135 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV559 @ SV1135 @ SV1622 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1622 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5380,plain,
! [SV2085: $i,SV1953: $i,SV562: $i,SV1625: $i,SV1138: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
= $false )
| ( ( ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
| ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5381,plain,
! [SV2141: $i,SV563: $i,SV1139: $i,SV2086: $i,SV1626: $i,SV1954: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true )
| ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5281]) ).
thf(5382,plain,
! [SV1628: $i,SV1141: $i,SV2142: $i,SV2087: $i,SV1956: $i,SV565: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 ) )
= $true )
| ( ( ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true )
| ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5283]) ).
thf(5383,plain,
! [SV1957: $i,SV2088: $i,SV1143: $i,SV1630: $i,SV567: $i] :
( ( ( c_Fun_Oinj__on @ SV567 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV1630 @ tc_bool ) ) @ SV1143 ) @ SV2088 ) @ SV1630 @ SV1957 )
= $false )
| ( ( SV1143 = SV2088 )
= $true )
| ( ( ( c_Set_Oimage @ SV567 @ SV1143 @ SV1630 @ SV1957 )
= ( c_Set_Oimage @ SV567 @ SV2088 @ SV1630 @ SV1957 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5284]) ).
thf(5384,plain,
! [SV2212: $i,SV2193: $i,SV2172: $i,SV2143: $i,SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
!= ( c_Fun_Ocomp @ SV2143 @ SV2172 @ SV2193 @ SV1958 @ SV2089 ) )
| ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SV2212 ) )
= ( hAPP @ SV2143 @ ( hAPP @ SV2172 @ SV2212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5285]) ).
thf(5385,plain,
! [SV2173: $i,SV2144: $i,SV2090: $i,SV1959: $i,SV1636: $i,SV1151: $i,SV575: $i] :
( ( ( ( c_Fun_Ocomp @ SV575 @ SV1151 @ SV1636 @ SV1959 @ SV2090 )
= ( c_Fun_Ocomp @ ( c_Fun_Oid @ SV1959 ) @ SV2144 @ SV1959 @ SV1959 @ SV2090 ) )
= $false )
| ( ( ( hAPP @ SV575 @ ( hAPP @ SV1151 @ SV2173 ) )
= ( hAPP @ SV2144 @ SV2173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5386,plain,
! [SV576: $i,SV1637: $i,SV1152: $i,SV2091: $i,SV1960: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1960 ) @ SV2091 ) @ SV1152 ) )
= $false )
| ( ( ( hAPP @ SV1637 @ SV2091 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1152 @ SV1637 @ SV1960 @ ( tc_fun @ SV576 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5287]) ).
thf(5387,plain,
! [SV2092: $i,SV1963: $i,SV584: $i,SV1643: $i,SV1158: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
= $false )
| ( ( ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
| ~ ( c_lessequals @ SV2092 @ SV1963 @ SV584 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5388,plain,
! [SV2145: $i,SV586: $i,SV1160: $i,SV2093: $i,SV1645: $i,SV1965: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true )
| ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5289]) ).
thf(5389,plain,
! [SV2146: $i,SV587: $i,SV1161: $i,SV2094: $i,SV1646: $i,SV1966: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true )
| ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(5390,plain,
! [SV2194: $i,SV2174: $i,SV2147: $i,SV2095: $i,SV1972: $i,SV1655: $i,SV1170: $i,SV596: $i,SV10: $i] :
( ( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SV2095 @ SV2147 @ SV2174 @ SV2194 @ SV1170 @ SV596 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(5391,plain,
! [SV2195: $i,SV2175: $i,SV2148: $i,SV2096: $i,SV1973: $i,SV1656: $i,SV1171: $i,SV597: $i,SV11: $i] :
( ( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SV2096 @ SV2148 @ SV2175 @ SV1171 @ SV2195 @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5294]) ).
thf(5392,plain,
! [SV1174: $i,SV600: $i,SV2176: $i,SV14: $i,SV2149: $i,SV2097: $i,SV1974: $i,SV1659: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 ) )
= $true )
| ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5297]) ).
thf(5393,plain,
! [SV1176: $i,SV602: $i,SV16: $i,SV1660: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1660 @ SV16 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV16 ) @ SV602 ) @ SV1660 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV602 ) @ SV1176 ) @ ( c_Finite__Set_Ofold @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV16 ) @ SV1176 @ SV1660 @ SV16 @ SV16 ) @ SV16 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5394,plain,
! [SV607: $i,SV1665: $i,SV1181: $i,SV21: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV21 @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV21 @ ( c_Set_Oinsert @ SV607 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) ) @ SV1181 @ ( tc_fun @ SV1665 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV607 ) @ SV21 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV21 @ ( c_Set_Oinsert @ SV607 @ SV1181 @ SV1665 ) @ ( tc_fun @ SV1665 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5299]) ).
thf(5395,plain,
! [SV624: $i,SV1193: $i,SV1672: $i,SV38: $i,SV1977: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5300]) ).
thf(5396,plain,
! [SV627: $i,SV1195: $i,SV1674: $i,SV1978: $i,SV41: $i,SV2098: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2098 @ SV41 @ SV1978 @ ( tc_fun @ SV1674 @ tc_bool ) ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1978 ) @ SV627 ) @ SV2098 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV41 @ SV627 ) @ SV1195 @ ( tc_fun @ SV1674 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(5397,plain,
! [SV2150: $i,SV1980: $i,SV633: $i,SV47: $i,SV1201: $i,SV1677: $i,SV2099: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2099 ) @ SV1677 ) @ SV1201 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV2099 ) @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV1980 @ SV2099 @ SV2150 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SV2099 @ SV2150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5302]) ).
thf(5398,plain,
! [SV2213: $i,SV2196: $i,SV2177: $i,SV2151: $i,SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ! [SY6162: $i] :
( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SV2177 @ SV2196 @ SV1982 @ SV2213 @ SY6162 @ SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5303]) ).
thf(5399,plain,
! [SV2214: $i,SV2197: $i,SV2178: $i,SV2152: $i,SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ! [SY6163: $i] :
( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SV2178 @ SV1983 @ SV2197 @ SV2214 @ SY6163 @ SV1680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5304]) ).
thf(5400,plain,
! [SV1699: $i,SV1994: $i,SV72: $i,SV658: $i,SV2104: $i,SV1226: $i] :
( ( ( ~ ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 ) )
= $true )
| ( ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(5401,plain,
! [SV1228: $i,SV1701: $i,SV74: $i,SV1996: $i,SV2105: $i,SV660: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV660 @ SV2105 @ SV1996 @ SV74 ) @ SV1701 @ ( tc_fun @ SV74 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1996 ) @ SV1228 ) @ SV2105 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV74 ) @ ( hAPP @ SV660 @ SV1228 ) ) @ SV1701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5310]) ).
thf(5402,plain,
! [SV1241: $i,SV89: $i,SV1711: $i,SV675: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1711 @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1711 @ SV1241 @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV675 @ SV1241 @ SV89 )
= $true )
| ( ( class_Orderings_Opreorder @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5311]) ).
thf(5403,plain,
! [SV677: $i,SV91: $i,SV1243: $i,SV1713: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1713 @ SV1243 @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1713 @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1243 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5404,plain,
! [SV112: $i,SV1260: $i,SV698: $i] :
( ( ( c_lessequals @ SV698 @ SV1260 @ ( tc_fun @ SV112 @ tc_bool ) )
= $false )
| ( ( SV698
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV1260 @ SV112 )
= $false )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ SV698 @ SV112 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV1260 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5405,plain,
! [SV1276: $i,SV129: $i,SV1732: $i,SV715: $i] :
( ( ( c_lessequals @ SV715 @ SV1732 @ SV129 )
= $false )
| ( ( c_lessequals @ SV1276 @ SV1732 @ SV129 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 ) @ SV715 ) @ SV1276 ) @ SV1732 @ SV129 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5406,plain,
! [SV1279: $i,SV132: $i,SV1733: $i,SV718: $i] :
( ( ( c_lessequals @ SV718 @ SV1733 @ SV132 )
= $false )
| ( ( c_lessequals @ SV1279 @ SV1733 @ SV132 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV132 ) @ SV718 ) @ SV1279 ) @ SV1733 @ SV132 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5316]) ).
thf(5407,plain,
! [SV1280: $i,SV133: $i,SV1734: $i,SV719: $i] :
( ( ( c_lessequals @ SV719 @ SV1734 @ SV133 )
= $false )
| ( ( c_lessequals @ SV1280 @ SV1734 @ SV133 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV133 ) @ SV719 ) @ SV1280 ) @ SV1734 @ SV133 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5408,plain,
! [SV2198: $i,SV2179: $i,SV2153: $i,SV2109: $i,SV2005: $i,SV1735: $i,SV1286: $i,SV725: $i,SV139: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SV2109 @ SV2153 @ SV2179 @ SV2198 @ SV1735 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SV2153 @ SV2109 @ SV2198 @ SV2179 @ SV1735 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5318]) ).
thf(5409,plain,
! [SV733: $i,SV2006: $i,SV2110: $i,SV1739: $i,SV1294: $i,SV147: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SV2110 @ SV2006 @ SV2006 )
= $false )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SV2110 ) @ SV2006 @ SV2006 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5320]) ).
thf(5410,plain,
! [SV227: $i,SV812: $i,SV1363: $i] :
( ( ( c_lessequals @ SV1363 @ SV812 @ ( tc_fun @ SV227 @ tc_bool ) )
= $false )
| ( ( SV1363
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV227 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV812 @ SV227 )
= $false )
| ( ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ SV812 @ SV227 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV1363 @ SV227 ) @ SV227 )
= $true )
| ( ( class_Orderings_Olinorder @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5328]) ).
thf(5411,plain,
! [SV2215: $i,SV2199: $i,SV2180: $i,SV2154: $i,SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ! [SY6164: $i] :
( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SV2180 @ SV2199 @ SV2013 @ SV2215 @ SY6164 @ SV1781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5329]) ).
thf(5412,plain,
! [SV2216: $i,SV2200: $i,SV2181: $i,SV2155: $i,SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ! [SY6165: $i] :
( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SV2181 @ SV2014 @ SV2200 @ SV2216 @ SY6165 @ SV1782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5330]) ).
thf(5413,plain,
! [SV1789: $i,SV241: $i,SV1376: $i,SV826: $i] :
( ( ( c_lessequals @ SV826 @ SV1376 @ SV241 )
= $false )
| ( ( c_lessequals @ SV826 @ SV1789 @ SV241 )
= $false )
| ( ( c_lessequals @ SV826 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV241 ) @ SV1376 ) @ SV1789 ) @ SV241 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5332]) ).
thf(5414,plain,
! [SV1790: $i,SV242: $i,SV1377: $i,SV827: $i] :
( ( ( c_lessequals @ SV827 @ SV1377 @ SV242 )
= $false )
| ( ( c_lessequals @ SV827 @ SV1790 @ SV242 )
= $false )
| ( ( c_lessequals @ SV827 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV242 ) @ SV1377 ) @ SV1790 ) @ SV242 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5333]) ).
thf(5415,plain,
! [SV1791: $i,SV243: $i,SV1378: $i,SV828: $i] :
( ( ( c_lessequals @ SV828 @ SV1378 @ SV243 )
= $false )
| ( ( c_lessequals @ SV828 @ SV1791 @ SV243 )
= $false )
| ( ( c_lessequals @ SV828 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV243 ) @ SV1378 ) @ SV1791 ) @ SV243 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5334]) ).
thf(5416,plain,
! [SV852: $i,SV1807: $i,SV267: $i,SV1399: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1399 @ SV267 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV267 ) @ SV1807 ) @ SV1399 ) )
= $false )
| ( ( c_lessequals @ ( c_Finite__Set_Ofold @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV852 @ SV1399 @ SV267 @ SV267 ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV267 ) @ SV1807 ) @ SV852 ) @ SV267 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5335]) ).
thf(5417,plain,
! [SV855: $i,SV1809: $i,SV1402: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV270 @ ( c_Set_Oinsert @ SV855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) ) @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV270 @ SV1402 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Set_Oinsert @ SV855 @ SV1402 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(5418,plain,
! [SV2116: $i,SV1410: $i,SV279: $i,SV1810: $i,SV864: $i,SV2020: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5337]) ).
thf(5419,plain,
! [SV1811: $i,SV280: $i,SV1411: $i,SV2021: $i,SV2117: $i,SV865: $i] :
( ( ( c_Fun_Oinj__on @ SV865 @ SV2117 @ SV2021 @ SV1411 )
= $false )
| ( ( c_Fun_Oinj__on @ SV280 @ ( c_Set_Oimage @ SV865 @ SV2117 @ SV2021 @ SV1411 ) @ SV1411 @ SV1811 )
= $false )
| ( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ SV280 @ SV865 @ SV1411 @ SV1811 @ SV2021 ) @ SV2117 @ SV2021 @ SV1811 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5338]) ).
thf(5420,plain,
! [SV1413: $i,SV2157: $i,SV2022: $i,SV2118: $i,SV1812: $i,SV868: $i,SV283: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ SV1812 @ SV2118 @ SV2022 @ SV2157 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2022 ) @ SV1413 ) @ SV1812 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV283 @ SV868 @ ( c_Set_Oinsert @ SV1413 @ SV1812 @ SV2022 ) @ ( hAPP @ ( hAPP @ SV283 @ SV1413 ) @ SV2118 ) @ SV2022 @ SV2157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5339]) ).
thf(5421,plain,
! [SV2158: $i,SV2025: $i,SV2119: $i,SV1817: $i,SV1419: $i,SV874: $i,SV289: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2025 @ SV2119 @ SV2158 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2119 ) @ SV1817 ) @ SV1419 ) ) )
= $true )
| ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SV2119 @ SV2158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5340]) ).
thf(5422,plain,
! [SV1852: $i,SV921: $i,SV337: $i,SV1464: $i,SV2122: $i,SV2034: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2034 ) @ SV2122 ) @ SV1464 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( hAPP @ SV1852 @ SV2122 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV337 ) @ SV921 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1464 @ SV1852 @ SV2034 @ ( tc_fun @ SV337 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5343]) ).
thf(5423,plain,
! [SV1853: $i,SV922: $i,SV338: $i,SV1465: $i,SV2123: $i,SV2035: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2035 ) @ SV2123 ) @ SV1465 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( hAPP @ SV1853 @ SV2123 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV338 ) @ SV922 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1465 @ SV1853 @ SV2035 @ ( tc_fun @ SV338 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5344]) ).
thf(5424,plain,
! [SV2217: $i,SV2201: $i,SV2182: $i,SV2159: $i,SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ! [SY6166: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SV2217 @ SY6166 @ SV2041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5345]) ).
thf(5425,plain,
! [SV2218: $i,SV2202: $i,SV2183: $i,SV2160: $i,SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ! [SY6167: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SV2218 @ SY6167 @ SV2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5346]) ).
thf(5426,plain,
! [SV1861: $i,SV2043: $i,SV931: $i,SV347: $i,SV2126: $i,SV1474: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1474 ) @ SV2126 ) @ SV347 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV931 @ SV2126 ) @ SV2043 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV347 @ SV931 @ SV1474 @ ( tc_fun @ SV1861 @ tc_bool ) ) @ SV2043 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(5427,plain,
! [SV1862: $i,SV2044: $i,SV932: $i,SV348: $i,SV2127: $i,SV1475: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1475 ) @ SV2127 ) @ SV348 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV932 @ SV2127 ) @ SV2044 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV348 @ SV932 @ SV1475 @ ( tc_fun @ SV1862 @ tc_bool ) ) @ SV2044 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(5428,plain,
! [SV2219: $i,SV2203: $i,SV2184: $i,SV2161: $i,SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ! [SY6168: $i] :
( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SV2219 @ SY6168 @ SV2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5349]) ).
thf(5429,plain,
! [SV2220: $i,SV2204: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ! [SY6169: $i] :
( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SV2220 @ SY6169 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5350]) ).
thf(5430,plain,
! [SV2221: $i,SV2205: $i,SV2186: $i,SV2163: $i,SV2130: $i,SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
| ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SV2205 @ SV1486 @ SV1869 @ SV2221 @ SV2048 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5351]) ).
thf(5431,plain,
! [SV2222: $i,SV2206: $i,SV2187: $i,SV2164: $i,SV2131: $i,SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
| ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SV2206 @ SV2222 @ SV1870 @ SV2049 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5352]) ).
thf(5432,plain,
! [SV962: $i,SV379: $i,SV1503: $i,SV1882: $i] :
( ( ( c_lessequals @ SV1882 @ SV1503 @ SV379 )
= $false )
| ( ( c_lessequals @ SV962 @ SV1882 @ SV379 )
= $false )
| ( ( c_lessequals @ SV962 @ SV1503 @ SV379 )
= $true )
| ( ( class_Orderings_Oorder @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(5433,plain,
! [SV963: $i,SV380: $i,SV1504: $i,SV1883: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1883 @ SV1504 @ SV380 )
= $false )
| ( ( c_lessequals @ SV963 @ SV1883 @ SV380 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV963 @ SV1504 @ SV380 )
= $true )
| ( ( class_Orderings_Oorder @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5434,plain,
! [SV964: $i,SV381: $i,SV1505: $i,SV1884: $i] :
( ( ( c_lessequals @ SV1884 @ SV1505 @ SV381 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1884 @ SV381 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV964 @ SV1505 @ SV381 )
= $true )
| ( ( class_Orderings_Oorder @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5435,plain,
! [SV1506: $i,SV382: $i,SV1885: $i,SV965: $i] :
( ( ( c_lessequals @ SV965 @ SV1885 @ SV382 )
= $false )
| ( ( c_lessequals @ SV1885 @ SV1506 @ SV382 )
= $false )
| ( ( c_lessequals @ SV965 @ SV1506 @ SV382 )
= $true )
| ( ( class_Orderings_Opreorder @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5356]) ).
thf(5436,plain,
! [SV1515: $i,SV395: $i,SV1892: $i,SV978: $i] :
( ( ( c_lessequals @ SV978 @ SV1892 @ SV395 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1892 @ SV1515 @ SV395 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV978 @ SV1515 @ SV395 )
= $true )
| ( ( class_Orderings_Opreorder @ SV395 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5437,plain,
! [SV1516: $i,SV396: $i,SV1893: $i,SV979: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1893 @ SV396 )
= $false )
| ( ( c_lessequals @ SV1893 @ SV1516 @ SV396 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV979 @ SV1516 @ SV396 )
= $true )
| ( ( class_Orderings_Opreorder @ SV396 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5438,plain,
! [SV1520: $i,SV2053: $i,SV402: $i,SV1897: $i,SV2133: $i,SV985: $i] :
( ( ( ~ ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 ) )
= $true )
| ( ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5361]) ).
thf(5439,plain,
! [SV2223: $i,SV2207: $i,SV2188: $i,SV2165: $i,SV2134: $i,SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SV2165 @ SV2188 @ SV2207 @ SV2223 @ SV1521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5362]) ).
thf(5440,plain,
! [SV2224: $i,SV2208: $i,SV2189: $i,SV2166: $i,SV2135: $i,SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SV2166 @ SV2189 @ SV2208 @ SV2224 @ SV1522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(5441,plain,
! [SV1531: $i,SV996: $i,SV1906: $i,SV2167: $i,SV413: $i,SV2136: $i,SV2060: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SV2167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
= $true )
| ( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SV2167 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SV2167 @ SV2136 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5365]) ).
thf(5442,plain,
! [SV2209: $i,SV2190: $i,SV2169: $i,SV2138: $i,SV2069: $i,SV1924: $i,SV1571: $i,SV1046: $i,SV464: $i] :
( ( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SV2138 @ SV2169 @ SV2190 @ SV2209 @ SV1571 @ SV1046 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5367]) ).
thf(5443,plain,
! [SV2210: $i,SV2191: $i,SV2170: $i,SV2139: $i,SV2070: $i,SV1925: $i,SV1572: $i,SV1047: $i,SV465: $i] :
( ( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SV2139 @ SV2170 @ SV2191 @ SV1572 @ SV2210 @ SV1047 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(5444,plain,
! [SV1082: $i,SV502: $i,SV1591: $i,SV1935: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__valids @ SV1935 @ SV1591 @ t_a )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ ( v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 @ SV1935 @ SV502 ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ SV1082 ) @ SV1591 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV502 @ SV1082 @ t_a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5370]) ).
thf(5445,plain,
! [SV1599: $i,SV1112: $i,SV535: $i,SV2073: $i,SV1936: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5371]) ).
thf(5446,plain,
! [SV2081: $i,SV1948: $i,SV550: $i,SV1614: $i,SV1127: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5376]) ).
thf(5447,plain,
! [SV2225: $i,SV2211: $i,SV2192: $i,SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ! [SY6170: $i] :
( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SV2192 @ SV2211 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SV2225 @ SV2192 @ SY6170 ) @ SV2140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5377]) ).
thf(5448,plain,
! [SV1950: $i,SV555: $i,SV2083: $i,SV1619: $i,SV1132: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 )
= $true )
| ( ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5378]) ).
thf(5449,plain,
! [SV1138: $i,SV1625: $i,SV562: $i,SV1953: $i,SV2085: $i] :
( ( ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
= $true )
| ( ( ~ ( c_lessequals @ SV1625 @ SV1138 @ SV562 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5380]) ).
thf(5450,plain,
! [SV2141: $i,SV563: $i,SV1139: $i,SV2086: $i,SV1626: $i,SV1954: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
| ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true )
| ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5381]) ).
thf(5451,plain,
! [SV1628: $i,SV1141: $i,SV2142: $i,SV2087: $i,SV1956: $i,SV565: $i] :
( ( ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
= $false )
| ( ( ( SV1141 = SV1628 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true )
| ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5382]) ).
thf(5452,plain,
! [SV2212: $i,SV2193: $i,SV2172: $i,SV2143: $i,SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
!= ( c_Fun_Ocomp @ SV2143 @ SV2172 @ SV2193 @ SV1958 @ SV2089 ) )
= $true )
| ( ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SV2212 ) )
= ( hAPP @ SV2143 @ ( hAPP @ SV2172 @ SV2212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5384]) ).
thf(5453,plain,
! [SV1963: $i,SV2092: $i,SV584: $i,SV1158: $i,SV1643: $i] :
( ( ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
= $true )
| ( ( ~ ( c_lessequals @ SV2092 @ SV1963 @ SV584 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5387]) ).
thf(5454,plain,
! [SV2145: $i,SV586: $i,SV1160: $i,SV2093: $i,SV1645: $i,SV1965: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
| ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true )
| ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5455,plain,
! [SV2146: $i,SV587: $i,SV1161: $i,SV2094: $i,SV1646: $i,SV1966: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
| ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true )
| ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5389]) ).
thf(5456,plain,
! [SV596: $i,SV1170: $i,SV2194: $i,SV2174: $i,SV2147: $i,SV2095: $i,SV1972: $i,SV10: $i,SV1655: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1655 @ SV10 @ SV1972 @ SV2095 @ SV2147 @ SV2174 @ SV2194 @ SV1170 @ SV596 )
= $false )
| ( ( ( hAPP @ SV10 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV596 @ tc_bool ) ) )
= SV1170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5457,plain,
! [SV597: $i,SV2195: $i,SV1171: $i,SV2175: $i,SV2148: $i,SV2096: $i,SV1973: $i,SV1656: $i,SV11: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV11 @ SV1656 @ SV1973 @ SV2096 @ SV2148 @ SV2175 @ SV1171 @ SV2195 @ SV597 )
= $false )
| ( ( ( hAPP @ SV11 @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ SV597 @ tc_bool ) ) )
= SV1171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5458,plain,
! [SV1174: $i,SV600: $i,SV2176: $i,SV14: $i,SV2149: $i,SV2097: $i,SV1974: $i,SV1659: $i] :
( ( ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
| ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 ) )
= $true )
| ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5392]) ).
thf(5459,plain,
! [SV624: $i,SV1193: $i,SV38: $i,SV1672: $i,SV1977: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1977 @ SV1672 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1977 @ SV38 @ SV1672 @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1672 ) @ SV624 ) @ SV1977 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV38 @ SV624 ) @ SV1193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5460,plain,
! [SV2150: $i,SV1980: $i,SV2099: $i,SV1677: $i,SV1201: $i,SV633: $i,SV47: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ ( c_Set_Oinsert @ SV1677 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV2099 ) @ ( tc_fun @ SV2099 @ tc_bool ) ) @ SV1980 @ SV2099 @ SV2150 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2099 ) @ SV1677 ) @ SV1201 ) )
= $false )
| ( ( c_Finite__Set_Ofold__graph @ SV47 @ SV633 @ SV1201 @ ( hAPP @ ( hAPP @ SV47 @ SV1677 ) @ SV1980 ) @ SV2099 @ SV2150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5461,plain,
! [SV2226: $i,SV2213: $i,SV2196: $i,SV2177: $i,SV2151: $i,SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SV2177 @ SV2196 @ SV1982 @ SV2213 @ SV2226 @ SV1679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5398]) ).
thf(5462,plain,
! [SV2227: $i,SV2214: $i,SV2197: $i,SV2178: $i,SV2152: $i,SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SV2178 @ SV1983 @ SV2197 @ SV2214 @ SV2227 @ SV1680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5399]) ).
thf(5463,plain,
! [SV1699: $i,SV1994: $i,SV72: $i,SV658: $i,SV2104: $i,SV1226: $i] :
( ( ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 ) )
= $true )
| ( ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5400]) ).
thf(5464,plain,
! [SV1735: $i,SV2179: $i,SV2198: $i,SV2109: $i,SV2153: $i,SV2005: $i,SV1286: $i,SV139: $i,SV725: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV725 @ SV139 @ SV1286 @ SV2005 @ SV2153 @ SV2109 @ SV2198 @ SV2179 @ SV1735 )
= $false )
| ( ( c_Complete__Lattice_Ocomplete__lattice @ SV139 @ SV725 @ ( c_COMBC @ SV1286 @ SV1735 @ SV1735 @ tc_bool ) @ ( c_COMBC @ SV2005 @ SV1735 @ SV1735 @ tc_bool ) @ SV2109 @ SV2153 @ SV2179 @ SV2198 @ SV1735 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5408]) ).
thf(5465,plain,
! [SV733: $i,SV2110: $i,SV1739: $i,SV1294: $i,SV2006: $i,SV147: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV147 @ SV2006 )
= $false )
| ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV1294 @ SV1739 @ SV2110 @ SV2006 @ SV2006 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2006 ) @ SV1294 ) @ SV1739 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV147 @ SV733 @ ( c_Set_Oinsert @ SV1294 @ SV1739 @ SV2006 ) @ ( hAPP @ ( hAPP @ SV147 @ SV733 ) @ SV2110 ) @ SV2006 @ SV2006 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5466,plain,
! [SV2228: $i,SV2215: $i,SV2199: $i,SV2180: $i,SV2154: $i,SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SV2180 @ SV2199 @ SV2013 @ SV2215 @ SV2228 @ SV1781 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5411]) ).
thf(5467,plain,
! [SV2229: $i,SV2216: $i,SV2200: $i,SV2181: $i,SV2155: $i,SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SV2181 @ SV2014 @ SV2200 @ SV2216 @ SV2229 @ SV1782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(5468,plain,
! [SV864: $i,SV2020: $i,SV2116: $i,SV1810: $i,SV1410: $i,SV279: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5418]) ).
thf(5469,plain,
! [SV2158: $i,SV2025: $i,SV874: $i,SV289: $i,SV1419: $i,SV1817: $i,SV2119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2119 ) @ SV1817 ) @ SV1419 ) )
= $false )
| ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ ( c_HOL_Ominus__class_Ominus @ SV1419 @ ( c_Set_Oinsert @ SV1817 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2119 ) @ ( tc_fun @ SV2119 @ tc_bool ) ) @ SV2025 @ SV2119 @ SV2158 )
= $false )
| ( ( c_Nitpick_Ofold__graph_H @ SV289 @ SV874 @ SV1419 @ ( hAPP @ ( hAPP @ SV289 @ SV1817 ) @ SV2025 ) @ SV2119 @ SV2158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5421]) ).
thf(5470,plain,
! [SV2230: $i,SV2217: $i,SV2201: $i,SV2182: $i,SV2159: $i,SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SV2217 @ SV2230 @ SV2041 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5424]) ).
thf(5471,plain,
! [SV2231: $i,SV2218: $i,SV2202: $i,SV2183: $i,SV2160: $i,SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SV2218 @ SV2231 @ SV2042 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(5472,plain,
! [SV2232: $i,SV2219: $i,SV2203: $i,SV2184: $i,SV2161: $i,SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SV2219 @ SV2232 @ SV2046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5428]) ).
thf(5473,plain,
! [SV2233: $i,SV2220: $i,SV2204: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SV2220 @ SV2233 @ SV2047 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5429]) ).
thf(5474,plain,
! [SV2221: $i,SV2205: $i,SV2186: $i,SV2163: $i,SV2130: $i,SV2048: $i,SV1869: $i,SV1486: $i,SV943: $i,SV359: $i] :
( ( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SV2205 @ SV1486 @ SV1869 @ SV2221 @ SV2048 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5475,plain,
! [SV2222: $i,SV2206: $i,SV2187: $i,SV2164: $i,SV2131: $i,SV2049: $i,SV1870: $i,SV1487: $i,SV944: $i,SV360: $i] :
( ( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SV2206 @ SV2222 @ SV1870 @ SV2049 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5431]) ).
thf(5476,plain,
! [SV1520: $i,SV2053: $i,SV402: $i,SV1897: $i,SV2133: $i,SV985: $i] :
( ( ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 ) )
= $true )
| ( ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5477,plain,
! [SV2223: $i,SV2207: $i,SV2188: $i,SV2165: $i,SV2134: $i,SV2054: $i,SV1898: $i,SV1521: $i,SV986: $i,SV403: $i] :
( ( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SV2165 @ SV2188 @ SV2207 @ SV2223 @ SV1521 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5439]) ).
thf(5478,plain,
! [SV2224: $i,SV2208: $i,SV2189: $i,SV2166: $i,SV2135: $i,SV2055: $i,SV1899: $i,SV1522: $i,SV987: $i,SV404: $i] :
( ( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SV2166 @ SV2189 @ SV2208 @ SV2224 @ SV1522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5440]) ).
thf(5479,plain,
! [SV1531: $i,SV996: $i,SV1906: $i,SV2167: $i,SV413: $i,SV2136: $i,SV2060: $i] :
( ( ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 )
= $false )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SV2167 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
= $true )
| ( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SV2167 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SV2167 @ SV2136 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5441]) ).
thf(5480,plain,
! [SV1046: $i,SV1571: $i,SV2209: $i,SV2190: $i,SV2169: $i,SV2138: $i,SV2069: $i,SV1924: $i,SV464: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV464 @ SV1924 @ SV2069 @ SV2138 @ SV2169 @ SV2190 @ SV2209 @ SV1571 @ SV1046 )
= $false )
| ( ( ( hAPP @ SV464 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1046 @ tc_bool ) ) )
= SV1571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5481,plain,
! [SV1047: $i,SV2210: $i,SV1572: $i,SV2191: $i,SV2170: $i,SV2139: $i,SV2070: $i,SV465: $i,SV1925: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1925 @ SV465 @ SV2070 @ SV2139 @ SV2170 @ SV2191 @ SV1572 @ SV2210 @ SV1047 )
= $false )
| ( ( ( hAPP @ SV465 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1047 @ tc_bool ) ) )
= SV1572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5482,plain,
! [SV2073: $i,SV1936: $i,SV535: $i,SV1599: $i,SV1112: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1112 @ SV1599 @ SV535 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1936 @ SV2073 @ SV535 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1112 @ SV1599 @ SV535 )
= ( c_HOL_Ominus__class_Ominus @ SV1936 @ SV2073 @ SV535 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5483,plain,
! [SV1614: $i,SV1127: $i,SV550: $i,SV2081: $i,SV1948: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1948 @ SV2081 @ SV550 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1127 @ SV1614 @ SV550 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1127 @ SV1614 @ SV550 )
= ( c_HOL_Ominus__class_Ominus @ SV1948 @ SV2081 @ SV550 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV550 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5484,plain,
! [SV2234: $i,SV2225: $i,SV2211: $i,SV2192: $i,SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SV2192 @ SV2211 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SV2225 @ SV2192 @ SV2234 ) @ SV2140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5447]) ).
thf(5485,plain,
! [SV1950: $i,SV555: $i,SV2083: $i,SV1619: $i,SV1132: $i] :
( ( ( c_Fun_Oinj__on @ SV1132 @ SV1619 @ SV2083 @ SV555 )
= $false )
| ( ( c_Fun_Oinj__on @ SV1132 @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV1619 ) @ SV1950 ) @ SV2083 @ SV555 )
= $true )
| ( ( c_Fun_Oinj__on @ SV1132 @ SV1950 @ SV2083 @ SV555 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV555 @ tc_bool ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1619 @ SV1950 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) ) @ ( c_Set_Oimage @ SV1132 @ ( c_HOL_Ominus__class_Ominus @ SV1950 @ SV1619 @ ( tc_fun @ SV2083 @ tc_bool ) ) @ SV2083 @ SV555 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5486,plain,
! [SV1953: $i,SV2085: $i,SV562: $i,SV1138: $i,SV1625: $i] :
( ( ( c_lessequals @ SV1625 @ SV1138 @ SV562 )
= $false )
| ( ( c_lessequals @ SV2085 @ SV1953 @ SV562 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1138 @ SV1625 @ SV562 )
= ( c_HOL_Ominus__class_Ominus @ SV1953 @ SV2085 @ SV562 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5449]) ).
thf(5487,plain,
! [SV1626: $i,SV2141: $i,SV563: $i,SV2086: $i,SV1139: $i,SV1954: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
= $false )
| ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5450]) ).
thf(5488,plain,
! [SV2142: $i,SV565: $i,SV1956: $i,SV2087: $i,SV1628: $i,SV1141: $i] :
( ( ( SV1141 = SV1628 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
= $false )
| ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5451]) ).
thf(5489,plain,
! [SV2212: $i,SV2193: $i,SV2172: $i,SV2143: $i,SV2089: $i,SV1958: $i,SV1634: $i,SV1148: $i,SV572: $i] :
( ( ( ( c_Fun_Ocomp @ SV572 @ SV1148 @ SV1634 @ SV1958 @ SV2089 )
= ( c_Fun_Ocomp @ SV2143 @ SV2172 @ SV2193 @ SV1958 @ SV2089 ) )
= $false )
| ( ( ( hAPP @ SV572 @ ( hAPP @ SV1148 @ SV2212 ) )
= ( hAPP @ SV2143 @ ( hAPP @ SV2172 @ SV2212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5452]) ).
thf(5490,plain,
! [SV1158: $i,SV1643: $i,SV584: $i,SV1963: $i,SV2092: $i] :
( ( ( c_lessequals @ SV2092 @ SV1963 @ SV584 )
= $false )
| ( ( c_lessequals @ SV1643 @ SV1158 @ SV584 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1158 @ SV1643 @ SV584 )
= ( c_HOL_Ominus__class_Ominus @ SV1963 @ SV2092 @ SV584 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5453]) ).
thf(5491,plain,
! [SV1645: $i,SV2145: $i,SV586: $i,SV2093: $i,SV1160: $i,SV1965: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(5492,plain,
! [SV2146: $i,SV587: $i,SV1646: $i,SV2094: $i,SV1161: $i,SV1966: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) ) )
= $true )
| ( ( ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
= $false )
| ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5455]) ).
thf(5493,plain,
! [SV1174: $i,SV600: $i,SV2149: $i,SV1659: $i,SV2176: $i,SV14: $i,SV2097: $i,SV1974: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
= $false )
| ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5494,plain,
! [SV2226: $i,SV2213: $i,SV2196: $i,SV2177: $i,SV2151: $i,SV2100: $i,SV1982: $i,SV1679: $i,SV1203: $i,SV635: $i,SV49: $i] :
( ( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SV2177 @ SV2196 @ SV1982 @ SV2213 @ SV2226 @ SV1679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5461]) ).
thf(5495,plain,
! [SV2227: $i,SV2214: $i,SV2197: $i,SV2178: $i,SV2152: $i,SV2101: $i,SV1983: $i,SV1680: $i,SV1204: $i,SV636: $i,SV50: $i] :
( ( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SV2178 @ SV1983 @ SV2197 @ SV2214 @ SV2227 @ SV1680 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5462]) ).
thf(5496,plain,
! [SV1699: $i,SV1226: $i,SV1994: $i,SV658: $i,SV2104: $i,SV72: $i] :
( ( ( c_Fun_Oinj__on @ SV72 @ SV2104 @ SV658 @ SV1994 )
= $false )
| ( ( c_lessequals @ SV1226 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1699 @ SV2104 @ ( tc_fun @ SV658 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV72 @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV658 @ tc_bool ) ) @ SV1226 ) @ SV1699 ) @ SV658 @ SV1994 )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ SV1994 @ tc_bool ) ) @ ( c_Set_Oimage @ SV72 @ SV1226 @ SV658 @ SV1994 ) ) @ ( c_Set_Oimage @ SV72 @ SV1699 @ SV658 @ SV1994 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5463]) ).
thf(5497,plain,
! [SV2228: $i,SV2215: $i,SV2199: $i,SV2180: $i,SV2154: $i,SV2111: $i,SV2013: $i,SV1781: $i,SV1365: $i,SV814: $i,SV229: $i] :
( ( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SV2180 @ SV2199 @ SV2013 @ SV2215 @ SV2228 @ SV1781 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5498,plain,
! [SV2229: $i,SV2216: $i,SV2200: $i,SV2181: $i,SV2155: $i,SV2112: $i,SV2014: $i,SV1782: $i,SV1366: $i,SV815: $i,SV230: $i] :
( ( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SV2181 @ SV2014 @ SV2200 @ SV2216 @ SV2229 @ SV1782 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5467]) ).
thf(5499,plain,
! [SV864: $i,SV2020: $i,SV2116: $i,SV1810: $i,SV1410: $i,SV279: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
= $false )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5468]) ).
thf(5500,plain,
! [SV2230: $i,SV2217: $i,SV2201: $i,SV2182: $i,SV2159: $i,SV2124: $i,SV2041: $i,SV1859: $i,SV1471: $i,SV928: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SV2217 @ SV2230 @ SV2041 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5470]) ).
thf(5501,plain,
! [SV2231: $i,SV2218: $i,SV2202: $i,SV2183: $i,SV2160: $i,SV2125: $i,SV2042: $i,SV1860: $i,SV1472: $i,SV929: $i,SV345: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SV2218 @ SV2231 @ SV2042 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5471]) ).
thf(5502,plain,
! [SV2232: $i,SV2219: $i,SV2203: $i,SV2184: $i,SV2161: $i,SV2128: $i,SV2046: $i,SV1867: $i,SV1484: $i,SV941: $i,SV357: $i] :
( ( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SV2219 @ SV2232 @ SV2046 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5472]) ).
thf(5503,plain,
! [SV2233: $i,SV2220: $i,SV2204: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV2047: $i,SV1868: $i,SV1485: $i,SV942: $i,SV358: $i] :
( ( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SV2220 @ SV2233 @ SV2047 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5473]) ).
thf(5504,plain,
! [SV2221: $i,SV1869: $i,SV1486: $i,SV2205: $i,SV2186: $i,SV2163: $i,SV359: $i,SV2130: $i,SV2048: $i,SV943: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV943 @ SV2048 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SV2205 @ SV1486 @ SV1869 @ SV2221 @ SV2048 ) )
= $true )
| ( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5474]) ).
thf(5505,plain,
! [SV1870: $i,SV2222: $i,SV2206: $i,SV1487: $i,SV2187: $i,SV2164: $i,SV2131: $i,SV360: $i,SV2049: $i,SV944: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV944 @ SV2049 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SV2206 @ SV2222 @ SV1870 @ SV2049 ) )
= $true )
| ( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5475]) ).
thf(5506,plain,
! [SV1520: $i,SV985: $i,SV2053: $i,SV1897: $i,SV2133: $i,SV402: $i] :
( ( ( c_Fun_Oinj__on @ SV402 @ SV2133 @ SV1897 @ SV2053 )
= $false )
| ( ( c_lessequals @ SV985 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1520 @ SV2133 @ ( tc_fun @ SV1897 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV402 @ ( c_HOL_Ominus__class_Ominus @ SV985 @ SV1520 @ ( tc_fun @ SV1897 @ tc_bool ) ) @ SV1897 @ SV2053 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV402 @ SV985 @ SV1897 @ SV2053 ) @ ( c_Set_Oimage @ SV402 @ SV1520 @ SV1897 @ SV2053 ) @ ( tc_fun @ SV2053 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5476]) ).
thf(5507,plain,
! [SV986: $i,SV1521: $i,SV2223: $i,SV2207: $i,SV2188: $i,SV2165: $i,SV2134: $i,SV2054: $i,SV403: $i,SV1898: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1898 @ SV403 @ SV2054 @ SV2134 @ SV2165 @ SV2188 @ SV2207 @ SV2223 @ SV1521 )
= $false )
| ( ( ( hAPP @ SV403 @ ( c_Set_Oinsert @ SV986 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1521 @ tc_bool ) ) @ SV1521 ) )
= SV986 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5477]) ).
thf(5508,plain,
! [SV987: $i,SV1522: $i,SV2224: $i,SV2208: $i,SV2189: $i,SV2166: $i,SV2135: $i,SV2055: $i,SV1899: $i,SV404: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV404 @ SV1899 @ SV2055 @ SV2135 @ SV2166 @ SV2189 @ SV2208 @ SV2224 @ SV1522 )
= $false )
| ( ( ( hAPP @ SV404 @ ( c_Set_Oinsert @ SV987 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) )
= SV987 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5509,plain,
! [SV1531: $i,SV996: $i,SV1906: $i,SV2136: $i,SV2060: $i,SV2167: $i,SV413: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV413 @ SV2167 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV2060 @ SV2136 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2136 ) @ SV1906 ) @ SV2060 ) )
= $true )
| ( ( ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ ( c_Set_Oinsert @ SV1906 @ SV2060 @ SV2136 ) @ SV2167 @ SV2136 )
= ( hAPP @ ( hAPP @ SV413 @ ( hAPP @ SV996 @ SV1906 ) ) @ ( c_Finite__Set_Ofold__image @ SV413 @ SV996 @ SV1531 @ SV2060 @ SV2167 @ SV2136 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5479]) ).
thf(5510,plain,
! [SV2234: $i,SV2225: $i,SV2211: $i,SV2192: $i,SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
!= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SV2192 @ SV2211 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SV2225 @ SV2192 @ SV2234 ) @ SV2140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5484]) ).
thf(5511,plain,
! [SV1626: $i,SV2141: $i,SV563: $i,SV2086: $i,SV1139: $i,SV1954: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
| ( SV1139 = SV1626 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
= $false )
| ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5487]) ).
thf(5512,plain,
! [SV2142: $i,SV565: $i,SV1141: $i,SV1956: $i,SV1628: $i,SV2087: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true )
| ( ( SV1141 = SV1628 )
= $true )
| ( ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
= $false )
| ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(5513,plain,
! [SV1645: $i,SV2145: $i,SV586: $i,SV2093: $i,SV1160: $i,SV1965: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
| ( SV1160 = SV1645 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5514,plain,
! [SV2146: $i,SV587: $i,SV1646: $i,SV2094: $i,SV1161: $i,SV1966: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
= $false )
| ( ( ( SV1161 = SV1646 )
| ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
= $false )
| ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5492]) ).
thf(5515,plain,
! [SV1174: $i,SV600: $i,SV2149: $i,SV1659: $i,SV2176: $i,SV14: $i,SV2097: $i,SV1974: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
= $false )
| ( ( ~ ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
= $false )
| ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5516,plain,
! [SV1203: $i,SV635: $i,SV1679: $i,SV2226: $i,SV2213: $i,SV1982: $i,SV2196: $i,SV2177: $i,SV2151: $i,SV49: $i,SV2100: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2100 @ SV49 @ SV2151 @ SV2177 @ SV2196 @ SV1982 @ SV2213 @ SV2226 @ SV1679 )
= $false )
| ( ( ( hAPP @ SV49 @ ( c_Set_Oinsert @ SV635 @ ( c_Set_Oinsert @ SV1203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1679 @ tc_bool ) ) @ SV1679 ) @ SV1679 ) )
= ( hAPP @ ( hAPP @ SV1982 @ SV635 ) @ SV1203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5517,plain,
! [SV1204: $i,SV636: $i,SV1680: $i,SV2227: $i,SV2214: $i,SV2197: $i,SV1983: $i,SV2178: $i,SV2152: $i,SV2101: $i,SV50: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV50 @ SV2101 @ SV2152 @ SV2178 @ SV1983 @ SV2197 @ SV2214 @ SV2227 @ SV1680 )
= $false )
| ( ( ( hAPP @ SV50 @ ( c_Set_Oinsert @ SV636 @ ( c_Set_Oinsert @ SV1204 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1680 @ tc_bool ) ) @ SV1680 ) @ SV1680 ) )
= ( hAPP @ ( hAPP @ SV1983 @ SV636 ) @ SV1204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5518,plain,
! [SV1365: $i,SV814: $i,SV1781: $i,SV2228: $i,SV2215: $i,SV2013: $i,SV2199: $i,SV2180: $i,SV2154: $i,SV229: $i,SV2111: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2111 @ SV229 @ SV2154 @ SV2180 @ SV2199 @ SV2013 @ SV2215 @ SV2228 @ SV1781 )
= $false )
| ( ( ( hAPP @ SV229 @ ( c_Set_Oinsert @ SV814 @ SV1365 @ SV1781 ) )
= ( hAPP @ ( hAPP @ SV2013 @ SV814 ) @ ( hAPP @ SV229 @ SV1365 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5519,plain,
! [SV1366: $i,SV815: $i,SV1782: $i,SV2229: $i,SV2216: $i,SV2200: $i,SV2014: $i,SV2181: $i,SV2155: $i,SV2112: $i,SV230: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV230 @ SV2112 @ SV2155 @ SV2181 @ SV2014 @ SV2200 @ SV2216 @ SV2229 @ SV1782 )
= $false )
| ( ( ( hAPP @ SV230 @ ( c_Set_Oinsert @ SV815 @ SV1366 @ SV1782 ) )
= ( hAPP @ ( hAPP @ SV2014 @ SV815 ) @ ( hAPP @ SV230 @ SV1366 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5520,plain,
! [SV864: $i,SV2116: $i,SV1810: $i,SV1410: $i,SV2020: $i,SV279: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV279 @ SV2020 )
= $false )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV1410 @ SV1810 @ SV2116 @ SV2020 @ SV2020 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV864 ) @ SV1810 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2020 ) @ SV1410 ) @ SV1810 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV279 @ SV864 @ ( c_Set_Oinsert @ SV1410 @ ( c_HOL_Ominus__class_Ominus @ SV1810 @ ( c_Set_Oinsert @ SV864 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ ( tc_fun @ SV2020 @ tc_bool ) ) @ SV2020 ) @ SV2116 @ SV2020 @ SV2020 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5521,plain,
! [SV2230: $i,SV2217: $i,SV2201: $i,SV2182: $i,SV2159: $i,SV344: $i,SV2124: $i,SV928: $i,SV1471: $i,SV1859: $i,SV2041: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SV2217 @ SV2230 @ SV2041 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5500]) ).
thf(5522,plain,
! [SV2231: $i,SV2218: $i,SV2202: $i,SV2183: $i,SV2160: $i,SV345: $i,SV1472: $i,SV2125: $i,SV1860: $i,SV929: $i,SV2042: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SV2218 @ SV2231 @ SV2042 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5501]) ).
thf(5523,plain,
! [SV941: $i,SV2232: $i,SV2219: $i,SV357: $i,SV2203: $i,SV2184: $i,SV2161: $i,SV1484: $i,SV2128: $i,SV2046: $i,SV1867: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SV2219 @ SV2232 @ SV2046 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5502]) ).
thf(5524,plain,
! [SV942: $i,SV2233: $i,SV2220: $i,SV2204: $i,SV358: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV1485: $i,SV2047: $i,SV1868: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SV2220 @ SV2233 @ SV2047 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5503]) ).
thf(5525,plain,
! [SV2221: $i,SV1869: $i,SV1486: $i,SV2205: $i,SV2186: $i,SV2163: $i,SV359: $i,SV2130: $i,SV2048: $i,SV943: $i] :
( ( ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SV2205 @ SV1486 @ SV1869 @ SV2221 @ SV2048 ) )
= $true )
| ( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5504]) ).
thf(5526,plain,
! [SV1870: $i,SV2222: $i,SV2206: $i,SV1487: $i,SV2187: $i,SV2164: $i,SV2131: $i,SV360: $i,SV2049: $i,SV944: $i] :
( ( ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SV2206 @ SV2222 @ SV1870 @ SV2049 ) )
= $true )
| ( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5505]) ).
thf(5527,plain,
! [SV2234: $i,SV2225: $i,SV2211: $i,SV2192: $i,SV2171: $i,SV2140: $i,SV2082: $i,SV1949: $i,SV1618: $i,SV1131: $i,SV554: $i] :
( ( ( ( hAPP @ SV554 @ ( hAPP @ SV1131 @ SV1618 ) )
= ( hAPP @ SV1949 @ ( hAPP @ SV2082 @ SV2140 ) ) )
= $false )
| ( ( ( hAPP @ ( c_Fun_Ocomp @ SV554 @ SV1131 @ SV2171 @ SV2192 @ SV2211 ) @ SV1618 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1949 @ SV2082 @ SV2225 @ SV2192 @ SV2234 ) @ SV2140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5510]) ).
thf(5528,plain,
! [SV1626: $i,SV1139: $i,SV2141: $i,SV1954: $i,SV2086: $i,SV563: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 ) )
= $true )
| ( ( SV1139 = SV1626 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
= $false )
| ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5511]) ).
thf(5529,plain,
! [SV2142: $i,SV565: $i,SV1141: $i,SV1956: $i,SV1628: $i,SV2087: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) ) )
= $true )
| ( ( SV1141 = SV1628 )
= $true )
| ( ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
= $false )
| ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5530,plain,
! [SV1645: $i,SV1160: $i,SV2145: $i,SV1965: $i,SV2093: $i,SV586: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 ) )
= $true )
| ( ( SV1160 = SV1645 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5513]) ).
thf(5531,plain,
! [SV2146: $i,SV1966: $i,SV2094: $i,SV587: $i,SV1646: $i,SV1161: $i] :
( ( ( SV1161 = SV1646 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
= $false )
| ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5514]) ).
thf(5532,plain,
! [SV1174: $i,SV600: $i,SV2149: $i,SV1659: $i,SV2097: $i,SV1974: $i,SV2176: $i,SV14: $i] :
( ( ( c_OrderedGroup_Oab__semigroup__mult @ SV14 @ SV2176 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1974 @ SV2097 )
= $false )
| ( ( c_Fun_Oinj__on @ SV1659 @ SV1974 @ SV2097 @ SV2149 )
= $false )
| ( ( ( c_Finite__Set_Ofold__image @ SV14 @ SV600 @ SV1174 @ ( c_Set_Oimage @ SV1659 @ SV1974 @ SV2097 @ SV2149 ) @ SV2176 @ SV2149 )
= ( c_Finite__Set_Ofold__image @ SV14 @ ( c_Fun_Ocomp @ SV600 @ SV1659 @ SV2149 @ SV2176 @ SV2097 ) @ SV1174 @ SV1974 @ SV2176 @ SV2097 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(5533,plain,
! [SV2230: $i,SV2217: $i,SV2201: $i,SV2182: $i,SV2159: $i,SV344: $i,SV2124: $i,SV928: $i,SV1471: $i,SV1859: $i,SV2041: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SV2217 @ SV2230 @ SV2041 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5521]) ).
thf(5534,plain,
! [SV2231: $i,SV2218: $i,SV2202: $i,SV2183: $i,SV2160: $i,SV345: $i,SV1472: $i,SV2125: $i,SV1860: $i,SV929: $i,SV2042: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SV2218 @ SV2231 @ SV2042 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5522]) ).
thf(5535,plain,
! [SV941: $i,SV2232: $i,SV2219: $i,SV357: $i,SV2203: $i,SV2184: $i,SV2161: $i,SV1484: $i,SV2128: $i,SV2046: $i,SV1867: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SV2219 @ SV2232 @ SV2046 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5523]) ).
thf(5536,plain,
! [SV942: $i,SV2233: $i,SV2220: $i,SV2204: $i,SV358: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV1485: $i,SV2047: $i,SV1868: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SV2220 @ SV2233 @ SV2047 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5537,plain,
! [SV943: $i,SV2048: $i,SV2221: $i,SV1869: $i,SV1486: $i,SV2205: $i,SV2186: $i,SV2163: $i,SV359: $i,SV2130: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2130 @ SV359 @ SV2163 @ SV2186 @ SV2205 @ SV1486 @ SV1869 @ SV2221 @ SV2048 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV943 @ SV2048 )
= $false )
| ( ( ( hAPP @ SV359 @ SV943 )
= ( c_Finite__Set_Ofold @ SV1486 @ SV1869 @ SV943 @ SV2048 @ SV2048 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5538,plain,
! [SV944: $i,SV2049: $i,SV1870: $i,SV2222: $i,SV2206: $i,SV1487: $i,SV2187: $i,SV2164: $i,SV2131: $i,SV360: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV360 @ SV2131 @ SV2164 @ SV2187 @ SV1487 @ SV2206 @ SV2222 @ SV1870 @ SV2049 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV944 @ SV2049 )
= $false )
| ( ( ( hAPP @ SV360 @ SV944 )
= ( c_Finite__Set_Ofold @ SV1487 @ SV1870 @ SV944 @ SV2049 @ SV2049 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(5539,plain,
! [SV1626: $i,SV1139: $i,SV2141: $i,SV1954: $i,SV2086: $i,SV563: $i] :
( ( ( c_Fun_Oinj__on @ SV563 @ SV2086 @ SV1954 @ SV2141 )
= $false )
| ( ( SV1139 = SV1626 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1139 ) @ SV2086 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1954 ) @ SV1626 ) @ SV2086 ) )
= $false )
| ( ( ( hAPP @ SV563 @ SV1139 )
= ( hAPP @ SV563 @ SV1626 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5528]) ).
thf(5540,plain,
! [SV2142: $i,SV565: $i,SV1628: $i,SV1956: $i,SV1141: $i,SV2087: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1141 ) @ SV1956 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2087 ) @ SV1628 ) @ SV1956 ) )
= $false )
| ( ( SV1141 = SV1628 )
= $true )
| ( ( c_Fun_Oinj__on @ SV565 @ SV1956 @ SV2087 @ SV2142 )
= $false )
| ( ( ( hAPP @ SV565 @ SV1141 )
= ( hAPP @ SV565 @ SV1628 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5529]) ).
thf(5541,plain,
! [SV1645: $i,SV1160: $i,SV2145: $i,SV1965: $i,SV2093: $i,SV586: $i] :
( ( ( c_Fun_Oinj__on @ SV586 @ SV2093 @ SV1965 @ SV2145 )
= $false )
| ( ( SV1160 = SV1645 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1160 ) @ SV2093 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1965 ) @ SV1645 ) @ SV2093 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1160 )
= ( hAPP @ SV586 @ SV1645 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5530]) ).
thf(5542,plain,
! [SV1646: $i,SV1161: $i,SV2146: $i,SV1966: $i,SV2094: $i,SV587: $i] :
( ( ( c_Fun_Oinj__on @ SV587 @ SV2094 @ SV1966 @ SV2146 )
= $false )
| ( ( SV1161 = SV1646 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1161 ) @ SV2094 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1966 ) @ SV1646 ) @ SV2094 ) )
= $false )
| ( ( ( hAPP @ SV587 @ SV1161 )
= ( hAPP @ SV587 @ SV1646 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(5543,plain,
! [SV1471: $i,SV1859: $i,SV2041: $i,SV2230: $i,SV2217: $i,SV2201: $i,SV2182: $i,SV2159: $i,SV344: $i,SV2124: $i,SV928: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV928 @ SV2124 @ SV344 @ SV2159 @ SV2182 @ SV2201 @ SV2217 @ SV2230 @ SV2041 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2041 ) @ SV1859 ) @ SV1471 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV344 @ ( hAPP @ SV928 @ SV1471 ) ) @ SV1859 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5544,plain,
! [SV1860: $i,SV929: $i,SV2042: $i,SV2231: $i,SV2218: $i,SV2202: $i,SV2183: $i,SV2160: $i,SV345: $i,SV1472: $i,SV2125: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2125 @ SV1472 @ SV345 @ SV2160 @ SV2183 @ SV2202 @ SV2218 @ SV2231 @ SV2042 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2042 ) @ SV929 ) @ SV1860 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV929 ) @ ( hAPP @ SV1472 @ SV1860 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5534]) ).
thf(5545,plain,
! [SV941: $i,SV1867: $i,SV2046: $i,SV2232: $i,SV2219: $i,SV357: $i,SV2203: $i,SV2184: $i,SV2161: $i,SV1484: $i,SV2128: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2128 @ SV1484 @ SV2161 @ SV2184 @ SV2203 @ SV357 @ SV2219 @ SV2232 @ SV2046 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1867 @ SV2046 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV357 @ SV941 ) @ ( hAPP @ SV1484 @ SV1867 ) )
= ( c_Finite__Set_Ofold @ SV357 @ SV941 @ SV1867 @ SV2046 @ SV2046 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5535]) ).
thf(5546,plain,
! [SV942: $i,SV1868: $i,SV2047: $i,SV2233: $i,SV2220: $i,SV2204: $i,SV358: $i,SV2185: $i,SV2162: $i,SV2129: $i,SV1485: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1485 @ SV2129 @ SV2162 @ SV2185 @ SV358 @ SV2204 @ SV2220 @ SV2233 @ SV2047 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1868 @ SV2047 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV358 @ SV942 ) @ ( hAPP @ SV1485 @ SV1868 ) )
= ( c_Finite__Set_Ofold @ SV358 @ SV942 @ SV1868 @ SV2047 @ SV2047 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5547,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1233,5546,5545,5544,5543,5542,5541,5540,5539,5538,5537,5532,5527,5520,5519,5518,5517,5516,5509,5508,5507,5506,5496,5490,5489,5486,5485,5483,5482,5481,5480,5469,5465,5464,5460,5459,5457,5456,5444,5437,5436,5435,5434,5433,5432,5427,5426,5423,5422,5420,5419,5417,5416,5415,5414,5413,5410,5407,5406,5405,5404,5403,5402,5401,5396,5394,5393,5386,5385,5383,5379,5375,5374,5373,5372,5369,5366,5364,5360,5357,5342,5341,5331,5327,5326,5325,5324,5323,5322,5321,5319,5313,5309,5307,5306,5305,5296,5295,5292,5291,5282,5273,5272,5271,5269,5267,5266,5260,5259,5258,5257,5255,5254,5253,5252,5251,5250,5249,5248,5247,5246,5245,5242,5235,5234,5233,5232,5230,5225,5224,5223,5222,5221,5220,5215,5208,5207,5206,5205,5204,5203,5202,5201,5199,5198,5196,5194,5188,5187,5186,5185,5184,5183,5182,5181,5176,5171,5170,5169,5165,5163,5161,5160,5159,5158,5157,5149,5148,5146,5144,5143,5142,5140,5138,5137,5136,5132,5131,5130,5114,5108,5103,5098,5097,5093,5089,5078,5076,5073,5072,5071,5070,5069,5068,5063,5062,5051,5050,5045,5044,5036,5032,5018,5012,5007,5006,5005,5004,5003,5000,4999,4997,4996,4994,4993,4992,4981,4980,4979,4964,4952,4951,4950,4949,4945,4944,4941,4939,4938,4937,4936,4925,4924,4923,4922,4921,4920,4919,4918,4909,4908,4902,4901,4893,4885,4884,4883,4880,4879,4876,4874,4872,4870,4869,4867,4859,4857,4853,4851,4849,4848,4844,4834,4828,4816,4815,4814,4812,4798,4788,4785,4781,4777,4771,4751,4750,4742,4741,4740,4720,4719,4716,4710,4709,4704,4703,4697,4696,4691,4690,4686,4681,4673,4672,4671,4670,4662,4661,4660,4654,4633,4626,4625,4624,4623,4615,4613,4609,4600,4599,4598,4597,4595,4592,4590,4587,4585,4579,4578,4577,4566,4565,4563,4558,4557,4556,4555,4542,4541,4531,4530,4529,4514,4512,4500,4497,4496,4492,4490,4478,4475,4474,4473,4471,4466,4464,4461,4460,4459,4457,4444,4421,4420,4399,4382,4381,4376,4364,4363,4341,4340,4339,4336,4335,4324,4322,4321,4316,4315,4314,4313,4301,4295,4294,4290,4289,4286,4280,4276,4275,4269,4266,4254,4253,4252,4251,4250,4249,4241,4238,4237,4236,4230,4229,4215,4213,4212,4211,4210,4207,4206,4200,4199,4194,4185,4179,4170,4148,4145,4139,4138,4132,4128,4125,4104,4100,4095,4094,4060,4059,4058,4057,4056,4055,4054,4052,4051,4050,4049,4048,4036,4035,4034,4033,4032,4030,4029,4028,4024,4023,4022,4021,4020,4019,4018,4017,4015,4014,3973,3966,3965,3963,3955,3954,3937,3925,3924,3862,3852,3840,3838,3786,3784,3783,3782,3776,3775,3772,3771,3767,3766,3765,3746,3722,3721,3719,3716,3705,3703,3702,3696,3691,3690,3668,3654,3650,3647,3646,3645,3644,3640,3637,3636,3568,3551,3550,3549,3548,3546,3544,3542,3541,3540,3531,3528,3527,3526,3525,3523,3521,3515,3425,3423,3422,3415,3411,3389,3388,3387,3358,3342,3337,3336,3333,3331,3311,3310,3296,3281,3264,3258,3229,3228,3214,3211,3210,3204,3195,3194,3168,3155,3154,3112,3110,3107,3098,3074,3065,3063,3043,3019,2989,2983,2980,2979,2978,2970,2968,2967,2965,2964,2962,2961,2960,2954,2923,2908,2889,2873,2872,2858,2812,2787,2763,2754,2739,2725,2687,2676,2675,2583,2576,2520,2519,2513,2436,2380,2370,2364,1901,1843,1842,1841,1840,1839,1838,1837,1836,1835,1834,1833,1832,1831,1830,1829,1828,1827,1826,1825,1824,1823,1822,1821,1802,1779]) ).
thf(5548,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV856-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 16:45:31 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 99.18/16.89 ....
% 99.18/16.89
% 99.18/16.89 No.of.Axioms: 614
% 99.18/16.89
% 99.18/16.89 Length.of.Defs: 0
% 99.18/16.89
% 99.18/16.89 Contains.Choice.Funs: false
% 99.18/16.89 ...........................................................................................................................................................................................................................
% 99.18/16.89
% 99.18/16.89 ********************************
% 99.18/16.89 * All subproblems solved! *
% 99.18/16.89 ********************************
% 99.18/16.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:614,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5547,loop_count:0,foatp_calls:1,translation:fof_full)
% 99.18/16.89
% 99.18/16.89 %**** Beginning of derivation protocol ****
% 99.18/16.89 % SZS output start CNFRefutation
% See solution above
% 16.79/16.93
% 16.79/16.93 %**** End of derivation protocol ****
% 16.79/16.93 %**** no. of clauses in derivation: 5548 ****
% 16.79/16.93 %**** clause counter: 5547 ****
% 16.79/16.93
% 16.79/16.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:614,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5547,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------